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Modern
Communications
By
THOMAS Η. CROWLEY
GERARD G. HARRIS
STEWART E. MILLER
JOHN R. PIERCE
JOHN P. RUNYON
N E W Y O R K A N D L O N D O N 1 9 6 2
C O L U M B I A UNIVERSITY PRESS

Copyright © 1962 Columbia University Press
Library of Congress Catalog Card Number: 62-18618
Manufactured in the United States of America

Foreword
THE POSITION of man on the evolutionary ladder is, in
part, described by the range and complexity of the stimuli that
the human organism is capable of receiving, interpreting, and
communicating to his fellows. It seems unlikely that man's
ability to generate and communicate ideas is rapidly changing,
except in so far as each generation is heir to a larger cultural
heritage and to a larger range of devices that may extend the
range and power of his senses.
The degree of elaboration of the processes of communication
among men is an indication of the state of development of civili-
zation. The growth of language with an ever-increasing capacity
to describe the knowledge that man may achieve of the world
about him was perhaps the most important ingredient in man's
social and cultural evolution. The development of writing, not
only in the form in which we think of it today but also in the
more primitive forms which have yielded much knowledge
about civilizations millenia old, greatly expanded man's ability
to communicate with others at other places and also at other
times; man's sense of having a past stems from the written rec-
ord. The invention of printing greatly expanded the dimensions
of the group with which a single individual could communicate.
The rise of mathematics rendered much more efficient the com-
munication of certain kinds of information. The increased pos-
sibility and speed of travel have, as an important social conse-
quence, an increase in the ease and effectiveness of communica-
tion.
One of the great triumphs of science and technology has been
the development, within little more than a century, of virtually
instantaneous communication by electrical methods, between

vi Foreword
almost any two points on the globe. From the first commercial
installation of a telegraph line in 1844 to the transmission by
telephone of the first complete spoken sentence, "Mr. Watson,
come here, I want you," took thirty-two years. Twenty-two more
years were to elapse before the first paid radio message was
transmitted in 1898. Since then the milestones in the develop-
ment of electrical and electronic techniques of communication
have been separated by ever-decreasing intervals. Long before
striking innovation in technique has become a commonplace
in the communications system, other innovations appear on the
horizon.
Sheer inventiveness could not, of itself, have brought our
communications system to its present excellence. Coupled to
inventiveness and to imaginative engineering was a determined
effort, often highly theoretical, to understand the nature of
communication, the qualities in man that lead to the ability and
need to communicate, and the basic laws of nature that govern
all communications systems.
The telephone and the arts and techniques that contribute
to its success as one of the devices that has formed the quality
of contemporary life are, of course, only a part of the modern
system of communications. Nevertheless, an understanding of
the basic principles of telephony contributes to an understand-
ing of almost all the other means of communications. The de-
velopment of the telephone system is a fascinating case history
of the interplay between inventiveness, imagination, theoretical
analysis, and even philosophic insight. It is a case history that
is typical of a great many of the profound technological and
scientific developments that have changed the dimensions and
the nature of the world that man inhabits.
No matter what excellence we may see in the modern tele-
phone system, it is certain that further improvements will be
made. One of the world's outstanding industrial research labora-
tories, Bell Telephone Laboratories, is dedicated to the ex-
ploration of ways and means of increasing the effectiveness of
the telephone system. This encompasses a great spectrum of
activities ranging from studies of the rotting of telephone poles

Foreword vii
to research in the behavior of metals in the superconducting
state, that very remarkable state at very low temperatures in
which the electrical resistance of the metal is zero. From such
work will come a system of increased reliability, convenience,
and speed, and perhaps a system based on wholly novel princi-
ples.
June, 1962 P O L Y K A R P K U S C H

Preface
THIS BOOK is intended to describe the principles of com-
munication technology in a way which will make them easily
understood by readers whose training is in other fields. It is
the outgrowth of notes prepared for a course designed to pro-
vide teachers of basic science with a concise fund of up-to-date
background information which is otherwise widely scattered.
It may also be of interest to trained engineers and scientists
who have to do with the subject matter of one or two of our
chapters and are curious to see how their specialty plays its role
in communication systems.
Communication technology is a branch of electrical engi-
neering. The electrical engineer who earned his degree a gen-
eraton ago will find the following chapters quite surprising.
It will seem to him that about half of the book has nothing to
do vith electrical engineering, or has at best a remote connec-
tion with it. On the other hand, a young electrical engineer
with the ink fresh on his diploma may not realize the extraor-
dinary fecundity of his subject. Indeed, an organized under-
standing of a major part of the book's content has been brought
about only during the past generation. The pace of change is
so great that it behooves us from time to time to try to explain
ourselves and our works in words which will speak to a broad
circe of interested but unspecialized persons.
The authors all work in the telephone industry. Naturally
we lave drawn the great majority of our examples from this
fiele. This may lend a somewhat parochial air to the book.
T o us "communication" is the sending of a signal from one
point to another, usually in a way which permits a two-way
"conversation" to take place. We have little knowledge of the

χ Preface
technical problems of those parts of the communications in-
dustry where a one-way message is "broadcast" to a large num-
ber of recipients, so we do not speak at all of newspapers or
advertising, and only to a limited extent of radio and tele-
vision broadcasting.
The book has been written by a committee, which makes
it modern in a second sense. None of us thinks that this is the
best way to write a book, but in this case it was the only way
it could be done in the time available. Although this has led
to some unevenness, we offer the book in the belief that it will
be useful.
We would be remiss if we did not acknowledge the debts we
owe our colleagues, at the Bell Telephone Laboratories and
elsewhere, who in recent years have created the subjects which
we here summarize. We would also like to thank all those who
helped so substantially in the preparation of the manuscript.
Chapters 13-15 are based on sections of Symbols, Signals and
Noise, by J. R. Pierce (New York, Harper & Brothers, 1961),
and include material from that book.
June, 1962 THE AUTHORS

Contents
Foreword by Polykarp Kusch ν
Preface ix
ι. Introduction and Orientation ι
2. Speech Communication 13
3. Speech and Other Signals in the Telephone System 41
4. Modulation Theory 64
5. Pulse Modulation 91
6. Multiplex System 110
7. Transmission Media 129
8. Amplification and Signal Generation 153
9. Transmission Systems 178
10. Trunking and Switching 220
11. Interconnecting Networks and Trunking Plans 242
12. Central Office Control 264
13. Communication Theory 283
14. The Noisy Channel 304
15. Continuous Signals and Channels 321
Index 335

I
Introduction and Orientation
THIS BOOK will discuss some of the knowledge and techni-
cal achievements necessary to produce the means of modern
communication. We are all familiar with the fact that the ability
to communicate rapidly and conveniently has greatly affected
our lives, but by and large we are unfamiliar with the technology
of modern communication systems. This technology is inti-
mately connected to the telephone system. The invention of the
telephone satisfied a need for person-to-person communication,
as evidenced by the immense growth of the telephone system
and its complex technology. Therefore, it is no wonder that
most of the problems found in modern communications are
also those which have had to be solved in the telephone system,
and that a discussion of the telephone system will provide a
useful framework for the subject of modern communications.
It will be helpful to start with an over-all view of the functions
that are present in any communication system. Shannon, who
contributed greatly to communication theory, has provided a
workable description which we shall adopt here.1 In this descrip-
tion every communication system consists of five functional
units:
Source, the originator of a message which has to be communi-
cated;
Transmitter, that unit which accepts the message from the
source and converts it to a form suitable for transmisson
on the channel;
Channel, the link through which the message travels;
Receiver, the unit that accepts the message from the channel
Ό , E. Shannon, The Mathematical Theory of Communication (Urbana, Illi-
nois, University of Illinois Press, 1948).

2
SOURCE
TRANSMITTER CHANNEL RECEIVER DESTINATION
units
and reproduces it in a form comprehensible to the destina-
tion;
Destination, the unit to which the message is to be com-
municated.
This description is simple and logical. Figure ι. ι gives some
examples of this classification. In a simple telephone conversa-

Introduction and Orientation 3
tion [Fig. 11(a)] the speaker is the source. The transmitter takes
the sound-wave message and changes it into an electrical signal.
T h e channel may be considered as the electrical connection
between the transmitter and receiver. It can be simply two
wires or it can also include many switches, telephone exchanges,
or even the whole transatlantic cable. The receiver changes the
electrical signals back into sound waves which are heard by the
destination or listener. Figure 1.1(b) shows the same type of
classification for a television program. In this example the chan-
nel is taken as that section of the radio spectrum allotted to
the station.
T h e particular way in which a communication system is
divided into these functional units will depend upon our view-
point. Figure 1.1(c) illustrates an example in which the mouth
acts as the transmitter, the air as the channel, and the ear as the
receiver. In this case, the brain of the talker would be the source
and the brain of the receiver the destination. One classification
may be useful at one time, another at another time.
We shall be discussing some of the physical properties of
communication, not the meaning behind what is being com-
municated. For our purposes, then, it will be useful to consider
the mouth as the source of the message and the ear as the des-
tination. It is easy to see from this picture that the properties
of the mouth-ear combination determine many of the require-
ments of a telephone network. For instance, the network needs
to be capable of transmitting only those properties of speech
which are important for perception.
The exact boundary between different functions is arbitrary.
This is particularly true for the concept of a channel. At one
time we may regard the whole link between a telephone trans-
mitter and receiver as the channel. At another time it may be
useful to regard only part of that link as the channel, as when
the transatlantic cable is viewed as a channel and the compli-
cated equipment at either end is viewed as the transmitter and
receiver.
The objective of any communication system is to transmit
messages correctly and as quickly as possible. Shannon has

4 Introduction and Orientation
shown that every channel has a finite capacity. T o show this
he first defined that which is being communicated and called
it information. Its precise mathematical definition will be con-
sidered in Chapter 13. Next, Shannon showed that a capacity of
a communication channel can be defined as the maximum rate
at which information can be sent over the channel without er-
ror. If we try to communicate at a rate faster than this we are
certain to make errors. If we communicate at a rate slower than
the channel capacity we may still make errors, but it is theo-
retically possible to send the message error-free. T o send a mes-
sage error-free requires sophisticated procedures and, from a
practical standpoint, the goal of error-free transmission of in-
formation can only be approached. Nonetheless, the viewpoint
of communication theory can be very useful in providing limits
for what can and cannot be done *vith a given type of com-
munication problem.
This over-all view of the communication problem will be
taken up in Chapters 13-15, after we have learned about the
contents of a communication system in some detail. The im-
portant point for us to grasp here is that in all communication
systems there are limits to the rates at which information can
be communicated. We wish to understand why these limits
exist because they are basic to problems in communication.
What are they? A simple illustration can be given in terms of
a transatlantic telegraph line.
The requirements of early telegraph lines were relatively
simple by today's standards. An electric current was used to
represent dots or dashes and the absence of current denoted a
space. The current was turned on three times longer for a dash
than a dot. Sequences of dots and dashes were used to represent
letters through the Morse code. The speed of the early telegraph
systems was limited mainly by the speed of the human oper-
ators.
That the telegraph line itself could be a limitation became
apparent with the laying of the first serviceable transatlantic
telegraph cable in 1866. Lord Kelvin correctly appreciated the
factors which limited the rate at which a message could be sent.

He found that the time required for any electrical operation
such as turning a current on or off was proportional to the
quantity RCl2 where R and C are the resistance and capaci-
tance per unit length of the cable and I is the length from trans-
mitter to receiver. The central wire of the cable has a certain
capacitance to ground which has to be charged and discharged
through the resistance of the cable itself. If a voltage is put on
the cable at one end, a voltage does not immediately appear at
the other end of the cable. It increases from zero to the maxi-
mum value as the capacity of the cable is charged up. If the
voltage at the transmitting end is impressed and then taken
away in too short a time, no detectable voltage change will
occur at the receiver.
The word detectable in the foregoing is important. You
might imagine that there would always be some voltage change,
but in actuality no signal is detected unless it is larger than a
certain threshold. This threshold is determined both by the
sensitivity of the receiving apparatus and by the magnitude of
the spurious voltage fluctuations which always occur on any
real communication link. These fluctuations are termed noise.
If the voltage fluctuation at the receiving end due to the signal
is sufficiently less than that due to noise, the signal will pass
undetected. Figure 1.2 illustrates this. The curves represent
the transmitted and received voltages plotted as a function of
time. At the transmitting end the voltage is turned on. At the
receiving end the voltage begins to rise, comes to a level which
is less than the transmitted voltage, and, when the transmitted
voltage is switched off, the received voltage slowly drops to zero.
The voltage fluctuations due to noise are added on to the re-
ceived signal. If the transmitted voltage is turned on and off
too fast, the received signal does not have a chance to rise to
a gieat enough value to be detected through the noise.
There are two factors here which limit the rate of communi-
cation:
There is always noise on the channel. The received signal
must be larger than the spurious fluctuations due to noise.

The received signal is always attenuated, i.e., the received
signal is always less than the transmitted signal. If the
signal is attenuated too much it will not be detected
through the noise.
We have mentioned one cause of this attenuation, i.e., the
resistance and capacitance of the transatlantic cable. There
can be other causes of attenuation. For instance, there is al-
SIGNAL DETECTED SIGNAL NOT DETECTED
TRANSMITTED SIGNAL
RECEIVED SIGNAL WITHOUT NOISE
TIME — •
RECEIVED SIGNAL WITH NOISE
Fig. 1.2. Schematic of signals from a transatlantic telegraph cable
ways some leakage resistance in an undersea cable which will
cause even a steady current to be less at the receiving end than
at the transmitting end.
Because of the resistance and capacitance in the telegraph
cable the received signal does not have the same form as the
transmitted signal. This is shown in Fig. 1.2. This type of
distortion can be shown to be another form of attenuation.
In one form or another the limitations due to noise, the
finite rate of signal change, distortion, and attenuation are
present in all communication channels. The study of ways of

dealing with these limitations will form a major portion of this
book.
The concept of noise is important in communication theory.
In general, noise can be considered as any unwanted sound or
signal. It usually interferes with comprehension of the message
and, unfortunately, it is often of such a nature that it cannot be
removed from the signal. There are many different types of
noise. The most basic type is thermal noise. This type occurs
everywhere because of thermal fluctuations and can never be
eliminated. Thermal noise, sometimes called white noise, will
be present at every point in the circuit where there is resistance.
However, it can be reduced by lowering temperatures.
Impulse noise occurs with uncontrolled spasmodic surges
of signal. The sudden closing of a switch can cause a surge of
current which is heard on a telephone line as a click, or as
static. In contrast to impulse noise, thermal noise sounds like
the center of a waterfall or heavy rain on a tin roof. Impulse
noise can also be said to sound like occasional raindrops on a
tin roof. Under proper conditions the flow of individual elec-
trons in a vacuum tube can be detected as impulse noise.
Crosstalk is another type of noise. The wires of two separate
telephone conversations may come close together and the elec-
trical currents on one line can induce voltages in the other line.
These induced voltages may be heard as a faint conversation
or garble in the background. It also is not limited to the tele-
phone system and can be used to describe any induced, un-
wanted signals.
We have talked about distortion, which is the altering of a
signal. Distortion is not always noise, but the addition of a
noise is always distortion. One cannot correct for noise; foi1
some distortions one can. For instance, suppose an amplifier
distorts a signal by amplifying the low frequencies more than
the high frequencies. It is possible to add another amplifier
which amplifies the high frequencies more than the low fre-
quencies. The net result of both amplifiers is an amplified, un-
distcrted signal. Noise changes the signal in an unpredictable

way—so, by its very nature, once it is present in the signal it
is difficult to eliminate. Thus, the problem with noise is to
see that it does not become mixed with the signal in the first
place, or at least to keep it as small as possible. We shall see
in the chapter on multiplexing that when many signals are
mixed together it is very important to have no distortion pres-
ent. In multiplexing, signals are mixed together, transmitted
as one signal, and separated into the original signals at the
other end. If distortion is present a complete separation cannot
be effected.
Noise is a major problem in communications because it is
always present and always unwanted. We need some means of
measuring the effect of noise. A quantity which has been found
to be very useful is the logarithm of the signal-to-noise ratio.
T h e signal-to-noise ratio is the signal power S divided by the
noise power N. T h e signal-to-noise ratio, S/N, is usually meas-
ured in decibels. T h e signal-to-noise ratio in decibels (db) is
given by
10 log,ο "Ι-
Α signal-to-noise ratio of 10 db means that the signal power
is ίο times the noise power. A signal-to-noise ratio of 20 db
means that the signal power is 100 times the noise power and
a ratio of —3 db means that the signal power is half the noise
power.
T h e example of the transatlantic telegraph has served to
illustrate how noise and attenuation limit the rate at which
information can be communicated. Throughout the book we
shall examine ways of dealing with the problems caused by
these factors. Of course, there exist other problems in the tele-
phone system, which are caused by its immense size, rapid rate
of growth, and complexity.
As the telephone system began to develop, an immediate
problem was the connecting of the different telephones. This
was done by a human operator. A line from each telephone
terminated on a board in front of the operator, who was able

Introduction and Orientation g
to connect any line with any other line. Such a procedure was
fine as long as the number of telephones remained small, but
problems arose as the number of telephones increased. An op-
erator's arm is only so long and it will span only a limited num-
ber of line connections. The next step was to have two or more
operators, each one with a number of phones and also a number
of lines interconnecting the two operator positions. It is clear
that the number of lines between the operators need not be
as large as the number of phones for each operator, as it would
be highly unlikely that all the phones of one operator would
wish to call all the phones of the other operator at the same
time. In order to decide how many lines there should be it is
necessary to know some of the statistics of telephone calls, such
as the number of calls made, when made, for how long, etc.
The function performed by the operators was gradually taken
over by electromechanical switches. At present, even with
switches, the same problem of growth occurs. Since every tele-
phone has to be able to be linked with every other telephone,
the number of links which must be provided increases as the
square of the number of telephones. If there are Ν phones, the
number of different calls possible is N(N — i)/2; yet, if there
were a link between every two phones, the equipment needed
for any person to call any other person would be unfeasible.
Therefore, a different principle is used—that of common equip-
ment. A number of links are shared by many phones and are
assigned to a specific phone only when needed. Such a system
is possible because each phone uses the equipment only a small
portion of the time. The problems of switching, switching sys-
tems, and traffic will be discussed in Chapters 10 through 12.
With the increase in the number of phones came an increase
in the distance over which messages were transmitted. Because
the signals were always attenuated and distorted, some means
of signal amplification and distortion correction became neces-
sary. To perform these functions repeaters were developed for
insertion into the telephone lines at appropriate positions.2
:
A repeater is a telephone system term for a device which not only amplifies
the signal but also corrects for distortion.

ΙΟ Introduction and Orientation
On one cross-country telephone channel there may be up to
750 repeaters, or one every 4 miles. Because of this large num-
ber of repeaters, each repeater must amplify and transmit the
signal with practically no distortion so that the total distortion
effect of many repeaters is not noticeable. Moreover, the types
of electronic circuits which are used have to be very stable and
nondefective. Thus, the subject of signal amplification and dis-
tortion correction becomes important.
Traditionally, phones have been connected by means of a
circuit consisting of a pair of copper wires. This is efficient for
short distances, and also for long distances if repeaters are used,
but it was found to be very inefficient if a separate circuit was
used for each cross-country conversation. Consequently, as many
conversations as possible were put on a single circuit. This
meant that some way of combining several conversations at one
end of the circuit and separating them at the other had to be
developed. Such methods are grouped under the general head-
ing of multiplexing.
We will see that there are three main categories of multiplex-
ing: space-division multiplexing, which means that the different
conversations are separated in space (this is just a fancy name
for separate wires or physically separate channels); time-division
multiplexing, which means that the different conversations are
allotted different segments of time; and frequency-division mul-
tiplexing. The exact significance of these three types of multi-
plexing will not be clear until they have been discussed in
detail. It should be evident that multiplexing techniques play
an important role in modern communications. For instance,
television signals and telephone conversations are carried across
the country on a system consisting of microwave relay channels.
In such a system, microwave radio signals are beamed from the
transmitter to a receiver about 25 miles away. The signal is then
amplified and retransmitted to another receiver 25 miles fur-
ther along the route, and so on across the country. One micro-
wave relay channel can handle as many as 2000 simultaneous
telephone conversations, or a television program in place of

looo telephone conversations. This requires extensive multi-
plexing equipment at each end of the country, but generally it
is far more economical than providing individual repeaters for
each telephone circuit.
T h e most common circuits for carrying conversations con-
sist of pairs of wires. Although they are good for carrying con-
versations over short distances they are not adequate over long
distances. Other transmission media have been developed. The
microwave system mentioned above is one. Coaxial cables are
also used. Perhaps in the future waveguides and microwaves
relayed by satellites will come into use. Each transmission medi-
um has its own set of advantages and disadvantages which make
it the most appropriate choice for a particular application.
Since the present telephone system was developed to trans-
mit the human voice in the form of electrical signals, much of
the telephone system was designed around the properties of
the voice and of conversation. But modern communication is
the transmission of electrical signals, and there are important
signals other than voice—as in television, for example. The
transmission of data is another important use of a communica-
tion system, and its main requirements are speed and accuracy.
The properties of these signals are quite different from those
of voice signals. The question can be asked: What form of
electrical signals is best for sending each type of source? Thus,
the study of what type of encoding is used in a communication
system becomes essential. We shall see that different types of
encoding are appropriate for different types of transmission
media.
As a final question we can ask: How does one plan and design
a vast and complicated collection of interconnected equipment
such as the telephone network? Not only must all the separate
parts function by themselves, but they must also function prop-
erly when interconnected. Many factors enter into the design
of a system. Standards of performance must be attained, the
quality of transmission must be satisfactory, the equipment
must be reliable, and it must not be too expensive. There may

be many ways of setting up a communication system to perform
a specified job. Finding the best way is a formidable task—this
is the function of systems analysis.
In closing this introduction a word of warning is appropriate.
We are going to delve into the details of communications sys-
tems and in doing so there is danger of losing an over-all per-
spective. Somewhere in the back of our minds we should main-
tain an awareness of the function of communication. An anal-
ogy can be made between the relationship of the human being
and the human nervous system on the one hand, and a civiliza-
tion and its means of communication on the other hand. The
human nervous system is unbelievably complicated. Its function
is to integrate the parts of the body into one whole. The nerv-
ous system is not concerned with what the body does. It is not
important in itself, but only as a tool to the human being.
Similarly, the means of communication, fascinating though they
are, are not important in themselves. They are only important
as a tool to civilization. The important question concerns the
use to which they will be put. Unfortunately, this vital question
cannot be answered by technology.

2
Speech Communication
SPEECH COMMUNICATION is made physically possible by
a complicated and interrelated pair of organs: the mouth and
vocal tract, which act in combination as a transmitting appa-
ratus, and the ear, which acts as a receiving apparatus. In a
very real sense the telephone system is merely an extension in
space of the distance between the mouth and ear. Much of the
design of telephone and radio systems has been made with this
fact implicitly in mind. However, communication systems are
not exclusively designed for speech. There is also music for the
ear and the whole world for the eye. Communication systems
are not even designed exclusively for human beings. Communi-
cation between machine and machine is becoming increasingly
important. A system consisting of a machine on each end of a
communication link has vastly different requirements from a
system with a human being on either end. But even though
speech communication is not by any means the whole of the
subject, it is sufficiently important to deserve considerable at-
tention.
There is another reason why the study of speech communica-
tion will be useful. The proper understanding of such a highly
technical phenomenon as a communication system requires a
considerable degree of sophistication. There are a number of
mathematical techniques and new points of view which must be
presented. It is not the purpose of this discussion to be mathe-
matically elaborate, but such concepts as Fourier analysis, signal
representation, modulation, and noise, to name a few, must be
introduced. The study of speech communication will require
these concepts and will provide a convenient basis for their un-
derstanding.

14 Speech Communication
r
Fig. 2.1. X ray of male vocal tract
THE MOUTH AS A MESSAGE SOURCE
WASAL CAVITY
fiiil
VOCAL CORDS
T R A C H E A
10/iotsf
2o mr.
The vocal tract (Fig. 2.1) operates in the following manner.
Air from the lungs comes up through the trachea and passes
through a constriction called the glottis, which is formed by

Speech Communication 15
the space between the vocal cords. The air continues up
through the vocal tract, consisting of the throat and mouth, and
then flows out through the mouth. Two major types of sounds
can be produced—voiced sounds and unvoiced sounds. The
vowels a, e, i, o, u, are examples of voiced sounds. In voiced
sounds the acoustic energy is produced by the vocal cords, which
open and close rapidly, sending puffs of air through the vocal
tract. The rate at which the vocal cords open and close deter-
mines the pitch of the voice. For male voices the vocal cords
usually vibrate at a frequency between 80 and 120 cps, whereas
female voices usually range between 120 and 240 cps. The air
puffs, if heard by themselves, make a sound something like
a buzz. This sound cannot be heard in a pure form but only
as altered by its passage through the vocal tract. Thus, the
sounds which come from the mouth have different character-
istics depending on the shape of the vocal tract. You can make
experiments with your own mouth by repeating different voiced
sounds and sensing the shape of your mouth and throat. It is
possible to vary the pitch, keeping the same shape of the vocal
tract, and vice versa, to vary the shape of the vocal tract while
keeping your pitch constant. In your natural speaking voice do
you use the same pitch for the different vowels? Can you dis-
cover why the vowel in the word heed is called a front vowel
and why the vowel in the word hoot is called a back vowel?
The other main category of sounds, unvoiced sounds, is pro-
duced by a turbulence at some point in the vocal tract. The
consonants h, t, s, and ρ are examples of unvoiced sounds: h is
produced by a closure at the back of the mouth, t by the tongue
at the front teeth, s by front teeth and tongue, and ρ by the
front lips. Some consonants are combinations of voiced and
unvoiced sounds; ρ and b are an example of an unvoiced-voiced
consonant pair. The two consonants are produced with the
same mouth movements except that the latter has voicing added.
How many different sounds are there in English? There are
about 40 different phonemes, such as ρ and b, which are rec-
ognized as different, and which can change a word if one is

i6 Speech Communication
substituted for another, as the words pat and bat. But each
phoneme can be spoken in many different ways, depending
upon which other phonemes precede and follow it.
Since the sounds of speech are made by the rapid change in
shape of the mouth, the question can be asked: How fast can
a person speak? The mouth and throat are rather large, massive
organs and the muscles which move them have their limitations
of strength. Also, the nerve system of the body, which activates
the muscles, has its own speed of working. These factors com-
bine to limit the rate of speech to a maximum of about 10 dif-
ferent syllables per second or about 20-30 different sounds per
second. This is the rate of sound production.
How can we characterize the different sounds of speech? A
so-called parametric description would be on" way. If we could
find some parameters which adequately des. ribe the shape of
the vocal tract, together with the positic 1 of the lips and
tongue, we would be making a good start. Of course, the pitch
of the vocal cords would also have to be specified. We will come
back to such a description when we discuss voice synthesizers,
or vocoders.
There is another very useful way of describing the different
types of sounds. This is in terms of a time and frequency analy-
sis. We will here digress from our main line of description in
order to introduce those parts of frequency analysis or Fourier
analysis, as it is called, which will be of use to us. Fourier
analysis will not only be useful in describing speech, but will
also be of immense value in describing what happens to signals
in any electrical circuits.
FOURIER ANALYSIS
Figure 2.2 shows a graph of a short segment of speech. The
distance along the vertical axis is proportional to the pressure
of the sound wave. The distance on the horizontal axis repre-
sents time. In general, the variations of pressure with time in
speech are extremely complicated and very few regularities can
be detected. In order to see how to analyze speech we will first
consider some variations with time which are more regular.

One of the simplest types of regularities is exhibited by the
motion of a point on the circumference of a wheel moving at
constant speed. T h e motion is periodic which means that after
a certain time ( Τ , called the period) the motion repeats itself.
In the case of the revolving wheel the period Τ is the time of
Fig. 2.2. Sound-pressure variations as a time function
one complete revolution of the wheel. T h e frequency f of a
periodic function is the number of repetitions per second and
is given by the reciprocal of the period, f = i/T.
If the motion of the point on the circumference of the wheel
is projected onto a vertical line which passes through the center
of the wheel, a particularly simple form of periodic motion
0 = 2 7 7 f t
Y = A SIN 2 7 r f t f = Y
Fig. 2.3. Plot of sine 2nft and cosine 2π/ί

i8 Speech Communication
results. A graph of this motion is shown in Fig. 2.3. It is called
a sine function and can be represented by the formula
Y(t) = A sin (271-/Ο, (2.1)
where Y(t) is the displacement of the projected point and is
a function of the time t, and A is the amplitude of the sine
function corresponding to the maximum displacement. In our
example, A would be the radius of the wheel and / is the fre-
quency of rotation in cycles per second. The quantity 2irft is
the angle of rotation θ measured in radians.
A different type of periodic motion can be obtained by pro-
jecting the motion of a point on the circumference of a wheel
onto a horizontal axis instead of a vertical axis. This motion
is also shown in Fig. 2.3 and is represented by the formula
x(l) = A COS (Q7t/0· (2.2)
It is apparent that the sine function and the cosine function
are related by a rotation of the point one-fourth of the way
around the circle, or by an angle θ = π/2 rad. This can be ex-
pressed by the formula
sin [27r/i + (7Γ/2)] = COS (27r//). (2.3)
If the sine function is rotated through an arbitrary angle φ,
it can be expressed as a sum of both a sine and a cosine function,
sin (2π/< + φ) = cos <p-sin 27rfl + sin φ-cos 2π/ΐ, (2.4)
where φ is called the phase angle. Figure 2.4 shows this relation
graphically.
Sine and cosine functions are useful mathematical tools for
understanding natural phenomena. The small-amplitude move-
ment of a pendulum, and almost all small elastic vibrations,
are examples of motions which can be represented by sine
functions. Their immense importance, however, is due to a
property discovered by Fourier and embodied in the Fourier
theorem. This theorem states that a periodic time function of
period T, F(t), no matter how complicated, can be considered
as a sum of sine functions whose frequencies are integer mul-

0.86 SIN
2 7 7 t
SIN ( ^ γ ^ + *> ) = COS y> SIN ^ γ — + SIN y> COS ^ ψ ^ ·
tiples of the fundamental frequency /T. Each frequency
2jtm/T will have a specified amplitude Sn and a specified phase
<pn. This theorem can be written as
m = s 0 + s, sin ζ φ + + & sin ( ^ ψ + φ^
+ ü sin ( ψ + J . sin ( * ψ + + · · ·.
The dots represent missing terms and S„ sin [(2writ/ Τ) + φη] rep-
resents a general or nth term. This sum can be abbreviated by

using a summation symbol £ which indicates that all terms
n-0
from η = 0,1,2,3, e t c
> U
P t o
infinity, should be summed,
m = + (2.5)
The multiples of the fundamental frequency are called har-
monics. In practice, the amplitude of the terms which repre-
sent high harmonics (i.e., large n) are usually quite small. This
means that most time functions can be approximated quite well
by a reasonable number of terms. Figure 2.5 shows a straight-line
time function and the Fourier series which represents this func-
tion. One term of the series does not give a good approxima-
tion, whereas four terms represent the function closely.
Fourier series are of immense use in dealing with periodic
functions. It is a fact, however, that most variations which oc-
cur are not strictly periodic. Thus, our analysis has to be
extended to include nonperiodic functions. Without going into
the details we will say that this can be done by replacing the
sum over the harmonic frequencies, fn = nf=n/T, by an
integral over all frequencies. Thus, F(t) is given by the integral
F(t) = JT- S(f) sin 21rft + φ(/) ] df, (2.6)
where S(f) is the amplitude of the sine function whose fre-
quency is /, and <p(f) is the phase which also depends on the
frequency.
Two concepts, energy and power, are important for the study
of communication. All forms of communication take place by
energy exchange, and so it is of interest to see in what way and
with what power the energy is transferred from one place to
another. Power is energy divided by time, or the rate at which
energy is exchanged. For instance, we can ask: What is the
power in speech?
The energy £ in a function of time is proportional to the
integral
Ε = f*m F*{t) dt. (2.7)

TERM

V V
ν
2 TERMS-'' F (1) = COS 277t +£· COS 877-t +
COS 10/71 C
O
S (477 "t +
S. · · · + COS 277nt +
n= t,3,5,7
N
•^«SS. PERIODIC FUNCTION
BEING APPROXIMATED
/ V
' ' PORTION
(^-"PLOTTED
4 TERMS
. PER100,Τ .
t = i
Fig. 2.5. Successive approximations of a truncated
Fourier series to a periodic function

2 2 Speech C o m m u n i c a t i o n
RECTANGULAR
TIME PULSE
k—to—Μ TIME — •
Fig. 2.6. Rectangular pulse with associated energy-density spectrum
A good example of this is the energy in a voltage pulse which
is placed across a resistance R. T h e power Ρ is Ρ — V2(t)/R
and the energy developed across the resistance is
Ε = j " Pit = I j " V*{t)dt,
which has the form of (2.7). It can be shown that where the
impedance of the medium is independent of frequency, the
energy is also given by an integral over the frequency domain,
Ε = f* S2(f) df. (2.8)
In words, the energy is proportional to the sums of the ampli-
tude of the sine function squared. Y o u will notice that the
energy does not depend on the phase of the sine function. It
is often convenient to plot S2 (f), called the energy-density spec-
trum, as a function of frequency. Figure 2.6 shows a function
of time and below it a plot of S2(f) for that function. Where

S2
(f) is large, there is a lot of energy at that frequency. It is
interesting to note that when the time function becomes almost
periodic the energy concentrates at those frequencies which are
multiples of the fundamental frequency. A truly periodic func-
tion has energy only at the harmonic frequencies.
At times it is more convenient to deal with power than with
energy. Then, the power is given by the integral of the power-
density spectrum
P = if0" df,
where S'2
(f) is the power-density spectrum.
SOUND S P E C T R O G R A M S AND S P E E C H
We will see how the power-density spectrum can give us
some insights into the nature of speech sounds. So far, we have
H
i S
O
O
O
t
o
3
y 20001—
0
S
H
O
U
L
D W
E
. 1 .
OA
C
H
A
S
E
T
S T
S 2.0 S
E
C
O
N
O
S
T
H
O
S
E Y
O
U
N
G OU--T-LAW C- - ΟW - - - B
O
Y - - - 5
Fig. 2.7. Spectrogram of a sentence of speech spoken by a male voice
only shown graphs of amplitude versus time, or energy density
versus frequency. The sound spectrogram is a plot of the power-
density spectrum as a function of time. Figure 2.7 shows such
a spectrogram of a sample of speech. Time flows along the hor-
izontal axis, while frequency is plotted along the vertical axis.
The scale goes from ο to about 3000 cps. A third variable,
power, is represented by the intensity of blackening. Pick an
instant of time; then, in the vertical direction, the power-

density spectrum is shown as degree of darkness. The black
regions are those frequencies which have most of the power.
At a slightly later instant of time conditions have changed, the
power is concentrated at different frequencies, and the spectrum
reflects these changes. You will notice vertical striations in the
sound spectrogram which indicate rapid fluctuations of energy
with time. These striations correspond to the pitch periods in
the voiced sections of the speech. Each dark vertical stripe cor-
responds to a puff of air passing through the vocal cords.
The sound spectrogram is produced by an electronic fre-
quency analyzer, called the sound spectrograph. Since it is im-
possible to build a device that will analyze the power-density
spectrum at an instant of time, a finite duration of time must
always be used. Thus, the power-density spectrum which is
plotted is the average power-density spectrum over a finite
duration of time. The time interval chosen for the analysis
must be shorter than the time period of important power
fluctuations, or otherwise these fluctuations will be averaged
out. For instance, in Fig. 2.7 the time duration must be less
than the time between pitch periods to permit the pitch periods
to appear. Here the time duration is about 5 msec, which is
shorter than the pitch period of about 10 msec. You can appre-
ciate that in order to see the detail of the power-density spec-
trum it is desirable to make the average over as small a time
interval as possible. However, too small a time interval has
great disadvantages since there is a most important interrela-
tionship between the time domain and the frequency domain.
Turn a sound spectrogram on end, and, instead of consider-
ing it as a frequency analysis at a given instant of time, con-
sider it as the time analysis of the power at a given frequency.
When we do this it is necessary to average over a definite range
of frequencies. If we want to see detail in the frequency domain
we must average over a small range of frequencies. However,
the range of frequencies which are averaged and the time dura-
tion which is averaged are not independent. If a small time
duration is used, the range of frequencies which is averaged
has to be large; and, vice versa, if the time duration is large

the range of frequencies has to be small. The product of the
time duration and the frequency range is about unity. Thus,
the spectrogram in Fig. 2.7 which has an average time of 5 msec
must be an average over a frequency range of 200 cps.
T h e interdependence of the frequency domain and the time
domain holds for all communication systems. T h e range of
frequencies which a communication system can transmit is
-
h
_
5000
Ο
Ζ
g 4000
£ 3000
1
0
m
d 2000
υ
OL-
L
0.5 1.0 1.5 SECONDS
150 CPS BUZZ 750 CPS BUZZ
Fig. 2.8. Spectrogram of a buzz source
called the bandwidth. A system with large bandwidth can
transmit much detail in a given interval of time, while a sys-
tem with small bandwidth can transmit little detail in the same
interval of time. In order to transmit Ν independent numbers
per second a bandwidth of N/2 cps will be needed.
Figure 2.8 shows a spectrogram of sound from a periodic
source which sounds like a buzz. These spectrograms clearly il-
lustrate the relationship of the fundamental and harmonics in
a periodic function. In this spectrogram the time average is over
a period of 50 msec. Consequently, the power-density spectrum
is averaged over a frequency range of only 20 cps. One differ-
ence between a voiced sound and a buzz is that the intensity of
the harmonics in the buzz falls off more or less uniformly as

2-9- Spectrogram of vowels spoken by a male voice
QNOD3S d3d S310AD

the frequency increases, whereas the energy of the harmonics
for the voiced sound tend to be concentrated in two or three
broad bands.
These bands of energy are easily seen in Fig. 2.7. The central
frequencies of these bands are called the formant frequencies
and they represent the resonances of the vocal tract. The effect
of the vocal tract is to concentrate the acoustic energy into fre-
quencies near these resonances. The individual harmonics due
to the pitch frequency cannot be seen in Fig. 2.7. In order to
bring out the formant frequencies clearly, it is necessary to
average the power spectrum over an interval of about 5 msec
and a frequency spread of about 200 cycles. Thus, individual
pitch harmonics are not visible.
The shape of the vocal tract changes as speech is uttered,
and this change is reflected in the spectrogram as a shift in for-
mant frequencies. Figure 2.9 shows a spectrogram of a male
voice speaking the vowels in the words hid, head, had, ah, note,
and hoot. The constancy of the formant frequencies for each
vowel and the difference between vowels is evident. One means
for specifying the acoustic nature of the vocal tract is the listing
of the formant frequencies. The first three formant frequencies
give an accurate enough description for speech. However, an
important limitation to this is that the formant frequencies dis-
appear during the silent and unvoiced portions of speech.
Notice the s sounds in Fig. 2.7. The sound energy is not
localized in any particular band of the spectrum. The energy
is predominantly in the higher frequencies, but there is no evi-
dence of any harmonic structure. This, then, is a source of
sound energy very different from that in voiced sounds. In con-
trast to a buzz source for voiced sounds, this type of source is
often called a hiss source. It is usually produced by a turbulence
around a constriction in the mouth or throat. A characteristic
of such sources is that all frequencies are present with com-
parable energy and that the time function shows no periodic
structure. Figure 2.10 shows a spectrogram of a source which
carries this characteristic to the extreme. All frequencies, at
least in the bandwidth 200-3000 cps, are present with equal

6ΟΟΟ1—
5000
a
ζ
ο 4000
Ο
UJ
10
S 3000
ID
ij 2000
>
ο
1000
Ο1
—
0.5 S E C O N D S
WHITE NOISE
Fig. 2.io. Spectrogram of a noise source
energy per unit time. Such a source is produced by thermal
noise and is often called a white noise source.
There are thus two types of energy sources found in speech
-—a buzz type of sound and a hiss type of sound. T h e buzz type
of sound is produced by the vocal cords and is used to excite
the vocal tract. T h e hiss type of sound is produced by turbu-
lence at constrictions in the vocal tract.
We are now in a position to ask: How rapidly can a message
be transmitted by speech? We will not be able to give an answer
for some time, but at least we can start by understanding the
question. What are some of the parameters needed to specify
speech? First, we will need information to specify the formant
frequencies. Besides the first three formant frequencies, it will
be necessary to specify the intensity of the speech and the type
of energy source, voiced or unvoiced. It is important that none
of these details change very rapidly. We have seen that if there
is much detail which needs to be specified per unit of time the

bandwidth needed is large. Correspondingly, if there is not
m u c h detail, i.e., if the information-bearing elements do not
change rapidly, then a small bandwidth is needed. In the chap-
ters on communication theory it will be seen that bandwidth is
not the best measure of the information needed to specify
speech but that it is a useful first approximation. A more ac-
curate picture must also take into account the signal power
to noise power ratio.
W e can thus rephrase the question: How rapidly can a mes-
5000
4000
3000
2000
1000
f 1 ρ
"Sft^'f!, •SEES'' -
0 0.5
SHOULD WE CHASE
Fig. 2.11. Spectrogram showing fluctuations of formant frequencies
sage be transmitted by speech? It becomes: W h a t is the band-
width needed to specify speech? A high-fidelity system which
transmits speech and music satisfactorily can be constructed
with a bandwidth of 10,000 cps. A long-distance telephone sys-
tem has a bandwidth of about 3000 cps. T h e speech quality with
this bandwidth is not high fidelity but it is quite acceptable.
T h e r e have been estimates that a bandwidth from about 300-
600 cps should be sufficient to transmit intelligible speech. Such
a statement has no meaning unless a device can be built which
will do the job satisfactorily. W e will see later how successful
such attempts have been. T o see some of the reasons why a
small bandwidth may be sufficient, turn to Fig. 2.11. It shows
a spectrogram of speech in which the variations of the first

go Speech Communication
three formant frequencies have been traced. One can see that
the formant frequencies do not vary at a rapid rate.
Let us assume, for the moment, that the bandwidth necessary
to transmit speech is much less than the bandwidth actually
used in nature. The question can then be asked: Why is such
an excess of bandwidth used? The reason lies in the properties
of the air and the ear, and in the requirements necessary to
recognize the directions of sound. Sound of low frequency does
not carry well. Also, it is difficult to get much energy into low-
frequency waves. Although the ear can hear low frequencies, its
sensitivity to them is small. These effects combine to make it
very inefficient to use low frequencies for human communica-
tion. To avoid these difficulties nature has used a clever device.
The buzz sound of the vocal cords or the turbulent hiss sound
contain high frequencies which carry well. It is also important
that a sufficient amount of acoustic energy can be produced by
these sources to serve as a carrier of the speech message. By them-
selves they do not contain speech information. The shape of the
vocal tract modulates the speech carriers. Thus, superimposed
on the carriers are the information-bearing variations of speech.
The ear somehow demodulates or decodes this carrier and sends
the information-bearing signals to the brain.
Modulation, which is the superimposing of an information-
bearing signal upon a carrier signal, is very important in modern
communication systems and will be dealt with later in the book.
It is interesting to see that modulation is not exclusively a man-
made device, but one which is extensively used in nature. The
concept of modulation is useful in understanding communica-
tion systems. This concept separates the information-bearing
variations in the signal from the carrier wave. The information-
bearing elements are quite distinct from the physical means of
transmitting them.
How much acoustical power is produced by a person speak-
ing? The power produced by the voice must be detected and
changed into electrical signals in order to be transmitted. Thus,
any voice communication equipment must be designed to use
the amount of power which is developed in everyday speech.

Figure 2.12 shows a time pattern of a sentence of speech. T h e
horizontal axis represents time, and the distance along the verti-
cal axis is proportional to the sound pressure. T h e intensity is
proportional to the square of the pressure. Figure 2.3 is the
same type of picture with the time axis greatly expanded. It is
seen that there are rapid fluctuations in the intensity of the
syllables. Speech is characterized by both rapid increase and
decrease of intensity of sound. It therefore makes a difference
whether one speaks of instantaneous speech power or of average
speech power. Figure 2.13 shows an intensity power plot of the
word "quiet" showing both instantaneous power and a mean
IΨ ff ^ V Ψ
1« 2 . 5 SEC o|
Fig. 2.12. Pressure-envelope pattern of the sentence
"Few thieves are never sent to the jug"
power averaged over 10 msec.1 T h e instantaneous power shows
sharp peaks of up to 1500 /iw at the pitch periods. T h e average
speech power is much less, rising to about 40 μν for the word
"quite" uttered at normal conversational level.
T h e average speech power for American conversation is ap-
proximately 10 μλν or one-hundred-thousandth of a watt. T o
produce this power the air particles near the mouth vibrate
through a distance of about io~''cm. This is very small compared
to our usual standards of power. A IOO-W lamp uses 10,000,000
times more power. When one talks as loudly as possible the
1 Adapted from H. Fletcher, Speech and Hearing (Princeton, New Jersey,
D. Van Nostrand C o m p a n y , Inc., 1929).

ιβοο
<
0
I- 1400
Ϊ
Ο
g 1200
i
ζ
^ 1000
I-
*η
£ 800
Ζ
<η
8 βοο
ul
Ζ
ζ 400
£
Ζ
200
1Λ I i
AVERAGE 50 r
INTENSITY 01
0.05 0.10
TIME IN SECONDS
0.15 0.20
Fig. 2.13. Speech-intensity plot of the word "quite" (Fletcher, 1929)
average speech power increases to about one-thousandth of a
watt. A soft whisper is about one-billionth of a watt. Different
sounds of speech have different average powers—for instance,
vowels have more power than consonants. In terms of decibels
there are about 70 db between a whisper and a shout, and a
normal voice is about 40 db above a whisper.
CHARACTERISTICS OF THE EAR
Before exploring how the properties of speech help determine
the structure of modern communication systems, it will be
necessary to look at the receiving end of speech communication,
the ear. The ear is a wonderful acoustical, mechanical, and elec-
trical transducer that is very well suited to our needs. Figure
2.14 shows a schematic of the ear, partly in cross section.2 The
2 From B. P. Bogert, "A network to represent the inner ear," Bell Labora-
tories Record, 28, 481-85 (1950).

EXTERNAL EAR I MIDOLE J I N T E R N A L EAR
, V E S T I B U L A R APPARATUS
WITH SEMICIRCULAR C A N A L S
H A M M E R
(MALLEUS)
A N V I L
( I N C U S ) ·'
STIRRUP
(STAPES) .
V E S T I B U L A R
V- NERVE .
COCHLEAR
: NERVE
P I N N A
AUDITORY
C A N A L
•FF-V ' ' E A R D R U M -"'"·. V>V
(TYMPANIC M E M B R A N E ) '
O V A L W I N D O W ' •;-;.·
ROUND W I N D O W - '
EUSTACHIAN TUBE
NASAL CAVITY
OVAL WINDOW
HELICOTREMA-
S T I R R U P
SCALA VgSTIBUlA
SCALA TTMPANi
R O U N D .
WINDOW
C O C H L E A R
PARTITION'
Fig. 2.14. Schematic diagram of the human ear (Bogert, 1950)
ear is functionally divided into three parts: the outer ear, the
middle ear, and the inner ear. Each part of the ear serves one or
more quite definite functions.
The outer ear consists of the "ear" which is called the pinna
and serves to collect the sound waves and direct them to the
auditory canal and on to the eardrum. The asymmetry of the
pinna also helps in distinguishing the direction of sound. With-
out this there would be a horizontal axis of symmetry pass-
ing through the ears so that sounds coming from the front and
from the back of the head would be heard in an identical
way.
The auditory canal serves the purpose of protecting the ear-
drum. It also provides a quarter-wave resonance at around
5000 cps which increases the sensitivity of the ear in this fre-
quency region.
The bones of the middle ear transmit the vibrations of the
eardrum to the oval window of the cochlea. They help couple

the motions of the air with the different motion of the liquid-
filled cochlea. By their mode of vibration the middle-ear bones
also serve to protect the inner ear from loud noises, that is, the
mode of vibration of these bones at high sound intensity is
different from their mode at low intensities.
The inner ear consists of the cochlea and the vestibular ap-
paratus with its associated semicircular canals. The semicircular
canals are part of the spatial orientation sense and are not con-
cerned with hearing, so they will not be discussed further.
Such a description is highly simplified but it may help to show
how remarkably well suited the ear is to its task.
The inner ear and its operation deserves more of our atten-
tion. The cochlea, so called because of its shell-like shape, con-
tains a remarkable wave-analyzing mechanism. A schematic of
an unrolled cochlea is shown in the lower part of Fig. 2.14. In
its essential details the cochlea consists of a tube separated into
halves by the cochlear partition, an important part of which is
the basilar membrane. The elastic constant of the basilar mem-
brane varies by a factor of about 100 over its length. It is stiffest
at its basal end near the oval and round windows, and it is most
stretchable or flabby at the apical end where there is an opening
connecting the upper and lower halves of the cochlea.
Suppose there is a displacement of the oval window. If the
movement is very slow, as would occur for low frequencies, the
liquid in the upper half flows from the basal to the apical end
of the upper vestibule, flows through the hole in the apex and
into the lower vestibule, then back to the basal end of the
cochlea where, having no other place to go, it displaces the round
window. During this whole process the membrane displaces but
slightly, as shown at the top of Fig. 2.15.
As the frequency of motion at the oval window is increased,
there is a dynamic conflict between the inertia of the liquid in
the cochlea and the force required to displace the elastic mem-
brane. If the membrane is displaced, the mass of liquid beyond
the point of displacement need not be set into motion. Because
the inertial forces increase with increased frequency, a higher

.OVAL WINDOW
2
DISPLACEMENT
OF OVAL
WINDOW
ZERO
FREQUENCY
-ROUND WINDOW
LOW
FREQUENCY
G
"UNROLLED"
COCHLEA "
BASILAR
MEMBRANE
HIGH
FREQUENCY
DISTANCE ALONG BASILAR MEMBRANE — •
ENVELOPE OF BASILAR MEMBRANE DISPLACEMENT
Fig. 2.15. Motion of fluid in the cochlea produced by the displace-
ment of the oval window, showing frequency-dependent displace-
ment of the basilar membrane
frequency is more likely to cause membrane displacement rather
than mass motion.
Because of the variation in elasticity along the basilar mem-
brane, the point of maximum displacement is a function of fre-
quency. High-frequency displacements occur only at the basal
end of the membrane while low-frequency movements cause the

membrane to move throughout its whole length but with great-
est displacement at the apical end. The curve at the bottom of
Fig. 2.15 shows the outline of the basilar membrane displace-
ment for pure sine-wave inputs of various frequencies. Low-
frequency tones displace the high-frequency region of the mem-
brane, but high-frequency tones do not affect the low-frequency
portion of the membrane. Thus, it is not surprising that low-
frequency tones can interfere with or mask high-frequency tones
while high-frequency tones do not have much effect on the hear-
ing of low-frequency tones.
The next stage in the hearing process is the production of
nerve impulses. Along the length of the basilar membrane are
found rows of thin cells called hair cells which are attached both
to the basilar membrane and to the beginnings of the auditory
nerve. Motion of the basilar membrane causes a stimulation of
the hair cells which in turn causes electrical impulses to travel
up the nerve toward the brain. These electrical impulses are
presumably analyzed by the brain, and in such a way we reach
a conclusion about what we hear.
The cochlea thus works as a mechanical frequency analyzer.
But it also acts as a time analyzer. In Helmholtz's theory of the
operation of the ear there were a number of resonant analyzers.
This would be analogous to the strings on a piano. There would
be a number of such strings, each resonant to a particular fre-
quency. We could thus determine the frequency by detecting
which string was resonating.
Suppose that a person listens to two tones alternately. One
tone is fixed in frequency at 1000 cps, the other tone can be
shifted in frequency. He tries to match the variable frequency
tone to the fixed 1000-cps tone. Most people find a match
within the range 996 to 1004 cps about half the time, and so
we say that the accuracy of determining pitch at 1000 cps is
plus or minus 4 cps. Thus, the bandwidth of our pitch detecting
mechanism is about 8 cps. But the time resolution of the ear
is about 1 msec. In order for this to be true, the basilar mem-
brane must not be a sharp frequency analyzer but must have a
bandwidth of 1000 cps or more. We can conclude from this

that the detection of pitch involves something more than
mechanical frequency analysis by the basilar membrane.
The fact that the time resolution of the ear is limited to about
1 msec is related to a change in the way frequencies above and
below 1000 cps are heard. For frequencies below 1000 cps the
time fluctuations corresponding to the pressure variations of
the sound wave can be observed in the nervous system, but this
is not so for frequencies above 1000 cps. In our hearing the
detailed time structure of the sound wave is lost. Another way
of expressing the same thing is to say that the ear is phase-
insensitive for high frequencies.
Because the phase of the high-frequency components of speech
are not perceptually important, a certain amount of phase dis-
tortion in telephone circuits is permissible. This simplifies the
design and construction of the circuits, but there are drawbacks
to such simplifications. The telephone system is now being used
for other signals besides speech, and a distortion which is not
important for speech may be undesirable for another type of
signal.
We have mentioned that the ear can accurately detect the
pitch of a pure tone. It does not have the same accuracy in
detecting the pitch period of speech. This fact is used in single-
sideband modulation. In this type of modulation, which will be
discussed in detail later, the processed speech is often shifted in
frequency by a few cycles per second. A frequency shift of a few
cycles per second is tolerated quite well by the ear, and so makes
this modulation scheme feasible.
The mouth only radiates a small amount of power, thus the
ear must be a very sensitive acoustical instrument. There are
different types of sensitivities which can be measured. One im-
portant measure of the ear's sensitivity is the threshold of audi-
bility for pure sinusoidal tones. This is the minimum intensity
at which a tone can be heard when no other sounds are present.
Figure 2.16 shows a curve of the threshold of audibility which
is given by the American Standards Association. The scale is
in terms of sound-pressure level in decibels with respect to
0.0002 dyne/cm2
which is taken as the zero db reference level.

140
2
120
<
n
ui
Ζ
5 100
Ν
ο
ο
Ο
ό βο
>
IU
_>
« 20
α
ο.
ο
ζ
Ο
1
0
- 2 0
•
•

/
THRESHOLD OF /
PHYSICAL SENSATION
20 40 60 <00 200 400 600 1000 2000
FREQUENCY IN CYCLES PER SECOND
4000 10,000
Fig. 2.16. Threshold of audibility as set by American Standards
Association
You will remember that db represents 10 logi0 of the power ratio
and so represents 20 logi0 of the pressure ratio. Zero db sound-
pressure level corresponds to a power of i o ~ u w/cm2 or 0.01
/n/tw/cm2, a very small power indeed. This curve is an average
of many ears. Individual ears will vary considerably from this
curve. It is well known that as a person grows older sensitivity
of the ear to high-frequency tones decreases.
Communication rarely takes place in absolutely quiet sur-
roundings, so it is important to find out what effects the extra-
neous sounds or noise have on the ability to hear sounds, and
speech in particular. Extraneous sounds have the general effect
of raising the threshold of hearing. This effect is called partial
masking. If the noise is loud enough, it may totally mask the
desired sound. T h e amount of masking one sound has on an-
other depends both on the composition of the masking sound
and on the nature of sound that is masked. It will not be possible
to go into the subject of masking in any detail but one illustra-

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as a most decided opponent of Eugenius IV., and wrote in
A.D. 1439 from this point of view his history of the council. In
A.D. 1442 he entered the service of the then neutral Emperor
Frederick III., was made Poeta laureatus and imperial
councillor, and as such still fought for the independence of the
German church. But in A.D. 1445, with all the diplomatic arts
which were so abundantly at his disposal, he wrought to
secure the subjection of the emperor and German princes
under the pope (§ 110, 10). Made bishop of Siena in
A.D. 1450, he was raised to the cardinalate by Calixtus III. in
A.D. 1456, and two years later ascended the papal throne as
Pius II. The lasciviousness of his earlier life is mirrored in his
poems, novels, dialogues, dramas, and letters. But as pope,
old and weak, he maintained an honourable life, and in a bull
of retractation addressed to the University of Cologne
exhorted Christendom Æneam rejicite, Pium recipite!
§ 118.7. Reforms in Church Policy in
Spain.―Notwithstanding the church feeling awakened by the
struggle with the Moors, a vigorous opposition to papal
pretensions was shown during the 14th century by the
Spanish princes, and after the outbreak of the great schism
the anti-pope Clement VII., in A.D. 1381, purchased the
obedience of the Spanish church by large concessions in
regard to appointment to its bishoprics and the removal of
the abuses of papal indulgences. The popes, indeed, sought
not unsuccessfully to enlist Spain in their favour against the
reformatory tendencies of the councils of the 15th century,
until Ferdinand of Aragon [Arragon], A.D. 1479-1516, and
Isabella of Castille [Castile], A.D. 1474-1504, who had on
account of their zeal for the Catholic cause been entitled by
the pontiff himself “their Catholic majesties,” entered so
vigorous a protest against papal usurpations, that toward the
end of the 15th century the royal supremacy over the Spanish
church had won a recognition never accorded to it before.
They consistently refused to acknowledge any bishop

appointed by the pope, and forced from Sixtus IV. the
concession that only Spaniards nominated by the Crown
should be eligible for the highest ecclesiastical offices. All
papal rescripts were subject to the royal approval,
ecclesiastical tribunals were carefully supervised, and appeals
from them were allowed to the royal judicatures. The church
had also to give ordinary and extraordinary tithes of its goods
and revenues for State purposes. The Spanish inquisition
(§ 117, 2), thoroughly recognised in A.D. 1483, was more of a
civil than an ecclesiastical institution. As the bishops and
inquisitors were appointed by the royal edict, the orders of
knights (§ 98, 13), by the transference of the grand-
mastership to the king, were placed in complete subjection to
the Crown; and whether he would or not Alexander VI. was
obliged to accord to the royal commission for church and
cloister visitation and reform the most absolute authority. But
in everything else these rulers were worthy of the name of
“Catholics,” for they tolerated in their church only the purely
mediæval type of strict orthodoxy. The most distinguished
promoter of their reforms in church polity was a Franciscan
monk, Francis Ximenes, from A.D. 1492 confessor to
Isabella, afterwards raised by her to the archbishopric of
Toledo, made a Roman cardinal by Alexander VI., and grand-
inquisitor of Spain in A.D. 1507. He died in A.D. 1517.

§ 119. Evangelical Efforts at Reform.
Alongside of the Parisian reformers, but far in
advance of them, stand those of the English and
Bohemian churches represented by Wiclif and Huss.
The reformation aimed at by these two was
essentially of the same kind, Wiclif being the more
original, while Huss was largely dependent upon his
great English precursor. For in personal endowment,
speculative power, rich and varied learning,
acuteness and wealth of thought, originality and
productivity of intellect, the Englishman was head
and shoulders above the Bohemian. On the other
hand, Huss was far more a man for the people, and
he conducted his contention in a sensible, popular,
and practical manner. There were also powerful
representatives of the reform movement in the
Netherlands during this period, who pointed to
Scripture and faith in the crucified Saviour as the
only radical cure for the corruptions of the church.
While Wiclif and Huss attached themselves to the
Augustinian theology, the Dutchmen gave themselves
to quiet, calm contemplation and the acquirement of
practical religious knowledge. In Italy too a reformer
appeared of a strongly evangelical spirit, who did not

however show the practical sense of those of the
Netherlands.
§ 119.1. Wiclif and the Wiclifites.―In England the kings
and the Parliament had for a long time withstood the
oppressive yoke of the papal hierarchy. Men too like John of
Salisbury, Robert Grosseteste, Roger Bacon, and Thomas
Bradwardine had raised their voices against the inner
corruption of the church. John Wiclif, a scholar of
Bradwardine, was born about A.D. 1320. As fellow of the
University of Oxford, he supported in A.D. 1366 the English
Crown against the payment of tribute to the papal court then
at Avignon, admitted by John Lackland (§ 96, 18), of which
payment had now for a long time been refused. This secured
him court favour, the title of doctor, and a professorship of
theology at Oxford; and in A.D. 1374 he was chosen as
member of a commission which was to discuss at Brügge in
the Netherlands with the papal envoys the differences that
had arisen about the appointing to ecclesiastical offices. After
his return he openly spoke and wrote against the papal
“antichrist” and his doctrines. Gregory XI. now, in A.D. 1377,
condemned nineteen propositions from his writings, but the
English court protected him from the strict inquiry and
punishment threatened. Meanwhile Wiclif was ever becoming
bolder. Under his influence religious societies were formed
which sent out travelling preachers of the gospel among the
people. By their opponents they were called Lollards
(§ 116, 3), a name to which the stigma of heresy was already
attached. Wiclif translated for them the Scriptures from the
Vulgate into English. The bitterness of his enemies now
reached its height. Just then, in A.D. 1381, a rebellion of the
oppressed peasants that deluged all England with blood broke
out. Its origin has been quite gratuitously assigned to the
religious movement. When he had directly repudiated the
doctrine of transubstantiation, a synod at London, in

A.D. 1382, condemned his writings and his doctrine as
heretical, and the university also cast him out. Court and
Parliament could only protect his person. He now retired to
his rectory at Lutterworth in Leicestershire, where he died on
31st December, 1384.―For five centuries his able writings
were left unprinted, to moulder away in the obscurity of
libraries. His English works have now been edited by
Matthews, London, 1880. Lechler of Leipzig edited Wiclif’s
most complete and comprehensive work, the “Trialogus”
(Oxford, 1869), in which his whole theological system is
developed. Buddensieg of Dresden published the keen
antipapal controversial tract, “De Christo et suo adversario
Antichristo” (Leipzig, 1880). The Wiclif Society, instituted at
the fifth centenary of Wiclif’s death for the purpose of issuing
critical editions of his most important works, sent forth as
their first performance Buddensieg’s edition of “twenty-six
Latin controversial tracts of Wiclif’s from MSS. previously
unprinted,” in 2 vols., London, 1883. Among Wiclif’s
systematic treatises we are promised editions of the Summa
theologiæ, De incarnatione Verbi, De veritate s. Scr., De
dominio divino, De ecclesia, De actibus animæ, etc., some by
English, some by German editors.―As the principle of all
theology and reformation Wiclif consistently affirms the sole
authority of Divine revelation in the Holy Scriptures. He has
hence been called doctor evangelicus. Anything that cannot
be proved from it is a corrupting human invention.
Consistently carrying out this principle, he denounced the
worship of saints, relics, and images, the use of Latin in
public worship, elaborate priestly choir singing, the
multiplication of festivals, private masses, extreme unction,
and generally all ceremonialism. The Catholic doctrine of
indulgence and the sale of indulgences, as well as the ban
and the interdict, he pronounced blasphemous; auricular
confession he regarded as a forcing of conscience; the power
of the keys he explained as conditional, its binding and
loosing powerless, except when in accordance with the

judgment of Christ. He denied the real presence of the body
and blood of Christ in the Lord’s Supper, and affirmed, like
Berengar, a spiritual communication thereof, which however
he makes dependent, not only on the faith of the receiver, but
also on the worthiness of the officiating priest. The doctrine
of purgatory he completely rejected, and supported
Augustine’s predestinationism against the prevalent
semipelagianism. The papacy was antichrist; the pope has his
power only from the emperor, not from God. The hierarchical
system should be replaced by the apostolic presbyterial
constitution. Ordination confers no indelible character; a
priest who has fallen into mortal sin cannot dispense the
sacrament. Every believer is as such a priest. The State is a
representation of Christ, as the God-Man ruler of the
universe; the clergy represent only the poor and suffering life
of His humanity. Monkery is contrary to nature, etc.―Wiclif’s
supporters, many of them belonging to the noblest and most
cultured orders, were after his death subjected to violent
persecution, which reached its height when the House of
Lancaster in the person of Henry IV. ascended the English
throne in A.D. 1399. An act of parliament was passed in
A.D. 1400 which made death by fire the punishment of the
heresy of the Lollards. Among the martyrs which this law
brought to the stake was the noble Sir John Oldcastle, who in
A.D. 1418 was hung up between two beams in iron chains over
a fire and there slowly burnt. The Council of Constance in
A.D. 1415 condemned forty-five propositions from Wiclif’s
writings, and ordered his bones to be exhumed and scattered
abroad. Many germs sown by him continued until the
Reformation came.348
§ 119.2. Precursors of the Hussite Movement.―Owing to
its Greek origin (§ 79, 2, 3), the Bohemian church had a
certain character of its own and barely tolerated the Roman
constitution and ritual. In Bohemia too the Waldensians had
numerous supporters during the 13th century. And even

before the appearance of Huss three distinguished clergymen
in and around Prague by earnest preaching and pastoral work
had awakened in many a consciousness of crying abuses in
the church.
1. Conrad of Waldhausen was a famous preacher when
called by Charles IV. to Prague, where after fifteen years’
labour he died in A.D. 1369. Preaching in German, he
inveighed against the cupidity, hypocrisy, and immorality
of the clergy and monks, against the frauds connected
with the worship of images and relics and shrines, and
threw back upon his accusers the charge of heresy in his
still extant Apologia.
2. More influential than Conrad as a preacher of repentance
in Prague was John Milicz of Cremsier in Moravia, who
died in A.D. 1374. Believing the end of the world near and
antichrist already come, he went to Rome in A.D. 1367 to
place before Urban V. his scheme of apocalyptic
interpretation. Escaping with difficulty from the
Inquisition, he returned to Prague, and there applied
himself with renewed zeal to the preaching of
repentance. His preaching led to the conversion of
200 fallen women, for whom he erected an institution
which he called Jerusalem. But the begging friars
accused him before Gregory XI. as a heretic. Milicz
fearlessly went for examination to Avignon in A.D. 1374,
where he soon died before judgment had been passed.
The most important of his works is De Antichristo.
3. Matthias of Janow, of noble Bohemian descent, died in
A.D. 1374, after fourteen years’ work as a preacher and
pastor in Prague. His sermons, composed in Bohemian,
lashed unsparingly the vices of the clergy and monks, as
well as the immorality of the laity, and denounced the
worship of images and relics. None of his sermons are
extant, but we have various theological treatises of his on

the distinguishing of the true faith from the false and the
frequent observance of the communion. At a Prague
synod of A.D. 1389 he was obliged to retract several of his
positions, and especially to grant the propriety of
confessing and communicating half-yearly. Janow
however, like Conrad and Milicz, did not seriously contest
any fundamental point of the doctrine of the church.
§ 119.3. John Huss of Hussinecz in Bohemia, born
A.D. 1369, was Bachelor of Theology at Prague, in A.D. 1394,
Master of Liberal Arts in A.D. 1396, became public teacher in
the university in A.D. 1398, was ordained priest in A.D. 1400,
undertook a pastorate in A.D. 1402 in the Bethlehem chapel,
where he had to preach in the Bohemian language, was
chosen confessor of Queen Sophia in A.D. 1403, and was soon
afterwards made synodal preacher by the new archbishop,
Sbynko of Hasenburg. Till then he had in pious humility
accepted all the doctrines of the Romish Church, and even in
A.D. 1392 he offered his last four groschen for an indulgence,
so that for a long time dry bread was his only nourishment.
But about A.D. 1402 he reached an important crisis in his life
through the study of Wiclif’s theological works.―Bohemians
who had studied in Oxford brought with them Wiclif’s
philosophical works, and in A.D. 1348 the discussion on
realism and nominalism broke out in Prague. The Bohemians
generally sided with Wiclif for realism; the Germans with the
nominalists (§ 113, 3). This helped to prepare an entrance for
Wiclif’s theological writings into Bohemia. Of the national
party which favoured Wiclif’s philosophy and theology, Huss
was soon recognised as a leader. A university decree of
A.D. 1403 condemned forty-five propositions from Wiclif’s
works as heretical, and forbade their promulgation in lectures
or sermons. Huss however was still highly esteemed by
Archbishop Sbynko. In A.D. 1405 he appointed Huss, with
other three scholars, a commission to investigate a reputed
miracle at Wilsnack, where on the altar of a ruined church

three blood-red coloured hosts were said to have been found.
Huss pronounced the miracle a cheat, and proved in a tract
that the blood of Christ glorified can only be invisibly present
in the sacrament of the altar. The archbishop approved this
tract, and forbade all pilgrimages to the spot. He also took no
offence at Huss for uttering Wiclifite doctrine in his synod
sermon. Only when, in A.D. 1408, the clergy of his diocese
complained that Huss by his preaching made the priests
contemptible before the people, did he deprive him of his
function as synod preacher. When the majority of cardinals at
Leghorn in A.D. 1408 took steps to put an end to the schism,
king Wenzel determined to remain neutral, and demanded the
assent of the university as well as the clergy of his realm. But
only the Bohemian members of the university agreed, while
the rest, along with the archbishop, supported Gregory XII.
Sbynko keenly resented the revolt of the Bohemians, and
forbade Huss as their spokesman to preach within his
diocese. Huss paid no attention to the prohibition, but
secured a royal injunction, that henceforth in the university
Bohemians should have three votes and foreigners only one.
The foreigners then withdrew, and founded the University of
Leipzig in A.D. 1409. Huss was made first rector of the newly
organized University of Prague; but the very fact of his great
popularity in Bohemia caused him to be profoundly hated in
other lands.349
§ 119.4. The archbishop escaped prosecution only by
unreservedly condemning the doctrines of Wiclif, burning his
books, and prohibiting all lectures upon them. Huss and his
friends appealed to John XXIII., but this did not prevent the
archbishop burning in his palace yard about two hundred
Wiclifite books that had previously escaped his search. For
this he was hooted in the streets, and compelled by the
courts of law to pay the value of the books destroyed.
John XXIII. cited Huss to appear at Rome. King, nobles,
magistrates, and university sided with him; but the papal

commission condemned him when he did not appear, and the
archbishop pronounced anathema against him and the
interdict against Prague (A.D. 1411). Huss appealed to the
œcumenical council, and continued to preach. The court
forced the archbishop to become reconciled with Huss, and to
admit his orthodoxy. Sbynko reported to the pope that
Bohemia was free from heresy. He soon afterwards died. The
pope himself was the cause of a complete breach, by having
an indulgence preached in Bohemia in A.D. 1412 for a crusade
against Ladislaus of Naples, the powerful adherent of
Gregory XII. Huss opposed this by word and writing, and in a
public disputation maintained that the pope had no right to
grant such indulgence. His most stanch supporter was a
Bohemian knight, Jerome of Prague, who had studied at
Oxford, and returned in A.D. 1402 an enthusiastic adherent of
Wiclif’s doctrines. Their addresses produced an immense
impression, and two days later their disorderly followers, to
throw contempt on the papal party, had the bull of indulgence
paraded through the streets, on the breast of a public
prostitute, representing the whore of Babylon, and then cast
into the flames. But many old friends now withdrew from
Huss and joined his opponents. The papal curia thundered
against him and his followers the great excommunication,
with its terrible curses. Wherever he resided that place was
put under interdict. But Huss appealed to the one righteous
Judge, Jesus Christ. At the wish of the king he left the city,
and sought the protection of various noble patrons, from
whose castles he went forth diligently preaching round about.
He spread his views all over the country by controversial and
doctrinal treatises in Latin and Bohemian, as well as by an
extensive correspondence with his friends and followers. Thus
the trouble and turmoil grew from day to day, and all the
king’s efforts to restore peace were in vain.
§ 119.5. The Roman emperor Sigismund summoned Huss to
attend the Council of Constance (§ 110, 7), and promised him

a safe-conduct. Though not yet in possession of this latter,
which he only got at Constance, trusting to the righteousness
of his cause, for which he was quite willing to die a martyr’s
death, he started for Constance on 11th October, A.D. 1414,
reaching his destination on 3rd November. On 28th November
he was sentenced to imprisonment at a private conference of
the cardinals, on the pretended charge of an attempt at flight,
first in the Dominican cloister, then in the bishop’s castle of
Gottlieben, where he was put in chains, finally in the
Franciscan cloister. Sigismund, who had not been forewarned
when he was cast into prison, ordered his release; but the
council convinced him that Huss, arraigned as a heretic
before a general council, was beyond the reach of civil
protection. His bitterest enemies and accusers were two
Bohemians, Michael of Deutschbrod and Stephan of Palecz.
The latter extracted forty-two points for accusations from his
writings, which Huss from his prison retracted. D’Ailly and
Gerson were both against him. The brave knight John of
Chlum stood faithfully by him as a comforter to the last. For
almost seven months was he harassed by private
examinations, in which, notwithstanding his decided
repudiation of many of them, he was charged with all
imaginable Wiclifite heresies. The result was the renewed
condemnation of those forty-five propositions from Wiclif’s
writings, which had been condemned A.D. 1408 by the
University of Prague. At last, on 5th June, A.D. 1415, he was
for the first time granted a public trial, but the tumult at the
sitting was so great that he was prevented from saying a
single word. Even on the two following days of the trial he
could do little more than make a vain protest against being
falsely charged with errors, and declare his willingness to be
better instructed from God’s word. The humility and
gentleness of his demeanour, as well as the enthusiasm and
believing joyfulness which he displayed, won for him many
hearts even outside of the council. All possible motives were
urged to induce him to submit. Sigismund so exhorted him,

with the threat that if he did not he would withdraw his
protection. The third and last day of trial was 8th June,
A.D. 1415, and judgment was pronounced in the cathedral
church on the 6th July. After high mass had been celebrated,
a bishop mounted the pulpit and preached on Romans vi. 6.
He addressed Sigismund, who was present, “By destroying
this heretic, thou shalt obtain an undying name to all ensuing
generations.” Once again called upon to recant, Huss
repeated his previous protests, appealed to the promise of a
safe-conduct, which made Sigismund wince and blush, and
kneeling down prayed to God for his enemies and unjust
judges. Then seven bishops dressed him in priestly robes in
order to strip him of them one after another amid solemn
execrations. Then they put on him a high pyramidal hat,
painted with figures of devils, and bearing the inscription,
Hæresiarcha, and uttered the words, “We give thy soul to the
devil.” He replied: “I commend it into the hands of our
Saviour Jesus Christ.” On that same day he was given over by
Sigismund to Louis Count-palatine of the Rhine, and by him to
the Constance magistrates, and led to the stake. Amid prayer
and praise he expired, joyfully, courageously, and confidently,
showing himself worthy to rank among the martyrs who in
the best times of Christianity had sealed their Christian
confession with their blood. His ashes were scattered on the
Rhine. The later Hussites, in accordance with an old Christian
custom (§ 39, 5), celebrated the day of his death as the dies
natalis of the holy martyr John Huss.―Jerome of Prague
had gone unasked to Constance. When he saw that his longer
stay would not help his friend, but only involve himself in his
fate, he left the city; but was seized on the way, and taken
back in chains in April, A.D. 1415. During a severe half-year’s
imprisonment, and wearied with the importunities of his
judges, he agreed to recant, and to acquiesce in the sentence
of Huss. But he was not trusted, and after as before his
recantation he was kept in close confinement. Then his
courage revived. He demanded a public trial before the whole

council, which was at last granted him in May, A.D. 1416.
There he solemnly and formally retracted his previous
retractation with a believer’s confidence and a martyr’s joy.
On May 30th, A.D. 1416, he, too, died at the stake, joyfully
and courageously as Huss had done. The Florentine humanist
Poggio, who was present, has given enthusiastic expression in
a still extant letter to his admiration at the heroic spirit of the
martyr.
§ 119.6. In all his departures from Romish doctrine Huss was
dependent upon Wiclif, not only for the matter, but even for
the modes of expression. He did not however separate
himself quite so far from the Church doctrines as his English
master. He firmly maintained the doctrine of
transubstantiation; he was also inclined to withhold the cup
from the laity; and, though he sought salvation only from the
Saviour crucified for us, he did not refuse to give any place to
works in the justification of the sinner, and even invocation of
the saints he did not wholly condemn. While he energetically
protested against the corruption of the clergy, he never
denied that the sacrament might be efficaciously administered
by an unworthy priest. In everything else however he was in
thorough agreement with the English reformer. The most
complete exposition of his doctrine is found in the Tractatus
de ecclesia of A.D. 1413. Augustine’s doctrine of predestination
is its foundation. He distinguishes from the church as a visible
human institution the idea of the church as the true body of
Christ, embracing all elected in Christ to blessedness from
eternity. Its one and only head is Christ: not Peter, not the
pope; for this church is no monster with two heads. Originally
and according to Christ’s appointment the bishop of Rome
was no more than the other bishops. The donation of
Constantine first gave him power and dignity over the rest. As
the church in the beginning could exist without a pope, so the
church unto the end can exist without one. The Christian can
obey the pope only where his commands and doctrines agree

with those of Christ. In matters of faith Holy Scripture is the
only authority. Fathers, councils, and popes may err, and have
erred; only the word of God is infallible.―That this liberal
reforming Council of Constance, with a Gerson at its head,
should have sentenced such a man to death is not to be
wondered at when we rightly consider how matters stood. His
hateful realism seemed to the nominalistic fathers of the
council the source of all conceivable heresies. It had even
been maintained that realism consistently carried out would
give a fourth person to the Godhead. His devotion to the
national interests of Bohemia in the University of Prague had
excited German national feeling against him. And, further, the
council, which was concerned only with outward reforms, had
little sympathy with the evangelical tone of his spirit and
doctrine. Besides this, Huss had placed himself between the
swords of two contending parties. The hierarchical party
wished, in order to strike terror into their opponents, to show
by an example that the church had still the power to burn
heretics; and the liberal party refused to this object of papal
hate all protection, lest they should endanger the cause of
reformation by incurring a suspicion of sympathy with
heresy.―The prophecy said to have been uttered by Huss in
his last moments, “To-day you burn a goose (this being the
meaning of Huss in Slavonian), but from its ashes will arise a
swan (Luther’s coat of arms), which you will not be able to
burn,” was unknown to his contemporaries. Probably it
originated in the Reformation age from the appeals of both
martyrs to the judgment of God and history. Huss had often
declared that instead of the weak goose there would come
powerful eagles and falcons.350
§ 119.7. Calixtines and Taborites.―During the
imprisonment of their leader the Hussite party was headed by
Jacob of Misa, pastor of St. Michael’s church in Prague. With
consent of Huss he introduced the use of the cup by the laity
and rejected the jejunium eucharisticum as opposed to

Matthew xxvi. 26. This led to an interchange of controversial
tracts between Prague and Constance on the withholding of
the cup. The council decreed that whoever disobeys the
Church on this point is to be punished as a heretic. This
decree, followed by the execution of Huss, roused Bohemia to
the uttermost. King Wenceslaw died in A.D. 1419 in the midst
of national excitement, and the estates refused to crown his
brother Sigismund, “the word-breaker.” Now arose a civil war,
A.D. 1420-1436, characterized by cruelties on both sides rarely
equalled. At the head of the Hussites, who had built on the
brow of a steep hill the strong fortress Tabor, was the one-
eyed, afterwards blind, John Ziska of Trocznov. The
crusading armies sent against the Hussites were one after
another destroyed; but the gentle spirit of Huss had no place
among most of his followers. The two parties became more
and more embittered toward one another. The aristocratic
Calixtines (calix, cup) or Utraquists (sub utraque), at whose
head was Bishop Rokycana of Prague, declared that they
would be satisfied if the Catholic church would concede to
them four articles:
1. Communion under both kinds;
2. Preaching of the pure gospel in the vulgar tongue;
3. Strict discipline among the clergy; and
4. Renunciation by the clergy of church property.
On the other hand, the Taborites would have no
reconciliation with the Romish church, regarding as
fundamentally corrupt in doctrine and worship whatever is
not found in Scripture, and passing over into violent
fanaticism, iconoclasm, etc. After Ziska’s death of the plague
in A.D. 1424, the majority of the Taborites elected Procopius
the Great as his successor. A small party that regarded no
man worthy of succeeding the great Ziska, refused him
allegiance, and styled themselves Orphans. They were the

most fanatical of all.―Meanwhile the Council of Basel had
met (§ 110, 8) and after long fruitless negotiations it was
resolved in A.D. 1433 that 300 Hussite deputies should appear
at Basel. After a fifty days’ disputation the four Calixtine
articles with certain modifications were accepted by the
council. On the basis of this Basel Compact the Calixtines
returned to the Romish church. The Taborites regarded this as
shameful treason to the cause of truth, and continued the
conflict. But in A.D. 1434 they were utterly annihilated at
Böhmischbrod, not far from Prague. In the Treaty of Iglau in
A.D. 1436 Sigismund swore to observe the compact, and was
recognised as king. But the concessions sworn to by church
and state were more and more restricted and ultimately
ignored. Sigismund died in A.D. 1437. In place of his son-in-
law, Albert II., the Utraquists set up a rival king in the person
of the thirteen year old Polish prince Casimir; but Albert died
in A.D. 1439. His son, Ladislaus, born after his father’s death,
had, in George Podiebrad, a Calixtine tutor. After he had
grown up in A.D. 1453, he walked in his grandfather’s
footsteps, and died in A.D. 1457. The Calixtines now elected
Podiebrad king, as a firm supporter of the compact. Pius II.
recognised him in the hope that he would aid him in his
projected war against the Turks. When this hope was
disappointed he cancelled the compact, in A.D. 1462. Paul II.
put the king under him, and had a crusade preached against
him. Podiebrad however still held his ground. He died in
A.D. 1471. His successor, Wladislaw II., a Polish prince, though
a zealous Catholic, was obliged to confirm anew to the
Calixtines at the Diet of Cuttenberg, in A.D. 1485, all their
rights and liberties. Yet they could not maintain themselves as
an independent community. Those of them who did not join
the Bohemian and Moravian Brethren gradually during the
16th century became thoroughly amalgamated with the
Catholic church.

§ 119.8. The Bohemian and Moravian Brethren.―George
Podiebrad took Tabor in A.D. 1453, and scattered the last
remnants of the Taborites. Joining with the evangelical
Friends of God, they received from the king a castle, where,
under the leadership of the local pastor, Michael of Bradacz,
they formed a Unitas fratrum, and called themselves
Bohemian and Moravian Brethren. But in A.D. 1461 Podiebrad
withdrew his favour, and confiscated their goods. They fled
into the woods, and met for worship in caves. In A.D. 1467 the
most distinguished of the Bohemian and Moravian Brethren
met in a Bohemian village, Shota, with the German
Waldensians, and chose three brethren by lot as priests, who
were ordained by Michael and a Waldensian priest. But when
the validity of their ordination was disputed, Michael went to
the Waldensian bishop Stephen, got from him episcopal
consecration, and then again ordained the three chosen at
Shota, one, Matthias of Conewald, as bishop, the other two as
priests. This led Rokycana to persecute them all the more
bitterly. They increased their numbers however, by receiving
the remnants of the Waldensians and many Utraquists, until
by the beginning of the 16th century they had four hundred
congregations in Bohemia and Moravia. Under Wladislaw II.
persecution was stopped from A.D. 1475, but was renewed
with great violence in A.D. 1503. They sent in A.D. 1511 a
confession of faith to Erasmus (§ 120, 6), with the request
that he would give his opinion about it; which he however,
fearing to be compromised thereby, declined to do. After the
death of Bishop Matthias, in A.D. 1500, a dislike of monarchy
led to the appointment of four Seniors instead of one bishop,
two for Bohemia and two for Moravia. The most important
and influential of these was Luke of Prague, who died in
A.D. 1518, rightly regarded as the second founder of the
union. He impressed a character upon the brotherhood
essentially distinct in respect of constitution and doctrine from
the Lutheran Reformation.―Continuation § 139, 19.

§ 119.9. The Waldensians.
1. The range of the missionary enterprise of the Lombard-
German Waldensians was widely extended during the
14th century. At the close of that period it stretched
“from western Switzerland across the southern borders of
the empire, from the upper and middle Rhine along the
Main and through Franconia into Thuringia, from
Bohemia up to Brandenburg and Pomerania, and with its
last advances reached to Prussia, Poland, Silesia,
Hungary, Transylvania, and Galicia.” The anonymous
writer of Passau, about A.D. 1260 or 1316, reports from
his own knowledge of numerous “Leonists,” who in forty-
two communities, with a bishop at Einzinspach, in the
diocese of Passau, were in his time the subject of
inquisitorial interference, and in theory and practice bore
all the characteristic marks of the Lombard Leonists. The
same applies to the Austrian Waldensians, of whose
persecution in A.D. 1391 we have an account by Peter of
Pilichdorf. We may also with equal confidence pronounce
the Winkelers, so called from holding their services in
secret corners, who about this time appeared in Bavaria,
Franconia, Swabia, and the Rhine Provinces, to be
Waldensians of the same Lombard type. Their confessors,
Winkelers in the narrower sense, were itinerant, celibate,
and without fixed abode, carrying on missionary work,
and administering the sacrament of penance to their
adherents. Although, in order to avoid the attentions of
the Inquisition, they took part in the Catholic services,
and in case of need confessed to Catholic priests, they
were nevertheless traced about A.D. 1400 to Strassburg.
Thirty-two of them were thrown into prison, and induced
under torture to confess. The Dominicans insisted that
they should be immediately burned, but the council was
satisfied with banishing them from the city. At a later
period the Hussites obtained an influence over them. One

of their most notable apostles at this time was Fr. Reiser
of Swabia. In his travels he went to Bohemia, attached
himself to the Hussites there, received from them priestly
ordination, and in A.D. 1433 accompanied their
representatives to the Basel Council. Then Procopius
procured him a call to a pastorate in the little Bohemian
town of Landscron, which, however, he soon abandoned.
Encouraged by the reformatory tendency of the council,
he now remained for a long time in Basel, then
conducted missionary work in Germany, at first on his
own account, afterwards at the head of a Taborite
mission of twelve agents, in which position he styled
himself Fridericus Dei gratia Episcopus fidelium in
Romana ecclesia Constantini donationem spernentium. At
last, in A.D. 1457, he went to Strassburg, with the
intention of there ending his days in peace. But soon
after his arrival he was apprehended, and in A.D. 1458,
along with his faithful follower, Anna Weiler, put to death
at the stake.―On the Waldensians in German
Switzerland, and the Inquisition’s oft repeated
interference with them, Ochsenbein gives a full report,
drawn from original documents, specially full in regard to
the great Inquisition trial at Freiburg, in A.D. 1430,
consisting of ninety-nine wearisome and detailed
examinations. Subsequently terrible persecutions, aiming
at their extermination, became still more frequent in
Switzerland. Also the Swiss Waldensians already bore
unmistakable marks of having been influenced by the
Hussites. Finally, Wattenbach has made interesting
communications regarding the Waldensians in Pomerania
and Brandenburg, based upon a manuscript once in the
possession of Flacius, but afterwards supposed to have
been lost, discovered again in the Wolfenbüttel library in
A.D. 1884, though in a very defective form, which contains
the original reports of 443 prosecutions for heresy in
Pomerania, Brandenburg, and Thuringia. By far the

greatest number of these trials were conducted between
A.D. 1373 and 1394, by the Cœlestine provincial Peter,
appointed inquisitor by the pope. From A.D. 1383 Stettin
was the centre of his inquisitorial activity, and on the
conclusion of his work he could boast that during the last
two years he had converted to the Catholic faith more
than 1,000 Waldensians. The victims of the Inquisition
belonged almost exclusively to the peasant and artisan
classes. Their objectionable doctrines and opinions are
essentially almost the same as those of their ancestors of
the 13th century. Although equally with their
predecessors they abhorred the practice of the Catholic
church, and declared all swearing and slaughter to be
mortal sin, they yet in great part, and as it seems even
without the application of torture, were persuaded to
abjure their heresy, and incurred nothing more than a
light penance. They did this, perhaps, only in the hope
that their indulgent confessors would absolve them from
their sin. The last protocols bring us down to A.D. 1458.
Since a great number of these heretics were found again
in Brandenburg, the elector caused one of their most
distinguished leaders, the tailor Matthew Hagen, and
three of his disciples to be taken prisoners to Berlin, and
commissioned the Bishop of Brandenburg to investigate
the case; but owing to his sickness this duty devolved
upon John Cannemann, professor and doctor of theology.
The elector was himself present at the trial. The
investigation showed that the Waldensians of
Brandenburg had evidently been influenced in their
opinions by the Bohemian Taborites, and that they were
constantly in close communion with them, and Hagen
confessed that he had been there ordained by Fr. Ryss or
Reiser to the clerical office. When Hagen persistently
refused to retract, he was delivered over to the civil
authorities for punishment, and was by them executed,
probably at the stake. His three companions abjured their

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Modern Communications Thomas H Crowley Gerard G Harris Stewart E Miller John R Pierce John P Runyon

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