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The Enjoyment of Math
The Enjoyment of
Math

BY HANS RADEMACHER AND

OTTO TOEPLITZ

TRANSLATED BY HERBERT ZUCKERMAN

With a new foreword by Alex Kontorovich

PRINCETON UNIVERSITY PRESS

PRINCETON OXFORD
 Published 1957 by Princeton University Press,
41 William Street, Princeton, New Jersey
In the United Kingdom: Princeton University Press,
99 Banbury Road, Oxford OX2 6JX

Foreword to theAll Princeton Science Library edition

Rights Reserved
copyright © 2023, by Princeton University Press
This is a translation from Von Zahlen undFiguren: Proben Mathematischen
Denkens fiir Liebhaber der Mathematik, by Hans Rademacher and Otto
Toeplitz, second edition originally published by Julius Springer, Berlin,
1933. Chapters 15 and 28 by Herbert Zuckerman have been added to the
English language edition.

First published 1957

New Princeton Science Library paperback edition,
with a new foreword by Alex Kontorovich, 2023
Paperback ISBN 9780691241548
E-book ISBN 9780691241531
LCCN: 2022942877

Cover design by Michael Boland for TheBolandDesignCo.com

Cover image: iStock

press.princeton.edu

Printed in the United States of America

 CONTENTS
Foreword by Alex Kontorovich vii
1
Preface
Introduction 5
1. The Sequence of Prime Numbers 9
2. Traversing Nets of Curves 13
3. Some Maximum Problems 17
4. Incommensurable Segments and Irrational Numbers 22
5. A Minimum Property of the Pedal Triangle 27
6. A Second Proof of the Same Minimum Property 30
7. The Theory of Sets 34
8. Some Combinatorial Problems 43
9. On Waring's Problem 52
10. On Closed Self-Intersecting Curves 61
11. Is the Factorization of a Number into Prime Factors Unique? 66
12. The Four-Color Problem 73
13. The Regular Polyhedrons 82
14. Pythagorean Numbers and Fermat's Theorem 88
15. The Theorem of the Arithmetic and Geometric Means 95
16. The Spanning Circle of a Finite Set of Points 103
17. Approximating Irrational Numbers by Means of Rational
Numbers 111
18. Producing Rectilinear Motion by Means of Linkages 119
19. Perfect Numbers 129
20. Euler's Proof of the Infinitude of the Prime Numbers 135
21. Fundamental Principles of Maximum Problems 139
22. The Figure of Greatest Area with a Given Perimeter 142
23. Periodic Decimal Fractions 147
24. A Characteristic Property of the Circle 160
25. Curves of Constant Breadth 163

v
 c ont e nt s
26. The Indispensability of the Compass for the Constructions
of Elementary Geometry 177
27. A Property of the Number 30 187
28. An Improved Inequality 192
Notes and Remarks 197

vi
 Foreword
The art form of mathe­matics is well-­known to have a marketing prob­
lem. The ­great German mathematician Carl Friedrich Gauss famously
said, “Mathe­matics is the queen of science.”1 And yet this queen, direct-
ly responsible for much of our modern existence and all its extranatural
comforts, is greatly underappreciated, if not outright despised, by most
of the educated public. I c­ an’t tell you how many ­people I’ve met who
have told me, “I hate math.” Upon further prodding, ­they’ll admit that
in fact they loved math up to Subject X (where X might be calculus, or
trigonometry, or algebra, or what­ever), and then Subject X + 1 was the
worst and ­they’ve hated math ever since. (Upon even further prodding,
it turns out they ­really hated their teacher in Subject X + 1, hence never
learning it properly, and every­thing thereafter was gobbledygook. Many
of them also admit that as adults, they love struggling to solve difficult
puzzles like Sudoku, KenKen, and so forth).
You ­don’t hear such statements nearly as often about a closely related
subject, physics. I’ve always wondered why. For one explanation, physics
is less often a requirement in school, so the only ­people subjected to its
rigors are ­there voluntarily. Another, perhaps, and much closer to the
discussion at hand, is that a g­ reat number of Nobel laureate physicists
write public accounts of their discoveries, wowing us with faraway galax-
ies, quantum field theories, Earth-­like Goldilocks planets, black holes,
quantum entanglement, and so on. The rec­ord for mathematicians of
the highest caliber “wasting” their im­mense talents and invaluable time
by trying to reason with the general public is far, far sparser.
This is what makes the pre­sent book all the more remarkable. H ­ ere
are two world-­ renowned mathematicians making a valiant attempt
at showing the public some true gems of our beloved subject. Hans
Rademacher and Otto Toeplitz ­were preeminent researchers who made
fundamental contributions to twentieth-­century mathe­matics. Toeplitz,
born in 1881 in Breslau (modern-­day Poland) to a Jewish ­family, cut his
teeth at the University of Gottingen, which was the mathematical home
of every­one from Gauss to Riemann to his own teachers Hilbert, Klein,
and Minkowski. When the Nazis came to power, Toeplitz was dismissed
from his professorship at Bonn, and he moved to the Hebrew Universi-
1
 ​He continued, “and Number Theory”—­which features heavi­ly in the book
before you—­“is the queen of Mathe­matics.”

vii
 f oreword
ty in Jerusalem, where he died in 1940 from tuberculosis. Rademacher,
about a de­cade Toeplitz’s ju­nior, hailed from the Hamburg area and
overlapped with his coauthor in Gottingen, where he earned his PhD
in 1916. While Rademacher was racially acceptable to the Nazis, his
pacifist views ­were not, and he was likewise dismissed from his position
at the University of Breslau. Rademacher moved to the United States to
take an assistant professorship at the University of Pennsylvania (despite
already having served a de­cade as a full professor in Germany), from
which he retired in 1962, passing away not long a­ fter in 1969. Their
combined interest in and passion for popularizing mathe­matics, crys-
talized over many lectures to the public, came to fruition as Von Zahlen
und Figuren, released in German in 1930 and translated into the text
before you in 1957.
The topics presented within are not the recreational material one
sometimes encounters; ­these are the “real deal.” The first chapter, for
example, begins with Euclid’s argument that the prime numbers are
plentiful: for any finite collection of them, more exist; this is followed
immediately with a contradistinction: one may chance upon an arbi-
trarily long distance between one prime to the next. Such issues are
quite deep, forming the basis of ongoing research ­today, and yet their
pre­sen­ta­tion ­here is completely “elementary,” in the sense of not re-
quiring any technical knowledge beyond the fifth grade. Instead, what
this book asks of its audience is a penchant for finding t­ hese questions
of interest, as well as the determination and stamina to chew over
the arguments presented ­until they coalesce. This duality of render-
ing advanced disciplines in an elementary style applies to most of the
topics presented, ranging from geometry and arithmetic to topology
and graph theory. Some chapters, like that describing the Four-­Color
Prob­lem (now a theorem, resolved only in 1976), describe the state of
­things in the 1930s but of course not our present-­day understanding.
Other chapters pre­sent topics that have since been showcased in new
ways to the public. For example, chapter 25 discusses curves of constant
breadth; ­today, someone wanting to learn about such curves can visit
the National Museum of Mathe­matics in New York City and take a spin
on some non-­spherical coasters which nonetheless ­ride smoothly.
Overall, the topics seem to me on the advanced side for t­oday’s
general audience. Maybe ­today we know more about what the general
public can and cannot typically follow. Or maybe previous generations
experienced so much more daily hardship that a few hours of strug­gle
with a mathematical chapter (or just a paragraph, or even a sentence)

viii
 f ore word
would, by comparison, not seem so insurmountable. On the other
hand, I’m reminded of a story that Keith Devlin, the author of Introduc-
tion to Mathematical Thinking and other popu­lar math books, told me
some time ago about the first time he wrote something and submitted it
to a local newspaper. The editor told him that he’d be delighted to have
him contribute something, but what Keith had written was way too com­
plicated for the audience. He’d need to craft something that ­people
could read for five minutes over a cup of coffee (and when Keith’s me­
dium moved to radio, he was similarly told that his topic needed to be
digestible while the average Joe was pumping his gas). Now, by keeping
his material accessible, Keith has been tremendously successful with
communicating with the public.
But the modern experience of mass media, with significantly less gate­­
keeping and editorializing, has shown several t­hings about the public
audience. In defiance of conventional media wisdom, audiences have an
appetite for long-­form content, ­whether it’s a fourteen-­hour Netflix
show or an extended series of podcasts, and this has proven true across
virtually all va­ri­e­ties of content form and subject ­matter. ­People ­will
gladly watch, by the millions and tens of millions, videos on very ad­
vanced graduate-­level mathe­matics, when presented by masters of expo­
sition like the YouTube channels 3Blue1Brown, Veritasium, and many
­others. All this is to say that, perhaps if this book ­were to be proposed
­today, its authors might be told by editors to water-­down the subjects
and discussion; but since it has already achieved a significant amount of
success, it has earned its right to be as it is, and it remains an essential
entry point for ­those audiences who hunger for a deeper exploration of
mathe­matics. I sincerely hope that you, dear reader, ­will give its message
the time required to strug­gle with the difficult, impor­tant, and timeless
material; you ­will be greatly rewarded.
We seem to be in a bit of a re­nais­sance for math exposition, both in
terms of mathematicians showing greater re­spect for expository writing
and in the appreciation of the general public for books like ­these. Let
us hope that another generation may be inspired by the writings within.

New Brunswick, New Jersey, 2022 ALEX KONTOROVICH

ix
 Preface

Otto Toeplitz, co-author of this book, died in Jerusalem on Fe­

bruary 19, 1940, after having left Germany in the Spring of 1939.
Toeplitz began his academic career in Gottingen as a disciple of
David Hilbert, was then professor in Kiel and later in Bonn. His
scientific work is centered around the theory of integral equations
and the theory of functions of infinitely many variables, fields to
which he has made lasting contributions.
The plan for this book arose at frequent meetings which the
authors had, while Toeplitz was in Kiel and I was at the University
of Hamburg. Both of us had repeatedly lectured about the subject
matter of this book to a wider public. The manuscript was rewritten
several times under mutual criticism. Toeplitz's great interest in the
history of mathematics is still visible in the present edition. I re­
member with warm feelings the summer days in 1929 at Bonn, when
together we put the last touches to the German manuscript. I am
sure that Toeplitz would have been pleased and proud of the present
English edition, a project of which he had often thought.
I wish to thank the translator Professor Herbert S. Zuckerman for
his painstaking and understanding work. Not only do I admire his
apt translation of the German text, but I also think that in his pre­
sentation of the content he has brought many of its arguments closer
to the English speaking reader. He has added two chapters (15 and
28) to the book, which faithfully reflect the spirit in which this book
was written.
My thanks go to my friends Emil Grosswald, D. H. Lehmer, and
Herbert Robbins for help and valuable advice, and also to the
publisher for his sympathetic cooperation.

Philadelphia, 1956 HANS RADEMACHER

The Enjoyment of Math
Another random document with
no related content on Scribd:
THE RESULT OF THE SIEGE: IN THE AMERICAN MINISTER’S HOUSE
 Copyright, M. S. Woodward

THE RESULT OF THE SIEGE: FRENCH LEGATION RUINS

Our gates are all closed tight, and occasionally we hear thundering
down Legation Street as whole troops of half-starved horses, ponies,
and donkeys (animals which have been left by their owners in their
stables, and which have managed by some means to free
themselves, either by looters untying them, or perhaps fire freeing
them), dash past at top speed all together in a fury of liberty
regained. And dangerous it is for anyone to be on the road when
one of these wild troops race down the street, for he will certainly be
trampled to death. After a time these mad collections of animals
become tame and quiet from hunger and exhaustion, and are willing
enough to be led into almost any courtyard. Everything is unusual in
this wonderful Peking. This morning I walked with Colonel Churchill
and Captain Mallory on the Tartar Wall and down it to the Ha Ta Men
Gate, where we went down the Ramp and walked all over the
tremendously exposed German and French lines with their
barricades and defences. In the German compound the havoc
wrought is unimaginable. Whole sides of the houses have been
battered down, in some instances one or two walls only left
standing; and as for the French compound, every house, every
building, and every wall has been levelled to old Mother Earth again,
and nothing but the little house of the concierge at the gate, which
flies the French flag, is left standing.
On seeing this one can understand why the French at the
conference not only wanted Peking to be looted and sacked, but to
be burnt as well. As the whole place can be inspected now, Mr.
Gamewell tells me that four big mines, almost completed, have been
found, and, had not the allies arrived when they did, that the
following night would have seen some terrific explosions in the
British Legation, the Hanlin Library, and on the Tartar Wall even. The
mortality of the siege would thus have been doubled by twenty-four
hours’ further delay by our troops.
Baron von Ketteler’s body was accidentally discovered on the 16th
by the Russian troops who were passing near the Tsung-li Yamen,
very near the spot where he had been murdered. The body had
been thrown into an old wooden box and left. The polite
communication which had been sent to the Baroness von Ketteler
during the semi-armistice days of the siege that her husband’s body
was lying in state at the Tsung-li Yamen was thus proved to be an
utter fabrication on their part. To-day his formal obsequies took
place in the German Legation, the doyen of the Corps, the Spanish
Minister, reading a short address, which was as well put as it was as
hard for Baroness von Ketteler to hear. I did not go to the ceremony,
however, for I felt as if I had attended more than enough to last me
the rest of a long life.
Although the allies arrived on the afternoon of the 14th, it was not
until the afternoon of the 16th that the Japanese troops went to the
relief of the Pei-t’ang, where Archbishop Favier had held his own so
long. They had had tremendous losses by attack and mines which
exploded in their midst—300 Chinese converts killed, 75 orphan
children, and 60 foreigners, including 2 French officers who had
been sent with the 20 French marines to help them at the beginning
of the siege.
This huge fortified cathedral was the only other mission in or
about Peking which was strong enough to hold out. At four o’clock
they were relieved, and at seven o’clock the French Minister arrived
to make inquiries about his compatriots. All the commanders who
have inspected the Pei-t’ang say its defence was a wonderful one.
At every meal now Mrs. Squiers’s guests are most numerous,
charming, and interesting. The servants seem to be all back, and
although the days are filled with incredible stories of what the
different nationalities are “doing” in Peking, our evenings are always
delightful, as they are made up of the companionship of the most
delightful men in Peking, who, when they arrive to dine, throw off
the disagreeable features of these war times, and devote themselves
with happiness to this opportunity, probably their first for many
weeks, of enjoying the ordinary cheerful amenities of life; and while
these nice parties smack of the camp—for everyone is in uniform—it
only makes things more interesting, for they help to cheer up the
tired siege people. It is the same everywhere in the different
Legations: each nationality is surrounded by its military, with a
sprinkling of more or less unattached secretaries and Ministers
Plenipotentiary, who are temporarily without Legations to go to or
troops to attend to.
Sir Robert Hart is very busy with his mountain-high accumulated
Customs work to be attended to, but he manages often to drop in to
tiffin or dinner.
Colonel Mills, General Chaffee’s Chief of Staff, an old friend of our
host’s, comes frequently to this hospitable house, as does Colonel
Waller, a delightful person, with his young officers, Lieutenant David
Porter and Lieutenant Harding. Colonel Mallory and Colonel Churchill,
the British Military Attaché to Tokyo, who is an old friend of mine,
and many other charming people, would make this list a long one
should I attempt to make it complete.

MRS. HOOKER, MISS ARMSTRONG, LADY MACDONALD’S LITTLE GIRLS, FARGO

SQUIERS, AND COLONEL ARTHUR CHURCHILL
 Colonel Churchill is returning, as I am, as soon as he can to Tokyo.
He intends to go down the river with Miss Armstrong and Sir
Claude’s little girls with the first convoy sent down by the British,
which will be a day after General Chaffee sends down his.
Fargo Squiers, my maid, and I, will then meet him and Miss
Armstrong and the children in Tien-tsin, and we will make our
journey to Japan by the first way that presents itself. He thinks that
Admiral Bruce, who is in command of the British fleet at Taku, will
put a despatch-boat at our disposal, and that we will be sent
immediately over to Yokohama.
In coming up to Peking Colonel Churchill brought me a very kind
invitation from Admiral and Mrs. Bruce—I had known them for some
time—to come to Mrs. Bruce at Wei Hai Wei, the British concession
near Chefoo, in case I was ill or needed a rest before starting for
Tokyo. So, with the letters to Colonel Moale, in command of our
troops in Tien-tsin, to do everything possible for us, Mr. Squiers, Mrs.
Squiers, and I, feel that Fargo and I will have an interesting and
reasonably comfortable trip over to Japan, where I know my sister is
counting the days until I return to her.
General Chaffee has delayed sending the first convoy down until
the 21st, which gives me a little more time before starting. It has
made me feel that really, after having been shot upon all summer
from the Imperial walls, I should like a peep inside before I leave
Peking.
The city has been portioned off to the different generals, and the
English and Americans have a district where there is very little to
loot. To-day a French officer of high rank, wishing to get treasure
out of a palace that was in our lines, came to Mr. Conger and asked
him if he would allow him to change the boundary a trifle. The
Minister naïvely agreed to the Frenchman’s purely disinterested
request, and the consequence is there are a lot of indignant
American military men wandering about trying to understand why
this change in the map should have been made without consulting
them.
 August 19.
I talked over with Mrs. Squiers my great wish to see something of
the wonderful Purple City before leaving, and while she was too busy
nursing little Bard to go with me, she saw no reason why, with
ample protection, and escorted by an officer, I should not ride
through this mysterious and beautiful park.
I had expected General Chaffee would give me an order to enter
by the Ch’ien Men Gate and its continuing three gates, and pass
practically through our own lines, upon his hearing that I wished to
do so. He was usually so amiable when I asked him for anything,
that this time, much to my surprise, he became very angry, and,
pounding his fist on the table, he assured me that he would not
allow me to even ride through the Imperial City, giving as his refusal
the only reason that “there were sights of war there which no
American girl should see,” and pounding his fist a second time to
emphasize the fact. All of which was ridiculous, as the sights of war
referred to were simply the heaps of corpses which surrounded the
different gates of the Imperial City by which the allies had entered,
and, as a consequence of the defeat of the Chinese, the dead were
still there. He was right, inasmuch as these are not pretty things to
see; but as I had been in the midst of war for two months, and had
seen all these things many times, I did not feel that it was just in
him to deny me the privilege now of being able to get a bird’s-eye
view of this wonderful park, which he might have done by allowing a
special permit to go round it on horseback before leaving. But one
can’t fuss with people who deny you things for what they think is for
your own good, especially when the person in question happens to
be General Chaffee.
After this sad refusal, the first person I met was Baron von
Rahden, who, on hearing my tale of woe, was delighted to hear that
it was one which was so easy to remedy. As General Chaffee had the
power to write a permit to go into the Forbidden City, so had the
Russian Commander-in-Chief. He flew off, and in a few minutes
returned, bearing an order from the headquarters of the Russian
troops giving him power to escort me through the Imperial City, with
a company of Cossacks as a military guard, so that we could come
to no possible harm from snipers or marauding parties.
I was all excitement to be off. I felt like a naughty child, and was
afraid to stop a moment, fearing something might still stop me. But
we could not start, as there was no horse or pony in the Legation,
and the Cossacks had only their necessary number. Von Rahden was
a resourceful person, and told me that while I was putting on a
riding-habit he would have a horse got ready for me. He sent his
men off with the word that some sort of an animal for me to ride
must be here in fifteen minutes, and when I was ready to go I found
the Cossacks all lined up and Von Rahden holding two of the
sorriest, thinnest-looking horses I had ever seen. His men had
stopped a stampeded troop of animals out in Legation Street, and
these two were the best. The horse he selected was half mad with
fear, but I finally managed to mount him, and off we started, lickety
split, Von Rahden and myself leading, and the half-company of
Cossacks thundering after us. This dashing down deserted streets
and rushing up slight grades made me realize that one was no
longer a prisoner, at any rate.
We rode for a long time through absolutely deserted streets, at all
moments on the qui vive for shots from closed doors, or for a
possible ambush at each turning in the road. Our horses shied at
corpses in our path, and we were listening for unheard noises from
apparently empty houses, many of which had tiny little foreign flags
flying from some window or a painted foreign flag roughly executed
over the door, the owners hoping these Western insignia might
protect their property from looters.
Before entering the Forbidden City we passed through three series
of walls, at the entrance to which were piled innumerable dead
Chinese, silent proof that many lives were given in the vain attempt
to protect the Imperial City; but after we were once inside, these
horrors were forgotten in the grandiose landscape gardening, which
almost overwhelmed us by its magnificent simplicity. We crossed the
wonderful white marble bridges which spanned the artificial
waterways, and the glorious lotus-flowers were all in bloom on the
banks and partially in the water. They are such gorgeous, big
flowers; they are like the Chinese architecture—wonderful in big,
sweeping lines. We rode on through this semi-cultured landscape,
where every detail was so carefully attended to that the ensemble
was a complete joy to the senses, and after the eight weeks we had
been barricaded in our Legation district this park seemed like
heaven.

COAL HILL

We climbed the Coal Hill, and got the only view I ever had of the
Purple City. We were at such a height that we could look right down
and get a good glimpse of the plan of these palaces, besides
obtaining a gorgeous general View of the whole Imperial City. On
descending the hill, I must say I was disappointed that the palaces
in this Holy of Holies were not more imposing. They were low, long
buildings constructed of the gorgeous Imperial yellow tiles. The
extraordinarily rich colouring of these buildings made one forget
momentarily the plainly low architectural lines. Unfortunately, we
had no permission to enter these closely-guarded, mysterious
precincts. We hated to leave this spot of beautiful trees, long
avenues and vistas, and, above all, the pure air, to return to our half-
burnt, wholly ill-smelling Legation district.
At nine o’clock all the Anglo-Saxons sang a Te Deum on the
tennis-court. Mr. Norris conducted the service, and Dr. Smith, the
author of “Chinese Characteristics,” made a most stirring address.
We all surely sang it with hearts full of a thankfulness we had rarely
ever before felt.

August 20.
To-day I took a walk all over the German lines with Mr. von
Bergen, Second Secretary of the Legation, and, in fact, all over our
old siege lines, and said a cheerful good-bye to it all. To-night Mrs.
Squiers has a farewell dinner, and to-morrow, at 6.30 a.m., we start
with ourselves and our baggage in United States Army schooners en
route to Tungchow, where we take primitive houseboats to sail down
the Pei-ho to Tien-tsin. A detachment from the 9th United States
Infantry is to accompany us, and everything is to be very military in
this escort for the first convoy. How absurd to compare my coming
to Peking and my leaving it! I came up on Sir Robert Hart’s private
car in a few hours, and will go down to the coast in an antiquated
Chinese boat, which will take as many days as the train took hours.
And so, floating down the river, I will have much time to think quietly
about this wonderful siege, to forget the disagreeable and the bad,
and to remember the great and the good.
 INDEX

American Legation. See Legations

Armstrong, Miss, 17, 23
Austrian Legation. See Legations

Belgian Legation. See Legations

Below, Von, Secretary to German Legation, 14;
effect of siege on, 100
Bergen, Von, Second Secretary to German Legation, 203
Boxers, the, rising of, 7, 16, 23;
captures of, 29, 35, 76, 152;
outrages by, 38, 57
Brent, Mrs., 17
British Legation. See Legations
Bruce, Admiral, 197
Bruce, Mount, 2;
ascent of, 4

Carles, Mr., British Consul at Tien-tsin, 148, 149

Cartier, M. de, 142
Cassini, Countess Marguerite, 5
Chaffee, General: arrival at Tien-tsin, 158;
the relief of Peking, 177, 181, 199;
a funeral incident, 184;
the convoy to Tien-tsin, 187, 197
Chamot, Swiss proprietor of the Peking Hotel, provides food for the
besieged, 114
Cheshire, Mr., American Legation, waiting for the relief troops, 15,
21;
his bravery, 77
Ch’ien Men Gate, burning of, 25;
firing of cannon from, 69;
arrival of the relief force, 179
China, Empress of, and Prince Ching, 132;
and Li Hung Chang, 163, 164
Ching, Prince, head of the Tsung-li Yamen, 69, 92;
correspondence with the besieged, 132, 137, 138
Christians, Chinese, outrages on, 35, 38;
located at the Fu, 75, 132;
their want of food, 161
Churchill, Colonel, British Military Attaché to Japan, 180, 196
Cologan, Señor, Spanish Minister at Peking, 43;
his illness, 120
Coltman, Dr. and Mrs., American physician at Peking, 20, 52, 79
Conger, Mr. and Mrs., American Minister at Peking, 52, 62, 120;
message from the Yamen, 136;
a funeral incident, 184;
his naïveness, 198

Dana Collection, the, 14

Dosio, Père, the Superior of Nan-t’ang, his loss of mind, 131;
Chinese outrage on, 176
Dutch Legation. See Legations

Favier, Archbishop, the Superior of Pei-t’ang, 37, 194

Feng-tai railway-station, 4;
burning of, 8
Fisher, a marine, death of, 125
Food-supply during the siege, 58, 73, 85, 106, 108, 109;
an amusing incident, 146
French Legation. See Legations
Fu, the, Chinese Christians located at, 72, 132, 161
Fukushima, General, commander of the Japanese relief forces, 167

Gamewell, Rev., a missionary, a mainstay to the besieged, 112, 193

Gaselee, General, commander of British relief forces, 149, 167, 176
German Legation. See Legations
Giers, M. de, Russian Minister at Peking, 43, 120;
message from the Yamen, 136;
and the Americans, 186
Giers, Madame de, her wonderful help in nursing, 143

Hanlin Library, the, 107, 116

Hart, Sir Robert, Inspector-General of Customs, 13, 18, 50;
death of Oliphant, 105;
letters from the Yamen, 139, 151
Ha Ta Men Gate, defence of, 22, 33, 92
Hsu Ching Cheng, Director of Imperial University, 156
“International” cannon, the, 116
Italian Legation. See Legations

James, Dr. H., 75;

murder of, 76
Japanese Legation. See Legations
Joostens, M., Belgian Minister, 141, 142
Jung Lu, communications with the besieged, 132, 134, 159

Kempff, Admiral, 14, 16, 17

Ketteler, Baron von, German Minister at Peking:
Boxer incident, 24, 25;
murder of, 45;
discovery of body, 194
Kettles, Mr., the Belgian Consul, 141
Knobel, M., Dutch Minister at Peking, 43, 120;
the chicken episode, 146, 147
Kroupensky, Mr., Russian Secretary, 23

Legations:
Boxer outrages, 7 et seq.;
arrival of the marines, 15;
weakness of the American, 18, 31;
waiting for the relief party, 21, 27;
attempts to burn, 25 et seq.;
alarming state of, 31;
rescue of Chinese Christians, 35 et seq.;
Chinese offer an escort to the coast, 42, 159;
murder of Baron von Ketteler, 45, 194;
strength of the British Legation, 48, 72;
American women and children transferred to the British, 48, 50;
American missionaries brought in, 49;
life in, 50 et seq., 119 et seq.;
evacuation and burning of the Belgian, 56;
attempt on the Dutch, 57;
supply of food, 58 et seq., 86, 108 et seq., 160;
in great danger, 61 et seq.;
evacuation of Austrian and fright of the French, 63;
general panic, 64;
fighting the fire, 65 et seq.;
the crowded hospital, 74, 90, 91, 102, 103, 105, 116, 142, 143;
a sortie, 75;
murder of Dr. James, 76;
armistice, 78;
renewed attacks on, 80 et seq.;
attack on German, 92 et seq.;
an unsuccessful sortie, 95;
racial friendships and animosities, 95, 96, 121, 122, 135;
Japanese valour, 97;
boldness of the Chinese, 98;
successful charge down the wall, 99, 100;
funerals, 102 et seq.;
discovery and successful use of an old cannon, 115, 116;
plague of flies, 123, 124;
Captain Strouts mortally wounded, 125;
a bad day, 125 et seq.,
wave of despondency, 129 et seq.;
a missionary becomes insane, 131;
communications with the Yamen, 132-134, 136, 145, 151, 159,
163, 169;
Chinese send in food, 138;
news of the relief force, 140;
a chicken episode, 146;
messenger sent to Tien-tsin, 149;
description of the barricades, 151 et seq.;
letters from Tien-tsin, 157;
 food running short, 160;
more severe attacks, 165, 168, 171;
good news, 167;
arrival of the relief force, 171 et seq.;
the question of loot, 191;
the state of the German Legation, 193;
discovery of mines, 193

Li Hung Chang, 163;

and the Empress of China, 164, 165;
purchase of guns, 171
Linqua Su, temple of, description of, 2;
defence of, 9, 10
Lippitt, Dr., 34;
wounded, 91, 142;
typhoid fever, 186

McCalla, Captain, in command of the Japanese marines, 15;

returns to Tien-tsin, 16;
and the relief party, 21, 34
Macdonald, Sir Claude, British Minister at Peking, elected
Commander-in-Chief, 120, 121;
and Von Rostand, 122;
Communications from the Yamen, 132, 133;
and the relief force, 173, 179, 186
Macdonald, Lady, and her children, 17;
and Baroness von Ketteler, 46;
lodges the American missionaries in the chapel 50;
food-supply, 85, 160
McKinley, President of the United States, forbids looting, 191
Magi-poo, rioting at, 14
Mallory, Colonel, sends news to the besieged, 158
Marines, the, arrival at Peking, 15;
on the sick-list, 34;
sorties, 35, 41, 99;
death of Captain Strouts, 126;
the relieving force, 179, 187
Martin, Dr. A. W. P., Director of Imperial University in Peking, 23;
and the fire at the Legations, 68
Melotte, Chevalier de, his gallant defence, 56;
arrival of the relief force, 175, 177
Merghelynckem, M., First Secretary of Belgian Legation, 56;
saves the life of the French commanding officer, 117
Methodist Mission, burning of, 57
Mills, Colonel, General Chaffee’s Chief of Staff, 196
Missions:
arming of, 34, 35;
removal into the Legations, 49, 51;
work of Protestant and Roman Catholic missionaries, 57;
burning of Methodist, 57
Morrison, Dr., Times’ correspondent:
his kindness, 9;
stoned by rioters, 14;
his advice to the Legation Ministers, 44;
his hard work and cheerfulness, 69;
and the Chinese Christians at the Fu, 75;
wounded, 126
Myers, Captain, commander of the American marines in Peking, 17,
18, 21;
makes successful sorties, 25, 99, 100;
his hardships, 33;
saves the Dutch Legation, 57;
wounded, 103, 186
Nan-t’ang, burning of the, 131
Narahara, death of, 142
Neih, Chinese General, defeat and suicide of, 141
Norregarde, a Swedish missionary, becomes insane, 131
Norris, Rev., English chaplain at Peking:
the funeral of Oliphant, 105;
works hard on the fortifications, 118;
holds thanksgiving service, 203

Oliphant, funeral of, 105

Pei-t’ang, the Roman Catholic fortress cathedral, 36, 37;

relief of, 194
Peking—see also Legations:
Boxer rising, 7 et seq.;
burning of Feng-tai, 8;
positions of the Legations, 12;
telegraph broken, 21;
assassination of the Japanese Chancellor, 22;
burning of the missions, etc., 24 et seq.;
fires in, 25 et seq.;
description of, 26;
treachery of the Imperial Chinese troops, 45, 47;
burning of the Belgian Legation, 56;
burning of the Hanlin Library, 71;
entry of the relief force, 173 et seq.;
looting, 192
Pethick, William, Li Hung Chang’s private secretary, 11;
his opinion of the state of China, 19, 20;
his advice on the Yamen communication, 132;
and the antique China episode, 165
Pichon, M., the French Minister in Peking, 43, 78, 87, 120;
the Legion of Honour, 139
Poole, Dr., surgeon to the British Legation, 50, 52, 53, 59;
the Legation fire, 68
Porcelain, antique, 14

Rahden, Baron von, commander of Russian Legation force, 25, 30,

96;
and his undrilled soldiers, 110;
the defences of the Legations, 152;
the forbidden city, 200
Reilly, Captain, death of, 184
Roman Catholics in Peking, 36, 114
Rostand, Von, Austrian Chargé d’Affaires, 117;
and Sir Claude Macdonald, 121
Russian Legation. See Legations

Salvago Raggi, Marquis, 43, 86, 120

Seymour, Admiral, 44, 51
Shiba, Colonel, Japanese commander at Peking:
a sortie, 75;
description of, 95, 148
Shimonoseki, Treaty of, 163
Squiers, Herbert, Secretary of the American Legation, 6;
en route for Peking, 10;
his collection of antique porcelains, 14;
his hospitality, 15, 49, 73;
beginning of the siege, 22;
sends communication to Tien-tsin, 28, 29, 34;
removal to the British Legation, 53;
 renovates an old cannon, 115;
becomes Sir Claude Macdonald’s chief of staff, 134;
communications with the Yamen, 136;
the defences of the Legations, 152;
leads a sortie, 179;
Sir Claude Macdonald’s opinion of, 186
Squiers, Fargo, his brave adventure, 58;
and the Legation fire, 68
Strouts, Captain, commander of the British marines in Peking, 18;
a sortie, 25;
Legation fire, 30;
mortally wounded, 125
Su, Prince, 98

Taku Forts, taking of, 49

Tien-tsin, first relief force sent to
Peking from, 15;
message received by besieged from, 140;
the capture of, 141, 158
Tsung-li Yamen, the Chinese Foreign Office, send a guard to protect
the temple of Linqua Su, 6;
Swedish missionary’s interview with, 131;
communicates with the Legations, 136 et seq., 145, 159, 166,
169;
send in food, 139
Tung Fu-hsiang, 51, 92
“Tungchou,” the Roman Catholic church, burning of, 24

Velde, Dr., German surgeon at Peking, the excellence of his work, 73,
109, 113, 143
Waller, Colonel, 177, 196
Warren, Mr., mortally wounded, 124
Water Gate, entry of Sikhs through the, 174

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