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The Project Physics Course

Reader

Light and Electromagnetism

The Project Physics Course

Reader

UNIT

4 Light and Electromagnetism

A Component of the
Project Physics Course

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Directors of Harvard Project Physics

Gerald Holton, Department of Physics,

Harvard University
F. James Rutherford, Capuchino High School,

San Bruno, California, and Harvard University
Fletcher G. Watson, Harvard Graduate School

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2 «

5 I

3 6

Picture Credits for frontispiece.

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Sources and Acknowledgments
Project Physics Reader 4

1. Letter from Thomas Jefferson, June, 1799, from
Scripta Mathematica, Volume 1, 1932, pages
88-90. Reprinted with permission from the
Manuscript Collection of Teachers College
Library, Columbia University. Also in Science and
the Common Understanding by J. Robert
Oppenheimer. Reprinted with permission of
Simon and Schuster, Inc.

2. On the Method of Theoretical Physics by Albert
Einstein from Essays in Science, pages 12-21,
Philosophical Library, New York, copyright 1934
by Estate of Albert Einstein. Reprinted with
permission.

3. Systems, Feedback and Cybernetics from
Introduction to Natural Science by V. Lawrence
Parsegian, Alan S. Meltzer, Abraham S. Luchins
and K. Scott Kinerson, copyright © 1968 by
Academic Press, Inc. Reprinted with permission.

4. Velocity of Light from Studies In Optics by A. A.
Michelson, copyright 1927 by The University of
Chicago Press. Reprinted with permission.

5. Popular Application of Polarized Light from
Polarized Light (Momentum #7) by William A.
Shurcliff and Stanley S. Ballard, copyright © 1964
by Litton Educational Publishing Inc. Reprinted
with permission of Van Nostrand Reinhold
Company.

6. Eye and Camera by George Wald from Scientific
American, August 1950, copyright © 1950 by
Scientific American, Inc. Reprinted with permis-
sion. All rights reserved.

7. The Laser — What It Is and Does from The Story
of the Laser by John M. Carroll, copyright © 1964
by E. P. Dutton & Co., Inc., Reprinted with permis-
sion of E. P. Dutton & Co., Inc., and Souvenir
Press Ltd.

8. A Simple Electric Circuit: Ohm's Law from The
New College Physics: A Spiral Approach by
Albert V. Baez. W. H. Freeman and Company,
copyright© 1967. Reprinted with permission.

9. The Electronic Revolution from Voices from the
Sky by Arthur C. Clarke, Harper & Row, Publishers,
New York, copyright © 1965. "The Electronic
Revolution," copyright © 1962 by The New York
Times Company. Reprinted with permission of the
author and his agent, Scott Meredith Literary
Agency, and David Higham Associates. Ltd .

10. The Invention of the Electric Light by Matthew
Josephson from Scientific American, November

11. High Fidelity from Reproduction of Sound by
Edgar Villchur, copyright © 1962 by Acoustic
Research, Inc., Cambridge, Massachusetts.
Copyright © 1965 by Dover Publications, Inc.
Reprinted with permission.

12. The Future of Direct Current Power Transmission
by N. L. Allen from Endeavor, Volume CCVI, No.
97, Imperial Chemical Industries Limited, London.
Reprinted with permission.

13. James Clerk Maxwell by James R. Newman,
Part II, from Scientific American, June 1955,
copyright © 1955 by Scientific American, Inc.
Reprinted with permission. All rights reserved.

14. On the Induction of Electric Currents from

A Treatise on Electricity and Magnetism by James
Clerk Maxwell, Volume 2, 1873, The Clarendon
Press, Oxford. Reprinted with permission.

15. The Relationship of Electricity and Magnetism
from Faraday, Maxwell, and Kelvin, by D. K. C.
MacDonald, copyright © 1964 by Educational
Services Incorporated. Reprinted with permission
of Doubleday & Company, Inc. (Science Study
Series.)

16. The Electromagnetic Field from The Evolution of

Physics by Albert Einstein and Leopold Infeld.
Published by Simon and Schuster, copyright©
1961. Reprinted with permission.

17. Radiation Belts Around the Earth by James A.
Van Allen from Scientific American, March 1959.
Copyright © 1959 by Scientific American, Inc.
Reprinted with permission. All rights reserved.
Available separately at 200 each as Offprint No.
248 from W. H. Freeman and Company, 666
Market Street, San Francisco, California 94104.

18. A Mirror for the Brain from The Living Brain by
W. Grey Walter, copyright 1953, © 1963 by W. W.
Norton & Company, Inc. Reprinted with permission
of W. W. Norton & Company, Inc., and Gerald
Duckworth & Co. Ltd.

19. Scientific Imagination from The Feynman Lectures
on Physics by Richard P. Feynman, Robert B.
Leighton and Matthew L. Sands, copyright©
1964 by Addison-Wesley Publishing Company,
Inc. Reprinted with permission.

20. Lenses and Optical Instruments from PSSC
Physics, D. C. Heath and Company, Boston.
Copyright © 1965 by Educational Services
Incorporated. Reprinted with permission.

21. Baffled, by Keith Waterhouse from Punch, July 10,
1968, copyright © 1968 Punch, London.

This is not a physics textbook. Rather, it is a physics
reader, a collection of some of the best articles and
book passages on physics. A few are on historic events
in science, others contain some particularly memorable
description of what physicists do; still others deal with
philosophy of science, or with the impact of scientific
thought on the imagination of the artist.

There are old and new classics, and also some little-
known publications; many have been suggested for in-
clusion because some teacher or physicist remembered
an article with particular fondness. The majority of
articles is not drawn from scientific papers of historic
importance themselves, because material from many of
these is readily available, either as quotations in the
Project Physics text or in special collections.

This collection is meant for your browsing. If you follow
your own reading interests, chances are good that you
will find here many pages that convey the joy these
authors have in their work and the excitement of their
ideas. If you want to follow up on interesting excerpts,
the source list at the end of the reader will guide you
for further reading.

Reader 4
Table of Contents

1 Letter from Thomas Jefferson 1

June 1799

2 On the Method of Theoretical Physics 5

Albert Einstein

3 Systems, Feedback, Cybernetics 1 5

V. Lawrence Parsegian, Alan S. Meltzer, Abraham S. Luchins, K. Scott Kinerson

4 Velocity of Light 51

A. A. Michelson

5 Popular Applications of Polarized Light 69

William A. Shurcliff and Stanley Ballard

6 Eye and Camera 89

George Wald

7 The Laser— What It Is and Does 99

J. M. Carroll

8 A Simple Electric Circuit: Ohm's Law 143

Albert V. Baez

9 The Electronic Revolution 155

Arthur C. Clarke

1 0 The Invention of the Electric Light 162

Matthew Josephson

11 High Fidelity 175

Edgar Villchur

1 2 The Future of Direct Current Power Transmission 191

N. L. Allen

13 James Clerk Maxwell, Part II 195

James R. Newman

14 On the Induction of Electric Currents

James Clerk Maxwell

229

1 5 The Relationship of Electricity and Magnetism

D. K. C. MacDonald

233

1 6 The Electromagnetic Field

Albert Einstein and Leopold Infeld

241

17 Radiation Belts Around the Earth

James Van Allen

249

18 A Mirror for the Brain

W. Grey Walter

259

19 Scientific Imagination

Richard P. Feynman, Robert B. Leighton, and Matthew Sands

285

20 Lenses and Optical Instruments

Physical Science Study Committee

289

21 Baffled!

Keith Waterhouse

301

VII

A great American writes about the significant role
of science in the education of the individual and in
the creation of American society.

Letter from Thomas Jefferson

June 1799

Monticello June 18. 99.

DEAR SIR,

I have to acknolege the reciept of your favor of
May 14. in which you mention that you have finished
the 6. first books of Euclid, plane trigonometry, sur-
veying and algebra and ask whether I think a further
pursuit of that branch of science would be useful to
you. There are some propositions in the latter books
of Euclid, and some of Archimedes, which are useful,
and I have no doubt you have been made acquainted
with them. Trigonometry, so far as this, is most
valuable to every man, there is scarcely a day in
which he will not resort to it for some of the purposes
of common life; the science of calculation also is
indispensible as far as the extraction of the square and
cube roots ; Algebra as far as the quadratic equation
and the use of logarithms are often of value in ordi-
nary cases ; but all beyond these is but a luxury ; a
delicious luxury indeed ; but not to be indulged in by
one who is to have a profession to follow for his sub-
sistence. In this light I view the conic sections,

curves of the higher orders, perhaps even spherical
trigonometry, Algebraical operations beyond the
2d dimension, and fluxions. There are other
branches of science however worth the attention of
every man : Astronomy, botany, chemistry, natural
philosophy, natural history, anatomy. Not indeed
to be a proficient in them ; but to possess their general
principles and outlines, so as that we may be able to
amuse and inform ourselves further in any of them as
we proceed through life and have occasion for them.
Some knowlege of them is necessary for our character
as well as comfort. The general elements of astro-
nomy and of natural philosophy are best acquired at
an academy where we can have the benefit of the
instruments and apparatus usually provided there:
but the others may well be acquired from books
alone as far as our purposes require. I have indulged
myself in these observations to you, because the
evidence cannot be unuseful to you of a person who
has often had occasion to consider which of his
acquisitions in science have been really useful to him
in life, and which of them have been merely a matter
of luxury.

I am among those who think well of the human
character generally. I consider man as formed for
society, and endowed by nature with those disposi-
tions which fit him for society. I believe also, with
Condorcet, as mentioned in your letter, that his mind
is perfectible to a degree of which we cannot as yet
form any conception. It is impossible for a man who
takes a survey of what is already known , not to see
what an immensity in every branch of science yet
remains to be discovered, and that too of articles to
which our faculties seem adequate. In geometry and
calculation we know a great deal. Yet there are
some desiderata. In anatomy great progress has
been made; but much is still to be acquired. In
natural history we possess knowlege; but we want
a great deal. In chemistry we are not yet sure of
the first elements. Our natural philosophy is in a
very infantine state; perhaps for great advances in
it, a further progress in chemistry is necessary.
Surgery is well advanced ; but prodigiously short of
what may be. The state of medecine is worse than
that of total ignorance. Could we divest ourselves of

Letter from Thomas Jefferson

every thing we suppose we know in it, we should start
from a higher ground and with fairer prospects.
From Hippocrates to Brown we have had nothing
but a succession of hypothetical systems each having
it's day of vogue, like the fashions and fancies of
caps and gowns, and yielding in turn to the next
caprice. Yet the human frame, which is to be the
subject of suffering and torture under these learned
modes, does not change. We have a few medecines,
as the bark, opium, mercury, which in a few well
defined diseases are of unquestionable virtue: but
the residuary list of the materia medica, long as it is,
contains but the charlataneries of the art ; and of the
diseases of doubtful form, physicians have ever had a
false knowlege, worse than ignorance. Yet surely
the list of unequivocal diseases and remedies is
capable of enlargement ; and it is still more certain
that in the other branches of science, great fields are
yet to be explored to which our faculties are equal,
and that to an extent of which we cannot fix the
limits. I join you therefore in branding as cowardly
the idea that the human mind is incapable of further
advances. This is precisely the doctrine which the
present despots of the earth are inculcating, and
their friends here re-echoing ; and applying especially
to religion and politics ; ' that it is not probable that
any thing better will be discovered than what was
known to our fathers '. We are to look backwards
then and not forwards for the improvement of
science, and to find it amidst feudal barbarisms and
the fires of Spital-fields. But thank heaven the
American mind is already too much opened, to listen
to these impostures ; and while the art of printing is
left to use, science can never be retrograde; what is
once acquired of real knowlege can never be lost.
To preserve the freedom of the human mind then and
freedom of the press, every spirit should be ready to
devote itself to martyrdom ; for as long as we may
think as we will, and speak as we think, the condition
of man will proceed in improvement. The genera-
tion which is going off the stage has deserved well of
mankind for the struggles it has made, and for having
arrested that course of despotism which had over-
whelmed the world for thousands and thousands of
years. If there seems to be danger that the ground

they have gained will be lost again, that danger comes
from the generation your contemporary. But that
the enthusiasm which characterises youth should lift
it's parracide hands against freedom and science
would be such a monstrous phaenomenon as I can-
not place among possible things in this age and this
country. Your college at least has shewn itself
incapable of it; and if the youth of any other place
have seemed to rally under other banners it has been
from delusions which they will soon dissipate. I
shall be happy to hear from you from time to time,
and of your progress in study, and to be useful to
you in whatever is in my power; being with sincere
esteem Dear Sir

Your friend & servt
Th : Jefferson

Einstein discusses some of the factors that lead to a
scientific theory.

On the Method of Theoretical Physics

Albert Einstein
An essay— 1934.

If you want to find out anything from the theoretical
physicists about the methods they use, I advise you
to stick closely to one principle : don't listen to their
words, fix your attention on their deeds. To him
who is a discoverer in this field the products of his
imagination appear so necessary and natural that he
regards them, and would like to have them regarded
by others, not as creations of thought but as given
realities.

These words sound like an invitation to you to
walk out of this lecture. You will say to yourselves,
the fellow's a working physicist himself and ought
therefore to leave all questions of the structure of
theoretical science to the epistemologists.

Against such criticism I can defend myself from
the personal point of view by assuring you that it
is not at my own instance but at the kind invitation
of others that I have mounted this rostrum, which
serves to commemorate a man who fought hard all
his life for the unity of knowledge. Objectively, how-
ever, my enterprise can be justified on the ground
that it may, after all, be of interest to know how one
who has spent a life-time in striving with all his

might to clear up and rectify its fundamentals looks
upon his own branch of science. The way in which he
regards its past and present may depend too much
on what he hopes for the future and aims at in the
present; but that is the inevitable fate of anybody
who has occupied himself intensively with a world
of ideas. The same thing happens to him as to the
historian, who in the same way, even though perhaps
unconsciously, groups actual events around ideals
which he has formed for himself on the subject of
human society.

Let us now cast an eye over the development of
the theoretical system, paying special attention to
the relations between the content of the theory
and the totality of empirical fact. We are concerned
with the eternal antithesis between the two insep-
arable components of our knowledge, the empirical
and the rational, in our department.

We reverence ancient Greece as the cradle of
western science. Here for the first time the world
witnessed the miracle of a logical system which pro-
ceeded from step to step with such precision that
every single one of its propositions was absolutely
indubitable — I refer to Euclid's geometry. This ad-
mirable triumph of reasoning gave the human intel-
lect the necessary confidence in itself for its subsequent
achievements. If Euclid failed to kindle your youth-
ful enthusiasm, then you were not born to be a
scientific thinker.

But before mankind could be ripe for a science
which takes in the whole of reality, a second funda-

On the Method of Theoretical Physics

mental truth was needed, which only became common
property among philosophers with the advent of Kep-
ler and Galileo. Pure logical thinking cannot yield
us any knowledge of the empirical world ; all knowl-
edge of reality starts from experience and ends in
it. Propositions arrived at by purely logical means
are completely empty as regards reality. Because
Galileo saw this, and particularly because he drummed
it into the scientific world, he is the father of modern
physics — indeed, of modern science altogether.

If, then, experience is the alpha and the omega of
all our knowledge of reality, what is the function of
pure reason in science?

A complete system of theoretical physics is made
up of concepts, fundamental laws which are supposed
to be valid for those concepts and conclusions to be
reached by logical deduction. It is these conclusions
which must correspond with our separate experiences ;
in any theoretical treatise their logical deduction
occupies almost the whole book.

This is exactly what happens in Euclid's geometry,
except that there the fundamental laws are called
axioms and there is no question of the conclusions
having to correspond to any sort of experience. If,
however, one regard Euclidean geometry as the sci-
ence of the possible mutual relations of practically
rigid bodies in space, that is to say, treats it as a
physical science, without abstracting from its original
empirical content, the logical homogeneity of geometry
and theoretical physics becomes complete.

We have thus assigned to pure reason and ex-

perience their places in a theoretical system of physics.
The structure of the system is the work of reason ; the
empirical contents and their mutual relations must
find their representation in the conclusions of the
theory. In the possibility of such a representation lie
the sole value and justification of the whole system,
and especially of the concepts and fundamental prin-
ciples which underlie it. These latter, by the way, are
free inventions of the human intellect, which cannot
be justified either by the nature of that intellect or
in any other fashion a priori.

These fundamental concepts and postulates, which
cannot be further reduced logically, form the essential
part of a theory, which reason cannot touch. It is the
grand object of all theory to make these irreducible
elements as simple and as few in number as possible,
without having to renounce the adequate representa-
tion of any empirical content whatever.

The view I have just outlined of the purely fictitious
character of the fundamentals of scientific theory
was by no means the prevailing one in the eighteenth
or even the nineteenth century. But it is steadily
gaining ground from the fact that the distance in
thought between the fundamental concepts and laws
on one side and, on the other, the conclusions which
have to be brought into relation with our experience
grows larger and larger, the simpler the logical struc-
ture becomes — that is to say, the smaller the number
of logically independent conceptual elements which
are found necessary to support the structure.

Newton, the first creator of a comprehensive,

On the Method of Theoretical Physics

workable system of theoretical physics, still believed
that the basic concepts and laws of his system could
be derived from experience. This is no doubt the
meaning of his saying, hypotheses non fingo.

Actually the concepts of time and space appeared
at that time to present no difficulties. The concepts
of mass, inertia and force, and the laws connecting
them seemed to be drawn directly from experience.
Once this basis is accepted, the expression for the
force of gravitation appears derivable from experi-
ence, and it was reasonable to hope for the same in
regard to other forces.

We can indeed see from Newton's formulation of
it that the concept of absolute space, which comprised
that of absolute rest, made him feel uncomfortable ;
he realized that there seemed to be nothing in ex-
perience corresponding to this last concept. He was
also not quite comfortable about the introduction of
forces operating at a distance. But the tremendous
practical success of his doctrines may well have pre-
vented him and the physicists of the eighteenth and
nineteenth centuries from recognizing the fictitious
character of the foundations of his system.

The natural philosophers of those days were, on
the contrary, most of them possessed with the idea
that the fundamental concepts and postulates of
physics were not in the logical sense free inventions
of the human mind but could be deduced from ex-
perience by "abstraction" — that is to say by logical
means. A clear recognition of the erroneousness of
this notion really only came with the general theory

of relativity, which showed that one could take ac-
count of a wider range of empirical facts, and that
too in a more satisfactory and complete manner, on
a foundation quite different from the Newtonian.
But quite apart from the question of the superiority
of one or the other, the fictitious character of funda-
mental principles is perfectly evident from the fact
that we can point to two essentially different prin-
ciples, both of which correspond with experience to
a large extent ; this proves at the same time that
every attempt at a logical deduction of the basic con-
cepts and postulates of mechanics from elementary
experiences is doomed to failure.

If, then, it is true that this axiomatic basis of theo-
retical physics cannot be extracted from experience
but must be freely invented, can we ever hope to
find the right way? Nay more, has this right way any
existence outside our illusions? Can we hope to be
guided in the right way by experience when there
exist theories (such as classical mechanics) which to
a large extent do justice to experience, without
getting to the root of the matter? I answer without
hesitation that there is, in my opinion, a right way,
and that we are capable of finding it. Our experience
hitherto justifies us in believing that nature is the
realization of the simplest conceivable mathematical
ideas. I am convinced that we can discover by means
of purely mathematical constructions the concepts
and the laws connecting them with each other, which
furnish the key to the understanding of natural phe-
nomena. Experience may suggest the appropriate

On the Method of Theoretical Physics

mathematical concepts, but they most certainly cannot
be deduced from it. Experience remains, of course,
the sole criterion of the physical utility of a mathe-
matical construction. But the creative principle resides
in mathematics. In a certain sense, therefore, I hold
it true that pure thought can grasp reality, as the
ancients dreamed.

In order to justify this confidence, I am compelled
to make use of a mathematical conception. The phys-
ical world is represented as a four-dimensional con-
tinuum. If I assume a Riemannian metric in it and
ask what are the simplest laws which such a metric
system can satisfy, I arrive at the relativist theory
of gravitation in empty space. If in that space I
assume a vector-field or an anti-symmetrical tensor-
field which can be inferred from it, and ask what
are the simplest laws which such a field can satisfy,
I arrive at Clerk Maxwell's equations for empty space.

At this point we still lack a theory for those parts
of space in which electrical density does not disappear.
De Broglie conjectured the existence of a wave field,
which served to explain certain quantum properties
of matter. Dirac found in the spinors field-magni-
tudes of a new sort, whose simplest equations enable
one to a large extent to deduce the properties of the
electron. Subsequently I discovered, in conjunction
with my colleague, that these spinors form a special
case of a new sort of field, mathematically connected
with the four-dimensional system, which we called
"semi vectors." The simplest equations to which such
semivectors can be reduced furnish a key to the

understanding of the existence of two sorts of ele-
mentary particles, of different ponderable mass and
equal but opposite electrical charge. These semivectors
are, after ordinary vectors, the simplest mathematical
fields that are possible in a metrical continuum of
four dimensions, and it looks as if they described, in
an easy manner, certain essential properties of elec-
trical particles.

The important point for us to observe is that all
these constructions and the laws connecting them can
be arrived at by the principle of looking for the mathe-
matically simplest concepts and the link between
them. In the limited nature of the mathematically
existent simple fields and the simple equations pos-
sible between them, lies the theorist's hope of grasp-
ing the real in all its depth.

Meanwhile the great stumbling-block for a field-
theory of this kind lies in the conception of the
atomic structure of matter and energy. For the theory
is fundamentally non-atomic in so far as it operates
exclusively with continuous functions of space, in
contrast to classical mechanics, whose most impor-
tant element, the material point, in itself does justice
to the atomic structure of matter.

The modern quantum theory in the form associated
with the names of de Broglie, Schrodinger, and
Dirac, which operates with continuous functions, has
overcome these difficulties by a bold piece of inter-
pretation which was first given a clear form by Max
Born. According to this, the spatial functions which
appear in the equations make no claim to be a mathe-

On the Method of Theoretical Physics

matical model of the atomic structure. Those func-
tions are only supposed to determine the mathematical
probabilities of the occurrence of such structures if
measurements were taken at a particular spot or in a
certain state of motion. This notion is logically un-
objectionable and has important successes to its
credit. Unfortunately, however, it compels one to use
a continuum the number of whose dimensions is not
that ascribed to space by physics hitherto (four) but
rises indefinitely with the number of the particles
constituting the system under consideration. I cannot
but confess that I attach only a transitory importance
to this interpretation. I still believe in the possibility
of a model of reality — that is to say, of a theory which
represents things themselves and not merely the
probability of their occurrence.

On the other hand it seems to me certain that we
must give up the idea of a complete localization of
the particles in a theoretical model. This seems to
me to be the permanent upshot of Heisenberg's
principle of uncertainty. But an atomic theory in the
true sense of the word (not merely on the basis of
an interpretation) without localization of particles
in a mathematical model, is perfectly thinkable. For
instance, to account for the atomic character of elec-
tricity, the field equations need only lead to the
following conclusions: A portion of space (three-
dimensional) at whose boundaries electrical density
disappears everywhere, always contains a total elec-
trical charge whose size is represented by a whole
number. In a continuum-theory atomic characteristics

would be satisfactorily expressed by integral laws
without localization of the formation entity which
constitutes the atomic structure.

Not until the atomic structure has been successfully
represented in such a manner would I consider the
quantum-riddle solved.

One process can cause another; that one in turn, can be
the cause of a further sequence of events— including the
modification of the original process itself. This article is a
primer to basic ideas in applied science, engineering, and
information theory.

3 Systems, Feedback, Cybernetics

V. Lawrence Parsegian, Alan S. Meltzer, Abraham S. Luchins,
K. Scott Kinerson

From the textbook, Introduction to Natural Science, 1 968.

the READER will recall that following
the quotation from Teilhard de Chardin
in Chapter 1, we proposed extending the
scope of our interests to include analysis
of relationship and interrelationship of
natural phenomena to each other. We
have come to a point that requires a
more formal development of such inter-
relationships.

6.1 Extension of "systems"

One of the accomplishments of the New-
tonian period was the strengthening
of the concept that in material or physical
situations at least, things do not happen
without a causing force. A stone does not
hegin to move or come to a stop of its
own volition. In this chapter we shall
utilize that concept, but with three ex-
tensions.

The first extension takes into account
the fact that in most situations surround-

ing an event (such as the hurling of a
stone), the immediate event is itself part
of a larger situation or system that in-
cludes various other articulating parts
or related events. (That is, there is a
person who throws the stone, and the
throwing has relation to some cause or
purpose.)

The second extension may perhaps
be thought of as related to the action-
reaction principle, namely, that within
the context of the system involving an
event (a stone is thrown) there is often a
feedback effect (for example, the one at
whom the stone is thrown may hurl it
back).

The third extension includes in the
system both material things (stones) and
human beings along with biological
processes and the less tangible thought
processes.

What do we mean by the term system?
We might refer to the weight suspended

from a spring as a system that executes
simple harmonic motion. The governor
that controls the speed of an engine is a
control system. We also speak of a sys-
tem of highways, the economic system
of a nation, a system of thought, and of
many others. The combination locks that
protect the vault of a savings bank make
up a protective system, but this can also
be said to be only a subsystem of the
banking institution. The banking institu-
tion is itself only a subsystem within the
larger community economics, and the
latter is a subsystem of national eco-
nomics. The chain of larger and larger
subsystems, or the nesting of subsystems
within larger subsystems, may lead to
very complex assemblies and relation-
ships.

While an accurate, all-encompassing
definition for the term is not easy to give,
we can note a few of the characteristics
that are usually present in what we call
a system:

(1) A system is likely to have two or
more parts, elements, or aspects, which
tend to have some functional relation to
each other (like the bolt and key of the
lock, or the president and staff of the
bank).

(2) Because systems are usually sub-
systems of larger units it is usually help-
ful (and often necessary) to confine one's
study to the smallest unit that encom-
passes the particular functional ele-
ments and interrelationships that are
under study. (For example, the locksmith
can quite properly repair a fault in the
lock system of the bank vaults without
considering the question of the merits
of socialism for the nation's banking
system.)

(3) A control system has within itself
regulatory functions for control of vari-
ables such as speed of a motor, the tem-

perature of a room, the price of commod-
ities, or international trade in narcotics.

(4) It is usually possible to identify an
"input" and an "output" portion (or
aspect) of a system. For example, a key
placed in a lock and turned (input) will
cause the bolts to move (output); or an
order from a president of an industrial
firm (input) can double the selling price
of its commercial products (output). We
shall find, however, that most systems
have more than one form of input, as well
as a variety of functional relationships
that produce quite varied output.

(5) Usually (nearly always in systems
that include regulatory functions) there
is some form of feedback from the output
to the input, which may greatly modify
the net output of the system. [For exam-
ple, when the selling prices of the com-
mercial products of paragraph (4) were
doubled, the consumers could have
initiated strong feedback by refusing to
buy the products; and the industry's
board of directors could have exerted
even stronger feedback by firing the
president and hiring another who would
hold the prices at a more acceptable
level.] The role of feedback will be given
considerable attention in the discussion
that follows.

We shall now turn to a more detailed
introduction to systems, feedback, and
control.

6.2 Cyclic character of
natural phenomena

In Chapter 5 we learned that a mass sus-
pended from a spring executes simple
harmonic motion when displaced slightly
from its equilibrum position. When the
motion was recorded on a moving sheet
of paper (to illustrate the motion as a
function of time), the oscillations were

Systems, Feedback, Cybernetics

recorded as sine or cosine waveforms.
It was shown that the motion was initiated
when potential energy was added to the
system of weight and spring (by manually
raising the weight from its rest position,
against the pull of gravity, or by pulling
it down and extending the spring). In
either case, the pull of gravity or the pull
of the spring alternately introduced a
restoring force, which tended to return
the displaced mass to its original position
(Fig. 5.24). But since force applied to
mass accelerates the mass and thereby
increases its velocity (Eq. 5-1), by the
time the mass reached the "zero" or initial
position it had acquired so much velocity
(because the potential energy we added
manually had become kinetic energy at
that point) that the mass moved past the
zero point to the other extreme. There
would have been few or no oscillations at
all, on the other hand, if the weight had
been subjected to so much frictional drag
that the added (potential) energy was
lost as heat.f (This might have been the
case if the weight moved in a viscous
liquid.)

What about cyclic behavior in other
phenomena of nature? A very common
form can be demonstrated in electric
circuits in which the electric energy
rapidly passes back and forth between
parts of an oscillating circuit until the
electric energy dissipates as heat or
radiates away from the circuit (as in the
transmission of radio waves).

We shall find that there can be many
forms of oscillatory behavior when a

t We shall learn in Chapter 10 that the kinetic
energy of the system goes into faster, random
motion of the molecules that make up the parts
of the system. The increased molecular motion
raises the temperature of the parts of the sys-
tem, as though it were heated by a flame.
There is therefore a correspondence or equiv-
alence between the energy in a flame and
mechanical motion of the system.

"disturbance" changes the energy level
of a system and introduces a restoring
force that causes the energy to convert
to another form rather than completely
dissipate into the heat energy of the en-
vironment. The term energy may apply
not only to mechanical, electrical, or
chemical characters in physical systems,
but also to institutional and personal
pressures in social situations.

Let us now go to other phenomena that
show cyclic or periodic variation. (See
Figs. 6.1(a) through 6.1(d), for graphical
examples of such cyclic variations.) We
might utilize various sensing devices to
record changes in the temperature of an
air-conditioned room as a function of
time, the height of the tides of the sea,
wind velocity, the automobile traffic on
a road, rainfall, the movements of a tall
building or of the long span of a bridge,
or the temperature of the earth. We might
also look up past statistics on wheat
production, the stock market, attendance
at church, tourist travel, populations of
animals, or the length of women's skirts,
and plot these in graph form as function
of time. We would find that many phe-
nomena in nature and in animal or social
activity have variations of an oscillating
character (Fig. 6.1). It can be demon-
strated that in all these situations which
show oscillations about some average
point, there is present a restoring force
that comes into play whenever there
is energy change in a system. To be sure,
the magnitude and shapes of these oscil-
lations and waves vary considerably from
the sine waves we observe with a weight
on a spring. The periods may vary from
10-15 sec in the case of light waves, to
several hours for the period of the tides,
and to many years in the case of other
cycles of nature and of some social cus-
toms. Nevertheless, all are subject to
some common influence, not the least of

3rd interglacial
period

1st glacial 2nd glacial
period period

3rd glacial 4th glacial
period period

6 5 4 3 2 10

Time in hundreds of thousands of years ago

Fig. 6.1. (a) Cyclic temperature
variations during the ice ages.
Current theory attributes these
long, slow temperature variations
to relatively minor changes in the
atmospheric carbon dioxide
content (see Chapter 15, Sec. 2).
(Adapted from graph in G. H.
Drury, The Face of the Earth,
Penguin (Pelican book), pg. 157.)

140^

Fig. 6.1. (b) Cyclic varia-
tions in numbers of species
of Lepidoptera (butterflies
and moths) captured in light
traps at Woking, Surrey in
1948-49. The number of
different species of captured
reveals seasonal cyclic
variations that are obviously
related to weather condi-
tions. Note peaks in
successive Julys, when
Lepidoptera conditions are
ideal, and low values in
winter when conditions are
poor. (From C. B. Williams,
Patterns in the Balance of
Nature, Academic Press,
1964, pg. 159.)

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Systems, Feedback, Cybernetics

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Fig. 6.1. (c) Cyclic char-
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which is the fact that nature is dynamic
and in a state of continuous change, and
indeed that static situations represent
special and almost trivial aspects of nature
and of man.

Is the presence of some restoring force
sufficient assurance that a system will
experience only moderate oscillations

without going to extremes? Indeed it is
not, as we can learn from the dramatic
example of the failure of the Tacoma
Narrows suspension bridge of Tacoma,
Washington. When the bridge was opened
to traffic on July 1, 1940, there were
observed, in addition to the ordinary oscil-
lations of the bridge, some unexpected

Hand holding
spring

nitial amplitude
ot mass

Motion of hand

— Opposite motion
of mass

Motion of the mass

becomes reduced in

amplitude

Motion of hand

— "In phase" with
motion of mass

Motion of the mass

builds to destructive

proportions

Fig. 6.2. What happens when the mass of a spring is given some additional energy
by movement of the hand in two different phase relationships? In the center figure
the hand is moved upward when the mass is moving downward. At the right, the hand
is moved upward when the mass is also moving upward, causing the mass to take
large swings.

transverse (vertical) modes of vibration.
On November 7 a wind velocity of 40 to
45 mph made the vibrations so severe
that the bridge was closed to traffic, and
by 11:00 A.M. the main span collapsed, f

t A 4-minute film produced by the Ohio
State University and distributed by The Ealing
Corporation of Cambridge, Massachusetts,
gives the very dramatic story of the final oscil-
lation of the bridge prior to its collapse. Everv
reader should see this film and the variation
it offers of "simple harmonic motion" involving
the twisting and turning of this huge span of
steel and concrete. The new bridge that was
built on the original anchorages and tower
foundations included deep stiffening trusses
instead of girders, and has been entirely
successful.

6.3 How oscillations increase
despite restoring forces

It is not necessary to resort to the com-
plex behavior of the original Tacoma
Narrows bridge to see how a system may
have within it strong restoring forces
while yet experiencing oscillations that
increase in amplitude to the point of
destruction. The reader can duplicate
the phenomenon with the simple weight
on a spring as follows (Fig. 6.2):

Choose a weight and spring combina-
tion that gives an oscillatory period be-
tween i and i sec. Hold the spring firmly
and steady in your hand, and observe that
the weight executes the usual simple

Systems, Feedback, Cybernetics

harmonic motion, eventually coming to
a stop. Now prepare to move your hold-
ing hand up or down in synchronism
with the motion of the weight and with
two alternative movements.

First, raise your hand (about a half-inch
will do) whenever the weight is moving
downward, and lower it an equal distance
whenever the weight is moving up. With
a little analysis you can see that the
weight tends to reduce amplitude be-
cause the movements of your hand in-
crease the restoring force on the weight.
Note that the movement of your hand is
180 deg out of phase with the motion of
the weight.

Next, repeat the experiment with the
same up-and-down motion of your hand,
but now change the timing to be in phase
with the motion of the weight. That is,
move your hand upward when the weight
is moving upward, and downward when
the weight is moving downward. There
still is restoring force, and the weight
continues to oscillate up and down; but
now the amplitude of oscillations in-
creases until it becomes dangerous to
continue the experiment.

Why did the same amount of motion of
your hand have such opposite effects,
depending only on its phase relationship
to the motion of the weight? The reason
is that in the second case the increments
of energy that were introduced by each
in-phase motion of your hand tended to
add to and increase the energy of the
system represented by the spring and
weight. Conversely, the hand motion that
was completely out of phase with the
motion of the weight detracted from the
energy of the system, t

t The reader is urged to perform this experi-
ment and to attempt a careful analysis of the
various factors (energies and forces) that be-
come involved in the two cases. For example,

We can now extend this experiment to
apply to the early Tacoma Narrows bridge
experience. Obviously, the energy of the
wind became converted to energy of
oscillation of the bridge. Why did the
wind energy not become absorbed in
the concrete and steel of the bridge? Un-
doubtedly much of it did become ab-
sorbed and changed to heat energy, but
not all of it. Apparently when the wind
blew to produce a movement of the span
at some point along the bridge, the con-
ditions were just right to cause this move-
ment to act as a traveling wave, which on
backward reflection returned to the same
point in just the right phase to support
(rather than oppose) a new movement at
that point, caused by the continued blow-
ing of the wind. Had the physical struc-
ture of the bridge been different in length
or mass, the returning wave could have
opposed (out of phase with) any new
movement at A, and thus would have
added to the stability of the system.

We see, therefore, that for a system to
be stable, the relationship of the forces
and time characteristics must be such that
the amplitude and energy of the system
will not increase. This calls for special
attention with respect to the phase re-
lationships that obtain between feed-
back of energy from one part of the sys-
tem to another part. When the feedback
opposes the direction of the initial change
that produced the feedback, the system
tends to be stable. In contrast, when the
returning feedback of energy supports
the direction of initial change, the system
tends to add to the initial energy gain and
to be unstable. This means we must
delve into the theory of system control.

in the second case the increments of energy are
added to the spring-weight system. Where
does the hand energy go in the first case?

6.4 Modifying cyclic changes:
controls

While most fluctuations of nature go their
own way without inviting human concern,
there are some important cases in which
it becomes necessary to interfere, that is,
to modify the natural pattern or to control
or hold the fluctuations to smaller
changes. For example, the farmer may
not want to depend entirely on natural
rainfall to assure a good crop, so he in-
tervenes by irrigating the fields when
there is not enough rainfall. Because in
the course of the year there are wide
fluctuations in the temperature of the
earth, he installs a control system in his
home to keep the temperature within
comfortable limits.

Many types of controls are involved
in our daily life. We shall learn that the
human body has a remarkable control
system to maintain its own temperature
within very close limits. The body's
motor functions, by which we move our
arms and legs in an accurate and deter-
mined manner, are possible only because
of the operation of fine control systems.
Industrial production relies heavily on
control of temperature, pressure, chemi-
cal composition, and similar factors. The
application of control principles extends
to community and national life. Despite
their variety, we shall find that there are
some common characteristics among
them. Also, within a specific control
system there can be intermixed a wide
variety of elements of widely different
types. Take, for example, the very com-
mon experience of driving an automobile.
Here, the steering control allows the
driver to follow the curvature of the road
effectively, and many other electrome-
chanical parts as well in the motor and
transmission systems affect the driving

operation. But we shall learn before long
that nearly every aspect of the driver's
being — his metabolism, muscle and nerve
action, his thinking process — and the life
of his community are all parts of the sys-
tem that encompasses the simple driving
experience.

6.5 Introduction to on-off control

We return to the harmonic motion of the
weight suspended from a spring and note
that, so far, we have neither tried to re-
strict the amplitude of the motion nor put
the movement to some useful application.
In each assembly the added energy is
converted and reconverted from kinetic
energy to potential energy and then back
again to kinetic energy. (If there were no
frictional losses, the motion would con-
tinue forever, since the system would
then be self-contained, that is, a closed
or isolated system that neither receives
energy from nor gives energy to the out-
side.) Such systems have limited value
except as one may use them in a clock or
metronome to tell time from the os-
cillations.!

If there were no frictional or other loss
of energy from the system, the motion
would have a periodicity of T seconds.
Since friction is present, the oscillations
become continually smaller in magni-
tude, and the period of each cycle be-
comes slightly longer (T + AT) until the
mechanical energy dissipates as heat
energy and the movement ceases al-
together (Fig. 6.3). In general, friction or
damping is likely to make a system more
stable.

We can design an oscillator to do some-

f Of course, as any such device requires
periodic additions ot energy to the driving
springs, and therefore the person who winds
the spring becomes part of the system.

Systems, Feedback, Cybernetics

3 1

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E '

i
1

""^^v

\ Time—*- /

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T + AT sec-

Fig. 6.3. How the period of
simple harmonic motion
changes when there is
friction in the system. (The
period of seconds increases
to T + AT sec, while the
amplitude of motion
decreases.)

thing more by adding an electric switch
so that the dropping weight sends an
electrical signal to some device. As we
know from common experience, the
simple operation of an electric switch
can initiate (or trigger) many motor or
relay functions that bring into play the
vast energy resources of electric power-
generating stations. Figure 6.4 illustrates
the relationship between input and out-
put, with a transform function that relates
the two along with a source of energy.

Suppose that we incorporate such an
electric switch as part of a control system
for automatically filling a bucket with
water. Figure 6.5 illustrates how the
dropping pail signals that the pail is full
and also turns off the stream of water.
This becomes a simple on-off control
system in which the electrical signal
provides a feedback function as part
of the control system. (Later we shall
introduce the idea that the feedback also
represents information.)

We examine this process of filling the
bucket in a little more detail. When the
water flows into the bucket at a very slow
rate, the bucket settles slowly and the
signal switch has time to stop the flow
of water and bring the bucket to a gentle
stop. This is shown as curve A of Fig. 6.6,
which shows very little dropping of the
bucket below the desired level (that is,
there is very little overshoot beyond the
desired control point). The behavior
becomes quite different when the water
flows into the bucket at a rapid rate,
however. The switch operates as it did
before, but the rapid dropping of the
bucket develops enough momentum to
overshoot the desired final position by a
substantial amount. The bucket will
oscillate violently above and below the
desired control height for some time and
the switch will open and close erratically
(curve B). In fact, if the response rates
and delays in the switching and valve
devices should turn out to be particularly

Energy source to make
amplification possible

lllll

A/ = input to system

This box establishes
relationship between output
and input — the transfer
function /(/)

bO = output of system

(For example, position of (For example, automobile motor
accelerator pedal of an develops large power to correspond
automobile or position of to accelerator position, or electric
an electrical switch) circuit brings large electric energy

into play)

Fig. 6.4. How a small input change (such as the operation of an electric switch) can
bring into play sources of energy and thereby produce an output that may be quite
different inform and magnitude from the input. Each such conversion can be referred
to as involving a transformation (transfer function or transform function).

unsuitable, the water would be turned
on and off in such erratic manner as to
recall the sad fate of the Tacoma Narrows
bridge; see curve B, dotted line, Fig. 6.6.
In the case of room-temperature control,
the thermostat is likely to be kept at one
temperature (for comfort), say, around
72°F. In the case of the baking oven, the
temperature setting will vary with the
requirements for baking a cake or roast-
ing meat. In either case, the temperature
will vary (or hunt) around the set control
point. The hunting or oscillations can be
decreased if the rate of heat input is slow.
But this would increase the time needed
to bring the room or oven to the desired
temperature. With on-off control, the
heating unit becomes fully hot whenever
the control switch turns it on. By the time
the temperature at the thermostat reaches
the desired temperature to turn off the
heat, the region of the heater units be-
comes much hotter than necessary, and

this excess heat drives the temperature
well above the desired temperature. A
similar delay in reactivating the heating
unit as the temperature drops below the
desired level causes continual hunting
above and below the desired temperature.
We shall appreciate more and more, as
we examine more cases, that the "control"
of a variable rarely results in an exact
holding of the variable to the desired
control value. Nearly always, the variable
will hunt or vary about that control
value. Therefore, the function of a suc-
cessful control system is to hold the
variable within acceptable departures
from the desired control value.

6.6 Negative versus
positive feedback

In all the examples given above, while it
is clear that control at a point usually ends
up as hunting around that point, even this

Systems, Feedback, Cybernetics

'/////////////////////

Fig. 6.5. A simple system for controlling the
filling of a bucket.

Spring

Valve to control water flow by
electric motor control

To motor valve

Electric switch, designed to turn off
water valve when bucket drops
down to close switch

Fig. 6.6. How the bucket of Fig. 6.5 behaves:
Bucket A is filled slowly and settles gradually to
its final level after switch cuts off water flow.
Bucket B (solid line) is filled rapidly and over-
shoots final position, rebounds, and hunts for an
equilibrium position that is lower than that for
bucket A because extra water was added after the
first rebound above the switch-off level. With a
different spring tension for bucket B (dotted line),
the hunting may cause addition of sufficient
extra water on each cycle so that the amplitude
steadily increases until the system collapses.

Excessive hunting results in collision

with upper support and final collapse

of controlled aspect of system

bucket

degree of control is achieved only when
negative feedback is present. Thus, in
the case of the full bucket, the switch
turns off the water (since it was the
"water-on" condition that filled the
bucket). In the case of room-temperature
control (which we shall discuss presently
in detail), the heaters must be turned on
when the room temperature is too low,
and off when the temperature is too high.

The examples of feedback, as well as
the limitations of on-off (sometimes called
bang-bang) control can be illustrated
further by the example of a blind person
walking down a street with his cane. As
he progresses along the sidewalk the
tapping of his cane tells him when he is
too close to the buildings on the right.
This information, when processed
through his brain and muscle system,
serves as feedback to change his direction.
Since his movements have taken him too
far to the right, now he must move to the
left and therefore the feedback must be
negative. If the influence of feedback
were positive, it would support or add
to the original direction that took him t&
the right and would take him even farther
to the right and directly into the wall. He
now continues to the left until his cane
warns that he is too close to the curb at
the left. This information again converts
to become negative feedback, which will
oppose the move that carried him too far
to the left and thereby will restore his
direction until a new signal calls for new
action.

Our blind person can negotiate the
walk fairly well as long as his movements
are slow enough to give him time to
receive the signal from his tapping, to
interpret these, and to translate them into
suitable feedback influence. But now
suppose he tries to run down the same
sidewalk. Very soon his rate of receiving
and responding to signals would be in-
adequate, and he would be running in a
zigzag or colliding with obstacles.

Such an experience, which the reader
can himself check rather dramatically,
illustrates several features of control
that apply fairly generally, namely:

(1) Stable control requires the pres-
ence of negative feedback influences.

(2) Stable control of a variable to a
"fixed" point usually means maintain-
ing the variable so that is does not hunt
around the point beyond acceptable
limits.

(3) To be effective for the control of
any variable, the control system must
be designed to have response rates that
are suited for the specific application.

These and other characteristics of
control systems will be illustrated in the
following sections.

6.7 Driving an automobile

To illustrate further the limitations of
on-off control, let us apply the technique
to driving an automobile in a lane of the
road that is marked with white lines. We
know from experience that an auto tends
to go from side to side (to hunt), and
requires continuous steering control.
Let us assume an unreal situation in
which we turn the steering wheel a
small, fixed amount to make the correc-
tion, and do this only when a front wheel
touches a white line. The experiment
would then be like the walk of a blind
person. When crawling along at a very
slow speed we would find that the car
does not go very much outside the lane,
but when driving at a moderate speed
we would find that this type of correction
(applying a fixed amount of adjustment
as on-off control) causes the car to weave
substantially in and out of the lane. If
we were to drive even faster, the car
would be likely to leave the road alto-
gether. The amount of overshoot would
depend on how slowly we respond to vis-
ual signals and take action (see Fig. 6.7).

Systems, Feedback, Cybernetics

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N v%/ X. /") S

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Fig. 6.7. Difficulty of driving an auto by on-off control technique.

Fortunately not many people drive in
this manner because control of an auto-
mobile utilizes a much more sophisticated
system of elements than is possible with
on-off control. In fact, not many automatic
industrial processes can compare with
the sophistication and effectiveness of
good auto driving, since human judgment
enters this operation to a remarkable
degree. To begin with, as the auto moves
to a new position or direction, the driver
is kept continually informed of the nature
of each new situation through his sense of
sight and general physical awareness.
That is, there is continuous feedback, or
information, reaching him to guide his
next move. The element of judgment or
experience also enters. He can vary the
sharpness of turn of the steering wheel
to conform to the sharp right turn. This
is called proportional control. In addition,
he can see a curve in the road ahead long
before the auto has reached the curve.
He can therefore anticipate the move

(anticipatory control) and thus reduce
delay in his action (Fig. 6.8).

The driver of an automobile is aware
of several elements that make control
more difficult. If the steering wheel has
looseness or "play" in the shaft or gear
system, the steering wheel must be turned
several degrees of angle before there is
any effect on the front wheel directions.
This play, or region of no response, is
sometimes called the dead zone of the
system. The driver himself may be a little
slow in judging the situation and taking
action. This "lag or slowness of response
together with looseness in the steering
system, can make for wider overshoot in
the movement of the car. If the throttle
sticks, the motor hesitates, or the brakes
seize, the driver will not be able to assure
smooth "feel" and ride. Finally, rough-
ness of the road can introduce random
fluctuations that add uncertainty to the
normal small feedback of information.
A driver is not likely to give delicate

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Systems, Feedback, Cybernetics

guidance to the auto when his whole
body is being shaken. This background
confusion is often called noise or static
when one is referring to transmission of
signal or of information. It exists in almost
every type of control circuit, sometimes
in the form of vibration of an automobile
or plant equipment. It occurs in the
normal radioactivity background of the
environment, which disturbs radiation
measurements. In very sensitive elec-
tronic circuitry it shows up in the random
movements of the electrons. Similar
phenomena are present in social situ-
ations and in biological organisms that
maintain balance in their internal func-
tions and with their environment.

Because cyclic and control aspects of
nature are exceedingly important, we
must consider control principles and no-
menclature in a little more detail before
looking at the several types of systems
that are common.

6.8 Some control principles —
nomenclature

Before beginning detailed discussion we
need some convenient terminology and
symbols for representing the elements
and functions that make up systems.
When the driver of an automobile engages
the gears and steps on the accelerator
pedal, the motor raeexumd the car moves
forward with an expenditure of energy
that is vastly greater than the energy ap-
plied to the pedal. The power is ampli-
fied. We may represent this by a diagram
such as Fig. 6.4. The input, AI in this case,
appears to be simply the change in posi-
tion of the pedal and the small energy
required to make the change. The box in
Fig. 6.4 represents the change or trans-
formation (ol function) that the input
A/ initiates or experiences; in this case
the function produces motor power at a
level that is related (and perhaps propor-
tional) to the position of the throttle or

accelerator pedal. We can refer to the box
as representing a transfer function /(/),
or converter, which produces AO.

What is the source of the energy that
makes this conversion possible? In this
case, the energy source is the chemical
energy in the tank of gasoline. The pedal,
therefore, is nothing more than a lever
device for controlling the use of this
chemical energy. When one includes the
tank of gasoline and the driver along with
the automobile, the system becomes a
closed (or conservative) system.} With-
out either one, the system would be in-
complete. (It is common practice to omit
the sources of energy from block diagrams
of control systems and to indicate only
the energy input and output for a system.)

The operator has freedom to depress
the accelerator pedal quickly or slowly,
as he wishes. A question that is frequently
important for analyzing the behavior of
control systems is the following: What is
the nature of the output response wher
the input is given a quick change? A
quick increment of input change, which
we may represent by A7, is usually called
an input step function.t Figure 6.9 illu-
strates what might happen. Usually there
is some lag in the rise of motor power, as
shown by the curved rise and fall of the
output. This lag will not be serious in
the case of the automobile, since the
input is not likely to be reversed rapidly
very often. In general it is desirable to
have as much lag as one can tolerate,
consistent with adequate control; other-
wise the system will be too ready to
"jump" and probably to overshoot the

f We neglect the fact that as gasoline is
used up it must be replaced, bringing the
entire petroleum industry into our system.
Likewise, food for the driver is neglected.

\ The term step function is often associated
with on-off changes because the change of
power or direction assumes the form of a sud-
den change. This is illustrated by the shape
of the heat input as it is turned on and off in
Figs. 6.9 and 6.10.

L-iX

Sudden increase of input

Sudden Decrease of input

Slow increase of output power level

Slow decrease of output power level

INCREASING TIME-

Fig. 6.9. When the input is given a quick change (step function), the response
of the output may be designed to be slow or rapid. In general, a slow response
of output produces less hunting than does rapid response.

mark and hunt badly before settling down.
The lower curve of Fig. 6.9 illustrates
the nature of the "hunting" that results
when the system is made to respond too
quickly to change in input. How the out-
put will respond depends on the charac-
teristics of the system and on the features
incorporated in the transform function
box of Fig. 6.4.

If the system of moving parts includes
large, heavy components such as the
flywheel and other parts of the automobi le
motor, we can appreciate that quicker
response is possible only if the motor is
designed to have adequate extra power
to give the desired acceleration. But
excessive power can make control less
smooth and more "jumpy," not to mention
excessively costly in gasoline and in the
complexity of the motor itself. The goal
for design of most systems is to find a

happy compromise that makes the system
adequately responsive and yet stable
against excessive hunting, and which is
not too expensive in dollars or in use of
energy.

The system we have been discussing
has the features of proportional control.
That is, the accelerator pedal may be
depressed to give large or small change,
and the motor power level will respond
with some proportional relationship. We
backtrack a little to discuss on-off control
before proceeding further.

6.9 More on on-off control

Earlier we discussed how difficult it
would be to hold an automobile within
the lane of the road if we applied on-off
control principles to adjust the steering.
Despite certain limitations, on-off control

Systems, Feedback, Cybernetics

devices are used very commonly in homes
and in industry because of their sim-
plicity. It is very easy to design an elec-
tric iron, an oven, or room-temperature
control, to operate an electric switch
to turn on (or off) the electric power
whenever the temperature falls below
(or rises above) set values. Figure 6.10
illustrates how this might apply to the
thermostat controls for heating a room in
the winter time.
As shown in Fig. 6.10(a), 72°F is the

temperature desired for this room. But
all thermostats and switching devices
require a differential zone of temperature
change in which to go on and off; other-
wise they would act too frequently and
probably erratically because of vibration
conditions and momentary temperature
fluctuations in the immediate neighbor-
hood of the thermostat. We start with the
temperature dropping in the upper curve
of this figure. When the temperature
reaches the lower edge of the differential

B 73'

8. 72c

$ 7r

Thermostat goes "off"
to cut off heat

Max room temperature

Thermostat
goes on to ca
for heat

w "off -on" zone

Actual range of
L temperature
change in room

Increasing time

Heater turns "off"

\7I

Heater turns "on"

Increasing time

(a)

Above desired level

Thermostat Warm air

Desired temperature level

Cool air

Radiator

Below desired level

Fig. 6.10. Relation of room
temperature and thermostat to
the power input to a room-
(b) temperature control system.

temperature zone (71°F in Fig. 6.10(a)),
the thermostat switch turns on the heater.
This assumes that there are no significant
time delays in the response of the thermo-
stat or the heater controls. (In actual
experience there are always some delays.)
The radiators around the room take much
more time to heat up, and the temperature
of the air in the room continues to drop
until it reaches some point which is well
below the lower limit of the control
range (about 70° in Fig. 6.10(a)).

As the hot radiators heat the air in the
room, the temperature at the thermostat
starts to climb again, and at the 73°F
level the heaters are turned off. But at that
point the radiators are fully hot, and the
air in the room continues to receive heat
and to rise to a maximum temperature
which is well above 73°F. The net result
is that the room temperature may vary
by as much as four or more degrees
Fahrenheit. In an actual system there will
be a little time lag between the temper-
ature at 71°F or 73°F and the response of
the thermostat and heater controls, which
can make the overshoot and hunting more
severe. Nevertheless, the simplicity and
relatively low cost of on-off systems makes
them very attractive for use in such oper-
ations as controlling temperatures, main-
taining water level in tanks, and many
other operations. Biological and some
social systems, as well as many industrial,
mechanical, and chemical processes,
usually require the more accurate control
that can be achieved through propor-
tional-type systems.

How much power can an on-off system
control? It is fairly clear that the switch
that turns the heater on and off can be
designed to handle any amount of elec-
tric or other form of energy. The amount
depends on the power requirements to
keep the variable that is being controlled
as close to the desired value as possible.

A general rule might be to design the
power level so that the controller calls
for heat about half the time, and the heater
remains off half the total time. Sometimes
the control is improved by supplying a
portion of the power continuously at a
low, fixed level, and allowing the control
system to add or subtract a smaller in-
crement of power as needed.

6.10 Characteristics of

proportional control

The on-off type of temperature control,
in which the power is usually turned
full-on or full-off, is inadequate for many
applications that cannot tolerate the wide
surges around the desired control point
that often accompany on-off systems. The
undesirable surges can be reduced if
the power is moderated in proportion
to the need. This is exactly what is
achieved in proportional control systems,
in which the heat input continues at
some intermediate level when the tem-
perature is near the desired control
point. As the temperature rises somewhat,
the controller reduces the heat input in
proportion to the departure from the set
control point. Similarly, the heat input is
increased in proportion to a fall in tem-
perature below the set control point. Of
course the system becomes more com-
plicated because now the temperature
detector must measure the magnitude of
departure from the control point. (In
on-off control, all that the detector has to
do is to note that the temperature is above
or below the set point.) Also, there must
be somewhat more complex intercon-
nection so that the proportionate (or step-
bv-step) changes in the temperature
detector can be translated into propor-
tionate (or step-by-step) action on the
part of the valve or motor that controls
the fuel or power input.

Systems, Feedback, Cybernetics

* 74°-

72°
70°--

Temperature of room near thermostat

Time *-

Response of proportional thermostat to room temperature

Time

<u c

TO °o

Heater power level in response to changes in temperature

Time

Fig. 6.11. In a proportional control system, the response of the thermostat is
proportional to the departure of room temperature from the desired control point
and the change in power input to the boiler is proportional to the response of
the thermostat.

Let us analyze the action of such a
system designed to control the temper-
ature in a room.

When the door of the room opens and
lets in a draft of cold air, the thermostat
responds as shown by the drop in the
upper curve of Fig. 6.11. As shown by
the middle curve, at that same time the
thermostat control calls for a propor-
tional increase of heat, and the heaters
respond as shown by the lower curve. As
the draft of cold air becomes warmed
somewhat by mixing with the warmer
air, the proportional thermostat cor-
respondingly reduces its demand for
heat. The net result is that the room tem-
perature is maintained much more closely
to the desired 72°F than is possible with
on-off control. But the proportional control
instruments and equipment tend to be
more expensive, and for that reason they

are not used where on-off control is
adequate.

A serious limitation develops in pro-
portional control systems when the load
demand changes so that a different
average power level must be applied to
hold the variable at the desired control
value. To understand this, we note that
in proportional control, the output AO
(Fig. 6.4) has a fixed ratio to the input
A/. This proportionality ratio, or gain,
may be represented by G = AO/A/. As-
sume that the room-temperature control
we have been discussing is set to control
at 72°F when the outdoor temperature is
around 50°F. We may assume that this
requires an average heat input of 10,000
Btu per hour. Suppose that the outdoor
temperature drops to 0°F. Obviously, the
heater system must provide a great deal
more heat to hold the temperature at

72°F, say, 30,000 Btu per hour. We there-
fore need an additional 30,000 - 10,000 =
20,000 Btu per hour to hold the temper-
ature at 72°F. But since in proportional
control more heat is provided only in pro-
portion to the temperature drop from the
control setting, how can the additional
heat be provided without the actual tem-
perature remaining well below the de-
sired control value?

Let us analyze the situation a little
more quantitatively. Suppose that the
gain of our control is set so that, for each
degree that the temperature drops,
the controller permits an additional 2000
Btu per hour to be supplied to the boiler.
This represents a gain or proportionality
ratio of 2000 Btu per hour per degree
fahrenheit. To get the additional 20,000
Btu would require that the temperature
of the room go down to 62°F. Or, alter-
natively, the thermostat setting would
have to be moved arbitrarily to about
80°F in order to supply enough heat to
hold the room temperature at 72°F as long
as the outdoor temperature remained at
zero.

This discrepancy could be reduced if
the gain were made higher (that is, 1°F
could turn on much more than an addi-
tional 2000 Btu per hour). But making the
gain higher also makes the system more
unstable. Other devices can be intro-
duced to change the responsiveness of
the controller, such as incorporating into
the system an outdoor thermostat that
introduces this equivalent of the arbitrary
shift of a thermostat setting. of 80°F. We
need not go into more detail beyond
recognizing this severe limitation of
proportional control systems.

6.11 Feedback

We must give a little more attention to
the important feedback function. When

the thermostat of a temperature-control
system demands more heat, the addi-
tional heat energy continues to pour into
the heater boilers and radiators until
feedback information (in the form of
rising air temperature in its neighbor-
hood) reverses the thermostat demand.
In the case of the driver of the automobile,
although his foot on the accelerator finds
good proportional power response on the
part of the motor, only feedback in the
form of vision (and the transformation of
that ii/ormation into suitable muscle
action) makes driving successful. Without
the presence of feedback, the driver
could not function as part of the system.

The kind as well as the timing (or
phase relationship; see Sect. 6.3) of feed-
back are rather important. In the case of
the temperature controller, the electrical
thermostat reactions must become trans-
formed into heat energy and transfer of
this energy to the room if there is to be
control of temperature. In the case of the
driver, the feedback which arrives in
the form of sensory information must be-
come interpreted and converted into
suitable muscle action on the accelerator
pedal to be effective.

In the case of temperature control the
feedback must always be negative. That
is, the rising room temperature causes the
thermostat to demand less heat, while a
dropping temperature causes it to de-
mand more heat. In the case of driving
an automobile, the feedback may be
negative (say, when the traffic light turns
red and the driver has to let up on the
accelerator) or positive (say, when the
way is clear for higher speed). When a
politician confronts his voting constitu-
ents on an important issue, he watches
their reactions as he talks, to get some
form of feedback, When the response
(or feedback) from the audience is "posi-

Systems, Feedback, Cybernetics

tive," he believes that his statements
have been received favorably, whereas
a "negative" feedback is likely to make
him cautious.

Feedback may take many forms and
many types of coupling. Figure 6.12 il-
lustrates a simple modification of an
earlier graph. In this illustration some of
the output energy is fed back to the input.
The box marked "feedback transfer"
determines how much of and in what
form the output will be fed back. The
input is represented by a long arrow with
positive increment. The feedback is
shown as a small arrow with negative
value. In such a setup the net input is
reduced by the amount of the negative
feedback. The effect is to restrain or to
limit the output. If the sign of the feed-
back were positive, the input and the
feedback would add and the output
would increase continually and build
up to destruction, or to the limit of the
energy input. A system with feedback is
often referred to as a closed-loop system.
Since such systems incorporate a measure
of self-correction, the exact value that
the input is permitted to have becomes
less critical. This self-correction factor
also applies to the automobile driver, who

does not have to have a gauge on the foot
pedal because the "feedback" of his eyes
and ears is enough to guide and restrain
his push on the foot pedal.

High values for gain in amplifiers or
control circuits tend to make a system
unstable, and time lags produce wider
oscillations. Negative feedback, on the
other hand, tends to stabilize the systems.

6.12 The elements of
control systems

Now that we have developed some famil-
iarity with control systems, we can iden-
tify the functional elements that make up
most systems.

THE VARIABLE TO BE CONTROLLED

First there is the variable that the
system is expected to cope with or to
control within prescribed limits. Actually
it is rare that only one variable is present
in a system. In the case of room-temper-
ature control the changes in the outdoor
temperature constitute an independent
variable, while the internal temperature
represents the controlled variable. Other
independent variables may be intro-
duced, such as children running in and

A70 =

input +-*-

Converter, amplifier,
transducer, or transfer
function /(/)

+"*~ A0 = OUtput

Fig. 6.12.
Addition of a
feedback transfer
function to the

Feedback
transfer function

transform function
of Fig. 6.4.

out of open doors, to cause variable
demands for more or less heating.

Similarly, the driver of the automobile
has control devices by which he steers
and starts and stops the car in relation
to the road. But all along the way he is
forced to comply with independent
demands, such as changing road and
traffic conditions, stop signs, and traffic
lights, all of which constitute independent
variables.

SENSOR DEVICES

Usually there must be some sensor
device by which the variable can be
measured or gauged. For example, in the
case of the temperature measurement we
shall learn in Chapter 10 that the tem-
perature of air is actually determined by
the velocity of the molecules that make
up air. But we cannot gauge the temper-
ature by measuring the velocity of mol-
ecules directly. What we can do is to
utilize some effect that changes with
changing molecule velocity. For example:
At high air temperature, molecules in a
material become more active and bump
each other harder and more frequently,
causing objects such as fluid in a ther-
mometer or a piece of metal in a thermo-
stat to warm up. A thermostat usually
includes a bimetal t that carries an elec-
trical contact; the bimetal changes its
position when the air temperature
changes and thus makes or breaks an
electric circuit.

Similarly, while the position and be-
havior of the automobile are the variables

t A bimetal strip is made up of two different
metals bonded together. Because the two
metals have different temperature expansion
coefficients, the bimetal will bend when
heated, thus causing the contact to switch on
the system. As it cools, it straightens and con-
tact is terminated.

to be controlled, we gauge these by the
use of sensory information (vision, hear-
ing) and the interpretive processes of
the brain. The economist also looks for
meaningful indices by which to gauge
the larger features of national product,
industrial trends, and public attitudes.
The public utilizes quality and creativity
as gauges to evaluate intrinsic or extrinsic-
return on investment.

ENERGY SOURCE

Whether one deals with a temperature-
control system, driving an automobile, or
any other situation that involves variables
and controls, there must be a source of
energy by which the job is performed.

MOTOR TRANSFORM DEVICE

In most instances the sensor function
must utilize the services of a motor device
to restore a variable to its proper value.
To do this the motor device, or motor
function, utilizes energy from an energy
source. In the temperature-control sys-
tem, the blowers and burners (which are
triggered into action by the thermostat)
begin to utilize fuel energy to heat the
boilers. In the automobile a number of
mechanisms come into play to burn the
gasoline, to power the steering, and to
perform other nondriver functions.

FEEDBACK

Finally there is a feedback device, or

feedback function, which in one way or
another relates the output to the input
and thus controls the net output.

The functional elements of a system
cannot always be identified individually
or even as subsystems, but they are
present in one form or another. One
characteristic that will be evident more
and more is the wide variety of trans-
formations (transform functions) that are

Systems, Feedback, Cybernetics

possible in systems. Molecular speeds
are transformed into mechanical bending
of a bimetal, which completes an electric
circuit and utilizes electric energy. This
in turn starts a motor and pump device
to feed and burn oil in a boiler, which
produces heat that is transported or trans-
ferred by various means to another area
by other motor devices. Similarly, all
the tangible and intangible features of
human physical energy and human brain
processes become involved with elec-
tromechanical and chemical systems in
driving an automobile. (For each of these
transformations we can apply the more
elegant phrase transform function, and
illustrate the nature of the transformation
by means of a mathematical equation, a
graph, a listing of data, or a simple
picture.)

6.13 Control concepts: cybernetics

The art and science of control theory has
had a long and slow history- In the early
days it found application in the sailing
and steering of ships. With the coming of
the steam engine a mechanical governor
was needed to keep the speed of the
engine constant. In more recent decades
a wide variety of instruments, valves, and
other equipment have been developed
to maintain uniformity in chemical pro-
duction processes. Servomechanisms
were introduced during World War I for
control of gunfire. Electric circuitry and
electromechanical systems were given in-
tensive study to improve their respon-
siveness and stability for purposes of
controlling high-speed operations. By
the 1940's the pace of automation had
quickened as the concepts of control
theory and of feedback received wider
application in the electrical, mechanical,
and processing industries. The term

high-fidelity became a byword in ampli-
fier design as a result of the introduction
of negative feedback.

But the concept of feedback seemed to
be basic and useful for a much wider
range of applications. In 1947 the mathe-
matician Norbert Wiener and Arturo
Rosenbleuth compared the phenomena
of control and of feedback, as used in
technology, to the nervous system and
muscle behavior of the human body.
They postulated a close coordination of
communication relationships between
the brain, the sensory organs, and the
muscles, and concluded that this resulted
from the extensive use of feedback
principles. It seemed that a feedback
function is responsible for one's ability
to reach down and pick up an object and
to know how much farther the hand must
move to complete the act. Moreover, they
found an identity between feedback and
information and the information content
of a signal above the noise level. They
gave the name cybernetics (from the
Greek kybernes for steersman) to the
entire field of control and communication
theory, whether in the machine or in the
animal, f

The concepts oi feedback and informa-
tion encompassed by cybernetics permit
very extensive applications to the bio-
logical and social world. Just as the driver
of the automobile performs functions in
response to the information he derives

t The broad concepts that make up the sci-
ence of cybernetics as developed by Wiener
and his associates were new. The word itself
had much older origin, however. It appears
that Plato often employed the word "cyber-
netics" to mean "the steermans art." His
comment in "Cleitophon," "the cybernetics
of men, as you, Socrates, often call politics,"
suggests a wider implication. In 1834 the
French physicist Ampere used the word as
"means of governing" people.

from seeing and hearing and evaluating
the driving situation, so his reactions
under other situations are the result of
his relationship or interaction with each
new environment. Information and feed-
back are essential to his every move,
every decision, almost every thought and
learning process.

We shall have many opportunities to
refer to the principles that have just
been introduced. There will be applica-
tions to strictly technical systems, to
systems that involve nature's resources,
to biological systems, and to social
situations.

The importance of the subject suggests
that we summarize a few of the ideas
that are most pertinent to our purposes.

1. Nature's processes are characterized
by continuous dynamic transformations
of energy, which may range from the
vast magnitudes of astrophysics to the
metabolic adaptation of the smallest
living organism to its environment.

2. Much of man's own activities also
involves the development of processes
for conversion and utilization of nature's
energy resources for purposes of assuring
his survival and comfort. Indeed, the
design of systems that integrate physical
and chemical variables into cooperative,
controlled systems constitutes a main
interest of science and industry to bring
about modern civilization and the current
standard of living of advanced nations.

3. It is now recognized that the ele-
ments that make up a controlled system
have common characteristics, whether
accomplished by machine components,
biological elements, thought processes,
or social situations.

4. In such systems, the element of
feedback, or information, which inter-
relates the output (or behavior) of the
system and the input variables, con-

stitutes a major factor for the effective
operation and stability of systems.

5. The design of every control system
requires careful analysis (and usually
compromise) to meet the needs of the
process. A prime requisite for most con-
trol systems is that they be adequately
responsive to changes, and that they be
stable. Also needed is an adequate source
of energy to perform all the functions
that are required of the system. The input
to the system may be some variable such
as temperature, liquid level, or pressure.
Or it may be information that is itself the
product of other operations, such as in
computer systems.

6. The system performs its function bv
transforming the input to produce an out-
put whose energy content is usually
amplified, the added energy being de-
rived from the source of energy of the
system. The character of the transforma-
tion is designed into the system and is
identified by its transform function to
give the change or amplification gain to
the output.

7. When a feedback (or information)
loop permits some of the energy of the
output to be fed back to the input, there
can be considerable influence on the
nature of the net output and on the
stability of the system. In general, feed-
back that opposes changes (negative) in
the input will improve the stability of
the system, while feedback that arrives
at the input in a manner that increases
its changes (positive feedback) tends to
reduce the stability of a system.

8. The stability of the system suffers
and the system "hunts" more violently
when the amplification or gain between
output and input is too high or when the
system responds too quickly to changes
in the input variable. The design must
include enough damping to reduce exces-
sive overshoot (or violent hunting) of

Systems, Feedback, Cybernetics

Energy (food)

Brain

Energy losses, work output

Physical
environment

and sensory
system

Physical
man

Information

■ ■ 1 1 ■

Social

Information feedback

or other influence

environment

Fig. 6.13. The
complex inter-
relationship of
man with his
environment.

the system while still providing adequate
response. On-off controls offer cost ad-
vantages and simplicity, but the need for
better control may dictate the use of
proportional control or of other controls
that have more sophisticated design.
There can be more than one input to a
system, more than one output, and a wide
variety of interrelated combinations. In
fact, the input may be the statistical
output of many interrelated elements or
variables.

6.14 Some examples of systems

In Fig. 6.13, which illustrates the rela-
tionship of man to his environment, we
have identified two aspects of man (his
brain and sensory motor system as dis-
tinguished from his physical being) and
two aspects of his enviornment (the
physical and social environments). There
is very intimate and extensive inter-
change between the two aspects of man
and between the two aspects of environ-
ment, as shown by the proximity and
multiple arrows connecting them. Man
draws energy and material from the
physical environment and returns in-

formation and other materials to both.f

In the case of the driving of an automo-
bile, it is difficult to identify all the ele-
ments that make up the input to this
system. The desire to drive, the sensory
activity that provides data to the brain,
and the muscle behavior that operates
the controls of the car, each is a complex
that includes and combines the product
of some other part of the system. The
energy involved in the seeing, hearing,
and judgement operations is negligibly
small, but these become greatly magni-
fied by the body's metabolic processes.
This transform function of the body is
most complex, and is itself made up of
innumerable subsystems.

The specific control principles and
systems we have discussed thus far are
given broader significance by the princi-
ples of cybernetics. Cybernetics deals

f It is not easy to distinguish work from
information and learning. Physical acts are
not readily distinguishable as being separate
from sensory response and interpretation that
leads to learning, judgment, and decision.
Certainly we cannot say that the throwing of
a ball, intake of food, reading of newsprint,
and a walk around the block are not so much
mental processes that lead to future decision
or action as they are physical acts.

with elements or variables that are related
to each other so intimately that a change in
one variable is likely to affect other vari-
ables in the system. The elements may
be parts of a machine or those of a chem-
ical process. Cybernetics can deal with
the very specific behavior of a single
molecule among vast numbers of gas
molecules or with the behavior of a
single cell of the vast numbers that make
up an organism. It can as readily (and in
general more usefully) consider the
statistical-behavior character of all the
gas molecules together, or all the cells
of the human body. It can provide a
method for analyzing the economic
relationship of a grocer and his customer,
or as readily attack questions pertaining
to the economics of a whole nation. It
establishes functional relationships in
the course of changes, emphasizing their
coordination, regulation, and control
within a systems concept.

From the point of view of cybernetics,
the aspect of systems behavior that is of
greatest interest is the system's response
to a disturbance. This disturbance may be
a normal change or a momentary depar-
ture (transient) of the input, say as a result
of the dropping of temperature of an in-
dustrial oven below its control setting
when cold material is poured into it. One
or more of the input variables or signals
may experience changes that sum up to
a signal sufficiently large to initiate a
major change. For example, many chem-
ical processes go on within the body,
such as food intake, digestion, blood cell
production, and oxygen utilization. They
are not unrelated and all must be con-
sidered contributory to whether a person
feels well or feels ill. Each process experi-
ences its own daily or hourly variations,
which nevertheless may constitute
normal operation and good health. There
can be occasions, however, when the

individual variations in the processes
add up to produce sickness of a sort that
represents serious imbalance or dis-
turbance of the total system.!

In general, systems are designed to
accept and to cope with very specific
variables and to effect reasonably quick
restoration whenever some change in
those variables upsets equilibrium. The
system is considered to be responsive
when it reacts with adequate speed to the
upset. A system that responds too quickly
or introduces corrective steps that are
too large is likely to produce instability
around the equilibrium point. A system
may also be too sensitive to small fluctu-
ations that are of the order of magnitude
of background "noise," and for that
reason will be unstable.

We might consider the design of an
electrical amplifier system such as that
used for a quality phonograph system.
Figure 6.12 represents a fairly simple
circuit for transforming an input through
some form of transducer to produce an
output. The feedback to the input in this
case was designed to counteract or oppose
the input, tending to reduce undesirable
excursions in the output due to variations
other than the sound signals to be ampli-
fied. The system constitutes a channel
for transmitting and transposing signals,
the input signals being information. To
be effective, the design must usually
incorporate suitable capabilities in such
terms as capacity, watts, voltage, range,
and frequency. These in turn provide the
basis for designing suitable constraints
into the system.

However, a control system is not likely

t As a simple example, the experience of
sitting in an awkward position can introduce
a combination of neural signals and mental
process that suggests the need for a new posi-
tion and thereby requires a complete readjust-
ment of nerve and muscle systems.

Systems, Feedback, Cybernetics

to be designed to control every variable
against every change. For example, the
body's control of the iris openings of the
eyes (to permit only adequate light to
reach the retina) has a very specific,
limited function and purpose, which
excludes sensitivity to other variations of
body conditions. The purpose of con-
straints is to reduce the response of the
system to variables that are not con-
sidered to be part of the information to
be transmitted. There are also natural
restraints or constraints on the information
and on the variety of information that a
channel may transmit. Among these are
the limitations and directions imposed

by the conservation of energy and the
laws of thermodynamics. When a system
combines several elements into an inte-
grated organizational and functional
interdependence, the interdependence
automatically imposes constraints, since
the elements are now no longer inde-
pendent of each other. An amplifier
system may have to contend with con-
straints in the form of costs, against which
the designer must balance extra quality
or fidelity or amplification.

With only minor modifications the dia-
gram of Fig. 6.12 can represent a quite
different system for communication of
information. Figure 6.14 illustrates some

Government offices

Editorial and

management

office

Radio and
television

"**] Financial support, etc

Printing
facilities

Distribution
facilities

The
listening

and
reading
public

Financial support, etc.

Fig. 6.14. Schematic representation of a system for communicating news to the
public.

of the elements that enter into a system
for communicating news to the general
public. News may be collected from
many areas and reported; this news
becomes input (iu i2, ■ ■ ■ i„) to the
editorial offices of a news agency. At
the editorial offices this information
undergoes modification and shaping, and
is put into printed form or given elec-
trical broadcast. There will be close
liaison among the several blocks that
make up the channels for this communi-
cation. There will be government in-
fluences as well as government sources
of information bearing on the editorial
and management offices, much of it in
the form of feedback reaction to the com-
munication. The listening and reading
public applies "feedback" influence
through financial support (or lack of
support) of the broadcast and publishing
services, through the editorial offices, and
through government offices to the sources
of information. The constraints in such a
system are many. They arise from national
and local government policies; from elec-
trical, chemical, mechanical restraints;
from the cultural habits and educational
level of communities; and from financial
considerations. As a total result, such a
communication system becomes not a
simple amplifier and distributor of simple
news information but also a combination
system for receiving, modifying, trans-
mitting, and generating of news with
built-in restraints and objectives.

One interesting characteristic of a
system of this sort arises from the fact
that any one of the multiple input signals
(h> h, k ■ • ■ in) can suddenly introduce
a major disturbance that overshadows all
other input signals and that can bring
about violent response in either the
forward channels or the feedback chan-
nels. Such a disturbance might be an
act of war, a strike, a catastrophe, or an

event that is especially disliked or espe-
cially desirable. There may be quite a few
surges of output beyond the desired
limits of control before the system set-
tles down again.

One may also conceive that the input
(t, . . . in) can be made up of very many
items and elements so that the overall
significance of the input is determined
by the statistical character of the input
rather than being overly influenced by
any one item.

6.15 Functional relationship:
notations

In its simplest form, a cause-and-effect
relationship is stated as a simple function
such as y =f(x) (meaning y is a function
/ of x, or O =/(/) (meaning output O is
a function of input /). In diagram form
this might be written! as representing a
transition of / into an output O. Relating

this to our earlier example of the auto-
mobile, the power of the motor, O, is
some function of the position of the ac-
celerator pedal, /. If we include the driver
as well, we have a more complete system
with feedback and our equation would
have to provide a different function for
output,

0=f(I)F(0)

In its simplest form the diagram would
be changed to become

' " o

The more interesting examples are not
likely to be so simple as to comprise

t The approach in this section is consider-
ably influenced by the treatment given by
W. Ross Ashbv.

Systems, Feedback, Cybernetics

only a single input and single output.
Within the total system that includes the
auto and driver, there are innumerable
smaller systems such as cells, neurons,
muscles, organs, machine parts, and
electrical controls. A study of such as-
semblies must set out clear objectives
before its approach or results can be
made significant. For example, are the
functions to be studied primarily those
that pertain to keeping the auto on the
road, or are they functions that deter-
mine the state of the driver's gall bladder,
heart beat, or temperature? These sub-
sidiary systems are certainly part of
the total system of man and auto, but their
details are independent of the specific
functions that go with driving the auto-
mobile. The situation would be different,
of course, if part of a study had to do with
the effect of heart or temperature func-
tion on the driving, for which purpose a
new set of elements would be involved
when making up the system to be studied.
The situation is illustrated by Ashby
in the following diagram, in which one
may trace twenty different! circuits.

Each subsidiary circuit may have its
own mode of feedback and control, and
may be either strongly or weakly linked
with neighboring circuits. In the case of
our driver, vision plays the dominant
role in telling him where the auto is
going, while his knowledge of the situ-
ation is helped by the senses of hearing

t It is suggested that the reader list the
twenty different ways in which a signal may
travel through the system, starting at A and
returning ultimately to A in each case. For
example, ABCDA or ABCBCDA.

and by the sensations of his body as the
car sways. All the input stimuli have
some relation to each other. One may
picture a strong relationship (or strong
coupling) between vision and hearing
and a weaker coupling between heart-
beat and vision, as far as driving the car
is concerned.

Any study must therefore seek first to
identify the functionally significant rela-
tionships that are the subject of the study,
to identify the elements that bear directly
on the functions under study, and to elimi-
nate from consideration those elements
that are independent of the selected
functions.! This is not easy to do in most
cases because there are many varieties
of influences and "couplings" that come
into play. Often the study must assume a
series of situations and obtain results and
estimates for a wide variety of combina-
tions of systems.

MODELS

Often it becomes necessary to simplify
a system or make it understandable by
use of a model or models. This becomes
imperative for nearly all biological sys-
tems, which are enormously complex.
But models can very quickly become
detrimental to progress when one loses
sight of the simplifications and limita-
tions that are inherent to each model.

6.16 "Black box" approach

Ashby considers the interesting case of
an experimenter approaching a "black
box" that is unknown to him with respect
to contents and functions. How should
he proceed to investigate and determine
the contents and character of the box?

t The importance of such an approach in the
study of human behavior is seen in the Gestalt
psychology view of phenomena.

Box

Experimenter

7ig. 6.15.

lack-box rela

tionship.

(The procedure can be especially impor-
tant if one imagines that the "black box"
could be an explosive bomb.) There is,
immediately, a relationship between the
experimenter and the box, of the type
shown in Fig. 6.15. The diagram illus-
trates the nature of exchanges and feed-
back that take place as the experimenter
explores the problem by various means.
The "means" presumably might include
such things as pushing and pulling of the
box and levers. For a systematic search,
each move would be recorded along with
the "state" of the box that accompanied
each move. In time the experimenter
would presumably be able to identify the
"state" of the box for each type of input,
and possibly also the function for each
type of input. Many of the systems with
which we deal are actually made up of
"black boxes," and the functional charac-
teristics of the total assembly may be de-
termined by the characteristics of each
box and by the nature of their coupling to-
gether, f But we may fail to characterize
the system because a combination of
black boxes may produce an unexpected
function that is quite unrelated to the
characteristics of any one box. An example
given by Ashbv is that the approximately
twenty amino acids in a bacterium do not
individually have the property of being
self-replicating, but their combination
does introduce this property.

Real-life problems tend to have main
"black boxes," often interconnected in
such manner as to obscure the specific
role of each box, each subsystem. One
may make progress in the analysis of the
total system and its parts by systematic
analysis of "responses" or "states" to
questions and input stimuli. One may
seek to discover factors that produce

t The reader may pic tun' the similar situ-
ation that exists when he first meets a person

who is to become liis associate on some project.

Systems, Feedback, Cybernetics

certain extreme "responses" of "states."
The use of computers helps handle large
quantities of data and identify common
elements or contrasts. But progress in
attacking complex problems depends
more often on good use of judgment,
experience, intuition or insight, per-
sistence, and some luck. It is not always
easy to identify and isolate the specific
functions that are of importance for the
system's functioning. There may be mul-
titudinous other elements within the
total system that do not bear on the spe-
cific functions under study.

6.17 The closed-loop amplifier
system^

It will be helpful to look a little more
closely at the quantitative aspects of a
system that has feedback characteristics.
Figure 6.16 illustrates a system in which
an input signal E, (which may be in volts

t The sections printed in color represent
optional reading material.

and related to temperature, pressure,
blood count, or other variable) constitutes
the control variable. The system may be
designed to do something that is propor-
tional to or determined by this control
variable i. If the system is a servomech-
anism, input £, may represent the angle
of rotation of a small motor and output
E0 the angle of rotation of a larger motor,
the objective being to keep the two motors
in step with each other. Or £, may be
the input voltage from a measuring circuit
that has high resistance and low power
and which is to be converted to an iden-
tical voltage in a low-resistance circuit
to operate a loudspeaker or solenoid or
some other device that requires more
power than is available at the input end
of the circuit. (Throughout this discus-
sion keep in mind that there must be a
source of energy to make this conversion
possible, as is illustrated in Fig. 6.16.)

The signal £, may have a fixed value
or may vary with time. It feeds into a
comparator element, where E, is com-
pared (added) to the signal coming as
feedback. It both the input signal and

Comparator
E

Input

Input signal which
serves as fixed or
variable point for
control purposes

Error or

difference

signal

Ef=(FR)xEc

Energy source

LiiiJ

Converter

amplifier

transformer

effector, etc.

with gain

Sensor with

feedback ratio

(FR)

Fig. 6.16. A closed-loop amplifying .system.

GiE.-Ef)

Eo=G(Ei-Ef) + ED

External
disturbance

Output

E0 = E

•(t

+ (FR)G

)+Ed\1+(FR)g)
(6-2)

For the above example,

E° = l (l+(lxlO)) + ° (l + 1 x lo)

10 ,
^volt

The error or difference voltage therefore
becomes E, - E, = 1 - (10/11) = 1/11
volt. The amplifier must be capable of
acting on this voltage if the system is de-
signed to work on such magnitudes of
error. One way to improve this is to in-
crease the gain G of the amplifier. If, in
this case, the gain G is increased from 10
to 100 while keeping the feedback ratio
and ED the same, the error voltage reduces
to 1/101 volt from 1/11 volt. It can be seen
that the gain can change markedly with-
out introducing serious error in such a
system.

Finally suppose there develops a dis-
turbance ED amounting to 0.5 volt, with
the gain G = 10 and FR = 1. From the
last term of Eq. (6-2), the effect of the
disturbance reduces to

0.5

1 + 1 x 10 11

as a result of the feedback. Figure 6.17
presents these figures applied directly
to the diagram of Fig. 6.16 (following the
example of James E. Randall, Elements of
Riophysics).

The examples thus far apply to static-
systems. The behavior of systems varies
considerably when the input voltage
changes too rapidly for the system to
follow the changes of E, or ED. The sub-
ject of controller stability has received a
great deal of attention in connection with

servomechanism design (for remote con-
trol of airplane movements, and similar
applications) and electric circuit design
for communication, but we cannot delve
into that aspect of controller theory.
However, one related consideration is
"noise," mentioned briefly in an earlier
discussion. This also has had considerable
study because of the important effect
on the capacity of circuitry • to convey
"information."

6.78 The nature of "living" systems

In the discussions of control systems thus
far we have not distinguished between
systems involving machine components
and those involving living systems. Nor
is it our intention to do so now. The fact
is that, except for varying complexity,
the very same concepts may be applied
to living as well as nonliving or machine
systems. Each of the sensor)' organs
through which we communicate with the
much vaster system of nature is itself
designed, oriented, and functionally
controlled to achieve certain specific
goals or "purposes." It does not matter
whether we discuss a nerve cell or an
electric wire connection. Both are motor-
sensors. Information may be transmitted
through the medium of voice, teletype,
wireless, visual signals, or the raising of
an eyebrow. Each may be an element of a
system, and a composite system may in-
clude many elements or subsystems. The
science of information theory must cope
with vast complications to determine the
maximum and minimum informational
content that an actual system can trans-
mit, even when the role and nature of
each link of the chain can be fairly under-
stood.

The acts of stretching the bodv or of
reaching to pick up an object entail the
function of a fairly complex system of

Systems, Feedback, Cybernetics

Comparator

sensitive to

change in sensor

Aldosterone

L Sensor
Na + concentration $ responsive
142 m-eq/l < to Na +
content

-(°).

Adrenal
cortex

production

(

ATF

• ADP

\ Intake of
NaCI

Kidney

' /^-—

NaCI loss through

sweating; varies

with activity

Fig. 6.18. A simplified
version of control of
sodium ion concentration
in the extracellular fluid.

Controlled loss
of NaCI

regulation and control. This has been
demonstrated by Karl Smith's! experi-
ments with delayed visual feedback in
visual motor behavior, which showed that
what a person sees is delayed in reaching
him when he is performing various other
tasks such as writing.

The intention to stretch or to pick up an
object is itself a complex function, de-
veloping in the mind as a product of
other activities and influences. The
command signal, in the form of nerve im-
pulses, originate in the motor cortex of
the brain and initiates action in the mus-
cle contractile proteins. There is an
amplification, G, which may be expressed
as change in muscle length for a unit
change in the motor neurons that initiate
the discharges. The muscle spindle acts
as a sensor-transducer to produce nerve
impulses, in proportion to muscle length
extension, to send back to the brain as

f See K. V. Smith.

feedback on the extension. The original
impulses and the feedback impulses are
integrated in the spinal cord and give
indication of the error or difference from
completion of the intended act. The
spindle proprioceptors serve to provide
constant information on the state and tone
of the muscle system, and assure smooth
action of the body. When an individual is
deprived of their help, muscle activity
tends to be abrupt rather than smooth,
requiring dependence on visual sense of
position to the extent that he cannot
stand when blindfolded.

A person suffering from Parkinson's
disease retains some benefit from propri-
oceptive information, but tends to over-
shoot when reaching for an object — a
motion that recalls damped oscillation.

In later studies of biological systems
we shall have occasion to study in some
detail a few of the regulatory systems on
which life depends. Figure 6.18 illus-
trates how the sodium ion concentration

is maintained constant in the fluid that
surrounds the individual cells. There is
an elaborate system for maintaining uni-
form pressure in the circulation of blood.
Pressure-sensitive transducers, located in
the aorta and carotid arteries, send infor-
mation about the magnitude of the pres-
sure to an integrating center within the
medullary portion of the brain. This
results in action that lowers blood pres-
sure by slowing the heart rate and also by
producing vascular dilatation.

For respiration there is needed a mini-
mal value for blood carbon dioxide and
an adequate supply of blood oxygen.
When carbon dioxide concentration in
the blood increases, the medullary res-
piratory center stimulates respiration to
eliminate carbon dioxide. The transit
time for the flow of blood between the
lungs and the respiratory center is only a
few seconds under normal conditions (see
Randall, p. 108). Body temperature is
maintained by a delicate balance between
heat loss (from warm-blooded or homeo-
thermic animals) and heat production
within the animal through metabolism.
The "thermostat" that controls this
balance is located in the hypothalmus of
the brain and receives information from
various temperature transducers of the
body to guide its own function.

The regulatory system can extend be-
yond the body to include the interactions
involving climate, geography, geology,
agriculture, theology, government, dis-
ease, or any other influences. The ele-
ments of determinate function, distur-
bances, control variables, amplification,
feedback, informational content, are all
three, but they may take the forms of
imposed law, self-imposed law, self-im-
posed restraints, religious restraints,
moral obligations, and many other forms
that are even less tangible.

The regulatory principles apply to

commercial production plants where
orders for goods become converted to
products for sale, with often quick and
direct feedback from consumer to pro-
ducer. The economist must be aware of
the relationship of the key elements of
a nation's economy in terms that are
identical to those discussed, if he is to
succeed in regulating the ups.and downs
of business within manageable propor-
tions. The problem becomes especially
severe when each of the elements of the
system is a result of statistical variations,
and the statistics lack the assurance of
experience or of numbers. The difficulties
too often savor of the uncertainties of
"black boxes," and yet one must select
a suitable model, suitably simple to be
manageable and not too far removed from
the realities of the situation.

The student is urged to study carefully
all the details that have been included in
this section on controls. In time he will
find that many of the topics that are to
come in later chapters will fall more
easily into place. For nature and man exist
and continue as a result of a balance of
forces and utilization of energy, the whole
constituting a system that is in a state
of reasonable balance and regulation and
yet continually changing toward wholly
new forms.

In conclusion, we hope that this brief
introduction to systems and cybernetics
will encourage each reader to view the
events of his life with keener appreciation
for the interrelationship of the factors
that bear on the events, and especially
for feedback influences. A word of caution
is in order, however, with respect to over-
extended use of the term cybernetics to
situations wherein the relationships are
too complex or too obscure, and wherein
there are not present the control systems
elements which we have discussed.

Systems, Feedback, Cybernetics

Questions/Discussions

The assignments for this chapter are
intended to give the reader opportunity
to discover for himself how broadly the
concepts and techniques involving sys-
tems, feedback, control, stability-insta-
bility, and cybernetics apply to phenom-
ena in nature and to all aspects of human
social relations. It is suggested that from
two to four weeks be allowed for comple-
tion of this work.

1. For purposes of review, tabulate the
five elements of control systems (de-
scribed in Sec. 6.12) that apply in the
following personal situations. Explain
also whether the feedback is positive or
negative in each case.

(a) The control of temperature of your
home.

(b) The factors that control your waking
up on a weekday morning.

(d) One situation or experience of your
day that includes strong positive
feedback.

(e) A situation or experience of your
day that includes strong negative
feedback.

2. Select three phenomena or situations,
taken from any three of the following
categories, and analyze their "systems"
aspects in the following terms:

(a) The dependent and independent
variables that are involved in each,
either as "input" to the system or
as disturbances.

(b) The sensor devices or transform
functions required at the input end
for each variable.

(d) The motor devices or processes,
and the related transform functions.

(e) The gain or amplification between
output and input.

(f) The nature of feedback influences
(distinguishing between positive
and negative feedback and phase
relationships) related to each input
and each output.

(g) The nature of subsystems that are
included.

(h) The factors that make for stability
and instability in the total system
or subsystems.
(i) The graphical representation of
the above elements and processes,
with indication of polarity (direc-
tion) of feedback between each out-
put and input.

The phenomena or situations are to be
drawn from any three of the following
seven categories:

I Electromechanical, pneumatic
systems, chemical or production
processes
II Geophysical or meteorological
processes

III Biological processes (plants, ani-
mals), ecological relationships

IV Medical, pathological experiences
V Economics (international, national,

or personal), business operations
VI Behavioral, cultural, ethical, moral,
theological, and psychological
aspects of social experiences

Note: It is suggested that each "case" be
given adequate discussion and one to
two pages of graphical representation.
Because of the importance of the subject
of "systems," it is suggested that these
analyses be given time for class discus-
sion. Group effort on the part of the stu-
dents is encouraged, although each must
present his own final case study.

The author, the first American Nobel Prize physicist,
traces the determinations of the velocity of light, one
of the handful of constants of nature.

Velocity of Light

A. A. Michelson

A chapter from his book, Studies in Optics, published in 1927.

The velocity of light is one of the most important of
the fundamental constants of Nature. Its measurement
by Foucault and Fizeau gave as the result a speed greater
in air than in water, thus deciding in favor of the undu-
latory and against the corpuscular theory. Again, the
comparison of the electrostatic and the electromagnetic
units gives as an experimental result a value remarkably
close to the velocity of light — a result which justified
Maxwell in concluding that light is the propagation of an
electromagnetic disturbance. Finally, the principle of
relativity gives the velocity of light a still greater im-
portance, since one of its fundamental postulates is the
constancy of this velocity under all possible condi-
tions.

The first attempt at measurement was due to Galileo.
Two observers, placed at a distance of several kilometers,
are provided with lanterns which can be covered or un-
covered by a movable screen. The first observer uncovers
his light, and the second observer answers by uncovering
his at the instant of perceiving the light from the first.
If there is an interval between the uncovering of the
lantern by the first observer and his perception of the
return signal from the second (due allowance being made
for the delay between perception and motion), the dis-
tance divided by the time interval should give the velocity
of propagation.

Needless to say, the time interval was far too small
to be appreciated by such imperfect appliances. It is
nevertheless worthy of note that the principle of the
method is sound, and, with improvements that are almost
intuitive, leads to the well-known method of Fizeau. The
first improvement would clearly be the substitution of a
mirror instead of the second observer. The second would
consist in the substitution of a series of equidistant aper-
tures in a rapidly revolving screen instead of the single
screen which covers and uncovers the light.

The first actual determination of the velocity of light
was made in 1675 by Romer as a result of his observation
of the eclipses of the first satellite of Jupiter. These
eclipses, recurring at very nearly equal intervals, could be
calculated, and Romer found that the observed and the
calculated values showed an annual discrepancy. The
eclipses were later by an interval of sixteen minutes and
twenty-six seconds1 when the earth is farthest from
Jupiter than when nearest to it. Romer correctly attrib-
uted this difference to the time required by light to trav-
erse the earth's orbit. If this be taken as 300,000,000 kilo-
meters and the time interval as one thousand seconds,
the resulting value for the velocity of light is 300,000
kilometers per second.

Another method for the determination of the velocity
of light is due to Bradley, who in 1728 announced an
apparent annual deviation in the direction of the fixed
stars from their mean position, to which he gave the name
"aberration." A star whose direction is at right angles to
the earth's orbital motion appears displaced in the direc-
tion of motion by an angle of 20T445. This displacement
Bradley attributed to the finite velocity of light.

With a telescope pointing in the true direction of such
a star, during the time of passage of the light from ob-

1 The value originally given by Romer, twenty-two minutes, is clearly
too great.

Velocity of Light

jective to focus the telescope will have been displaced in
consequence of the orbital motion of the earth so that the
image of the star falls behind the crosshairs. In order to
produce coincidence, the telescope must be inclined for-
ward at such an angle a that the tangent is equal to the
ratio of the velocity v of the earth to the velocity of light,

v
tan a=y ,

or, since v = tD/T, where D is the diameter of the earth's
orbit and T the number of seconds in the year,

tan o-=yf ,

from which the velocity of light may be found; but, as is
also the case with the method of Romer, only to the de-
gree of accuracy with which the sun's distance, §Z>, is
known; that is, with an order of accuracy of about i per
cent.1

In 1849 Fizeau announced the result of the first ex-
perimental measurement of the velocity of light. Two
astronomical telescope objectives Lz and L2 (Fig. 73) are
placed facing each other at the two stations. At the focus
of the first is an intense but minute image a of the source
of light (arc) by reflection from a plane-parallel plate N.
The light from this image is rendered approximately
parallel by the first objective. These parallel rays, falling
on the distant objective, are brought to a focus at the sur-
face of a mirror, whence the path is retraced and an
image formed which coincides with the original image a,
where it is observed by the ocular E. An accurately
divided toothed wheel W is given a uniform rotation,

1 The value of the velocity of light has been obtained, by experimental
methods immediately to be described, with an order of accuracy of one in
one hundred thousand, so that now the process is inverted, and this re-
sult is employed to find the sun's distance.

*s3

Fig. 73

thus interrupting the passage of the light at a. If, on
returning, the light is blocked by a tooth, it is eclipsed, to
reappear at a velocity such that the next succeeding
interval occupies the place of the former, and so on.

If n is the number of teeth and N the number of turns
per second, K the number of teeth which pass during the
double journey of the light over the distance D,

V =

2NnD
K

It is easier to mark the minima than the maxima of in-
tensity, and accordingly

if p is the order of the eclipse. Let bK be the error com-
mitted in the estimate of K (practically the error in esti-
mation of equality of intensities on the descending and
the ascending branches of the intensity curve). Then

dV = dK
V K '

Hence it is desirable to make K as great as possible. In
Fizeau's experiments this number was 5 to 7, and should

Velocity of Light

have given a result correct to about one three-hundredth.
It was, in fact, about 5 per cent too large.

A much more accurate determination was undertaken
by Cornu in 1872 in which K varied from 3 to 21, the re-
sult as given by Cornu being 300,400, with a probable er-
ror of one-tenth of 1 per cent. In discussing Cornu's re-
sults, however, Listing showed that these tended toward a
smaller value as the speed increased, and he assigns this
limit as the correct value, namely, 299,950. Perrotin,
with the same apparatus, found 299,900.

Before Fizeau had concluded his experiments, another
project was proposed by Arago, namely, the utilization
of the revolving mirror by means of which Wheatstone
had measured the speed of propagation of an electric
current. Arago's chief interest in the problem lay in the
possibility of deciding the question of the relative veloci-
ties in air and water as a crucial test between the undula-
tory and the corpuscular theories. He pointed out,
however, the possibility of measuring the absolute ve-
locity.

The plan was to compare the deviations of the light
from an electric spark reflected directly from the revolving
mirror with that which was reflected after traversing a
considerable distance in air (or in water). The difficulty
in executing such an experiment lay in the uncertainty in
the direction in which the two reflected images of the
spark were to appear (which might be anywhere in 3600).
This difficulty was solved by Foucault in 1862 by the
following ingenious device whereby the return light is
always reflected in the same direction (apart from the
deviation due to the retardation which it is required to
measure), notwithstanding the rotation of the mirror.

Following is the actual arrangement of apparatus by
which this is effected. Light from a source S falls upon
an objective L, whence it proceeds to the revolving mir-
ror R, and is thence reflected to the concave mirror C

Fig. 74

(whose center is at R), where it forms a real image of the
source. It then retraces its path, forming a real image
which coincides with the source even when the revolving
mirror is in slow motion. Part of the light is reflected from
the plane-parallel glass M , forming an image at a where
it is observed by the micrometer eyepiece E.

If now the revolving mirror is turning rapidly, the
return image, instead of coinciding with its original posi-
tion, will be deviated in the direction of rotation through
an angle double that through which the mirror turns while
the light makes its double transit. If this angle is a and
the distance between mirrors is D, and the revolving
mirror makes N turns per second,

a = 27riv-^- i

V =

4irND

In principle there is no essential difference between
the two methods. In the method of the toothed wheel the
angle a corresponds to the passage of K teeth, and is
therefore a = 2irK/n, so that the formula previously found,

V =

2NnD
K

j now becomes V =

4irND

the same as for the

Velocity of Light

revolving mirror. The latter method has, however, the
same advantage over the former that the method of mir-
ror and scale has over the direct reading of the needle of
a galvanometer.

On the other hand, an important advantage for the
method of the toothed wheel lies in the circumstance
that the intensity of the return image is one-half of that
which would appear if there were no toothed wheel,

nB
whereas with the revolving mirror this fraction is —

if the mirror has n facets) , where /3 is the angular aperture

of the concave mirror, and / is the focal length of the

mirror, r is the distance from slit to revolving mirror,

and D is the distance between stations.

In the actual experiments of Foucault, the greatest
distance D was only 20 m (obtained by five reflections
from concave mirrors), which, with a speed of five hun-
dred turns per second, gives only 160" for the angle 2a
which is to be measured. The limit of accuracy of the
method is about one second, so that under these condi-
tions the results of Foucault's measurements can hardly
be expected to be accurate to one part in one hundred and
sixty. Foucault's result, 298,000, is in fact too small by
this amount.1

In order to obtain a deflection 2a sufficiently large to
measure with precision it is necessary to work with a
much larger distance. The following plan renders this
possible, and in a series of experiments (1878) the dis-
tance D was about 700 m and could have been made much
greater.

1 Apart from the mere matter of convenience in limiting the distance
D to the insignificant 20 m (on account of the dimensions of the labora-
tory), it may be that this was in fact limited by the relative intensity of
the return image as compared with that of the streak of light caused by
the direct reflection from the revolving mirror, which in Foucault's
experiments was doubtless superposed on the former. The intensity of
the return image varies inversely as the cube of the distance, while
that of the streak remains constant.

The image-forming lens in the new arrangement is
placed between the two mirrors, and (for maximum in-
tensity of the return image) at a distance from the re-
volving mirror equal to the focal length of the lens. This
necessitates a lens of long focus; for the radius of meas-
urement r (from which a is determined by the relation
8 = r tan a, in which 8 is the measured displacement of the

image) is given by r = -= , if / is the focal length of the lens ;

whence r is proportional to/2. In the actual experiment,
a non-achromatic lens of 2 5-m focus and 20-cm diameter
was employed, and with this it was found that the in-
tensity of the return light was quite sufficient even when
the revolving mirror was far removed from the principal
focus.

With so large a displacement, the inclined plane-paral-
lel plate in the Foucault arrangement may be suppressed,
the direct (real) image being observed. With 250 to 300
turns per second, a displacement of 100 to 150 mm was
obtained which could be measured with an error of less
than one ten-thousandth.

The measurement of D presents no serious difficulty.
This was accomplished by means of a steel tape whose
coefficient of stretch and of dilatation was carefully deter-
mined, and whose length under standard conditions was
compared with a copy of the standard meter. The esti-
mated probable error was of the order of 1 : 200,000.

The measurement of the speed of rotation presents
some points of interest. The optical "beats" between the
revolving mirror and an electrically maintained tuning
fork were observed at the same time that the coincidence
of the deflected image with the crosshairs of the eyepiece
was maintained by hand regulation of an air blast which
actuated the turbine attached to the revolving mirror.
The number of vibrations of the fork plus the number of
beats per second gives the number of revolutions per

Velocity of Light

second in terms of the rate of the fork. This, however,
cannot be relied upon except for a short interval, and
it was compared before and after every measurement
with a standard fork. This fork, whose temperature co-
efficient is well determined, is then compared, as follows,
directly with a free pendulum.

For this purpose the pendulum is connected in series
with a battery and the primary of an induction coil whose
circuit is interrupted by means of a platinum knife edge
attached to the pendulum passing through a globule of
mercury. The secondary of the induction coil sends a
flash through a vacuum tube, thus illuminating the edge
of the fork and the crosshair of the observing microscope.
If the fork makes an exact whole number (256) of vibra-
tions during one swing of the pendulum, it appears at
rest; but if there is a slight excess, the edge of the fork
appears to execute a cycle of displacement at the rate of n
per second. The rate of the fork is then N±n per second
of the free pendulum. This last is finally compared with
a standard astronomical clock.1 The order of accuracy
is estimated as 1 : 200,000.

The final result of the mean of two such determina-
tions of the velocity of light made under somewhat similar
conditions but at a different time and locality is 299,895.

A determination of the velocity of light by a modifica-
tion of the Foucault arrangement was completed by
Newcomb in 1882. One of the essential improvements
consisted in the use of a revolving steel prism with square
section twice as long as wide. This permits the sending
and receiving of the light on different parts of the mirror,
thus eliminating the effect of direct reflection. It should
also be mentioned that very accurate means were pro-
vided for measuring the deflection, and finally that the

1 The average beat of such a clock may be extremely constant al-
though the individual "seconds" vary considerably.

speed of the mirror was registered on a chronograph
through a system of gears connected with the revolving
mirror. Newcomb's result is 299,860.

The original purpose of the Foucault arrangement was
the testing of the question of the relative velocities of light
in air and in water. For this purpose a tube filled with
water and closed with plane-parallel glasses is interposed.
There are then two return images of the source which
would be superposed if the velocities were the same. By
appropriately placed diaphragms these two images may
be separated, and if there is any difference in velocities
this is revealed by a relative displacement in the direction
of rotation. This was found greater for the beam which
had passed through the water column, and in which,
therefore, the velocity must have been less. This result
is in accordance with the undulatory theory and opposed
to the corpuscular theory of light.

The experiments of Foucault do not appear to have
shown more than qualitative results, and it should be of
interest, not only to show that the velocity of light is less
in water than in air, but that the ratio of the velocities
is equal to the index of refraction of the liquid. Experi-
ments were accordingly undertaken with water, the result
obtained agreeing very nearly with the index of refrac-
tion. But on replacing the water by carbon disulphide,
the ratio of velocities obtained was 1.75 instead of 1.64,
the index of refraction. The difference is much too great
to be attributed to errors of experiment.

Lord Rayleigh found the following explanation of the
discrepancy. In the method of the toothed wheel the dis-
turbances are propagated in the form of isolated groups
of wave-trains. Rayleigh finds that the velocity of a
group is not the same as that of the separate waves ex-
cept in a medium without dispersion. The simplest form
of group analytically considered is that produced by two

Velocity of Light

simple harmonic wave-trains of slightly different fre-
quencies and wave-lengths. Thus, let

y=cos (nt— mx)+cos (nj—nhx) ,

in which n = 2ir/T, and m = 2ir/\, T being the period and
X the wave-length. Let n—nz = dn, and m—mi=dm.
Then

y=2 cos %(dnt— dmx) cos (nt—tnx) .

This represents a series of groups of waves such as illus-
trated in Figure 75.

Fig. 75

The velocity of the waves is the ratio V = n/m, but
the velocity of the group (e.g., the velocity of propagation
of the maximum or the minimum) will be

V' = dn/dm,
or, since n = mV,

or, since w = 27r/X,

\ vd\J

The demonstration is true, not only of this particular
form of group, but (by the Fourier theorem) can be ap-
plied to a group of any form.

It is not quite so clear that this expression applies to
the measurements made with the revolving mirror. Lord
Rayleigh shows that in consequence of the Doppler effect
there is a shortening of the waves at one edge of the

beam of light reflected from the revolving mirror and a
lengthening at the opposite edge, and since the velocity
of propagation depends on the wave-length in a dispersive
medium, there will be a rotation of the individual wave-
fronts.

If to is the angular velocity of the mirror, and wx that
of the dispersional rotation,

= dV = dVd\
dy d\ dy '

where y is the distance from the axis of rotation. But

d\ X X dV

Ty^^f'-^^VdX'

The deflection actually observed is therefore

r(2w+a>i) ,

where T is the time required to travel distance 2D; or

/ ,\dV\
\1+Vdk)>

hence the velocity measured is

•"-'♦MS).

or, to small quantities of the second order,
V" =V' = group velocity -1

The value of ( H — -tt ) for carbon disulphide for
the mean wave-length of the visible spectrum is 0.93-.
Accordingly,

V V 0.93 0.93 ' '
which agrees with the value found by experiment.

' J. W. Gibbs {Nature, 1886) shows that the measurement is in reality
exactly that of groups and not merely an approximation.

f-l

Velocity of Light

RECENT MEASUREMENTS OF THE VELOCITY OF LIGHT

In the expression for V, the velocity of light as de-
termined by the revolving mirror, V = 4tND/cl, there are
three quantities to be measured, namely, N, the speed of
the mirror; D, the distance between stations; and a, the
angular displacement of the mirror. As has already been
mentioned, the values of N and D may be obtained to
one part in one hundred thousand or less. But a cannot
be measured to this order of accuracy. It has been pointed
out by Newcomb1 that this difficulty may be avoided by
giving the revolving mirror a prismatic form and making
the distance between the two stations so great that the
return light is reflected at the same angle by the next fol-
lowing face of the prism.

The following is an outline of a proposed attempt to
realize such a project between Mount Wilson and Mount
San Antonio near Pasadena, the distance being about
35 km. For this, given a speed of rotation of 1,060 turns
per second, the angular displacement of the mirror during
the double journey would be 900; or, if the speed were
half as great, an angle of 450 would suffice.2 Accordingly,
the revolving mirror may have the form of an octagon.
It is, of course, very important that the angles should be

equal, at least to the order
of accuracy desired.

This has already been
attained as follows. The
octagon, with faces pol-
ished and angles approxi-
mately correct, is applied
to the test angle a V made
up of a 450 prism ce-
mented to a true plane.
The faces btb are made
parallel by the interfer-
ence fringes observed in

Fig. 76

1 Measures of the Velocity of Light. Nautical Almanac Office, 1882.

2 It may be noted that with eight surfaces the resulting intensity will
be four times as great as with the revolving plane-parallel disk.

monochromatic light. In general, the faces aLa will not be
parallel, and the angle between them is measured by the
distance and inclination of the interference bands. The
same process is repeated for each of the eight angles, and
these are corrected by repolishing until the distance and
inclination are the same for all, when the corresponding
angles will also be equal. It has been found possible in
this way to produce an octagon in which the average
error was of the order of one-millionth, that is, about
one-tenth to one-twentieth of a second.1

Another difficulty arises from the direct reflection and
the scattered light from the revolving mirror. The former
may be eliminated, as already mentioned, by slightly
inclining the revolving mirror, but to avoid the scattered
b'ght it is essential that the return ray be received on a
different surface from the outgoing.

zee 3

Fig. 77.— Light path a, b, c, d, e, eufu U, e,f, g, h, i,j

1 It may be noted that while a distortion may be expected when the
mirror is in such rapid rotation, if the substance of the mirror (glass, in
the present instance) is uniform, such distortion could only produce a very
slight curvature and hence merely a minute change of focus.

Velocity of Light

Again, in order to avoid the difficulty in maintaining
the distant mirror perpendicular to the incident light, the
return of the ray to the home station may be accom-
plished exactly as in the Fizeau experiment, the only pre-
caution required being the very accurate focusing of the
beam on the small plane (better, concave) mirror at the
focus of the distant collimator.

Finally, it is far less expensive to make both sending
and receiving collimators silvered mirrors instead of
lenses.

In Figure 77 is shown the arrangement of apparatus
which fulfilled all these requirements.

Three determinations were undertaken between the
home station at the Mount Wilson Observatory and
Mount San Antonio 22 miles distant. The rate of the
electric tuning fork was 132.25 vibrations per second,
giving four stationary images of the revolving mirror
when this was rotating at the rate of 529 turns per second.
The fork was compared before and after every set of the
observations with a free pendulum whose rate was found
by comparison with an invar pendulum furnished and
rated by the Coast and Geodetic Survey.

The result of eight measurements in 1924 gave

Va= 299,735 .

Another series of observations with a direct compari-
son of the same electric fork with the Coast and Geodetic
Survey pendulum1 was completed in the summer of 1925
with a resulting value

Va = 299,690 .

A third series of measurements was made in which the
electric fork was replaced by a free fork making 528 vibra-

1 This comparison was made by allowing the light from a very narrow
slit to fall on a mirror attached to the pendulum. An image of the slit was
formed by means of a good achromatic lens, in the plane of one edge of the
fork, where it was observed by an ordinary eyepiece.

tions per second maintained by an "auction circuit," thus
insuring a much more nearly constant rate. The result
of this measurement gave

Va= 299,704 .

Giving these determinations the weights 1, 2, and 4,
respectively, the result for the velocity in air is

Va= 299,704 .

Applying the correction of 67 km for the reduction
to vacuo gives finally 7=299,771 .

This result should be considered as provisional, and
depends on the value of D, the distance between the two
stations which was furnished by the Coast and Geodetic
Survey, and which it is hoped may be verified by a repeti-
tion of the work.

It was also found that a trial with a much larger
revolving mirror gave better definition, more light, and
steadier speed of rotation; so that it seems probable that
results of much greater accuracy may be obtained in a
future investigation.

FINAL MEASUREMENTS

Observations with the same layout were resumed in
the summer of 1926, but with an assortment of revolving
mirrors.

The first of these was the same small octagonal glass
mirror used in the preceding work. The result obtained
this year was V— 299,813. Giving this a weight 2 and
the result of preceding work weight 1 gives 299,799 for
the weighted mean.

The other mirrors were a steel octagon, a glass 12-
sider, a steel 12-sider, and a glass 16-sider.

Velocity of Light

The final results are summarized in Table VII.
TABLE VII

Turns per Second

Mirror

Number of
Observations

Vel. of Light
in Vacuo

528

Glass oct.
Steel oct.
Glass 12
Steel 12
Glass 16

576
195
270
2l8

504

299,797
299,795
299,796
299,796
299,796

528

352

264

Weighted mean, 299,796 + 1

Table VIII shows the more reliable results of measure-
ments of V with distance between stations, method used
and the weight assigned to each.

TABLE VIII

Author

Method

Wt.

Cornu

23 km
12

0.6

6-5
35

Toothed wheel
Toothed wheel
Rev. mirror
Rev. mirror
Rev. mirror

1
1
1
3

299,990
299 , 900
299,880
299,81(7
299,800

Perrotin

Mr and M2

Newcomb*

* Newcomb's value omitting all discordant observations was 298,860.

Bees, water fleas, and horseshoe crabs navigate by
polarized light. Sunglasses, camera filters, and
glare-free auto headlights are among other applica-
tions.

Popular Applications of Polarized Light

William A. Shurcliff and Stanley S. Ballard

A chapter from the book Polarized Light published in 1964.

If there is a logical order in which the various applications of
polarizers and polarized light should be considered, the authors
have never discovered it. The policy adopted here is to consider
the most popular and "humanistic" applications first, and the
more scientific and esoteric applications last.

POLARIZATION AND THE HUMAN EYE

The most humanistic fact about polarization of light is that
it can be detected directly by the naked eye. Nearly anyone, if
told carefully what to look for, can succeed in this. Sometimes he
can even determine the form and azimuth of polarization.

What the observer actually "sees" is a certain faint pattern
known as Haidinger's brush and illustrated in Fig. 10-1. The
brush is so faint and ill-defined that it will escape notice unless
the field of view is highly uniform: a clear blue sky makes an
ideal background, and a brightly illuminated sheet of white
paper is nearly as good. The best procedure for a beginner is to
hold a linear polarizer in front of his eye, stare fixedly through
it toward a clear blue sky, and, after five or ten seconds, sud-
denly turn the polarizer through 90°. Immediately the brush is
seen. It fades away in two or three seconds, but reappears if the
polarizer is again turned through 90°. The brush itself is sym-

BLUE

, '. YELL9wJ§ffl| ^Syellow .* •* • ,

• • BLUE •- -

ABOUT 3 DEGREES

FIG. 10-1 Approximate appearance of Haidinger's brush when the
vibration direction of the beam is vertical.

metric, double-ended, and yellow in color; it is small, subtending
an angle of only about 2° or 3°. The adjacent areas appear blue,
perhaps merely by contrast. The long axis of the brush is approx-
imately perpendicular to the direction of electric vibration in the
linearly polarized beam, i.e., perpendicular to the transmission
axis of the polarizer used.

Circular polarization, too, can be detected directly by eye, and
even the handedness can be determined. When an observer fac-
ing a clear blue sky places a right circular polarizer in front of
his eye, he sees the yellow brush and finds that its long axis has
an upward-to-the-right, downward-to-the-left direction, i.e., an
azimuth of about +45°. This is true, of course, irrespective of the
orientation of the polarizer, since a circle has no top or bottom.
If he employs a left circular polarizer, he finds the brush to have
a —45° orientation. In each case the pattern fades away rapidly,
but can be restored to full vigor by switching to a polarizer of
opposite handedness. Instead of using a circular polarizer the
observer can use a single linear polarizer in series with a 90° re-
tarder, the latter being held nearer to the eye. Turning the
retarder through 90° reverses the handedness of the circular
polarization.

Some people see the brush easily; others have difficulty. A few

Popular Applications of Polarized Light

see the brush when looking innocently at the partially polarized
blue sky, i.e., without using any polarizer at all, and even with-
out meaning to see the brush. Some people see the brush more
distinctly by linearly polarized light than by circularly polarized
light, and for others the reverse is true. An observer may find
the brush to have a slightly different orientation depending on
which eye is used.

The spectral energy distribution of the light is important. If
the light is rich in short-wavelength (blue) radiation, the brush
is very noticeable, but if the short-wavelength radiation is elimi-
nated by means of a yellow filter, the brush fails to appear. Use
of a blue filter tends to accentuate the brush.

Although the phenomenon was discovered in 1844, by the
Austrian mineralogist Haidinger, the cause is not yet fully under-
stood. Presumably the thousands of tiny blue-light-absorbing
bodies in the central (foveal) portion of the retina are dichroic
and are oriented in a radial pattern, for example, a pattern such
that the absorption axis of each body lies approximately along
a radius from the center of the fovea. Incident linearly polarized
light will then be absorbed more strongly in some parts of the
pattern than in other parts and consequently some parts will
fatigue more than others. When the vibration direction of the
light is suddenly changed, the varying degrees of fatigue are
revealed as a subjective radial pattern. Presumably no such
dichroism or orientation pattern applies to longer wavelength
(yellow and red) light; consequently a yellow sensation domi-
nates in those regions where fatigue-to-blue has occurred.

The fact that circular polarization, also, may be detected per-
haps implies that some transparent portion of the eye is weakly
birefringent and acts like a retarder, converting circularly polar-
ized light to linearly or elliptically polarized light. The direc-
tion of the major axis of the ellipse depends only on the direc-
tion of the fast axis of the retarding layer and hence remains
fixed — unless the observer tips his head.

Perhaps physicists will some day write matrices to describe the
retarding layers and dichroic areas of the eye. Poets were the first
to see magic fire and jewels in the human eye; physicists will be
the first to see matricesl

Bees, too, can detect the vibration direction of linearly polar-
ized light. The experiments of the biologist K. von Frisch during
World War II showed that bees "navigate" back and forth be-
tween hive and source of honey by using the sun as a guide.
More interesting, when the sun is obscured by a large area of
clouds the bees can still navigate successfully if they can see a
bit of blue sky: they can detect the azimuth of linear polariza-
tion of the blue light and navigate with respect to it. One way of
demonstrating the bee's ability to detect the azimuth of polariza-
tion is to place the bee in a large box the top of which consists
of a huge sheet of linear polarizer, such as H-sheet. Each time the
experimenter turns the polarizer to a different azimuth, the bee
changes his direction of attempted travel correspondingly.

Certain other animals also can detect the polarization of sky-
light and navigate by it. This includes ants, beetles, and the
fruit fly Drosophila. Probably many other examples will be dis-
covered.

POLARIZATION OF SKY LIGHT

Blue-sky light traveling in a direction roughly at right angles
to the sun's rays is partially polarized. When an observer holds
a linear polarizer in front of his eye and gazes in a direction
perpendicular to the direction of the sun, he finds that rotating
the polarizer slowly causes the sky to change from bright to dark
successively. The degree of polarization of sky light may reach
70 or 80 percent when the air is clear and dust-free, the sun is
moderately low in the sky, and the observation direction is near
the zenith.

The polarization is a result of the scattering of the sun's rays
by the molecules in the air. Rayleigh's well-known inverse-fourth-
power law relating scattering intensity to wavelength accounts
for the blue color of the scattered light, and the asymmetry as-
sociated with the 90° viewing angle accounts for the polarization,
as explained in Chapter 5. Some multiple scattering occurs, and
this reduces the degree of polarization somewhat; when the
observer ascends to a higher altitude, the amount of air involved

Popular Applications of Polarized Light

is reduced, multiple scattering is reduced, and the degree of
polarization is increased. A further increase results when a
yellow or red filter is used to block the short-wavelength com-
ponent of the light and transmit the long-wavelength component
— the latter component is less subject to multiple scattering. (The
situation is very different for infrared radiation of wavelength
exceeding 2 microns: much of this radiation is produced by
emission from the air itself, rather than by scattering, and this
exhibits little or no polarization.)

Some persons are capable of detecting the polarization of sky
light directly by eye, by virtue of the Haidinger brush phe-
nomenon discussed in a preceding section; a few individuals
find the brush noticeable enough to be a nuisance. Ordinarily,
of course, it escapes notice and plays little part in the affairs of
man. Its practical use by bees, ants, etc., has been indicated, and
the importance to photographers is discussed in a later section.

POLARIZATION OF LIGHT UNDER WATER

A surprising fact about the polarization found in light present
beneath the surface of the ocean (or of a pond) is that the pre-
dominant direction of electric vibration is horizontal. The oppo-
site might be expected, since most of the light that enters the
water enters obliquely from above, and the most strongly re-
flected component of obliquely incident light is the horizontally
vibrating component. But oceanographers and biologists, work-
ing at depths of 5 to 30 feet in waters off Bermuda and in the
Mediterranean Sea, have found the main cause of submarine
polarization to be the scattering of the light by microscopic
particles suspended in the water. Sunlight and sky light enter
the water from above, and the average direction of illumination
is roughly vertical; consequently the polarization form of the
scattered light that travels horizontally toward an underwater
observer is partially polarized with the electric vibration direc-
tion horizontal. The situation is much the same as that discussed
in Chapter 5, except that the incident light has a more steeply
downward direction and the asymmetric scattering is by micro-
scopic particles instead of molecules.

Typically, the degree of polarization is 5 to 30 percent, an

amount found to be important to a variety of underwater life.
The water flea Daphnia tends to swim in a direction perpendicu-
lar to the electric vibration direction, for reasons not yet known.
When tests are conducted in a tank filled with water that is free
of suspended particles, so that the submarine illumination is
practically unpolarized, Daphnia ceases to favor any one direc-
tion. But if suspended matter is added, thus restoring the polar-
ization, Daphnia resumes the custom of traveling perpendicular
to the vibration direction.

The arthropod Limulus (horse shoe crab) easily detects the
polarization of the underwater light and is presumed to navigate
with respect to the electric vibration direction. The same is true
of the crustacean Mysidium gracile and various other forms of
marine life. Most tend to swim perpendicularly to the vibration
direction; some swim parallel to it; a few swim at different rela-
tive orientations depending on the time of day. For all of these
animals, polarization is a compass that works even under water!

POLARIZING SUNGLASSES

The lenses of ordinary sunglasses employ absorbing materials
that are isotropic, and accordingly the incident light is attenuated
by a fixed factor irrespective of polarization form. This is un-
fortunate. The fact is that "glare" consists predominantly of
light having a horizontal vibration direction. Why? For these
reasons:

(a) The main source of light (sun and sky) is overhead, and
consequently the main flux of light is downward.

(b) The surfaces that are most strongly illuminated by the
downward flux are horizontal surfaces.

(d) Most outdoor objects are of dielectric material.

(e) Light reflected obliquely from a horizontal dielectric sur-
face is partially linearly polarized with the dominant vibration
direction horizontal, as explained in Chapter 4.

Polarizing sunglasses take full advantage of this fact. The
lenses are made of dichroic material (H-sheet, usually) oriented
with the transmission axis vertical, as indicated in Fig. 10-2a, so

Popular Applications of Polarized Light

(o)

(b)

(c)

FIG. 10-2 Three types of polarizing spectacles. In (a) the transmission
axis is vertical, for eliminating glare reflected from horizontal surfaces.
In (b) the axis is horizontal, for eliminating reflections from vertical
windows of trains, store-fronts (show-windows), etc. In (c) the axis di-
rections are 45* and —45°, a standard arrangement used in viewing
polarization-coded stereoscopic pictures.

that almost all of the horizontal vibrations are absorbed. The
component having vertical vibration direction is transmitted.
Usually some isotropic absorber is included in the lenses to
absorb ultraviolet light strongly and blue and red light to a
moderate extent; the sunglasses then have a greenish hue which
has nothing to do with the polarization.

Motorists and vacationists find that polarizing sunglasses are
helpful not only in reducing the brightness of the field of view
as a whole, but also in enhancing the beauty of the scene. Be-
cause specularly reflected light is absorbed preferentially, roads,
trees, grassy fields, etc., appear softer and more deeply colored
through polarizers. Specularly reflected light tends to veil nature's
inherent beauty; polarizing sunglasses remove the veil.

Fishermen and boatsmen enjoy another benefit from wearing
polarizing sunglasses. They want to be able to see fish, rocks, etc.,
beneath the surface of the water, yet the light from such objects
is dim and is usually lost in the "noise" of the sky light reflected
obliquely from the surface. Since the reflected light is highly
polarized with horizontal vibration direction, the polarizing
sunglasses absorb this component strongly, and the visibility of

the underwater objects is greatly increased. The increase is great-
est when the viewing direction corresponds to the polarizing
angle, which, for water, is about 53° from the normal. When the
viewing direction is along the normal, i.e., straight down, there
is no increase at all.

There is one interesting situation in which polarizing sun-
glasses produce little increase in visibility of underwater objects
even when the angle of viewing is the polarizing angle. This situ-
ation occurs when the sky is clear and blue, the sun is low in
the sky, and the pertinent portion of the sky is at 90° from the
direction of the sun. Under these circumstances the light striking
the water is already linearly polarized at such an azimuth that
almost none of it is reflected. There is no task left for the sun-
glasses to perform — there is no reflected glare to suppress. The
underwater objects are seen with great clarity. Persons unfamiliar
with the polarization of sky light and with the dependence of
oblique reflection on polarization form are likely to ascribe the
remarkable clarity to "especially clear water" rather than to
absence of reflection.

CAMERA FILTERS

Photographers often wish to enhance the contrast between blue
sky and white clouds. Thirty years ago they did this by employing
a yellow filter, which absorbed most of the blue light from the
clear sky but transmitted most of the white light from the clouds.
Using ordinary black-and-white film, they obtained excellent
contrast by this method. Today, photographers are using color
film increasingly, and the use of yellow filters is no longer per-
missible since it would eliminate all blue colors from the finished
photograph.

The only known solution is to exploit the difference in polari-
zation between blue sky and white clouds. Light from most por-
tions of the blue sky is partially linearly polarized, as explained
in a preceding section, and light from clouds is unpolarized.
Therefore a neutral-color, linear polarizer mounted at the opti-
mum azimuth in front of the lens will absorb a large fraction
(e.g., 80 percent) of the sky light while transmitting a large frac-

Popular Applications of Polarized Light

tion (nearly half) of the light from the clouds; thus the contrast
is increased by a factor of two or three. The factor is less if the
air is hazy, and more if the air is extremely clear (as in Arizona)
and if the camera is aimed about 90° from the direction of the
sun.

The usual way of choosing the azimuth of the polarizer is
crude, but perhaps adequate. The photographer holds the polar-
izer in front of his eye, finds by trial and error which azimuth
maximizes the contrast of the clouds in question, and then at-
tempts to mount the polarizer on the camera without changing
the azimuth of the polarizer. One type of polarizing filter for
cameras is equipped with a small "satellite" polarizer mounted
at the end of a short arm and aligned permanently with the main
polarizer. The photographer installs the main polarizer in front
of the lens, looks through the small polarizer and turns the arm
to whatever azimuth maximizes the contrast. Both polarizers
then have this optimum orientation. The satisfactoriness of the
azimuth can be checked visually at any time. Instead of using
these empirical methods, a scientifically minded photographer
can proceed by dead reckoning, i.e., by following this well-known
rule: Mount the polarizer so that its transmission axis lies in the
plane determined by camera, sun, and object photographed. (So
oriented, the polarizer performs a valuable additional service: it
eliminates most of the specularly reflected light from trees, roads,
etc., and enhances the softness and depth of color of the scene.)

When a photographer standing on a sidewalk tries to photo-
graph objects situated behind a store window, the reflection of
the street scene from the window may threaten to spoil the
photograph. An excellent solution is to place the camera off to
one side so that the window is seen obliquely at about the polar-
izing angle, and mount a linear polarizer in front of the lens;
the polarizer is turned so that its transmission axis is horizontal,
and the polarized light reflected from the window is absorbed.
The authors have a friend who has applied this same principle
to a pair of special spectacles he wears while touring the country
by railroad. The lenses consist of polarizers oriented with the
transmission axis horizontal, as indicated in Fig. 10-2b; thus
when he gazes out of the train window in oblique forward direc-

tion, the reflected images of passengers and newspapers are wiped
out, and the scenery appears in its pristine glory.

USE OF CIRCULAR POLARIZERS IN ELIMINATING
PERPENDICULARLY REFLECTED LIGHT

Eliminating perpendicularly reflected lights is a different prob-
lem from that of eliminating obliquely reflected light. The proc-
ess of oblique reflection at Brewster's angle causes the reflected
beam to be linearly polarized, and accordingly a linear polarizer
can eliminate the reflected beam entirely. But the process of
normal reflection, i.e., with incident and reflected beams perpen-
dicular to the smooth glossy surface in question, produces no
polarization at all. How, then, can the specularly reflected light
be eliminated while light originating behind the surface is trans-
mitted freely?

The question is an important one to radar operators scanning
the cathode-ray-oscilloscope screens on which dim greenish spots
representing airborne objects appear. The screen proper is situ-
ated in a large evacuated tube, and the greenish light emerges
through a curved glass window at the front end of the tube.
(Sometimes the window is flat; sometimes a safety plate of glass
or plastic is mounted close in front of it.) Often the operator
has difficulty in seeing the greenish spots, not only because they
are faint, but also because they may be masked by various ex-
traneous images reflected by the front surface of the window, e.g.,
reflections of room lights and of people, clothing, papers, etc.,
situated near the operator. Extinguishing the room lights would
eliminate these reflections, but would make it impossible for
the operator to read instructions or make notes. What he needs
is some kind of filter that will transmit the light originating be-
hind the window and absorb the light reflected approximately
perpendicularly from it.

This need is filled by the circular polarizer. Such a device, if
mounted close in front of the window, will transmit nearly half
of the light that originates behind the window, yet will eliminate
about 99 percent of the room light that is reflected perpen-
dicularly from it. The circular polarizer acts on the room light
twice: it circularly polarizes room light that is approaching the

Popular Applications of Polarized Light

window, then absorbs the reflected component. The logic behind
this requires explanation. Two key facts must be kept in mind:

(1) A beam that is reflected perpendicularly and specularly by
a smooth glossy surface has the same degree of polarization as
the incident beam, since the reflection process does not intro-
duce randomness of any kind.

(2) The reflection process reverses the handedness of polariza-
tion, because handedness is defined with respect to the propaga-
tion direction and the reflection process reverses the propagation
direction.

If the polarizer is of right-circular type, as in the arrangement
shown in Fig. 10-3, room light that passes through and ap-

UNPOLARIZED
LIGHT

RETARDING

LAYER

SPECULARLY

REFLECTING

GLASS PLATE/7

POLARIZER

FIG. 10-3 Use of a circular polarizer in absorbing light reflected by a
surface approximately perpendicular to the incident beam. Note that
the reflection process reverses the handedness of circular polarization.

proaches the window is right-circularly polarized; the reflected
light is /e/f-circularly polarized and hence is totally absorbed by
the polarizer. In effect, the circular polarizer "codes" the light,
the window reverses the coding, and the polarizer then annihi-
lates the reverse-coded beam. If both faces of the window are
ideally flat and smooth, if the light is incident exactly along
the normal, and if the polarizer is truly of circular type, the

reflected light is totally absorbed. Usually the conditions are
less ideal: the rear surface of the window usually serves as sup-
port for the luminescent screen and has a matte appearance; the
window is usually curved and much of the troublesome room
light incident on the window makes an angle of 10° or 20° or
more with the normal; and the polarizer, although circular with
respect to some wavelengths, is elliptical with respect to others.
Nevertheless, the improvement provided by the polarizer is large,
and the amount of faint detail that the operator can see on the
screen is greatly increased.

One precaution must be mentioned: reflections from the polar-
izer itself must be avoided. This is usually accomplished by tilt-
ing the polarizer forward so that the only reflected images the
observer sees are images of a dark-colored floor or other dark
objects.

Television sets, also, have been equipped successfully with cir-
cular polarizers. If the set is used in a brightly lit room, or is used
outdoors, the circular polarizer performs a valuable service in
trapping the specularly reflected glare and thus increasing the
picture-vs-glare ratio by a factor of the order of 10.

VARIABLE-DENSITY FILTER

A pair of linear polarizers arranged in series is an almost ideal
device for controlling the transmitted intensity of light. Rotating
one polarizer through an angle 6 with respect to the other causes
the intensity of the transmitted light to vary approximately as
cos2 6. Because the transmittance is easily varied and easily calcu-
lated, the pair of polarizers has found much favor in the eyes of
designers of spectrophotometers and other devices for controlling
and measuring light intensity.

Specially designed sunglasses employing pairs of linear polar-
izers in place of lenses have been used successfully by aviators
and others. One polarizer of each pair can be rotated through
an angle as large as 90°, and a linkage connecting the two pairs
insures that the attenuation is the same for both eyes. By moving
one small lever, the wearer can vary the transmittance through-
out a range of about 10,000 to 1.

Controllable pairs of very-large-diameter polarizers have been

Popular Applications of Polarized Light

used as windows of railroad cars and ocean liners. A person
sitting near such a window turns a small knob to rotate one
polarizer with respect to the other and thus reduce the intensity
of the transmitted light to any extent desired.

One of the authors has experimented with a variable-density
filter employing three linear polarizers in series, in order that a
transmittance range of 108 to 1 could be achieved. The device
worked well and, as expected, obeyed a cosine-fourth, rather than
a cosine-square law.

THREE-DIMENSIONAL PHOTOGRAPHY AND THE USE
OF POLARIZERS FOR CODING

Millions of polarizers found their way into the motion picture
theaters of North America in 1952 and 1953 when stereoscopic
(three-dimensional, or 3-D) movies achieved brief prominence.
Each spectator wore a pair of polarizing spectacles called view-
ers, and polarizers were mounted in front of the projectors.

A photographer who enjoys looking at 3-D still pictures in his
living room needs no polarizers. Usually he employs a small view-
ing box containing a light source and two lenses, one for each
eye; a black partition, or septum, divides the box into right and
left halves. The picture, consisting of two small transparencies
mounted about two inches apart in a side-by-side arrangement on
a cardboard frame, is inserted in the box so that the right-eye
transparency lines up with the right lens and the left-eye trans-
parency lines up with the left lens. (The two transparencies are,
of course, slightly different because they were taken by cameras
situated about two or three inches apart; the spacing used ap-
proximates the spacing of the two eyes.) The side-by-side arrange-
ment of the two transparencies and the presence of the septum
insure that the observer's right eye sees only the right trans-
parency and the left eye sees only the left transparency. No
cross-communication, or "cross-talk," can occur. Consequently
the observer enjoys an impressively realistic stereoscopic illusion.

When 3-D motion-picture films are projected in a theater,
many complications arise. Separate projectors must be provided
for the right-eye and left-eye movie films, and the two projectors
must be synchronized within about 0.01 second. Since there is

just one large screen and this is to be viewed by hundreds of
spectators, there can be no septum. Indeed, no practical geometri-
cal method of preventing cross-talk is known.

Before the advent of mass-produced polarizers in the 1930's, an
analglyph system of preventing cross-talk was invented. It applied
wavelength coding to the two projected beams. The right-eye
picture was projected through a long-wavelength (red) filter, and
the left-eye picture was projected through a shorter-wavelength
(green) filter. The spectator's viewers contained right and left
lenses of red and green plastic, respectively, and accordingly each
lens transmitted light from the appropriate projector and ab-
sorbed light from the other. Thus each eye received just the
light intended for it. The system succeeded as a short-term
novelty: stereoscopic illusions were created. But the system had
two major defects: chromatic "retinal rivalry" between the two
eyes, and incompatibility with the showing of colored motion
pictures.

In the 1930's the problem was solved with £clat by a polariza-
tion-coding system, demonstrated with great impact at the New
York World's Fair of 1939 and improved in later years. As indi-
cated in Fig. 10-4, a linear polarizer oriented with its transmis-
sion axis at —45° is placed in front of the projector used for the
right-eye pictures, and a polarizer at +45° is placed in front of
the projector used for the left-eye pictures. Thus the two beams
striking the movie screen are orthogonally coded. The lenses
of the spectator's viewers consist of correspondingly oriented
linear polarizers, and so each eye receives only light that origi-
nates in the appropriate projector. Superb stereoscopic illusions
result. Since the polarizers perform well at all wavelengths in the
visual range, color movies can be presented as easily and faith-
fully as can black-and-white movies.

The polarizers placed in front of the projectors consist, ordi-
narily, of K-sheet; as explained in Chapter 3, K-sheet is highly
resistant to heat, and any polarizing filter placed close in front
of a powerful projector is bound to heat up considerably since it
necessarily absorbs about half the light. The lenses of the 3-D
viewers are usually of HN-38 sheet; it has high major trans-
mittance kx and small minor transmittance k2, and it is inex-

Popular Applications of Polarized Light

FIG. 10-4 Arrangement for projecting polarization-coded stereoscopic
motion-picture films by means of two side-by-side projectors. Films FR
and FL containing the "right-eye pictures" and "left-eye pictures" are
mounted in the right and left projectors, which are equipped with
linear polarizers PR and PL oriented at —45° and +45* respectively.
The viewer contains correspondingly oriented polarizers, and accord-
ingly each eye sees only the images intended for it.

pensive. The viewers are cheap enough (about 10^ each) that
they can be discarded after a single use.

The polarization-coding scheme has one limitation: if the
spectator tilts his head to one side, the polarizers in his viewers
no longer line up accurately with the respective polarizers on the
projectors. Thus cross-talk occurs: the right eye sees faintly the
image meant for the left eye, and vice versa: each eye sees a
faint ghost image in addition to the main image. The spectator
does not enjoy this. The difficulty could be avoided if the linear
polarizers were replaced by high-quality, achromatic circular
polarizers, but unfortunately no method is known for producing
achromatic circular polarizers economically.

The effectiveness of any polarization-coding projection system
is destroyed if the screen depolarizes the light appreciably.
Screens that have a smooth aluminum coating usually conserve

polarization to the extent of about 99 percent, but those having
a matte white surface or a rough metallic coating produce much
depolarization and hence much cross-talk between the two
images. Many of the screens used in the innocent days of 1952
and 1953 were of the wrong type, and the resulting ghost images
were a major annoyance. For that reason, and because of fre-
quent lack of care in maintaining synchronism between the two
projectors, movie-goers socn turned back to conventional 2-D
pictures. Some nostalgia remains, however. Persons who were
lucky enough to see a full-color, 3-D movie showing attractive
actors filmed against a background of gorgeous scenery look for-
ward to the time when well-made, well-presented 3-D movies,
with their almost miraculous realism and intimacy, will animate
the theaters once again.

THE VECTOGRAPH

The type of three-dimensional photography discussed in the
preceding section is parallel-projected 3-D photography. The
two motion-picture films are situated side-by-side, and two pro-
jectors are operated in parallel. During the late 1930's a radically
new approach, called vcctography, was developed by E. H. Land,
J. Mahler, and others. In this system, the two films are arranged
in series, bonded together. Because of the permanent series ar-
rangement, many problems disappear. Only one projector is
needed, and perfect synchronism is "guaranteed at the factory."
Each pair of pictures (each vectograph) is projected as a single
unit, in the same projector aperture and at the same time, and
onto the same area of the same screen. If the film breaks, it can
be spliced with no concern as to preservation of synchronism.

The method can succeed only if means are provided for pre-
serving the identity of the two coincident projected beams.
Again, polarization-coding is the answer. However, because the
two images are bonded together in series, the coding must occur
within the images themselves. In the system used by Land and
Mahler each image consists of varying quantities of linearly
dichroic molecules aligned in a common direction, and the direc-
tions employed in the two images are mutually at right angles.
Dark areas in any one image contain a high concentration of

Popular Applications of Polarized Light

dichroic molecules; light areas contain little or no dichroic
material; but irrespective of concentration, the alignment direc-
tion is always the same. For the other image, the alignment direc-
tion is always orthogonal to the first. It is to be noted that the
images contain no silver and no other isotropic absorber. Only
aligned absorbers having high dichroic ratio are used.

A communications engineer would describe the vectograph by
saying that it provides two distinct channels. Each is assigned to
one image. Each is independent of the other. Since the vecto-
graph images themselves perform the polarization coding, no
polarizer is used in front of the projector; indeed, the interpo-
sition of such a filter would play havoc with the system. As be-
fore, the screen must preserve the polarization and the spectator's
viewers must perform the appropriate decoding, or discrimi-
nating, act. Excellent stereoscopic effects are achieved. However,
the production of vectograph film is a costly undertaking involv-
ing very specialized equipment, and constant attention is needed
to maintain high enough dichroic ratio so that the channels are
truly independent and ghost images are avoided.

Vectograph pictures of the "still" type are easier and cheaper
to make than vectograph movies. Stereo pairs of aerial photo-
graphs of mountainous country, if presented in vectograph form,
give a navigator (wearing an appropriate viewer) a very realistic
impression of the terrain, and a map maker can prepare an accu-
rate contour map from the vectograph with ease.

POLARIZING HEADLIGHTS

It is ironic that the main goal of Land and others in develop-
ing high-quality, large-area, low-cost polarizers has never been
achieved. The polarizers are used with great success in dozens
of applications, but not the application that was uppermost in
the minds of the inventors.

Their goal was to eliminate glare from automobile headlights.
In an era when dual-lane highways, circumferential bypasses,
and other safety engineering advances were virtually unknown
and the aim and focus of automobile headlights were highly
erratic, the glare that confronted motorists at night was almost

unbearable, and was an important cause of accidents. As early
as 1920 several illumination engineers recognized that the glare
could be eliminated by means of polarizers — if large-area polar-
izers could somehow be produced. If every headlight lens were
covered by a linear polarizer oriented with the transmission
axis horizontal and every windshield were covered with a linear
polarizer oriented with its axis vertical, no direct light from the
headlights of Car A could pass through the windshield of on-
coming Car B. Drivers in both cars could see road-markings,
pedestrians, and so forth, but neither would experience any
glare from the other's headlights. Moreover, it would be per-
missible for each driver to use his high beam continuously, and
accordingly his ability to see pedestrians, etc., would be greater
than before, despite the fact that each polarizer would transmit
only about half of the light incident on it.

It was soon recognized that the analyzing polarizer should not
be made a permanent part of the windshield, but should be in-
corporated in a small visor situated just in front of the driver's
eyes. During the day, when headlights were not in use, the visor
could be swung out of the way. It was also recognized that care
should be taken to make sure the headlight polarizers had suffi-
cient light-leak, i.e., sufficiently large k2 value, that the head-
lights of oncoming cars would not disappear entirely!

Land and his colleagues moved rapidly. They invented a
whole series of polarizers, each superior to its predecessor. The
first successful type, J-sheet, employed aligned, microscopic crys-
tals of the dichroic mineral herapathite; the method of manu-
facture is described in Chapter 3. Then came H-sheet, which
was better in nearly every respect and in addition was easier to
make. Finally, K-sheet appeared; it had most of the superb
qualities of the earlier materials and the added virtue of being
unaffected by fairly high temperature, such as 215°F. To per-
sons seeking polarizers for use in headlights, K-sheet appeared
to be the pot of gold at the end of a polarized rainbow.

Concurrently, several better ways of orienting the polarizers
were proposed. One attractive scheme was to orient the head-
light polarizers and the visor polarizer at the identical azimuth,
namely —45°, as indicated in Fig. 10-5. Then, even a polariza-
tion-conserving object in the path of the headlights would appear

Popular Applications of Polarized Light

FIG. 10-5 Automobile equipped with headlight polarizers and a visor
polarizer oriented at —45°. When two such cars approach one another,
each driver is protected from the glare from the headlights of the other.

to the driver to be brightly illuminated. (This would not be the
case if his visor polarizer were crossed with his headlight polar-
izers.) The —45° system disposed of the headlight glare problem
adequately: if two cars A and B both equipped in this manner
approached one another at night, each driver's visor would be
crossed with the other car's headlight polarizers, and neither
driver would experience any glare.

Using the Mueller calculus, Billings and Land compared a
wide variety of polarizer orientation schemes, and found several
to be particularly attractive. Perhaps the best system was one
called " — 55°, —35°." The transmission axes of the headlight
polarizers and visor polarizer are at 55° and 35° from the vertical,
respectively, an arrangement that minimizes complications stem-
ming from the obliquity of the portion of the windshield situated
just in front of the driver.

Despite the successes on all technical fronts, the project bogged
down. To this day no one knows just why. Probably many little
reasons were responsible. Among these were the following:

(1) The polarizers absorbed slightly more than half of the
light incident on them, and accordingly the automobile manu-
facturers felt that they would have to increase the power of the
lamps themselves and perhaps use larger generators and batteries
also.

(2) Some windshields were moderately birefringent; therefore

they would act like retarders, alter the polarization form of the
incident light, and allow some glare to leak through.

(3) Nearly every year the automobile manufacturers increased
the backward tilt of the windshields; such tilt tends to alter the
polarization form of light having an oblique vibration direction,
and hence leads to glare-leak.

(4) Passengers, as well as drivers, would require visors, since
passengers also dislike glare.

(5) Pedestrians might find that the glare was worse than ever,
unless they too employed polarizing visors or spectacles.

(6) The system would succeed only if adopted by all car manu-
facturers, and therefore no one manufacturer would gain any
promotional advantage from it.

(7) The first few drivers to put the system to use would get
little benefit from it for at least a year or two, i.e., until millions
of other cars were similarly equipped.

(8) It was difficult to decide when and how to force the owners
of old cars to install the necessary polarizers on their cars.

(9) The patents on the only fully satisfactory polarizers were
held by a single company.

(10) To introduce the system would require formal, coordi-
nated action by all States.

(11) Improvements in headlight design and aiming, the in-
creasing numbers of dual-lane highways, and the brighter street
lamps used in cities and suburbs led some people to believe that
the need for a polarization-type of glare control was no longer
acute.

However, persons who have actually experienced the polariza-
tion method of glare removal are convinced that the drawbacks
are trivial compared to the benefits.

Perhaps some day the system will be tried out on a pilot scale
in a small, isolated community, where all the cars could be
equipped with polarizers in a few weeks. Perhaps an island of
moderate size would make a good test ground. If the system is
found to be highly successful there, it will presumably spread
throughout every country that teems with automobiles.

An explanation of how the eye works, by the

biologist who won a Nobel Prize for contributions to this field.

Eye and Camera

George Wald

A Scientific American article, 1950

OF all the instruments made by man,
none resembles a part of his body
more than a camera does the eye.
Yet this is not by design. A camera is
no more a copy of an eye than the wing
of a bird is a copy of that of an insect.
Each is the product of an independent
evolution; and if this has brought the
camera and the eye together, it is not
because one has mimicked the other, but
because both have had to meet the same
problems, and frequently have done so
in much the same way. This is the type
of phenomenon that biologists call con-
vergent evolution, yet peculiar in that
the one evolution is organic, the other
technological.

Over the centuries much has been
learned about vision from the camera,
but little about photography from the
eye. The camera made its first appear-
ance not as an instrument for making
pictures but as the camera obscura or
dark chamber, a device that attempted
no more than to project an inverted
image upon a screen. Long after the
optics of the camera obscura was well
understood, the workings of the eye re-
mained mysterious.

In part this was because men found
it difficult to think in simple terms about
the eye. It is possible for contempt to
breed familiarity, but awe does not help
one to understand anything. Men have
often approached light and the eye in a
spirit close to awe, probably because
they were always aware that vision pro-
vides their closest link with the external

world. Stubborn misconceptions held
back their understanding of the eye for
many centuries. Two notions were par-
ticularly troublesome. One was that ra-
diation shines out of the eye; the other,
that an inverted image on the retina is
somehow incompatible with seeing right
side up.

I am sure that many people are still
not clear on either matter. I note, for
example, that the X-ray vision of the
comic-strip hero Superman, while re-
garded with skepticism by many adults,
is not rejected on the ground that there
are no X-rays about us with which to
see. Clearly Superman's eyes supply the
X-rays, and by directing them here and
there he not only can see through opaque
objects, but can on occasion shatter a
brick wall or melt gold. As for the in-
verted image on the retina, most people
who learn of it concede that it presents
a problem, but comfort themselves with
the thought that the brain somehow
compensates for it. But of course there
is no problem, and hence no compensa-
tion. We learn early in infancy to asso-
ciate certain spatial relations in the
outside world with certain patterns of
nervous activity stimulated through the
eyes. The spatial arrangements of the
nervous activity itself are altogether
irrelevant.

It was not until the 17th century that
the gross optics of image formation in
the eye was clearly expressed. This was
accomplished by Johannes Kepler in
1611, and again by Rene Descartes in

1664. By the end of the century the first
treatise on optics in English, written by
William Molyneux of Dublin, contained
several clear and simple diagrams com-
paring the projection of a real inverted
image in a "pinhole" camera, in a cam-
era obscura equipped with a lens and
in an eye.

Today every schoolboy knows that the
eye is like a camera. In both instruments
a lens projects an inverted image of the
surroundings upon a light-sensitive sur-
face: the film in the camera and the
retina in the eye. In both the opening
of the lens is regulated by an iris. In
both the inside of the chamber is lined
with a coating of black material which
absorbs stray light that would otherwise
be reflected back and forth and obscure
the image. Almost every schoolboy also
knows a difference between the camera
and the eye. A camera is focused by mov-
ing the lens toward or away from the
film; in the eye the distance between the
lens and the retina is fixed, and focusing
is accomplished by changing the thick-
ness of the lens.

The usual fate of such comparisons is
that on closer examination they are ex-
posed as trivial. In this case, however,
just the opposite has occurred. The more
we have come to know about the mech-
anism of vision, the more pointed and
fruitful has become its comparison with
photography. By now it is clear that the
relationship between the eye and the
camera goes far beyond simple optics,
and has come to involve much of the

CONJUNCTIVA

FOVEA

CILIARY
MUSCLE

NERVE

SCLERA CHOROID RETINA

''>"/ /ti\\\\\\\\\

OPTICAL SIMILARITIES of eye and camera are ap-
|iurent in their cross sections. Both utilize ;i lens to
funis an inverted image on a light-sensitive surface.

Botli posses* .in iris to adjust to various intensities of

liplit. The single lens of the eye, however, cannot bring
li^lit of all colors to a focus at the same point. The
compound lens of the camera is better corrected for
color because it is composed of two kinds of glass.

WMtf

FORMATION OF AN* IMAGE on the retina of the human eye was diagrammed
hy Rene Descartes in 1664. This diagram is from Descartes' Dioptrics.

Eye and Camera

essential physics and chemistry of both
devices.

Bright and Dim Light

A photographer making an exposure
in dim light opens the iris of his camera.
The pupil of the eye also opens in dim
light, to an extent governed by the activ-
ity of the retina. Both adjustments have
the obvious effect of admitting more
light through the lens. This is accom-
plished at some cost to the quality of
the image, for the open lens usually de-
fines the image less sharply, and has less
depth of focus.

When further pressed for light, the
photographer changes to a more sensi-
tive film. This ordinarily involves a fur-
ther loss in the sharpness of the picture.
With any single type of emulsion the
more sensitive film is coarser in grain,
and thus the image cast upon it is re-
solved less accurately.

The retina of the eye is grainy just as
is photographic film. In film the grain is
composed of crystals of silver bromide
embedded in gelatin. In the retina it is
made up of the receptor cells, lying side
by side to form a mosaic of light-sensitive
elements.

There are two kinds of receptors in the
retinas of man and most vertebrates:
rods and cones. Each is composed of an
inner segment much like an ordinarv
nerve cell, and a rod- or cone-shaped
outer segment, the special portion of the
cell that is sensitive to light. The cones
are the organs of vision in bright light,
and also of color vision. The rods provide
a special apparatus for vision in dim
light, and their excitation yields only
neutral gray sensations. This is why at
night all cats are gray.

The change from cone to rod vision,
like that from slow to fast film, involves
a change from a fine- to a coarse-grained
mosaic. It is not that the cones are
smaller than the rods, but that the cones
act individually while the rods act in
large clumps. Each cone is usually con-
nected with the brain by a single fiber
of the optic nerve. In contrast large
clusters of rods are connected by single
optic nerve fibers. The capacity of rods
for image vision is correspondingly
coarse. It is not only true that at night
all cats are gray, but it is difficult to be
sure that they are cats.

Vision in very dim light, such as star-
light or most moonlight, involves only
the rods. The relatively insensitive cones
are not stimulated at all. At moderately
low intensities of light, about 1,000 times
greater than the lowest intensity to
which the eye responds, the cones begin
to function. Their entrance is marked bv
dilute sensations of color. Over an inter-
mediate range of intensities rods and
cones function together, but as the
brightness increases, the cones come to
dominate vision. We do not know that

SSfig&S

GRAIN of the photographic emulsion, magnified 2,500
times, is made up of silver-bromide crystals in gelatin.

"GRAIN" of the human retina is made up of cones and
rods (dots at far right). Semicircle indicates fovea.

the rods actually stop functioning at
even the highest intensities, but in bright
light their relative contribution to vision
falls to so low a level as to be almost
negligible.

To this general transfer of vision from
rods to cones certain cold-blooded ani-
mals add a special anatomical device.
The light-sensitive outer segments of the
rods and cones are carried at the ends of
fine stalks called myoids, which can
shorten and lengthen. In dim light the
rod myoids contract while the cone my-
oids relax. The entire field of rods is thus
pulled forward toward the light, while
the cones are pushed into the back-
ground. In bright light the reverse oc-
curs: the cones are pulled forward and
the rods pushed back. One could scarce-
ly imagine a closer approach to the
change from fast to slow film in a camera.

The rods and cones share with the
grains of the photographic plate another
deeply significant property. It has long
been known that in a film exposed to
light each grain of silver bromide given
enough developer blackens either com-
pletely or not at all, and that a grain is
made susceptible to development by the
absorption of one or at most a few quanta
of light. It appears to be equally true
that a cone or rod is excited by light to
yield either its maximal response or none
at all. This is certainly true of the nerve
fibers to which the rods and cones are
connected, and we now know that to
produce this effect in a rod— and possibly
also in a cone— only one quantum of light
need be absorbed.

It is a basic tenet of photochemistry
that one quantum of light is absorbed by,
and in general can activate, only one
molecule or atom. We must attempt to
understand how such a small beginning
can bring about such a large result as the
development of a photographic grain
or the discharge of a retinal receptor.
In the photographic process the answer
to this question seems to be that the ab-

sorption of a quantum of light causes the
oxidation of a silver ion to an atom of
metallic silver, which then serves as a
catalytic center for the development of
the entire grain. It is possible that a
similar mechanism operates in a rod or a
cone. The absorption of a quantum of
light by a light-sensitive molecule in
either structure might convert it into a
biological catalyst, or an enzyme, which
could then promote the further reactions
that discharge the receptor cell. One
wonders whether such a mechanism
could possibly be rapid enough. A rod
or a cone responds to light within a
small fraction of a second; the mecha-
nism would therefore have to complete
its work within this small interval.

One of the strangest characteristics of
the eye in dim light follows from some
of these various phenomena. In focusing
the eye is guided by its evaluation of the
sharpness of the image on the retina. As
the image deteriorates with the opening
of the pupil in dim light, and as the
retinal capacity to resolve the image falls
with the shift from cones to rods, the
ability to focus declines also. In very
dim light the eye virtually ceases to ad-
just its focus at all. It has come to resem-
ble a very cheap camera, a fixed-focus
instrument.

In all that concerns its function, there-
fore, the eye is one device in bright light
and another in dim. At low intensities all
its resources are concentrated upon sen-
sitivity, at whatever sacrifice of form; it
is predominantly an instrument for see-
ing light, not pattern. In bright light all
this changes. By narrowing the pupil,
shifting from rods to cones, and other
stratagems still to be described, the eye
sacrifices light in order to achieve the
utmost in pattern vision.

Images

In the course of evolution animals
have used almost everv known device

for forming or evaluating an image.
There is one notable exception: no ani-
mal has yet developed an eye based
upon the use of a concave mirror. An
eye made like a pinhole camera, how-
ever, is found in Nautilus, a cephalopod
mollusk related to the octopus and squid.
The compound eye of insects and crabs
forms an image which is an upright
patchwork of responses of individual
"eyes" or ommatidia, each of which
records only a spot of light or shade.
The eye of the tiny arthropod Copilia
possesses a large and beautiful lens but
only one light receptor attached to a thin
strand of muscle. It is said that the mus-
cle moves the receptor rapidly back and
forth in the focal plane of the lens, scan-
ning the image in much the same way as
it is scanned by the light-sensitive tube
of a television camera.

Each of these eyes, like the lens eye
of vertebrates, represents some close
compromise of advantages and limita-
tions. The pinhole eye is in focus at all
distances, yet to form clear images it
must use a small hole admitting very
little light. The compound eye works
well at distances of a few millimeters,
yet it is relatively coarse in pattern reso-
lution. The vertebrate eye is a long-
range, high-acuitv instrument useless in
the short distances at which the insect
eye resolves the greatest detail.

These properties of the vertebrate eye
are of course shared by the camera. The
use of a lens to project an image, how-
ever, has created for both devices a spe-
cial group of problems. All simple lenses
are subject to serious errors in image
formation: the lens aberrations.

Spherical aberration is found in all
lenses bounded by spherical surfaces.
The marginal portions of the lens bring
rays of light to a shorter focus than the
central region. The image of a point in
space is therefore not a point, but a little
"blur circle." The cost of a camera is
largely determined by the extent to

CONES of the catfish Ameiurus are
pulled toward the surface of the ret-
ina (top) in bright light. The rods
remain in a layer below the surface.

RODS advance and cones retreat in
dim light. This retinal feature is not
possessed by mammals. It is peculiar
to some of the cold-blooded animals.

which this aberration is corrected by
modifying the lens.

The human eye is astonishingly well
corrected— often slightly overcorrected—
for spherical aberration. This is accom-
plished in two ways. The cornea, which
is the principal refracting surface of the
eye, has a flatter curvature at its margin
than at its center. This compensates in
part for the tendency of a spherical sur-
face to refract light more strongly at its
margin. More important still, the lens is
denser and hence refracts light more
strongly at its core than in its outer
layers.

A second major lens error, however,
remains almost uncorrected in the hu-
man eye. This is chromatic aberration,
or color error. All single lenses made of
one material refract rays of short wave-
length more strongly than those of longer
wavelength, and so bring blue light to a
shorter focus than red. The result is that
the image of a point of white light is not
a white point, but a blur circle fringed
with color. Since this seriously disturbs
the image, even the lenses of inexpensive
cameras are corrected for chromatic
aberration.

It has been known since the time of
Isaac Newton, however, that the human
eye has a large chromatic aberration. Its
lens system seems to be entirely uncor-
rected for this defect. Indeed, living or-
ganisms are probably unable to manu-
facture two transparent materials of such
widely different refraction and disper-
sion as the crown and flint glasses from
which color-corrected lenses are con-
structed.

The large color error of the human eye
could make serious difficulties for image
vision. Actually the error is moderate
between the red end of the spectrum and
the blue-green, but it increases rapidly
at shorter wavelengths: the blue, violet
and ultraviolet. These latter parts of the
spectrum present the most serious prob-
lem. It is a problem for both the eye and
the camera, but one for which the eye
must find a special solution.

The first device that opposes the color
error of the human eye is the yellow lens.
The human lens is not only a lens but a
color filter. It passes what we ordinarily
consider to be the visible spectrum, but
sharply cuts off the far edge of the violet,
in the region of wavelength 400 milli-
microns. It is this action of the lens, and
not any intrinsic lack of sensitivity of
the rods and cones, that keeps us from
seeing in the near ultraviolet. Indeed,
persons who have lost their lenses in the
operation for cataract and have had
them replaced by clear glass lenses, have
excellent vision in the ultraviolet. They
are able to read an optician's chart from
top to bottom in ultraviolet light which
leaves ordinary people in complete
darkness.

The lens therefore solves the problem
of the near ultraviolet, the region of the

Eye and Camera

spectrum in which the color error is
greatest, simply by eliminating the re-
gion from human vision. This boon is
distributed over one's lifetime, for the
lens becomes a deeper yellow and makes
more of the ordinary violet and blue in-
visible as one grows older. I have heard
it said that for this reason aging artists
tend to use less blue and violet in their
paintings.

The lens filters out the ultraviolet for
the eye as a whole. The remaining de-
vices which counteract chromatic aber-
ration are concentrated upon vision in
bright light, upon cone vision. This is
good economy, for the rods provide such
a coarse-grained receptive surface that
they would be unable in any case to
evaluate a sharp image on the retina.

As one goes from dim to bright light,
from rod to cone vision, the sensitivity
of the eye shifts toward the red end of
the spectrum. This phenomenon was de-
scribed in 1825 by the Czech physiolo-
gist Johannes Purkinje. He had noticed
that with the first light of dawn blue ob-
jects tend to look relatively bright com-
pared with red, but that they come to
look relatively dim as the morning ad-
vances. The basis of this change is a
large difference in spectral sensitivity
between rods and cones. Rods have their
maximal sensitivity in the blue-green at
about 500 millimicrons; the entire spec-
tral sensitivity of the cones is transposed
toward the red, the maximum lying in
the yellow-green at about 562 millimi-
crons. The point of this difference for
our present argument is that as one goes
from dim light, in which pattern vision
is poor in any case, to bright light, in
which it becomes acute, the sensitivity
of the eye moves away from the region
of the spectrum in which the chromatic
aberration is large toward the part of the
spectrum in which it is least.

The color correction of the eye is com-
pleted by a third dispensation. Toward
the center of the human retina there is a
small, shallow depression called the fo-
vea, which contains only cones. While
the retina as a whole sweeps through a
visual angle of some 240 degrees, the
fovea subtends an angle of only about
1.7 degrees. The fovea is considerably
smaller than the head of a pin, yet with
this tiny patch of retina the eye accom-
plishes all its most detailed vision.

The fovea also includes the fixation
point of the eye. To look directly at
something is to turn one's eye so that
its image falls upon the fovea. Beyond
the boundary of the fovea rods appear,
and they become more and more nu-
merous as the distance from the fovea
increases. The apparatus for vision in
bright light is thus concentrated toward
the center of the retina, that for dim
light toward its periphery. In very dim
light, too dim to excite the cones, the
fovea is blind. One can see objects then
only by looking at them slightly askance

to catch their images on areas rich in
rods.

In man, apes and monkeys, alone of
all known mammals, the fovea and the
region of retina just around it is colored
yellow. This area is called the yellow
patch, or macula lutca. Its pigmentation
lies as a yellow screen over the light re-
ceptors of the central retina, subtending
a visual angle some five to 10 degrees in
diameter.

Several years ago in our laboratory at
Harvard University we measured the
color transmission of this pigment in the
living human eye by comparing the spec-
tral sensitivities of cones in the yellow
patch with those in a colorless peripheral
area. The yellow pigment was also ex-
tracted from a small number of human
maculae, and was found to be xaniho-
phyll, a carotenoid pigment that occurs
also in all green leaves. This pigment in
the yellow patch takes up the absorption
of light in the violet and blue regions of
the spectrum just where absorption by
the lens falls to very low values. In this
way the yellow patch removes for the
central retina the remaining regions of
the spectrum for which the color error is
high.

So the human eye, unable to correct
its color error otherwise, throws away
those portions of the spectrum that
would make the most trouble. The yel-
low lens removes the near ultraviolet for
the eye as a whole, the macular pigment
eliminates most of the violet and blue
for the central retina, and the shift from
rods to cones displaces vision in bright
light bodily toward the red. By these
three devices the apparatus of most
acute vision avoids the entire range of
the spectrum in which the chromatic
aberration is large.

Photography with Living Eyes

In 1876 Franz Boll of the University
of Rome discovered in the rods of the
frog retina a brilliant red pigment. This
bleached in the light and was resynthe-
sized in the dark, and so fulfilled the
elementary requirements of a visual pig-
ment. He called this substance visual
red; later it was renamed visual purple
or rhodopsin. This pigment marks the
point of attack by light on the rods: the
absorption of light by rhodopsin initiates
the train of reactions that end in- rod
vision.

Boll had scarcely announced his dis-
covery when Willy Kiihne, professor of
physiology at Heidelberg, took up the
.study of rhodopsin, and in one extraor-
dinary year learned almost everything
about it that was known until recently.
In his first paper on retinal chemistry
Kiihne said: "Bound together with the
pigment epithelium, the retina behaves
not merely like a photographic plate, but
like an entire photographic workshop, in
which the workman continually renews

PINHOLE-CAMERA EYE is found in Nautilus, the spiral-shelled mollusk
which is related to the octopus and the squid. This eye has the advantage
of being in focus at all distances from the object that is viewed. It has the
serious disadvantage, however, of admitting very little light to the retina.

COMPOUND EYE is found in insects. Each element contributes only a small
patch of light or shade to make up the whole mosaic image. This double
compound eye is found in the mayfly Chloeon. The segment at the top
provides detailed vision; the segment at the right, coarse, wide-angled vision.

SCANNING EYE is found in the arthropod Copilia. It possesses a large lens
I right I but only one receptor element (left). Attached to the receptor
are the optic nerve and a strand of muscle. The latter is reported to move
the receptor back and forth so that it scans the image formed by the len9.

Eye and Camera

SPHERICAL ABERRATION occurs when light is refracted hy a lens with
spherical surfaces. The light which passes through the edge of the lens is
brought to a shorter focus than that which passes through the center. The
result of this is that the image of a point is not a point but a "blur circle."

CHROMATIC ABERRATION occurs when light of various colors is re-
fracted by a lens made of one material. The light of shorter wavelength is
refracted more than that of longer wavelength, i.e., violet is brought to a
shorter focus than red. The image of a white point is a colored blur circle.

350 400 450 500 550 600 650

B G Y O R

WAVELENGTH

700

CHROMATIC ABERRATION of the human eye is corrected by various
stratagems which withdraw the cones from the region of maximum aberra-
tion, i.e., the shorter wavelengths. The horizontal coordinate of this diagram
is wavelength in millimicrons; the colors are indicated by initial letters.

the plate by laying on new light-sensitive
material, while simultaneously erasing
the old image."

Kiihne saw at once that with this pig-
ment which was bleached by hght it
might be possible to take a picture with
the living eye. He set about devising
methods for carrying out such a process,
and succeeded after many discouraging
failures. He called the process optogra-
phy and its products optograms.

One of Kiihne's early optograms was
made as follows. An albino rabbit was
fastened with its head facing a barred
window. From this position the rabbit
could see only a gray and clouded sky.
The animal's head was covered for sev-
eral minutes with a cloth to adapt its eyes
to the dark, that is to let rhodopsin ac-
cumulate in its rods. Then the animal
was exposed for three minutes to the
light. It was immediately decapitated,
the eye removed and cut open along the
equator, and the rear half of the eyeball
containing the retina laid in a solution
of alum for fixation. The next day Kiihne
saw, printed upon the retina in bleached
and unaltered rhodopsin, a picture of the
window with the clear pattern of its bars.

I remember reading as a boy a detec-
tive story in which at one point the de-
tective enters a dimly lighted room, on
the floor of which a corpse is lying.
Working carefully in the semidarkness,
the detective raises one eyelid of the
victim and snaps a picture of the open
eye. Upon developing this in his dark-
room he finds that he has an optogram
of the last scene viewed by the victim,
including of course an excellent likeness
of the murderer. So far as I know
Kiihne's optograms mark the closest ap-
proach to fulfilling this legend.

The legend itself has nonetheless
flourished for more than 60 years, and
all of my readers have probably seen or
heard some version of it. It began with
Kiihne's first intimation that the eye re-
sembles a photographic workshop, even
before he had succeeded in producing
his first primitive optogram, and it
spread rapidly over the entire world. In
the paper that announces his first suc-
cess in optography, Kiihne refers to thi:
story with some bitterness. He says: "1
disregard all the journalistic potentiali-
ties of this subject, and willingly sur-
render it in advance to all the claims of
fancy-free coroners on both sides of the
ocean, for it certainly is not pleasant to
deal with a serious problem in such com-
pany. Much that I could say about this
had better be suppressed, and turned
rather to the hope that no one will expect
from me any corroboration of announce-
ments that have not been authorized
with my name."

Despite these admirable sentiments
we find Kiihne shortly afterward en-
gaged in a curious adventure. In the
nearby town of Bruchsal on November
16, 1880, a young man was beheaded by

guillotine. Kiihne had made arrange-
ments to receive the corpse. He had
prepared a dimly lighted room screened
with red and yellow glass to keep any
rhodopsin left in the eyes from bleach-
ing further. Ten minutes after the knife
had fallen he obtained the whole retina
from the left eye, and had the satisfac-
tion of seeing and showing to several
colleagues a sharply demarcated opto-
gram printed upon its surface. Kiihne's
drawing of it is reproduced at the bot-
tom of the next page. To my knowledge
it is the only human optogram on record.
Kiihne went to great pains to deter-
mine what this optogram represented.
He says: "A search for the object which
served as source for this optogram re-
mained fruitless, in spite of a thorough
inventory of all the surroundings and
reports from many witnesses. The delin-
quent had spent the night awake by the
light of a tallow candle; he had slept

human eye as did the original subject of
the picture.

How the human eye resolves colors is
not known. Normal human color vision
seems to be compounded of three kinds
of responses; we therefore speak of it as
trichromatic or three-color vision. The
three kinds of response call for at least
three kinds of cone differing from one
another in their sensitivity to the various
regions of the spectrum. We can only
guess at what regulates these differences.
The simplest assumption is that the hu-
man cones contain three different light-
sensitive pigments, but this is still a
matter of surmise.

There exist retinas, however, in which
one can approach the problem of color
vision more directly. The eyes of certain
turtles and of certain birds such as chick-
ens and pigeons contain a great predomi-
nance of cones. Since cones are the or-
gans of vision in bright light as well as

RETINAL PHOTOGRAPH, or an optogram, was drawn in 1878 by the
German investigator Willy Kiihne. He had exposed the eye of a living rabbit
to a barred window, killed the rabbit, removed its retina and fixed it in alum.

from four to five o'clock in the morn-
ing; and had read and written, first by
candlelight until dawn, then by feeble
daylight until eight o'clock. When he
emerged in the open, the sun came out
for an instant, according to a reliable
observer, and the sky became somewhat
brighter during the seven minutes prior
to the bandaging of his eyes and his exe-
cution, which followed immediately.
The delinquent, however, raised his eyes
only rarely."

Color

One of the triumphs of modern pho-
tography is its success in recording color.
For this it is necessary not only to graft
some system of color differentiation and
rendition upon the photographic proc-
ess; the finished product must then ful-
fill the very exacting requirement that it
excite the same sensations of color in the

of color vision, these animals necessarily
function only at high light intensities.
They are permanently night-blind, due
to a poverty or complete absence of rods.
It is for this reason that chickens must
roost at sundown.

In the cones of these animals we find
a system of brilliantly colored oil glob-
ules, one in each cone. The globule is
situated at the joint between the inner
and outer segments of the cone, so that
light must pass through it just before en-
tering the light-sensitive element. The
globules therefore lie in the cones in the
position of little individual color filters.

One has only to remove the retina
from a chicken or a turtle and spread it
on the stage of a microscope to tee that
the globules are of three colors: red,
orange and greenish yellow. It was sug-
gested many years ago that they provide
the basis of color differentiation in the
animals that possess them.

In a paper published in 1907 the Ger-
man ophthalmologist Siegfried Garten
remarked that he was led by such retinal
color filters to invent a system of color
photography based upon the same prin-
ciple. This might have been the first in-
stance in which an eye had directly in-
spired a development in photography.
Unfortunately, however, in 1906 the
French chemist Louis Lumiere, appar-
ently without benefit of chicken retinas,
had brought out his autochrome process
for color photography based upon ex-
actly this principle.

To make his autochrome plates Lu-
miere used suspensions of starch grains
from rice, which he dyed red, green and
blue. These were mixed in roughly equal
proportions, and the mixture was strewn
over the surface of an ordinary photo-
graphic plate. The granules were then
squashed flat and the interstices were
filled with particles of carbon. Each dyed
granule served as a color filter for the
patch of silver-bromide emulsion that lay
just under it.

Just as the autochrome plate can ac-
complish color photography with a single
light-sensitive substance, so the cones of
the chicken retina should require no
more than one light-sensitive pigment.
We extracted such a pigment from the
chicken retina in 1937. It is violet in
color, and has therefore been named
iodopsin from ion, the Greek word for
violet. All three pigments of the colored
oil globules have also been isolated and
crystallized. Like the pigment of the hu-
man macula, they are all carotenoids: a
greenish-yellow carotene; the golden
mixture of xanthophylls found in chicken
egg yolk; and red astaxanthin, the pig-
ment of the boiled lobster.

Controversy thrives on ignorance, and
we have had many years of disputation
regarding the number of kinds of cone
concerned in human color vision. Manv
investigators prefer three, some four, and
at least one of my English colleagues
seven. I myself incline toward three. It
is a good number, and sufficient unto the
day.

The appearance of three colors of oil
globule in the cones of birds and turtles
might be thought to provide strong sup-
port for trichromatic theories of color
vision. The trouble is that these retinas
do in fact contain a fourth class of glob-
ule which is colorless. Colorless globules
have all the effect of a fourth color; there
is no doubt that if we include them, bird
and turtle retinas possess the basis for
four-color vision.

Latent Images

Recent experiments have exposed a
wholly unexpected parallel between vi-
sion and photography. Many years ago
Kiihne showed that rhodopsin can be ex-
tracted from the retinal rods into clear
water solution. When such solutions are

Eye and Camera

/^~~

Hg^

Mtt

Wv^

?rr ■•"

'Hi

i1'

'n i
i;ui

!(■•'

FROG OPTOGRAM showing a
haired pattern was made hy the Gei-
nian ophthalmologist Siegfried Gar-
ten. The retina is mounted on a rod.

HUMAN OPTOGRAM was drawn
hy Kiiluie after he had removed the
retina of a beheaded criminal. Kit line
could not determine what it showed.

exposed to light, the rhodopsin bleaches
just as it does in the retina.

It has been known for some time that
the bleaching of rhodopsin in solution is
not entirely accomplished by light. It is
started bv light, but then goes on in
the dark for as long as an hour at room
temperature. Bleaching is therefore a
composite process. It is ushered in by a
light reaction that converts rhodopsin to
a highly unstable product; this then
decomposes by ordinary chemical reac-
tions—"dark" reactions in the sense that
they do not require light.

Since great interest attaches to the
initial unstable product of the light re-
action, many attempts were made in our
laboratory and at other laboratories to
seize upon this substance and learn its
properties. It has such a fleeting exist-
ence, however, that for some time noth-
ing satisfactory was achieved.

In 1941, however, two English work-
ers, E. E. Broda and C. F. Goodeve, suc-
ceeded in isolating the light reaction by
irradiating rhodopsin solutions at about
—73 degrees Celsius, roughly the tem-
perature of dry ice. In such extreme cold,
light reactions are unhindered, but or-
dinary dark processes cannot occur.
Broda and Goodeve found that an ex-
haustive exposure of rhodopsin to light
under these conditions produced only a
very small change in its color, so small
that though it could be measured one
might not have been certain merely by
looking at these solutions that any
change had occurred at all. Yet the light
reaction had been completed, and when
such solutions were allowed to warm up
to room temperature they bleached in
the dark. We have recently repeated
such experiments in our laboratory. With
some differences which need not be dis-
cussed, the results were qualitatively as
the English workers had described them.

These observations led us to re-exam-
ine certain early experiments of Kiihne's.
Kiihne had found that if the retina of a
frog or rabbit was thoroughly dried over
sulfuric acid, it could be exposed even to
brilliant sunlight for long periods with-
out bleaching. Kiihne concluded that dry
rhodopsin is not affected by light, and
this has been the common understanding
of workers in the field of vision ever
since.

It occurred to us, however, that dry
rhodopsin, like extremely cold rhodop-
sin. might undergo the light reaction,
though with such small change in color
as to have escaped notice. To test this
possibility we prepared films of rhodop-
sin in gelatin, which could be dried
thoroughly and were of a quality that
permitted making accurate measure-
ments of their color transmission through-
out the spectrum.

We found that when dry gelatin films

of rhodopsin are exposed to light, the
same change occurs as in very cold rho-
dopsin. The color is altered, but so
slightly as easily to escape visual obser-
vation. In any case the change cannot
be described as bleaching; if anything
the color is a little intensified. Yet the
light reaction is complete; if such ex-
posed films are merely wetted with wa-
ter, they bleach in the dark.

We have therefore two procedures-
cooling to very low temperatures and
removal of water— that clearly separate
the light from the dark reactions in the
bleaching of rhodopsin. Which of these
reactions is responsible for stimulating
rod vision? One cannot yet be certain,
yet the response of the rods to light oc-
curs so rapidly that only the light reac-
tion seems fast enough to account for it.

What has been said, however, has a
further consequence that brings it into
direct relation with photography. Every-
one knows that the photographic process
also is divided into light and dark com-
ponents. The result of exposing a film
to light is usually invisible, a so-called
"latent image." It is what later occurs in
the darkroom, the dark reaction of de-
velopment, that brings out the picture.

This now appears to be exactly what
happens in vision. Here as in photog-
raphy light produces an almost invisible
result, a latent image, and this indeed is
probably the process upon which retinal
excitation depends. The visible loss of
rhodopsin's color, its bleaching, is the re-
sult of subsequent dark reactions, of
"development."

One can scarcely have notions like
this without wanting to make a picture
with a rhodopsin film; and we have been
tempted into making one very crude
rhodopsin photograph. Its subject is not
exciting— only a row of black and white
stripes— but we show it at the right for
what interest it may have as the first
such photograph. What is important is
that it was made in typically photo-
graphic stages. The dry rhodopsin film
was first exposed to light, producing a
latent image. It was then developed in
the dark by wetting. It then had to be
fixed; and, though better ways are
known, we fixed this photograph simply
by redrying it. Since irradiated rhodop-
sin bleaches rather than blackens on de-
velopment, the immediate result is a
positive.

Photography with rhodopsin is onlv
in its first crude stages, perhaps at the
level that photography with silver
bromide reached almost a century ago.
I doubt that it has a future as a practi-
cal process. For us its primary interest
is to pose certain problems in visual
chemistry in a provocative form. It does,
however, also add another chapter to the
mingled histories of eye and camera.

RHODOPSIN PHOTOGRAPH was made by the author
and his associates Paul K. Brown and Oscar Starobin.
Rhodopsin, the light-sensitive red pigment of rod vision,
had been extracted from cattle retinas, mixed with

gelatin and spread on celluloid. This was then dried and
exposed to a pattern made up of black and white stripes.
When the film was wetted in the dark with hydroxyhv
mine, the rhodopsin bleached in the same pattern.

A device that operates on the principles of optics and
molecular physics— and that has an astonishing range
of applications.

The Laser — What it is and Does

J. M. Carroll

A chapter from a popular book, 1964.
Introduction

In i960, electronics scientists and engineers began to see
things in a different light.

It was a rich ruby light: not "kindled in the vine," as
the Persian poet Omar Khayyam said, but emitted by the
atoms of a synthetic gem stone.

The light came from the laser, a new device with wide
potential application in science, medicine, industry, and
national defense.

what's in a name?

The word laser is an acronym, or a word made up of the
first letters of several other words. Laser stands for Light
Amplification by Stimulated Emission of Radiation. It was
coined by analogy with another acronym: maser. Maser
stands for Microwave Amplification by Stimulated Emis-
sion of Radiation.

The maser works on the same basic principle as the laser
but, of course, emits microwave energy rather than light.
Masers are used as input amplifiers ( preamplifiers ) of radio
telescopes and space-tracking receivers that magnify fee-
ble signals gleaned from outer space.

No one is completely satisfied with the name "laser"
because lasers do not really amplify light in a strict sense;

instead they generate light with particular characteristics
that engineers and scientists find useful. In electronics
terminology a device that generates radiation is called
an oscillator, not an amplifier.

Furthermore, most lasers do not emit visible light at all
but rather infrared, or invisible, light. It is conceivable
that devices working on the same principle as the laser and
maser may someday emit ultraviolet or so-called black
light, X rays, or even gamma rays.

Scientists who moved from maser research into laser
research insist on calling the laser an optical maser. But
it can be argued that it is ridiculous to talk of "optical
microwave amplification by stimulated emission of radia-
tion" since "optical" means one thing and "microwave"
quite another.

Proponents of the term "optical maser" counter by say-
ing that "maser" doesn't stand for microwave amplification
by stimulated emission of radiation at all, but rather for
molecular amplification by stimulated emission of radia-
tion.

To the comment that masers do not amplify molecules
comes the answer that they depend for their action on the
behavior of the molecules of the substance.

Well, some masers and lasers do depend on molecular
effects. But more depend on the behavior of submolecular
particles: atoms, ions (atoms that have lost one or more
electrons), perhaps even electrons themselves.

Recently the term quantum device has been applied
to both masers and lasers, and this seems to make sense,
since the action of both the laser and the maser can be
explained by the science of quantum mechanics. In fact,
some scientists and engineers interested in lasers and
masers are attempting to form within the Institute of Elec-
trical and Electronics Engineers a professional group on

TOO

The Laser — What it is and Does

quantum electronics. And though for the present the term
"laser" seems deeply ingrained in the scientific vocabulary,
let's remember that the science we call electronics was
once known as thermionic engineering!

what's special about a laser?

The important thing about laser light is that it is co-
herent. The individual light rays are all of the same wave-
length or color, and are all in step. A laser beam differs
from a beam of ordinary light in both character and ef-
fectiveness in the same way that a platoon of well-drilled
soldiers differs from a ragtag, disorganized mob.

When light waves from a laser march in step, they can
perform amazing feats. The reason is that their energy is
not dissipated as the beam spreads out. This makes for an
intense concentration of energy at a very sharply defined
point. It also greatly extends the range of a light source.

Three of the many spectacular achievements of the laser
demonstrate how the properties of coherent light can be
put to work:

• Because its light does not spread out even at great
distances, a laser can illuminate the surface of the moon
with a two-mile- wide circle of light.

Laser beam on moon (black dot)
compared with area of radar
beam (shaded area) (Raytheon)

101

• Because its energy is concentrated at a fine point, it
can send a short, searing pinpoint of light into the human
eyeball to weld a detached retina back into place and re-
store sight.

• And since its radiation is so intense, it can burn holes
in a steel plate Ys inch thick at a distance of several feet.

These abilities have given rise to a whole range of ap-
plications. Laser range finders are used both by artillery
officers to sight their guns and by surveyors. In outer space,
where there is no atmosphere to absorb the light, the
laser will supplement conventional radar and radio for
space-vehicle navigation and communications.

Lasers can cut metal and other materials. But it is highly
unlikely that a laser will ever replace an engine lathe or
an oxyacetelene torch in most machining and metal-cut-
ting operations. Lasers are being used in the precision
machining of metals and in machining brittle materials
such as diamonds.

A laser can weld metals as well as retinas. But here, too,
its use is for precise work, as in making microelectronic
circuits. Nevertheless, large lasers mounted atop high
mountain peaks are being developed to provide a defense
against intercontinental-ballistic-missile warheads.

To the scientist, the laser is already a valuable tool in
absorption spectroscopy or the identification of compounds
by the particular wavelengths of light that they absorb.

Radiant Energy

How can a beam of light burn a hole in a steel plate?
It can do so because light is a form of radiant energy, and a
laser concentrates much radiant energy in a very tiny
spot. Radiant energy exists in many forms besides visible
light. It exists as radio waves, ultraviolet and infrared
light, X rays, gamma rays, and even cosmic rays.

102

The Laser — What it is and Does

WAVELENGTH AND FREQUENCY

It is sometimes convenient to think of radiant energy
as waves, that is, electromagnetic waves. Then the differ-
ent forms of radiant energy can be classified by their
wavelengths and arranged according to wavelength in a
spectrum. We have all seen the waves made by a pebble
thrown into a quiet pond. They are a series of alternating
crests and troughs. The wavelength is defined as the dis-
tance between two adjacent crests or two adjacent troughs.

Now, when a wave goes from crest to trough and back
to crest again, it is said to have gone through one cycle,
or alternation. The number of cycles that a wave executes
in one second is known as the frequency of the wave.

Light waves and all other electromagnetic waves travel
at the same speed, which is 186,000 miles, or 300,000,000
meters, a second. All scientific measurements are made in
metric system. In the metric system the basic unit of length
is the meter— a little over three feet.

RADIO SPECTRUM

The alternating current supplied by the power com-
pany is an electromagnetic wave that executes 60 cycles a
second; thus, in 1/60 of a second, or the time of one alter-
nation, the wave will travel 300,000,000/60, or 5,000,000
meters— roughly the distance from New York to Los An-
geles. The electromagnetic spectrum arranges the differ-
ent kinds of electromagnetic energy according to decreas-
ing wavelength.

Everyone is familiar with the red, orange, yellow, green,
blue, and violet spectrum of the rainbow after a spring
shower. The same separation of white light into its color
components occurs when we pass light through a glass
prism. A spectrum arranges the frequency components of
white light according to decreasing wavelengths. Similar

103

ELECTROMAGNETIC SPECTRUM

X-RAYS VISIBLE INFRARED

Jil^^

MICROWAVES RADIO

RUBY LASER

( ) lipS^

RUBY MASER

Electromagnetic spectrum from radio frequencies to X rays (Hughes)

spectra exist in the infrared and ultraviolet regions, but we
can't see them. They can, however, be photographed by
using special film. Radio waves also form part of the
electromagnetic spectrum.

A radio broadcasting station with a frequency of 1,000
kilocycles per second (or cycles per second times 1,000)
has a wave 300 meters long. A radar set used for naviga-
tion at sea has a wavelength of about 10 centimeters (one
centimeter equals 1/100 meter), or approximately 4 inches.

VISIBLE SPECTRUM AND INFRARED

Radiant energy is invisible to the human eye only until
we get to a wavelength of 0.00000075 meter, which we
see as red light. Since the meter is an ungainly unit for
measuring wavelengths of light, physicists use what is
called the angstrom unit, abbreviated A. One angstrom
equals 1/10,000,000,000 meter. Therefore we can say the
visible spectrum extends from 7,500 A ( deep red ) to 4,000
A, or blue. In between are regions of orange (about 6,000
A), yellow (about 5,900 A), and green (about 5,300
A).

The visible spectrum is bounded by longer waves of

104

The Laser — What it is and Does

infrared that we sense as heat. For example, a jet engine
exhaust has a wavelength of 40,000 A, while the heat of
the human body has a wavelength of about 99,000 A.

FROM SUN TANS TO COSMIC RAYS

The short wavelength, or blue end of the spectrum, is
bounded by the ultraviolet region. Sun-tanning ultraviolet
rays have a wavelength of about 3,000 A. Still shorter
are X rays ( 150 to 10 A) and gamma rays (1.4 to 0.1 A).
Gamma rays are associated with nuclear reactions, and
account for some of the deadly effects of atomic and hy-
drogen bombs and of radioactive waste materials. At the
high end of the spectrum are cosmic rays (0.01 to 0.001
A), those weird visitors from outer space whose effects
(they can cause biological mutations) are awesome in-
deed but about which very little is understood.

Scientists have known for a long time that the energy
of radiation is proportional to its frequency. We cannot
sense the presence of radio waves even though we stand
close by the antenna of a powerful broadcasting station.
Yet if we put a hand in front of a radar antenna, we may
feel a slight sensation of warmth. The energy of ultraviolet
waves will become painfully evident to some who sun
bathe not wisely but too well. The penetrating power of
X rays and gamma rays makes them useful for making
shadowgraphs of the human skeleton and internal organs
for medical diagnosis and for inspecting manufactured
parts for hidden flaws. Indeed, hard, or short, X rays and
gamma rays are used to destroy malignant tissue in the
treatment of cancer and related diseases.

The energy of each wavelet of radiation is called a
"quantum." It is measured by the frequency of the radia-
tion multiplied by Planck's constant (this is equal to
6.625 X 10~27 erg seconds— 26 zeros in front of the first

105

6). The intensity of a source of radiation depends upon
the number of quanta emitted from it that pass a desig-
nated boundary at a given time.

FLUORESCENCE

The action of the laser is allied to another, more familiar,
phenomenon, that of fluorescence. Fluorescence is said
to occur when radiant energy hits the atoms or molecules
of some particular material and in turn causes that sub-
stance to emit further radiant energy. Fluorescence has
this important property: the emitted radiation is always at
a lower frequency (longer wavelength) than the initial
radiation.

Here's how scientists explain fluorescence: Every atom
and molecule has certain energy states that it can occupy.
When the atoms absorb energy, they move to higher en-
ergy states. Conversely, when they return to lower energy
states, they give up energy, or emit radiation.

Imagine an atom to be a coil spring. When there is no
compression on the spring, it is in its ground, or rest, state.
When you compress the spring, you add potential energy
to the system. When you release the spring, it bounces
back and vibrates, giving up what is called its kinetic
energy.

In the picture tube of your television set, electrons
bombard a phosphor screen on the back of the faceplate.
The kinetic energy, or energy of motion of the rapidly
moving electrons, excites the atoms of the phosphor. As
these atoms relax, the faceplate of the picture tube glows,
and you see the television program because of fluorescence.

When a radiologist examines you with a fluoroscope, X
rays penetrate your body and excite the atoms of a phos-
phor screen. As the atoms of the phosphor coating relax,
the fluoroscope screen glows green, producing a shadow-
graph of the part of the body being visualized.

106

The Laser — What it is and Does

In a neon sign, an alternating current creates an elec-
tromagnetic field that agitates the molecules of neon gas
filling the tube. Because collisions of rapidly moving neon
molecules raise these molecules to higher energy levels,
they relax, emitting the orange-red glow characteristic of
a neon sign.

Of course, the common fluorescent lamp works on the
same principle of energy exchange. The inner walls of the
lamp tube are coated with beryllium oxide. Inside the
tube, there is an intense arc discharge between electrodes
at either end of the lamp tube. This arc discharge is rich
in ultraviolet light that energizes the phosphor molecules.
As these molecules relax, the lamp emits a blue-white light
similar to natural daylight.

We now have seen several examples of quantum energy
exchanges, but no one ever burned a hole in a steel plate
or illuminated the moon with a neon sign or with a fluores-
cent lamp. What, then, does the laser have that its less
powerful cousins lack?

Frequency Coherence

The answer is: the laser's coherence. In all the previous
examples of the phenomenon of fluorescence, the emitted
radiation had a broad spectrum. Because it was emitted
in random fashion, some wavelets added together while
others opposed each other.

Frequency coherence makes a big difference. It means
that all the emitted energy has the same wavelength. When
this happens, you can have a useful output indeed. Take
the babble of voices at a cocktail party as an example
of incoherent sound. The sound doesn't carry very far and
it is not especially meaningful. But if you were to concen-
trate all that sound energy into the blast of a police whistle
or siren, you could awaken half a city.

107

(WV

time

Frequency coherent radiation, top, and frequency incoherent radia-
tion, bottom (Raytheon)

Engineers learned many years ago that they could com-
municate more efficiently and more meaningfully when
they concentrated all the output of a radio transmitter at
a single frequency. But frequency coherence has other ad-
vantages besides efficiency. A beam of coherent light can
be modulated much as a radio signal can be. Modulation
is a process by which intelligence such as music or speech
is impressed upon a so-called carrier signal such as a radio
wave.

An incoherent light beam can be modulated in only the
most elementary manner— such as by switching it on and
off, as with the visual blinker lights used to send Morse
code between ships. But the frequency-coherent laser
beam can be modulated by such complex signals as speech,
music, or even a television picture.

Frequency-coherent light also lends itself to frequency
multiplication, the technique whereby a closely controlled
but relatively low radio frequency can be raised to a
higher output frequency. The output of a rubv laser at

108

The Laser — What it is and Does

6,943 A has been doubled to 3,472 A. The input was deep
red and the output blue-violet, almost ultraviolet. The
reason the wavelengths of laser light are given so pre-
cisely is that the emission of laser light depends on the
shifting of electrons between atomic orbits, and each
wavelength is characteristic of one particular orbital shift,
or so-called quantum jump.

Laser beams can also be mixed. For example, a ruby
laser operates in two slightly different modes. These modes
can be mixed in a microwave phototube. The frequency
difference between the modes yields a microwave signal
that can be handled by conventional radio or television
techniques. This property has permitted some engineers
to modulate laser beams with television pictures and to
recover the television signal after transmission for several
feet.

Scientists find the frequency coherence of the laser
especially gratifying. Before the discovery of the laser,
only signals in the lower, or radio, end of the spectrum
could be produced coherently. Radio techniques were
limited to producing signals whose wavelength was on the
order of a millimeter or so.

If monochromatic (or single-frequency) signals were
desired anywhere else in the spectrum, they had to be
produced by placing an appropriate filter in front of an
incoherent source. This method was unsatisfactory for
two reasons: it was very inefficient, since the source had to
produce many times the energy that could be usefully
employed; and, second, since no filtered output is ever
truly coherent, modulation, frequency multiplication, and
mixing were always unsatisfactory. But now a whole new
section of the spectrum, ranging from the "near" (to
visible light, that is) infrared to near ultraviolet, is open
to investigation, and there is evidence that the existing

109

gaps at the high and low ends of this laser operating range
can be filled by using related techniques.

SPATIAL COHERENCE

Frequency coherence is only part of the picture. The
output of a laser is also spatially coherent. This means that
all wavelets start in step with each other. Spatial coher-
ence also adds to the efficiency of a device. The difference

Spatially coherent radiation, top, and spatially incoherent radiation,
bottom (Raytheon)

between spatial incoherence and spatial coherence is like
the difference between a disorganized group of castaways
of a raft each paddling in his own way and the smooth,
efficient performance of a well-trained crew rowing an
eight-oared racing shell.

Ruby Lasers

The ruby laser was the first device to generate coherent
light successfully. The rubies used in lasers are synthetic
gem stones. They are made by fusing aluminum and

110

The Laser — What it is and Does

chromium oxides to produce large crystals. The amount
of chromium in a synthetic ruby is small— about five hun-
dredths of 1 percent. But it is that chromium upon which
laser action depends.

The ruby crystal is cylindrical, about )i inch in diameter
and i/2 to 2 inches long. It appears pink to the eye. That
is because there are two absorption bands in a ruby— one
at 5,600 A and the other at 4,100 A— which means that
when you hold a ruby up to the light, yellow-green light
and blue light are absorbed. This subtraction of yellow,
green, and blue from white light (which is a mixture of
all colors) gives the remaining light transmitted to the
eye its distinctive pink hue. Actually, there is also some
natural fluorescence in a ruby, but it is all but imper-
ceptible to the eye.

A laser crystal must be polished to optical flatness on
both ends. Both ends are also silvered, one with a heavy
coat while the other, or output end, is lightly silvered
with a coat that permits it to reflect only about 92 percent
of light incident on it.

Exploded view of ruby laser showing ruby, mirrors, and helical
flashtube (Hughes)

SILVER
MIRROR

RED LIGHT WAVES TRAPPED BETWEEN MIRRORS

111

The ruby rod is now placed within a helical-shaped
xenon flashtube, the kind of tube widely used in elec-
tronic flash attachments for cameras. The process of ir-
radiating the ruby rod with a xenon flashtube is called
optical pumping. The output of the flash lamp is rich
in the yellow-green region.

The energy level of an atom ( an ion is just an atom that
has lost one or more electrons) depends upon the condi-
tion of its electrons. Now, an atom is like a miniature solar
system. It has a positive nucleus at its center in place of
the sun, and a specific number of planet-like electrons.
These electrons revolve around the nucleus and spin on
their own axes. Unlike the planets of the solar system,
however, each electron can occupy not just one but sev-
eral orbits. Moreover, the electrons can revolve around the
nucleus with different azimuthal momenta (speed) and
even change their direction of spin. Each change in orbit,
momentum, or spin corresponds to a discrete energy
level.

For example, when energy is imparted to an atom, an
electron may move to an orbit more remote from the
nucleus. The atom is said to absorb energy and to have
been raised to a higher or more excited energy state or
level. If the electron then returns to its original orbit, the
atom gives up energy; it may now emit light of a certain
precise wavelength. The atom is said to relax to a lower
or less excited energy state or level. When light wavelets,
or photons, at 5,600 A from the flashtube irradiate the
ruby rod, they raise the energy of some of the chromium
ions dissolved in the ruby from ground state (1) to various
levels lying within the absorption band. Then the chromium
ions immediately begin to drop from these higher energy
levels. Some drop right back to the ground state— level (T)
—as they do in natural fluorescence. But others drop to

112

The Laser — What it is and Does

20 r

5 15

rO
O

? 10

uj 5

■- "A

i"M

_L_L.

.1 I I I I I I I I I 1 1

6,925 R2

"I
WAVELENGTH IN A

6,950

6,925 R2

Hi i ■ i i ■ I

WAVELENGTH

IN A

6,950

(B)

Energy level transitions in a ruby laser as described in text (A); low-
level pumping (B) and high-level pumping (C) showing how latter
mode concentrates energy at one wavelength (Electronics)

an intermediate or so-called metastable state ©. If left
alone, the latter chromium ions would continue their drop
to level ©, and the result would just be natural fluores-
cence. But these ions dally for a short but measurable
time in level ©, and this is what makes laser action
possible.

While the chromium ions are trying to get back to level
©, the flashtube keeps on irradiating more chromium ions.

113

In fact, the two-step movement from state (T) to state @
and down to state (2) is much faster than the movement
from state (2) to state (7). Thus there develops a chromium-
ion traffic jam at energy level (2).

STIMULATED EMISSION

As the pile-up of chromium ions in level (2) continues,
another situation develops: soon there are more chromium
ions in level (2) than in level (1). This is called population
inversion, and is essential for laser action.

When you have inversion of the chromium ion popula-
tion, the laser resembles a spring that is wound up and
cocked. It needs a key to release it. This is what is meant
by stimulated emission of radiation: the stimulus is the
key that releases the cocked spring.

The key is a photon of light of exactly the wavelength
to be emitted (6,943 A). Emission begins when a random
chromium ion spontaneously falls from level (2) to level
(1) emitting a photon at 6,943 A. The photon strikes
neighboring metastable (level (2)) ions, causing them to
emit additional photons, and these in turn trigger other
metastable ions.

As the photons travel along the rod, some emerge from
the sides of the cylinder and are lost. Others hit the sil-
vered ends of the cylinder and are reflected back into
the rod. The reflections tend to favor those photons that
are traveling parallel to the long axis of the cylinder. And
so, there is now a stream of photons bouncing back and
forth between the silvered ends of the cylinder. The pho-

Two following pages: How a ruby laser works. Pumping light ir-
radiates ruby rod (A) raising some atoms to their metastable state
(B). One atom spontaneously emits coherent radiation (C) triggering
other nearby atoms (D). Photons emitted parallel to sides bounce
back and forth between mirrors triggering other atoms (E) until
light pulse (F) bursts from slightly transparent end (Electronics)

114

The Laser — What it is and Does

PUMPING LIGHT

V_J / /\ \ I / \

° I

nVV

SLIGHTLY-TRANSPARENT MIRROR
(A) RUBY ROD^

115

(D)

•

• o

•

A
O

? 5 ■

•

• o

(E)

•* — #-o ■* — *• # < — * o *—
•* — »■ o •* — *• • < — *■ o *-

— • —

-► o *-

A
— O —

— >
— ►

« — » o « * 0 *__* o «-

-* • *-

^ O —

— *•

(F)

400 800

TIME IN MSEC

1,200

116

The Laser — What it is and Does

tons become more numerous, and consequently the light
beam grows more intense as the photons already in the
stream trigger still more metastable chromium ions into
emitting their radiation.

Eventually the photon stream builds up sufficient in-
tensity so that it bursts from the partially silvered end of
the ruby as a single pulse of monochromatic ( single color
or frequency), spatially coherent light.

PARALLEL RAYS

The light beams coming out of the partially silvered
end of the ruby rod are almost exactly parallel, and it is
this factor that makes it possible for a laser beam to reach
the moon. Conventional light sources such as an in-
candescent lamp are point sources: their light rays are
emitted in a spherical pattern. Conventional rays can be
made parallel by use of focusing mirrors and lenses, but
such optical systems are far from efficient: the light beam
diverges, and consequently loses its intensity at great dis-
tances. But since the beams coming from a laser are
parallel to begin with, they remain essentially parallel
even at exceedingly great distances.

Liquid and Plastic Lasers

The ruby laser was the first laser, but today it is only
one member of the class of optically pumped lasers.
Furthermore, there are many varieties of ruby lasers. The
original ruby lasers worked at room temperature. Later
devices have been designed to work at cryogenic tempera-
tures, or temperatures close to absolute zero ( — 273 de-
grees centigrade). Cryogenic temperatures are usually
achieved by immersing the laser in liquid nitrogen or
liquid helium. Lasers cooled this way can put out a con-
tinuous beam of coherent light instead of a series of flashes.

117

Other optically pumped lasers include many different
crystalline materials, most of which are doped: made im-
pure by the infusion of small quantities of some other
material— either a rare-earth element, such as europium
or neodymium, or an actinide element— a class of heavy
metals that includes uranium. Some optically pumped
lasers have been made of doped glass ( glass to which im-
purities have been added), of liquid or gas in a quartz
cavity or of bundles of plastic fibers.

Gaseous Lasers

The gaseous laser represents a second general class of
laser. The working medium is a mixture of helium and
neon gas at very low pressure (o.i millimeter of mercurv

Helium-neon gas laser (Raytheon)

118

The Laser — What it is and Does

of neon and 1.0 millimeter of mercury of helium). The gas
is contained in a cylindrical Pyrex tube about one meter
long and 17 millimeters in diameter. At each end of the
tube is a quartz plate ground optically flat and with a
13-layer dielectric (or electrically nonconductive ) coat-
ing on its inner face: this coating produces the same effect
as the lightly silvered end of the ruby rod. The spacing of
the quartz-plate mirrors can be changed with precision
for optimum internal reflection, thanks to an arrangement
known as a Fabrtj-Perot interferometer. The laser beam is
emitted from both ends of the apparatus.

ELECTRICAL PUMPING

The gas laser is not optically pumped, nor is it pulsed
at the rate of three or four times a second as is the ruby
laser. Instead it operates in a continuous-wave mode, its
excitation supplied by a radio-frequency field— though in
some gas lasers, direct current has been used to produce
the required discharge. In a typical gas laser the source
is a 50-watt transmitter operating on a carrier frequency
of 29 megacycles per second. This frequency was selected
simply because it lies within a band provided by the Fed-
eral Communications Commission for industrial, scientific,
and medical use; another frequency would do equally well.
The transmitter is coupled to the gas tube by three metal
loops.

The radio-frequency generator produces an electrical
discharge through the gas that raises the helium gas atoms
to an excited state designated as the 23S state. This is a
metastable state that the helium atoms retain for a finite
period of time.

When the helium metastables collide with neon atoms
in the ground state, the helium atoms transfer their energy
to the neon atoms and drop immediately to the ground

119

25,

o
cr.

g '6

24.6

19.81

He'

23S

Ne +

Energy levels in a helium-neon laser (Electronics)

state. Simultaneously, the neon atoms are raised to the
so-called 2S state because the energy level of the 2s state
in neon is nearly equal to the energy level of the 23S
state in helium.

There are three excited states in neon that are involved
in this reaction: the 2S, 2p, and is states. We are primarily
interested in the transition between the 2S (higher) and
2p (lower) states. The 2s state is a metastable state. Ac-
tually, there are four substates in the 2S band and ten
substates in the 2p band. Theoretically there are 30 possi-
ble transitions, or downward changes in energy level, that
could occur, with each giving off radiation at its character-
istic wavelength. Actually, only five of these transitions
have as yet figured importantly in stimulated emissions;
all correspond to wavelengths in the near-infrared region.
The strongest of these emissions is one at 11,530 A.

As in the case of the ruby laser, neon atoms tend to pile

120

The Laser — What it is and Does

up in the 2s state, and the threshold energy is the amount
of input energy that makes the population of neon atoms
in the 2S state equal to that in the 2p state. When some
random neon atom spontaneously makes the transition
from the 2s state to the 2p state, radiation at 11,530 A
stimulates coherent emission.

The photon at 11,530 A stimulates nearby metastable
neon atoms, and they, too, go down the chute and emit
their photons at the same wavelength. Photons emitted
perpendicular to the Fabry-Perot mirrors bounce back
and forth between the mirrors until they acquire sufficient
intensity to break out. Photons emitted in other direc-
tions are lost through the walls of the tube and do not
participate in coherent emission.

When in operation, a gas laser is bathed in an orange-
red glow, but this light has nothing to do with its laser
action. Most of the coherent output of the gas laser is in
the infrared region and is invisible to the eye. The visible
glow results from spontaneous transitions of excited neon
atoms that do not enter into the stimulated emission of
radiation. In fact, the glow is identical to that of any neon
sign.

Injection Lasers

The third basic type of laser is the injection laser. An
injection laser consists of a semiconductor diode made of
gallium arsenide or of gallium arsenide-phosphide.

A diode is an electronic part that has the property of
conducting current easily in one direction but almost not
at all in the opposite or reverse direction. The injection
laser is a forward-biased semiconductor diode. It conducts
current in its easy direction.

A semiconductor is a material that does not conduct
electricity so well as something like copper does, but does

121

so better than an insulator such as sulphur. The most com-
mon semiconductors are the metals silicon and germanium,
but some compounds can also be used, and, for the injec-
tion laser, gallium arsenide has proved useful. Because
gallium is a little better conductor than silicon, and arsenic
a little poorer, when mixed together they give roughly
the same effect as silicon.

Now, to make a diode out of a block of semiconductor
material, it is necessary to dope it. This is done by allow-
ing the two impurities— tellurium and zinc— to diffuse into
the block at high temperature. Because the tellurium atom
has one more valence (combining) electron than does
arsenic, when tellurium atoms replace some of the arsenic
atoms in the gallium-arsenic block, there are a few free
electrons left over. Since the electron has a negative
charge, tellurium-doped gallium arsenide is called N-type,
or negative, gallium arsenide.

Because zinc, on the other hand, has one less valence
electron than gallium, when some zinc atoms replace a
few of the gallium atoms, there are several holes, or elec-
tron deficiencies, left over. Therefore, zinc-doped gallium
arsenide is called P-type, or positive, gallium arsenide.

The boundary where the regions of N-type and P-type
gallium arsenide meet is called the semiconductor junc-
tion. If you connect the positive terminal of a battery or
electronic power supply to the P-type region of a semi-
conductor diode and connect the negative terminal to the
N-type region, the diode will be biased in the forward
direction, and current will flow easily across the semi-
conductor junction. If the power supply is connected with
its negative terminal going to the P-region and its positive
terminal going to the N-region, the diode will be biased
in its reverse direction, and little, if any, current will flow
across the semiconductor junction.

122

The Laser — What it is and Does

HOW DOES IT WORK?

Scientists are not yet sure just what energy transitions
occur in the injection laser. But laser action seems to be
most pronounced on the P-side of the junction. This might
indicate that some energetic electrons making up the cur-
rent flowing across the junction recombine with holes and
give up energy in the recombination process.

The injection laser emits coherent light by passing ex-
tremely high current between the terminals of the semi-
conductor diode, so that light is emitted along the line
that defines the semiconductor junction. The light comes
out incoherently at first, but as the intensity of the current
is increased, the emission becomes coherent. Of course, all

Semiconductor injection laser design as developed by IBM (Elec-
tronics)

INTENSITY

(ARBITRARY UNITS)
I50t

pTYPE GaAs

100

n TYPE GaAs

(ABOVE THRESHOLD

8.13 AMPS 50

Oo^ (AT THRESHOLD) 8.03 AMPS

70 60 50 40 30 20 10
ANGLE OF ROTATION (DEGREES)

123

this electrical current passing through the relatively small
diode makes the diode heat up rapidly. Since such extreme
heating could destroy the semiconductor junction, before
the diode is operated it is usually immersed in a cryostat,
or double bottle, the inner bottle filled with liquid helium
and the outer one with liquid nitrogen. Furthermore, the
current is usually pulsed rather than passed continuously.

A typical injection laser is a rectangular parallelopiped
(six-sided solid block whose opposite faces are parallel)
about ten times as long as it is wide. Dimensions of a
typical unit are 1/10 by 1/10 by lM millimeters. The sides
are finely polished and tend to reflect light back into the
laser so that the emission of coherent light comes out in
parallel rays from the square sides of the block. Silvering
is not required because the block itself is metallic, and
when its sides are polished they will reflect the light rays
generated within the block.

Current is applied to opposite rectangular sides of the
block. The current flow is perpendicular to the semicon-
ductor junction, which is a narrow plane or region cutting
the block along its long axis.

The reflection of waves at the polished sides of the diode
tends to favor the waves coming out of the square ends
parallel to the junction. Furthermore, since the recom-
bination process takes place all along the semiconductor
junction plane, coherent-light waves traveling along the
junction stimulate radiation from other hole-electron pairs,
and the wave grows in intensity before it bursts from the
square sides of the laser.

A gallium-arsenide laser emits coherent light at 8,400 A
in the near-infrared region. This light is invisible to the
human eye. Gallium arsenide-phosphide lasers have emit-
ted coherent light at 7,000 A, in the deep-red region.
Furthermore, by varying the amount of phosphorus in the

124

The Laser — What it is and Does

laser, the color can be changed throughout the near-
infrared and deep-red regions of the spectrum. Several
other intermetallic compounds involving indium and anti-
mony as well as gallium, arsenic, and phosphorus show
promise of producing laser action. A silicon-carbide diode
was reported to have emitted blue-violet light, but proof
of this accomplishment is as yet inconclusive.

The current passed through the particular laser we have
described may vary from 10 to 25 amperes or more. At
lower currents, the emission is incoherent and involves
only a small part of the junction area. As current is in-
creased, the area of incoherent sparkling or sporadic emis-
sion of light spreads out along the junction, and coherent
emission can be noticed near the center of the junction.

Comparison

Thus there are three main types of lasers: optically
pumped lasers, which may be crystalline, glass, liquid,
gaseous, or plastic; radio-frequency or direct-current-
pumped gas lasers; and semiconductor diode lasers
pumped by injection of high current.

GASEOUS LASERS

The gas laser emits coherent light, usually in the infra-
red region. Gas lasers are used mostly in scientific investi-
gations, such as spectroscopy, and for experiments in space
and time, such as verification of some of the consequences
of the theory of relativity. The gas laser is useful in these
investigations because its output is the most nearly co-
herent of all lasers and because continuous output is
conveniently available from gas lasers even at room tem-
perature.

Because gaseous lasers operate in the continuous wave
mode rather than through pulsation, they have proved

125

better than optically pumped lasers for many communi-
cations experiments, such as the transmission of speech
and music or television pictures.

Furthermore, since gas lasers produce the most nearly
coherent output of any laser— the only thing that can cause
a helium-neon gas laser to deviate from its 11,530 A center
frequency is mechanical vibration of the apparatus— they
have been used for scientific studies, such as checking the
experimental evidence of Einstein's theory of relativity
and for constructing a precise gyroscope.

OPTICALLY PUMPED LASERS

Optically pumped lasers are used when high energy is
required, such as for burning metal, performing delicate
eye operations, precision welding or machining. The most
used optically pumped laser is still the ruby laser. It is
one of the few lasers that can give visible output. Nearly
all gas lasers, and most types of optically pumped lasers,
work in the infrared region. Most optically pumped lasers
emit pulses at a relatively low repetition rate. Continuous
output can be achieved only by putting the laser in a
cryostat, or double bottle of liquid helium and nitrogen.
Although the physical form of a ruby laser is simpler than
that of a gas laser, its excitation system is somewhat more
complex. The gas laser needs only a simple radio trans-
mitter, while the ruby laser requires an electronic flashgun
and either a special xenon flashtube or a carefully designed
system of reflectors.

INJECTION LASERS

The injection laser is physically simpler than either the
ruby or gas laser. For excitation, it actually needs only a
rudimentary direct-current power supply, but it is usually
operated in a cryostat. Injection lasers can produce a
whole range of coherent output frequencies within the red

126

The Laser — What it is and Does

and infrared regions of the spectrum. They deliver con-
tinuous or nearly continuous output, and they, too, have
been found useful in communications experiments in
which speech, music, or even television pictures have been
transmitted. Gallium-arsenide diodes operated at lower
current and at room temperature are already being used
in portable communications systems. Although the infra-
red output of these devices is not coherent, they have
permitted communications over a range of thirty miles.

Universal Coherence

Sciences have long dreamed of generating coherent
emission at all frequencies of the electromagnetic spec-
trum. Quantum devices have made important contribu-
tions toward this end, but a great deal remains to be done.
It has been suggested that variations of the word "maser"
be coined for all the new devices, including the ones yet
to come. There might be rasers ( radio-frequency ) , masers
(microwave), irasers (infrared), lasers (Zight), uuasers
( ultraviolet ) , xasers (X ray), and gasers (gamma-ray).
One prominent scientist jocularly suggested the name
"daser," standing for "darkness amplification by stimu-
lated emission of radiation."

All this points up the advantage of talking about quan-
tum devices (and specifying whether they are oscillators,
amplifiers, or harmonic generators) and designating the
wavelength of interest rather than playing with acronyms.
It does, nevertheless, seem to be a fact of life that the term
"maser" will continue to be used both for amplifiers and
for oscillators not only in the microwave region (roughly
1,000 megacycles per second) but perhaps for devices
operating at even lower frequencies, when and if such de-
vices are developed.

Likewise, it seems that the term "laser" will continue to

127

be used to refer both to amplifiers and to oscillators that
operate in the near-infrared, visible, and near-ultraviolet
portions of the spectrum. Neither extension of laser action
into the far-infrared ( near microwaves ) nor into the far-
ultraviolet (near X rays) will result in a change in termi-
nology.

But possibly, when we can successfully generate co-
herent X rays and gamma rays, another term will be used,
for already, as mentioned above, the word "gaser" is being
bandied about.

MASERS

Masers are usually true amplifiers instead of the gen-
erators that lasers are. This means that they receive a
weak signal and pass it on at a higher power level. Masers
operate between 300 megacycles per second ( 100 centi-
meters or 1 meter wavelength) and 100,000 megacycles
per second (3 millimeters).

We might remark parenthetically that there is other
millimeter-wave research going on that does not involve
masers. One special microwave tube, the Tornadotron,
has been reported to have an output of 500,000 mega-
cycles per second, or a wavelength of 0.6 millimeter.

A typical maser consists of a crystal containing chro-
mium that is pumped by the output of a microwave tube
operating at a frequency much higher than the one to be
received. The microwave signal pumps the chromium ions
to an elevated energy level that is metastable.

Incoming signals at a certain lower microwave fre-
quency stimulate the chromium ions to fall from their ele-
vated energy level to an intermediate level before the
ground state. In so doing, they emit radiation at the fre-
quency of the incoming signal and thus amplify it.

To avoid the introduction of noise or unwanted signals,

128

The Laser — What it is and Does

maser amplifiers are placed between the pole pieces of a
powerful magnet, and are operated in a double bottle with
liquid helium on the inside and liquid nitrogen on the
outside.

About a dozen radio astronomical observatories
throughout the world use maser amplifiers to pick up
radio-frequency emissions from distant planets, stars, and
nebulae. Several stations use maser amplifiers for tracking
satellites and space probes. So do some of the stations that
receive radio and television signals from orbiting com-
munications satellites such as Telstar and Relay. It is
possible that maser amplifiers are used in special military
radar and communications applications, but if so, the
Department of Defense isn't saying!

INFRARED LASERS ( IRASERS )

Various kinds of lasers cover the near-infrared spectrum
from nearly 13,000 A right up to visible light. This leaves
a gap in the spectrum from 3 millimeters wavelength to
0.013 millimeter. This gap includes the millimeter and
submillimeter-wave regions of the radio spectrum and the
far-infrared band that encompasses radiation from warm
and lukewarm objects.

NEW COLORS IN LASERS

Progress has not been so good in the visible region.
Only a few lasers produce visible light, and most of that,
as we have noted, is deep red. There is, of course, the ruby
laser. Red light has been produced by several other meth-
ods as well: by a laser consisting of a crystal of calcium
fluoride with the rare-earth samarium dissolved in it; from
europium chelate (rhymes with "tea late") embedded in
a plastic tube (a chelate is a complex organic or hydro-
carbon molecule containing a metal atom, in this case an
atom of the rare-earth europium); with the gallium ar-

129

senide-phosphide laser; and with some helium-neon gas
lasers.

There is a demand for lasers to produce other colors
besides red. The Navy would like to have a blue-green
laser because blue-green light is best for penetrating sea-
water and because a blue-green laser could be used as
part of an underwater television system to help navigators
of nuclear submarines detect the presence of friendly or
hostile submarines or other underwater objects.

So far, the only progress in that direction has been the
development of "blue-violet lasers," produced by doubling
the output frequency of a deep-red laser. (Doubling the
output frequency is the same thing as dividing the wave-
length by two.) Likewise, there are "green lasers,"
achieved by doubling the output frequency of lasers op-
erating in the near-infrared region.

But when you double the output frequency of a laser,
you lose 8/10 or more of its energy, and what's left will
hardly perform the job the Navy has in mind. Therefore
the search for different colored lasers continues, with
scientists now studying not only rare-earth and actinide
metals but even various organic compounds. They feel
that, given the right conditions, any substance that will
fluoresce can be made to lase. This leaves them with thou-
sands of compounds to investigate.

ULTRAVIOLET LASERS ( UVASERS )

So far the story of the ultraviolet laser is short and
sweet. One optically pumped laser, using a glass rod in
which a small quantity of the rare-earth gadolinium has
been dissolved, lases at 3,125 A in the near ultraviolet.

GAMMA-RAY LASERS ( GASERS )

Nothing has been announced officially about X-ray
lasers, but certain work is going on with gamma-ray lasers

130

The Laser — What it is and Does

under Navy auspices, though the work has not progressed
very far as yet. The Russians have also announced work
in this field.

The approach is to use a gamma-ray-emitting isotope
of ruthenium to raise a radioactive isotope of rhodium to
a higher energy state that is metastable. After a half-life
of some 40 days, the level of energy emitted by the
ruthenium will drop to that of the metastable state of the
rhodium isotope, and trigger emission at roughly 0.3 A.

There are many problems in the way, however. First,
one has to find a way to make a crystal containing the
appropriate isotopes without changing their essential
characteristics. Next comes the problem of containing the
gamma rays (they will penetrate just about anything) so
as to achieve spatial coherence. If achieved, a gamma-ray
laser would be a death ray in every sense of the word.
Gamma rays have several times the burning power of
X rays, which are, of course, harmful when improperly
applied.

The Future of the Laser

As we have seen, the laser has the advantage of provid-
ing a monochromatic or single-color light source. Further-
more, its beam is so collimated that all its energy can be
focused on a very small spot. It is also highly directive,
with little or no tendency for the beam to bend or spread
out even over the astronomical distances of outer space.
These properties have suggested a great many uses in na-
tional defense, industry, medicine, and science.

Lasers may be developed into devastating antiperson-
nel weapons for use on the battlefield. They may be sent
into space on special platforms to fight intercontinental
ballistic missiles or to destroy hostile space stations or
satellites. The laser may also be used to modify chemical

131

compounds or even to change the genetic characteristics
of the protein molecules of living organisms.

Someday special fiber-optic light pipes or other optical
wave guides, such as evacuated tubes with an internal
mirror system, may carry laser signals much as coaxial
cables now carry telephone conversations and network
television programs between cities. A fiber-optic light pipe
is a very fine glass, plastic, or arsenic-trisulfide rod pol-
ished on the outside; its walls reflect light back inside so
that it can bend around corners and still carry a light
beam.

One way to put a TV signal on a laser beam is first to
impress the complete TV picture and sound (the video
signal) on a microwave carrier. The microwave carrier is
then used to excite a special crystal situated in a micro-
wave cavity or special metal box. When the laser beam
traverses the crystal, entering and leaving the cavity
through small side windows, the beam is modulated or
made to vary in accordance with the modulated micro-
wave signal. At the receiver, the beam of a microwave
traveling-wave amplifier phototube is similarly made to
vary in accordance with the variations of the laser light
striking the traveling wave tube's photocathode. We now
have again the microwave carrier with the video signal
riding on it. This signal is demodulated, using conven-
tional electronic circuits to give the original TV picture
and sound.

A wideband video channel can be divided into many
subchannels, actually some 600, each of which can carry
a telephone conversation. Electronic circuits called filters
slice up the video channel into so-called voice channels.
Each voice channel is about o to 2,000 cycles per second
wide. Each incoming telephone signal is heterodyned, or
moved up, in frequency to fit a specific voice channel at

132

The Laser — What it is and Does

the transmitting end, then moved down in frequency and
routed out on its proper telephone line at the receiving
end.

A laser communications system would greatly expand
the capabilities of our nationwide telecommunications
network. Tiny lasers may also function as parts of the
memory system of a computer. Such a computer would
literally work with the speed of light.

Who knows? You may even one day have a laser igni-
tion system in your automobile!

MILITARY USES

One of the first uses that occurs to most people is to
build a big, superpower laser and use it to shoot down
ballistic missile nose cones. This would, they reason, make
our nation secure from the terrors of thermonuclear war.

But it isn't as easy as all that. Even the most powerful
lasers can at present penetrate only /8-inch of high-carbon
( easily burnable ) steel. And the holes they make are mere
pinpricks. Furthermore, burning requires that the laser be
only a distance of a few feet from the steel. At longer
ranges, the water vapor and dust in the atmosphere se-
verely reduce the effective power of the light ray.

Nevertheless, the Air Force is hard at work trying to
develop big lasers and figuring out how to deploy them
effectively outside the earth's atmosphere: atop mountain
peaks, aboard orbiting satellites, or even on antimissile
missiles.

Meanwhile, the military and space agencies have other,
more prosaic, but none the less vital uses for the laser.
When the Apollo lunar capsule carries the first Americans
to the vicinity of the moon, the two-man crew aboard the
Lunar Excursion Module that will make the actual land-
ing on the moon will probably use a laser altimeter to feel

133

their way onto the lunar surface. Before that, astronauts
in Project Gemini will use laser radar to practice rendez-
vous and docking of satellites in space. Already a large
laser at Wallops Island, Virginia, has tracked an orbiting
satellite 1,000 miles up. Incidentally, at that range the
laser beam was only 200 feet in diameter.

The Army has ordered several laser range finders for
use on the battlefield. They will be able to measure the
distance to targets far more accurately than their optical
or radar counterparts.

During World War II the Army made effective use of
sniperscopes and snooperscopes, infrared devices that lo-
cated targets even at night. But for such devices to be
effective, the target had to be a good deal warmer than
the background. Now, with an infrared laser, it would be
possible to scan the target and get a picture regardless of
its temperature.

During World War II the Navy used infrared "Nancy"
equipment (usually Nerst tubes or hot filaments enclosed
by a black metal hood and placed behind a deep ruby
lens) for short-range communications between ships. But
the laser affords a much more efficient and less easily de-
tectable source of infrared.

The Armed Forces have a project under way to see just
how fast a computer can operate. Some people think that
the result will be a new high-speed giant brain for our
ballistic missile early-warning system. But a better guess
is that such a computer will be used to crack secret enemv
codes and ciphers. Anyway, one part of this project is a
laser computer, sponsored by the Air Force, in which light
pulses would do the counting instead of electrical signals.
Such a computer would be faster by several orders of
magnitude than any computer now available, since light
travels faster than electrical current, which is slowed

134

The Laser — What it is and Does

down by the action of reactive elements, such as capacitors
and inductors in the circuit.

INDUSTRIAL APPLICATIONS

Industry is already using lasers to perform delicate
machining and welding operations in the manufacture of
microelectronic circuits.

A microelectronic circuit is fabricated on a thin wafer
of silicon. Sometimes forty circuits are made at one time
on a wafer only an inch in diameter. Each circuit can do
the work of, say, a five-tube radio or perhaps a computer
stage.

The circuits are made by allowing certain selected im-
purities to diffuse into the silicon wafer in prescribed pat-
terns. These patterns are formed by first allowing a film
of silicon dioxide ( glass ) to grow over the silicon wafer—
usually by applying steam to the surface— then selectively
etching away portions of the film.

Selective removal of the oxide is accomplished by first
coating the oxide with so-called photoresist— a film that
becomes tough and acid-resistant when exposed to light-
then masking the wafer with a diffusion mask and expos-
ing the unprotected photoresist to light. The wafer is next
etched with strong acid, and its silicon-dioxide coat is
eaten away except where it is protected by light-hardened
photoresist.

Preparation of the diffusion mask is a critical operation,
and laser machining of metallic foil is expected to allow
making sharper and more precise pattern outlines. Possibly
lasers may be used to remove the oxide itself, thus saving
several steps in the process of manufacturing micro-
circuits.

Laser light sources could be valuable in high-speed
photography where chromatic aberration or the unequal

135

bending of light of different wavelengths through the
camera lens can cause a blurred image.

Since different components of the atmosphere absorb
different wavelengths of light to a greater or lesser extent,
a bank of lasers used at an airport as a transmissometer
could disclose not only the visibility at the end of the
runway— as the optical devices already in use do— but also
the makeup of the atmosphere at any particular time. Such
a laser device could also be useful in air-pollution studies.
( Transmissometers are used even though the end of the
runway may indeed be visible from the control tower; the
view from the tower is not what an approaching pilot sees;
besides, the instrument, unlike a human observer, remains
on duty around the clock. )

In a chemical process, a laser might be created so that
its beam is absorbed to a great extent by the desired prod-
uct. The laser could be focused permanently through the
output pipe, and automatic control equipment could be
adjusted so that the product absorbs maximum light from
the beam. This would assure that the product in the output
pipe has precisely the desired chemical composition.

The ability of a laser beam to carry an almost infinite
amount of information has set communications engineers
to speculating about its possible use for trunkline or inter-
city communications. Today, these are handled by coaxial
cables or microwave links. One microwave link can earn1
four television programs simultaneously or replace any
one of the television channels with up to 600 telephone
conversations. But a laser beam could carry many times
this amount of information.

Nevertheless, since dust and water vapor in the atmos-
phere severely reduce the effective power of a laser beam,
a serious problem still remains before lasers can be used
for practical communications. Of course, short-distance

136

The Laser — What it is and Does

communications would indeed be possible, as would com-
munications to and from communications satellites. In the
latter case, the beam travels in the earth's atmosphere for
only a relatively short distance, although the total trip
might be 1,000 miles or even more.

One answer to abetting laser communications would be
to use light pipes or evacuated tubes with mirrors arranged
to conduct the beam around corners where necessary.

A laser telephone exchange has been contemplated.
Here the light pulses would be conducted by fiber optic
strands. These strands carry light around comers just as
copper wires carry electrical current. Though a fiber-optic
strand severely cuts down the power of the light being
transmitted, in a telephone exchange the length of the
interconnecting strands can be kept short by design. The
big advantage of a laser telephone exchange would be
that there would be no crossed wires or unwanted pickup
between adjacent optical fibers so that you would not
occasionally hear fragments of another conversation on
your line.

MEDICAL USES

Lasers have been regarded as a major boon to medi-
cine. Thousands of Americans suffer each year from a de-
tached retina. In this condition the retina, the light or
sensitive area at the rear of the eye, comes loose from the
inner surface or choroid coating of the eyeball. The fluid,
or humor, with which the eye is filled works in behind
the retina and aggravates the condition. Initially, the con-
dition causes distorted vision, but if the retina becomes
completely loose from the optic nerve, blindness results.
A laser beam can be focused through the lens of the eye
so that it makes small scars around the periphery of the
retina and thus welds it back into place.

137

A laser can also burn out small tumors in the eye. In
fact, a laser beam can be made as narrow in diameter as
the diameter of a single human cell. Some surgeons see
the laser, therefore, as a device that can burn out tumors
with minimum risk of damage to surrounding healthy tis-
sue. Lasers have also been considered for suturing wounds
through heat. The laser would cauterize the wound as it
sutured it. It could also be used to disinfect small areas
quickly. Dentists have experimented recently with laser
drills; they are fast, sure, and painless.

It is conceivable that laser beams can be made even
narrower in diameter than a single protein molecule. Such
a laser beam might be used to alter the genetic properties
of living organisms.

A team of medical scientists has reported that irradia-
tion by a laser beam has altered the electrical conductiv-
ity of whole human blood. Just what this means or how
it occurs has not yet been made apparent.

SCIENTIFIC APPLICATIONS

Perhaps some of the most far-reaching effects of the
laser will be in the fields of pure and applied science. The
laser may profoundly affect man's understanding of his
natural environment.

Our most basic quantities of measurement are length,
mass, and time. Two of these, length and time, are related
by a constant, the velocity of light in a vacuum, and yet
the value of this constant is only imperfectly known.

Our national standard of frequency is calibrated from
the same astronomical observations that give us our meas-
ure of time, since the frequency of cycles per second that
a wave executes is intimately related to time.

When dealing with radiation in the visible region, scien-
tists measure wavelength instead of frequency. But if the

138

The Laser — What it is and Does

standard radio frequencies could be doubled, redoubled,
and then redoubled again as many times as necessary to
reach the visible-light region, then length and time would
be one and the same thing irrespective of our uncertainty
as to the exact speed of light in a vacuum.

Another basic scientific problem is the question of
whether ether exists or not. You recall that we explained
electromagnetic waves by comparing them to waves in a
pond. Many scientists have found it equally hard to con-
ceive of waves without postulating some substance or
medium in which the waves could move or propagate.

Accordingly, they postulated ether— a colorless, odorless
substance filling all space— in which electromagnetic
waves could propagate just as waves propagate in a pond.
For years now, scientists have been trying to relegate ether
to the same never-never land as phlogiston and other
weird substances once postulated by alchemists to explain
physical phenomena they could not understand.

The first experiment to disprove the existence of ether
was the Michaelson-Morley experiment: If the earth is
rotating in a stationary sea of ether, the ether will drift
by the earth in a direction counter to the earth's rotation.
Now, suppose two light beams are transmitted at right
angles to each other in such a way that the ether drift will
add to the speed of one beam while the other beam will
travel perpendicular to the ether drift and therefore be
unaffected by it. Then any difference in velocity caused by
ether drift could be detected by measuring the difference
in frequency of the two beams. To make the measurement
more precise, the apparatus emitting the light beam is
next turned around so that the ether drift will oppose the
speed of the beam instead of adding to it; the frequency
difference (if any) can again be measured. If the sum
of the two frequency differences were significant, an ether

139

drift could be said to exist. This experiment has been car-
ried out with the use of gas lasers, but no significant
frequency difference has been noticed that could substan-
tiate the existence of an ether.

In the realm of applied science, the laser shows greatest
promise in spectroscopy. We have referred at many times
to absorption of infrared, light, and ultraviolet frequencies
by certain substances. The exact frequencies absorbed de-
pend upon the chemical composition of the substance and
the structure of its molecules. The totality of frequencies
absorbed or the absorption spectrum of a substance is as
individual as your fingerprints. Therefore spectroscopy is
a basic tool for physicists and chemists studying the prop-
erties of matter. But better discrimination in spectroscopy
is needed, and to get it, scientists must know the exact
frequencies with which a substance is irradiated. As the
number of laser materials increases, and consequently the
number of available coherent light frequencies increases,
spectroscopists can look forward to more efficient tools
that will enable them to gain greater and greater insight
into the basic makeup of matter.

Conclusion

In this chapter we have explained the continuum of
the electromagnetic spectrum in terms of both frequency
and wavelength. We have come to grips with some of the
basic concepts of quantum mechanics and have seen how
they explain the action of the three basic types of lasers:
optically pumped, gaseous electrically pumped, and injec-
tion. We have discussed the phenomenon of fluorescence
and have seen how laser action is related to fluorescence
but differs from it because of ( a ) its frequency coherence
or monochromaticity and ( b ) its spatial coherence, or the
fact that all wavelets keep in step.

140

The Laser — What it is and Does

(Incidentally, this last gem of knowledge now makes
you smarter than a certain covey of investors with more
spare cash than technical knowledge. They lost several
kilobucks supporting a glib physicist with a lab full of
bottles of fluorescent material that he passed off as lasers
completely covering the visible spectrum! Of course, they
weren't lasers at all. )

Finally, we have looked at the whole electromagnetic
spectrum in terms of how coherent radiation is or might
be produced by quantum devices, and have placed a
special emphasis on a possible gamma-ray laser. And we
have seen the impact of lasers on national defense, indus-
try, medicine, and science.

Now we shall look backward and see how the laser
actually came into being.

141

One basic law rules the operation of all devices that use
electric currents. A fine introduction to the study of electricity.

8 A Simple Electric Circuit: Ohm's Law

Albert V. Baez

A chapter from the textbook The New College Physics, a Spiral Approach.

WE BEGIN this chapter by considering the
operational steps we might take, in an elementary
laboratory, in order to learn more about electric
current. We shall then try to build up a theory
that accounts for our observations.

40.1. A Simple Series Circuit: Measurement
of Potential Difference

Figure 40.1 shows what our apparatus looks
like: A, a six-volt storage battery; B, a lamp in a
socket; C, a knife switch; D, a voltmeter; £, an
ammeter; F, some connecting wires. From now on

we shall, as much as possible, use the shorthand
of conventional diagrams, as in Figure 40.2, which
shows battery A, lamp B (the zigzag line is actu-
ally the symbol for an element with resistance),
and switch C connected in series. When the switch
is closed, the lamp lights up. We say that there
is an electric current or that there is a flow of
electric charge, but we don't, of course, see any-
thing flowing. The fact that the bulb lights up
when the switch is closed is the only outward
sign that anything flows.

It is not uncommon to begin such an experiment
with little or no knowledge of what is inside the
magic boxes A, B, D, and E (Fig. 40.1). All we

r --— ~

/js;

ft o &

■$*'

FIG

40.1. Apparatus needed for a simple experiment with electric circuits: A, ^^f^f'j^^uS

C, a knife switch; D, a voltmeter; E, an ammeter; F, typical connecting wires, two oj the clips on winch

are called alligator clips.

143

fig. 40.2. Schematic diagram of a series circuit includ-
ing a battery, A, connected to a lamp, B (shown here
as a resistor), through a switch, C.

know is that D measures potential difference and
that E measures current. In this chapter we shall
look inside B, D, and E. The battery, A, however,
will have to remain just an electron pump; I
shall leave its inner details out of the discussion
because they involve the complicated molecular
mechanism by which chemical energy is converted
into electrical energy.

We want to understand why the voltmeter read-
ings of Figure 40.3 are what they are at different
places. We are going to limit ourselves in this
chapter to an understanding of the simple circuit
of Figure 40.2. We shall move more slowly than
is customary in a chapter on electric circuits, and
only when we peek inside the voltmeter and the
ammeter shall we see slightly more complicated
circuits in series and in parallel. Our immediate
objective is limited ; but, if you understand all the
details of this discussion, you will have a firm
grasp of fundamentals.

We first notice, as we consider the reading of
the voltmeter in different parts of Figure 40.3,
that we do not need to disturb the circuit when we
take a voltmeter reading. We simply connect the
voltmeter to two points of the circuit.

Next we observe and record the data, and then
we try to explain them by theory. When the volt-
meter (Fig. 40.3) is connected across the bat-
tery (A), it reads 6 volts if the switch is open;
with the switch closed (B) it reads 5.45 volts.
Connected across the lamp, it reads 0 if the switch
is open (C) and 5.45 volts if the switch is closed
(D). Connected across one of the connecting wires,
it reads 0 whether the switch is open (E) or
closed (F).

If the voltmeter is telling the truth, the potential

144

difference across the terminals of the battery is
6 volts when there is no current in the circuit (A).
The potential difference across the battery drops
when there is current (B). There is no potential
difference across the terminals of the lamp (C)
until the switch is closed (D), and there is never
a measurable potential difference across one of
the connecting wires. Our theory of what is going
on must account for all these readings (and a lot
more).

Let's begin our description of what we think
is going on. We have already encountered a mo- i
mentary flow of charge in electrostatic experi-
ments, but something different is obviously hap-
pening here, for this current can flow for a long
time. Something replenishes the charge; something '
maintains a potential difference that produces a
steady flow of charge. This something, in our
experiment, is the battery. The terminals of the
battery are charged in the very sense in which we
used the word in electrostatics. If our battery has
only two terminals, an electric field surrounds

6 V (almost)

5.45 V

Zero volts

5.45V

fig. 40.3. Readings on a voltmeter as it is connected to
different parts of a series circuit that is sometimes
open and sometimes closed.

A Simple Electric Circuit: Ohm's Law

fig. 40.4. (A) The electric field lines in air surrounding the terminals of a battery. (B) The electric field lines
within a wire connecting the two terminals of a battery through a lamp.

them as if they constituted an electric dipole.
Figure 40.4.A shows the electric field between the
two battery terminals. It looks very much like the
electric field between two charged metal balls on
insulating stands; but there is a difference in
what happens to these fields if the terminals are
connected with a wire. A wire connecting one
charged ball to the other would carry current
only for an instant, for the potential difference
between them would soon be zero, and the field
would vanish. If the terminals of the battery are
connected, a large current can exist in the wire
for a much longer time, and the field between the
terminals will still be like that of Figure 40.4.A
after the wire is removed. In Figure 40.4. B we
see the electric field lines (E) that come into exist-
ence within the wire that runs from one terminal
through the lamp to the other terminal. I said
earlier that there can be no electric field within a
conductor, but that is true only in the electro-
static case. Charges move in the wire of Figure
40.4.B because there is an electric field within it.

Since the lamp gets hot, it is obvious that energy
is involved. It looks very much as if something
were playing the role that friction plays in me-
chanics. Something is playing that role; it is
called resistance (defined in § 40.3), and we shall
soon consider it in some detail.

Let us now recall the definition of electric field,
E, as F/q, the force per unit charge (§ 4.4). An

electron finding itself in electric field E experi-
ences the force F = — eE. It should experience
the acceleration a = F/m, and it does, but it
cannot pick up much speed, for it collides with
other electrons. The average behavior of many
electrons, starting and stopping, is, nevertheless,
a general drift in the direction of — eE. Statis-
tically, the free electrons drift at an average speed
determined by the magnitude of the force — eE.

The idea of motion at a constant speed under
the action of balanced forces can be perfectly il-
lustrated by the falling of small spheres (such as
marbles) through a tall glass beaker containing
glycerin (Fig. 40.5.A); balls of the right weight
and dimensions achieve a terminal velocity. The
force of gravity, mg, pulls them downward, but a
viscous frictional force, f, pushes them upward.
When wg = f, the acceleration is zero (see § 5.2).

A positive charge, q, in electric field E feels the
force qE (Fig. 40.5. B). If it also feels an equal
retarding force, f, it can move at a constant
speed. What happens in a wire is somewhat like
this. For two reasons, however, you must not
take any such picture literally. First, no electron
travels for long without hitting another, and the
concept of drift velocity is therefore purely statis-
tical. (It takes a lot of kinetic energy to carry an
electron into contact with another, even when the
other is anchored to an atom. What I have called
hitting just means being decelerated by a force

145

fig. 40.5. (A) The gravitational field lines running
through a tall glass beaker containing glycerin; little
spheres fall through it at a constant speed. (B) The
electric field lines in a wire; electric charges move
with a constant average speed within the wire.

field. Here it would pay you to re-read § 3.7,
dealing with the concept of contact.) Second,
electrons have a negative charge and move op-
posite to E, but this does not damage the model
of Figure 40.5.

Traditionally, the direction of current in a wire
has been taken as from the positive to the negative
pole (in the part of the circuit outside the battery).
In this book, since it is now known that in a wire
the electrons do the moving, I have broken with
tradition by assigning to / the direction of elec-
tron flow. But I shall use the symbol /(= -/) for
the conventional direction (from positive to nega-
tive) whenever it can simplify the wording of
statements. All the left-hand rules I gave in the
study of magnetism relate to /. If we associate
the right hand with /, similar rules apply. In
other words, / is the direction in which positive
charges would move in a wire. Since positive
charges tend to move from a region of high elec-
tric potential to one of low potential, it is con-

venient to use the traditional symbol for current, j
/, in these cases. (We simply need to remember
that the electrons in metallic conductors move in
the opposite direction; in liquids, however, posi-
tive as well as negative charged bodies move.)
Whenever we use the symbol q without any further
specification, it will represent a positive charge.
The electronic charge will, of course, be written as
— e.

There are two ways of expressing the reason
why a ball moves downward through the beaker
of glycerin. One is to say that it moves down
because wg points downward; the other is to say
that it has a tendency to move from a region of
high potential to one of low potential. The same
language applies to positive charges in an electric
field: they move from A to B in Figure 40. 5. B
because qE points that way, or (since an applied
force would do work in moving a positive charge
from B to A) they move from a region of high
potential to one of low potential.

Potential difference, V, is measured in volts,
which we identified earlier (§ 37.2) with joules per
coulomb. The work that will move charge Iq
through distance x from B to A is (by the formula
"work equals force times distance") MJ = (Aq)Ex.
The work per unit charge is AU Aq = Ex. The left-
hand side has the units joules per coulomb, or i
volts. The right-hand side has newtons per cou-
lomb times meters for units. This equivalence is
worth remembering. We may write

V = Ex
E = V/x

[40.1

[40.2

Now we are getting somewhere. The quantities
on the right-hand side of the second equation
are measurable, V with a voltmeter (we'd better
find out how it works), x with a meter stick.

If we connected a voltmeter across points A
and B of Figure 40.5. B, would it show a reading?
I said earlier (Fig. 40.3. F) that there is no de-
tectable reading across a wire carrying current.
You will have to take my word for it that a cer-
tain very sensitive kind of voltmeter would indi-
cate a small potential difference between points
A and B if there were a current in the wire.

146

A Simple Electric Circuit: Ohm's Law

EXAMPLE 40.1. A sensitive voltmeter indicates a
potential difference of 10-6 V between points A and
B of Fig. 40.5. B. The distance between the points
is x = 2 m. We wish to know (1) what force, in
newtons, an electron feels within the wire; (2) what
acceleration it experiences; (3) what the increment
in its speed is if it travels for 10-7 sec.
1. The force on a charge, q, is F = Eq. Since, by
equation 40.2, E = V/x, we know that F = Vq/x.
We are given that

V = 10~6 V

q = -e = -1.60Xl0-19coul
x = 2m
Therefore, if we drop the minus sign,
10~6 X 1.60X10"19

F =

= 8Xl0-26nt
2. The acceleration is a = F/m. We know that
F = 8xl0"26nt
m = 9.11Xl0-31kg

Therefore

8Xl0~26nt
" 9.11XlO"31kg

= 8.78xl04m/sec2

3. We know that

Av/At = a
Therefore

Av = a(At)

- 8.78 XlO4 m/sec2 X lO"7 sec
= 8.78X10-3 m/sec

There are experimental reasons for believing that
this is of the right order of magnitude for the aver-
age speed of electrons in a wire.

40.2. Electromotive Force

We can extend the analogy of balls falling
through glycerin to a simple electric circuit.

In Figure 40. 6. A we see balls rolling and falling
under the action of the earth's gravitational field,
g. If the balls are to keep moving at a constant
rate, work has to be done against gravitational
force as each ball is lifted from D to A. The energy
is supplied by the man, who acquires it by the
complicated chemical process that transforms food
energy into mechanical energy. Notice that there
is a small difference in gravitational potential,
g(Ahi), between points A and B, a large differ-

Ah,

I Ah,

— <

fig. 40.6. Analogy between the effect of the earth's gravitational field and that of an electric field.

147

■*"" — 5"*"

2. 73 amp

FIG. 40.7. How an ammeter will read when connected
in different parts of a circuit.

ence, g(Ah2), between points B and C, and a small
difference again, g(Ah3), between points C and D.
In this arrangement a "potential-difference meter"
(analogous to a voltmeter) could consist of an
ordinary meter stick.

The frictional force on each ball as it falls in
the glycerin from B to C is equal to its weight.
This makes the resultant force zero, which is
what is required for descent at a constant speed.
The frictional force on each ball in AB and CD
is much smaller than its weight. This is suggested
by the small slope of the inclined planes in these
regions. The man has to do work mgh (/; =
A/?i + A/z2 + A/73) on each ball to move it from
D back to A so that it can start the cycle again.

In Figure 40.6. B we have the electrical counter-
part of Figure 40.6. A, a complete electric circuit,
ABCD. Electric charges are moving under the
influence of the electric field, E. The potential
difference between points A and B is very small
because the charges encounter only a slight re-
sistance to their motion in this region. The poten-
tial difference between points B and C is great
because the resistance there is great; the letter R
signifies, in fact, that this portion of the circuit,
like the lamp in Figure 40.2, is a resistor (a con-
ductor with relatively large resistance). There is
only a small potential difference between C and D.
The charges have a low potential at D, and it
takes energy, which is supplied by the battery,
to lift them to a high potential at A. The battery
transforms chemical into electrical energy by a
complicated process, which I shall not analyze

any more than I analyzed the internal workings
of the man of Figure 40. 6. A.

The ability of the battery to raise positive
charges from a low potential at D to a high po-
tential at A is measured by the number of joules
per coulomb, AW/Aq, it needs in order to do this.
(It is actually electrons, with negative charges,
that are moving — and the other way round; but
this poses only semantic problems. We could talk
the whole thing out by using different words, but
we are here adhering to the classical idea that
current consists of positive charges whose poten-
tial is raised in going from D to A.) The ratic
AW/Aq is called the electromotive force (abbrevi-
ated as emf) of the battery and is symbolizec
as 8. It is the work per unit charge done by the
battery in moving positive charges against the
electric field within the battery. It is not, ot
course, a force in the Newtonian sense; it i<
measured in joules per coulomb, or volts, not ir
newtons; but the word "force" has become firmh
established in the vocabulary of electricity. Since
AW/Aq is measured in volts, you might ask wh\
we do not simply say that 8 is the difference ir
potential between points D and A. The answei
is that the battery itself may have internal re
sistance, and that the potential difference betweer
points D and A may therefore be somewhat les:
than 8, depending on how much internal re
sistance there is. Ideally, with no internal resist
ance, 8, measured in volts, would be equal t(
the difference in potential between points D and A
Let us return, for illustration, to Figure 40.3
The voltmeter showed (B) a potential different
of 5.45 volts between D and A when there wa.
electric current in the circuit. This was not, how
ever, the emf of the battery. The potential differ
ence across the terminals of a battery is neve
exactly equal to its emf when there is curren
through the battery. When the switch is open (A)
the potential difference is almost 6 volts. We hav
to hedge here because some charges flow evei
when the voltmeter alone is connected across th
battery; the potential difference is not quite equa
to the emf unless the resistance of the voltmete
is infinite — that is, unless the voltmeter draw> n
current. A good voltmeter, obviously, has a ver
high resistance.

148

A Simple Electric Circuit: Ohm's Law

I have been using the term "resistance" in a
qualitative way. In order to define it precisely, I
have to measure current. Notice that the argu-
ment so far has not depended upon current. I
have talked only of potential difference ("volt-
age" in the vernacular of the electrician). But
perhaps our rolling-ball analogy (Fig. 40.6) has
shown why the reading of the voltmeter in Fig-
ure 40.3. F was zero. (It corresponded to a van-
ishingly small Ahi.) The potential rise (8 = ArV/Aq)
within the battery — that is, the emf — must equal
the sum of the potential drops (AV) in the complete
circuit or loop. We let VAB mean "the potential
difference between points A and 5." Since VAD
and VCd (Fig. 40.6. B) are both practically zero,
the voltmeter readings of Figure 40.3.B,D are
practically identical. We now imagine (Fig. 40.6)
connecting one terminal of the voltmeter to point
A. We then touch points B, C, and D with a wire
connected to the other terminal of the voltmeter.
We read that VAB = 0, that VAC = 5.45 volts,
and that VAD = 5.45 volts. The reason for this is
that

VAD = VAB + VBC + VCD

= 0 + 5.45 V + 0 = 5.45 V

Before we can proceed, we need to define resist-
ance in terms of potential difference and current.

40.3. Ohm's Law

We shall now use the ammeter in the circuit of
Figure 40.3. To use an ammeter, you must break
into the circuit at some point and allow the current
to pass through the ammeter.^ Figure 40.7 shows
that the ammeter reads 2.73 amperes in each of
four different positions. This simply means that
charges are conserved. The number of charges
flowing per second past any point in the circuit
must be the same as the number flowing per sec-
ond past any other point; otherwise charges would
be either accumulating or leaking away. If, for

t Two interesting exceptions to this statement are: (1) a
special alternating-current ammeter that just clamps its
coil round the current-carrying wire; (2) a special direct-
current meter, used by automobile electricians, that works
essentially like Oersted's experiment; it is simply clipped
onto the battery-charging line.

fig. 40.8. The sum of inward currents at a junction is
equal to the sum of outward currents.

fig. 40.9. One way to connect an ammeter and a volt-
meter to measure the resistance of a resistor.

example (Fig. 40.8), we have a junction, O, where
the currents are T, /->, h, and /4, it must be true
that 2/ = 0— that is, that h + 72 + h + h = 0—
if we consider "coming into O" as positive and
"leaving 0" as negative.

So far Figure 40.7 simply confirms the fact that
the current in a single loop is the same every-
where, including the battery. Outside the battery,
positive charges tend to flow from regions of high
to regions of low potential; inside the battery,
the energy supplied by the battery makes it pos-
sible for positive charges to flow against the
electric field that is naturally there (compare DA
in the rolling-ball analogy, Figure 40.6. A).

We now need an experimental fact about metal-
lic conductors. If such a conductor (labeled BC)
is connected as in Figure 40.9, the ammeter will
show the current in it, and the voltmeter will
show the voltage across it. If different currents, I,
are made to flow through it, different voltages,
V, will appear across it. A plot of V agaiust / is
a straight line going through the origin (Fig.
40.10); that is, the ratio of V to I is constant.
(This is not true of all kinds of conductors; it is

149

not true, for example, of vacuum tubes or of
certain types of crystals.) I shall now define, by
the following equation, the quantity called the
resistance, R, of the conductor BC:

R =

[40.3

For some materials (for many different kinds
of metallic wires, for example) and under certain
conditions (at constant temperature, for exam-
ple) the resistance defined in this way is a con-
stant, independent of /. For other kinds of
conductors (vacuum tubes, for example) the R
defined in this way is not independent of /. In
all cases the resistance defined by equation 40.3
is measured in ohms. Obviously, "volts divided
by amperes" is equivalent to ohms. Equation 40.3
is known as Ohm's law after Georg Simon Ohm,
a German physicist (1787-1854).

If the current is / and the cross-sectional area

■MMMiinim maw— ummmw i asMmmmnsi

fig. 40.10. A plot of voltage against current in an olvnie
conductor.

— — 7^\%*i

fig. 40.1 1. Illustrating the definition of current density.

150

fig. 40.12. The voltage drop between Vv and P: is sc
small that the bird feels no shock.

of the wire is A, the current density, j, has the
magnitude

J =

[40.4-

and is measured in amperes per square meter.
For the class of conductors I have been talking
about (called ohmic conductors) it is an experi-
mental fact that the electric field intensity, E^
established inside the wire (Fig. 40.1 1) is prop
tional to the current density in the wire. In ot
words, experiments show that

por-

Eoc j

[40 J

(I have written j as a vector because E is a vector.)
There must be a constant of proportionality, p,.
such that

E = pj [40.6\

Remembering that E is measured in volts per
meter (equation 40.2), let us find the potential
difference, V, across a length, /, of wire as follows.
Dropping the vector notation, we have

El = pjl [40./ 1

Using equation 40.4, we get

£/ = „-/

[40.6:

But, according to equation 40.2, El = V. There-
fore

K=p-/

[40.9

A Simple Electric Circuit: Ohm's Law

fig. 40.13. The voltage drop between Qi and Q2 might be great enough to kill the bird.

Pi
A

[40.10

But this is the ratio that defines resistance, R
; (equation 40.3). Hence

R-pl
R~A

[40.11

That is, the resistance of a wire is directly propor-
tional to its length and inversely proportional to
its cross-sectional area. [I could have introduced
p by means of equation 40.11, but I wanted to
emphasize, once again (equation 40.6), the exist-
ence of an electric field within a wire carrying a
current.] The constant of proportionality, p, is

' called the resistivity of the material. Resistivity is
the inverse of conductivity. Table 37.2 lists the

; resistivities of some common substances.

EXAMPLE 40.2. We wish to find the resistance of a
piece of copper wire 1 km long and 1 mm in di-
ameter.
We know that

p = 0.172 X10-7 ohm-meter
/ = 103m
d = 10-3 m

Therefore

A = ?$- = 7.85 X 10-7 m2
4

and (equation 40.11)

0. 1 72 Xl0~7 ohm-meter X 103m

R =

7.85X10"
= 21.9 ohms

(The filament of an ordinary 100-W light bulb
has a resistance of about 100 ohms.)

We can now consider the voltage drop in wires
carrying current. You have seen birds perched on
such wires without being killed and apparently
without feeling any shock. Now, one of the harm-
ful things in electric shock, to birds or to people,
is the current through the body. This current
obeys, approximately, Ohm's law, which implies
that we get big currents through the body if we
touch points with large potential differences.

There is a voltage drop, V = IR (see equation
40.3), in a wire, but the potential difference (Fig.
40.12) between points Pi and P2, where the bird's
feet rest on the wire, is exceedingly small. In
Example 40.2 we saw that the resistance of 1,000
meters of a certain copper wire was 21.9 ohms.
The resistance of 10 centimeters would be only
21.9X 10~4 ohm. Even if the wire carried a current
of 100 amperes (very unlikely), the potential drop
from Pi to P2 would be only 0.219 volt. Such a
small potential difference could not send enough
current through the bird to do much harm.

A great potential drop might occur (Fig. 40.13)
across some distant load — a motor, M, perhaps.

151

Hence the potential difference between points Qx
and Qi on wires carrying the same current might
be very great indeed. If the bird could put one
foot at Q\ and the other at Q2, it might be killed.
We can now consider our original circuit sym-
bolically. In Figure 40.14 the battery, B, with its
internal resistance, r, is enclosed in a dashed
line; the lamp, L, has resistance R. The current,
/, is the same in both B and L. The potential
drop in L is IR (equation 40.3); the potential drop
in B is Ir. The charges leave point P at the same
potential at which they arrive there. The work per
unit charge done by the battery, 8 = AW/Aq,
must therefore exactly equal the drop in potential,
IR + Ir. Hence

Ir = IR

[40.12

Now Figure 40.3 indicates (D) that IR = 5.45
volts and (B) that 8 — Ir = 5.45 volts. From
Figure 40.7 we see that / = 2.73 amperes. There-
fore

5 45 V

R = z^ = 2 ohms [40.13

2.73 amp L

From Figure 40.3. A we know that S is almost
6 volts. Therefore, using the equation

8 - Ir - 5.45 V [40.14

we get

Ir = (6 - 5.45) V

- 0.55 V [40.15

But / = 2.73 amperes. Therefore

= 0.55 V
2.73 amp

= 0.2 ohm

We have now accounted for the voltage readings
of Figure 40.3, and we have learned something
about electric circuits in the process.

40.4. How the Ammeter and the Voltmeter
Work

I have already told how a galvanometer works;
it is a coil, mounted between the poles of a mag-
net, whose dipole moment experiences a torque
when it carries current (§ 38.4). If (Fig. 40. 15.A,C)
a low-resistance conductor, S (called a shunt), is
connected across the coil, C, in parallel with it,
most of the current flows through S, and we have

fig. 40.14. Our original series circuit treated symboli-
cally. The internal resistance of the battery is shown
as r. // 8 is the emf of the battery, 8 — Ir = IR.

an ammeter. The combination, which has a low
resistance, can be designed to measure even a
large current, for very little of the current flows
through the coil.

The same galvanometer can be converted into
a voltmeter (Fig. 40.15.B,D). If the coil, C, is
connected in series with a resistor, M, of high
resistance (called a multiplier), even a large poten-
tial difference, V, across the terminals A and B
will produce only a small current through the
coil, C, since / = V/R and R here includes the
resistance of both M and C. The whole device
has, as a good voltmeter must have, a high resist-
ance. The details may be clarified by reference to
Problems 40.15, 40.16, and 40.17.

It is also left for Problem 40.14 to prove that,
when two resistors are connected in series, the
resistance of the combination is simply the sum
of the two resistances, but that, when they are
connected in parallel, the reciprocal of the combi-
nation is the sum of the reciprocals of the indi-
vidual resistors. For resistors in series (as in
Fig. 40.15.B.D)

R = Ri + /?- [40.16

For resistors in parallel (as in Fig. 40. 15. A, C)

R /?, R2

[40.17

40.5. Electric Power Dissipated as Heat

The analogy of balls falling through glycerin
(Fig. 40.6.A) is useful, for we see immediately
that the loss in potential energy must appear as
heat. Similarly, the loss in potential energy of
charges moving in the resistor, R, of Figure 40.6.B
can appear in the form of heat. The work re-

152

A Simple Electric Circuit: Ohm's Law

quired to lift a bail in Figure 40.6. A is W = mgh.
The work per unit mass is W/m = gh. Similarly,
the work required to move the positive charge
Aq from B to A is

AW = (Aq)VBA = coulombs X volts
joules

coulombs X

joules

[40.18

coulomb
The rate of doing work, P (for power), is

At At BA

But Aq/At is the current, /, in amperes. Hence
P = IV B a- This must be in joules per second, or
watts. If all this power goes into heating the
resistor, we may write

Pj = IV [40.19

The subscript J is for "joule," to remind us that
heat is being generated. Thus "amperes times
volts" is equivalent to "watts." Since 4.184
joules = 1 calorie, we may use the expression
IV/4AS4 to compute the calories per second gen-
erated in a resistor.

From Ohm's law (equation 40.3) we know that
V = IR ; so we may write

Pj = i(iR) = pr [40.20

Since, if several resistors are connected in series,
they all carry the same /, this form of the equation
(Pj = PR) is useful.

On the other hand, since / = V/R, we may
write

V V2

P< = -V = —

J R R

[40.21

A/WWV

■ — >■

92?

1ZZ

A 9

92?

! nfooo<n i

Ammeter

FIG. 40.15. Symbolic representation of the components (A, C) of an ammeter and (B, D) of a voltmeter.

153

Since, if several resistors are connected in parallel,
each has the same potential drop as the others,
this form (Pj = V2/R) is applicable to such com-
binations.

40.6. Summary

A battery has the ability to raise positive charges
from a low potential to a high potential. Positive
charges in an external electric circuit connected
to this battery tend to flow from the region of
high potential to that of low potential. This flow
is called current. Actually, in wires, negative
charges (electrons) flow in the opposite direction,
but the logic is not affected.

The work per unit charge done by the battery
is called its electromotive force, 8; it is the ratio
AW/Aq, measured in joules per coulomb, or volts.

The potential rise in the battery must equal the
sum of all the potential drops, AV, in the whole
circuit. The potential drop across an ohmic re-
sistor of resistance R in which there is current /
is V — IR (Ohm's law). The resistance of a wire is
directly proportional to the product of its length
and its resistivity and is inversely proportional to
its cross-sectional area.

The flow of charges in a wire is very similar to
the flow of a liquid in a pipe. When several wires
meet at a point, for example, the sum of the in-
ward currents is equal to the sum of the outward
currents.

In both pipes and wires energy can be dissipated
in the form of heat. If the potential drop in a wire
is V, the work it takes to move charge q across
it is qV, and the rate of doing work, or power, is
P = IV. The power that goes into heating a
resistor may be written as PR or as V2/R.

154

A brief, informal review of the electronic age, past
and present.

The Electronic Revolution

Arthur C. Clarke

An excerpt from his book, Voices from the Sky, originally published
in the New York Times in 1962.

The electron is the smallest thing in the universe; it would
take thirty thousand million, million, million, million of them
to make a single ounce. Yet this utterly invisible, all but
weightless object has given us powers over nature of which
our ancestors never dreamed. The electron is our most ubiqui-
tous slave; without its aid, our civilization would collapse in a
moment, and humanity would revert to scattered bands ol
starving, isolated savages.

We started to use the electron fifty years before we dis-
covered it. The first practical application of electricity (which
is nothing more than the ordered movement of electrons)
began with the introduction of the telegraph in the 1840's.
With really astonishing speed, a copper cobweb of wires and
cables spread across the face of the world, and the abolition of
distance had begun. For over a century we have taken the
instantaneous transfer of news completely for granted; it is
very hard to believe that when Lincoln was born, communi-
cations were little faster than in the days of Julius Caesar.

Although the beginning of "electronics" is usually dated
around the 1920^, this represents a myopic view of tech-
nology. With the hindsight of historical perspective, we can
now see that the telegraph and the telephone are the first two
landmarks of the electronic age. After Alexander Graham Bell
had sent his voice from one room to another in 1876, society
could never be the same again. For the telephone was the first

155

electronic device to enter the home and to affect directly the
lives of ordinary men and women, giving them the almost
godlike power of projecting their personalities and thoughts
from point to point with the speed of lightning.

Until the closing years of the nineteenth century, men used
and handled electricity without knowing what it was, but in
the 1890's they began to investigate its fundamental nature,
by observing what happened when an electric current was
passed through gases at very low pressures. One of the first,
and most dramatic, results of this work was the invention of
the X-ray tube, which may be regarded as the ancestor of all
the millions of vacuum tubes which followed it. A cynic
might also argue that it is the only electronic device wholly
beneficial to mankind— though when it was invented many
terrified spinsters, misunderstanding its powers, denounced
poor Rontgen as a violator of privacy.

There is an important lesson to be learned from the X-ray
tube. If a scientist of the late Victorian era had been asked
"In what way could money best be spent to further the
progress of medicine?" he would never by any stretch of the
imagination have replied: "By encouraging research on the
conduction of electricity through rarefied gases." Yet that is
what would have been the right answer, for until the dis-
covery of X rays doctors and surgeons were like blind men,
groping in the dark. One can never predict the outcome of
fundamental scientific research, or guess what remote and
unexpected fields of knowledge it will illuminate.

X rays were discovered in 1895— the electron itself just one
year later. It was then realized that an electric current consists
of myriads of these submicroscopic particles, each carrying a
minute negative charge. When a current flows through a solid
conductor such as a piece of copper wire, we may imagine the
electrons creeping like grains of sand through the interstices
between the (relatively) boulder-sized copper atoms. Any
individual electron does not move very far, or very fast, but it
jostles its neighbor and so the impulse travels down the line at

156

The Electronic Revolution

speeds of thousands of miles a second. Thus when we switch
on a light, or send a Morse dash across a transatlantic cable,
the response at the other end is virtually instantaneous.

But electrons can also travel without wires to guide them,
when they shoot across the empty space of a vacuum tube like
a hail of machine-gun bullets. Under these conditions, no
longer entangled in solid matter, they are very sensitive to the
pull and tug of electric fields, and as a result can be used to
amplify faint signals. You demonstrate the principle involved
every time you hold a hose-pipe in your hand; the slightest
movement of your wrist produces a much greater effect at the
far end of the jet. Something rather similar happens to the
beam of electrons crossing the space in a vacuum tube; they
can thus multiply a millionfold the feeble impulses picked up
by a radio antenna, or paint a fluorescent picture on the end
of a television screen.

Until 1948, electronics was almost synonymous with the
vacuum tube. The entire development of radio, talkies, radar,
television, long-distance telephony, up to that date depended
upon little glass bottles containing intricate structures of wire
and mica. By the late logo's the vacuum tube had shrunk
from an object as large as (and sometimes almost as luminous
as) an electric light bulb, to a cylinder not much bigger than a
man's thumb. Then three scientists at the Bell Telephone
Laboratories invented the transistor and we moved from the
Paleoelectronic to the Neoelectronic Age.

Though the transistor is so small-its heart is a piece of
crystal about the size of a rice grain-it does everything that a
radio tube can do. However, it requires only a fraction of the
power and space, and is potentially much more reliable. In-
deed, it is hard to see how a properly designed transistor can
ever wear out; think of little Vanguard I, still beeping away
up there in space, and liable to continue indefinitely until
some exasperated astronaut scoops it up with a butterfly net.
The transistor is of such overwhelming importance because
it (and its still smaller successors) makes practical hundreds

157

of electronic devices which were previously too bulky, too ex-
pensive or too unreliable for everyday use. The pocket radio is
a notorious example; whether we like it or not, it points the
way inevitably to a day when person-to-person communica-
tion is universal. Then everyone in the world will have his
individual telephone number, perhaps given to him at birth
and serving all the other needs of an increasingly complex
society (driving license, social security, credit card, permit to
have additional children, etc. ) . You may not know where on
Earth your friend Joe Smith may be at any particular mo-
ment; but you will be able to dial him instantly— if only you
can remember whether his number is 8296765043 or
8296756043.

Obviously, there are both advantages and disadvantages in
such a "personalized" communication system; the solitude
which we all need at some time in our lives will join the
vanished silences of the pre-jet age. Against this, there is no
other way in which a really well-informed and fast-reacting
democratic society can be achieved on the original Greek
plan— with direct participation of every citizen in the affairs
of the state. The organization of such a society, with feedback
in both directions from the humblest citizen to the President
of the World, is a fascinating exercise in political planning. As
usual, it is an exercise that will not be completed by the time
we need the answers.

A really efficient and universal communications system,
giving high-quality reception on all bands between all points
on the Earth, can be achieved only with the aid of satellites.
As they come into general use, providing enormous informa-
tion-handling capacity on a global basis, today's patterns of
business, education, entertainment, international affairs will
change out of all recognition. Men will be able to meet face
to face (individually, or in groups) without ever leaving their
homes, by means of closed circuit television. As a result of
this, the enormous amount of commuting and traveling that
now takes place from home to office, from ministry to United

158

The Electronic Revolution

Nations, from university to conference hall will steadily de-
crease. There are administrators, scientists and businessmen
today who spend about a third of their working lives either
traveling or preparing to travel. Much of this is stimulating,
but most of it is unnecessary and exhausting.

The improvement of communications will also render obso-
lete the city's historic role as a meeting place for minds and a
center of social intercourse. This is just as well anyway, since
within another generation most of our cities will be strangled
to death by their own traffic.

But though electronics will ultimately separate men from
their jobs, so that (thanks to remote manipulation devices)
not even a brain surgeon need be within five thousand miles
of his patient, it must also be recognized that few of today's
jobs will survive long into the electronic age. It is now a cliche
that we are entering the Second Industrial Revolution, which
involves the mechanization not of energy, but of thought.
Like all cliches this is so true that we seldom stop to analyze
what it means.

It means nothing less than this: There are no routine, non-
creative activities of the human mind which cannot be carried
out by suitably designed machines. The development of com-
puters to supervise industrial processes, commercial transac-
tions and even military operations has demonstrated this
beyond doubt. Yet today's computers are morons compared to
those that they themselves are now helping to design.

I would not care to predict how many of today's professions
will survive a hundred years from now. What happened to the
buggywhip makers, the crossing sweepers, the scriveners, the
stonebreakers of yesteryear? (I mention the last because I can
just remember them, hammering away at piles of rock in the
country lanes of my childhood. ) Most of our present occupa-
tions will follow these into oblivion, as the transistor inherits
the earth.

For as computers become smaller, cheaper and more re-
liable they will move into every field of human activity. Today

159

they are in the office; tomorrow they will be in the home.
Indeed, some very simple-minded computers already do our
household chores; the device that programs a washing ma-
chine to perform a certain sequence of operations is a special-
ized mechanical brain. Less specialized ones would be able to
carry out almost all the routine operations in a suitably de-
signed house.

Because we have so many more pressing problems on our
hands, only the science-fiction writers— those trail-blazers of
the future— have given much thought to the social life of the
later electronic age. How will our descendants be educated for
leisure, when the working week is only a few hours? We have
already seen, on a worldwide scale, the cancerous growths
resulting from idleness and lack of usable skills. At every
street corner in a great city you will find lounging groups of
leather-jacketed, general-purpose bioelectric computers of a
performance it will take us centuries and trillions of dollars to
match. What is their future— and ours?

More than half a century ago H. G. Wells described, in
The Time Machine, a world of decadent pleasure lovers,
bereft of goals and ambitions, sustained by subterranean ma-
chines. He set his fantasy eight hundred thousand years in the
future, but we may reach a similar state of affairs within a
dozen generations. No one who contemplates the rising curve
of technology from the Pilgrim fathers to the Apollo Project
dare deny that this is not merely possible, but probable.

For most of history, men have been producers; in a very few
centuries, they will have to switch to the role of consumers,
devoting their energies 100 per cent to absorbing the astro-
nomical output of the automated mines, farms and factories.

Does this really matter, since only a tiny fraction of the
human race has ever contributed to artistic creation, scientific
discovery or philosophical thought, which in the long run are
the only significant activities of mankind? Archimedes and
Aristotle, one cannot help thinking, would still have left their
marks on history even if they had lived in a society based on

160

The Electronic Revolution

robots instead of human slaves. In any culture, they would be
consumers of goods, but producers of thought.

We should not take too much comfort from this. The elec-
tronic computers of today are like the subhuman primates of
ten million years ago, who could have given any visiting
Martians only the faintest hints of their potentialities, which
included the above mentioned Archimedes and Aristotle.
Evolution is swifter now; electronic intelligence is only dec-
ades, not millions of years, ahead.

And that— not transistor radios, automatic homes, global
TV— is the ultimate goal of the Electronic Revolution.
Whether we like it or not, we are on a road where there is no
turning back; and waiting at its end are our successors.

161

No. 223,898.

T. A. EDISON.
Electric-Lamp.

Patented Jan. 27, 1880.

€%

i::!'

dnwvrUot
3llC/fU^ (I. SdtdCTV

/" ^^^Tfro^i^O

<«'J.

EDISON'S PATENT on the incandescent lamp was accompanied thickened ends of filament (c), platinum wires Id), clamp, In),

by this drawing. The labeled parte are the carbon filament (o), leading wire, (x), copper wire, (e), tube to vacuum pump (m).

162

Thomas Edison's incandescent lamp, generally as-
sumed to be the product of inspired tinkering, was
actually only one element in a more far-reaching in-
vention: an entire system of lighting.

The Invention of the Electric Light

Matthew Josephson

An article trom Scientific American, 1959.

can hire mathematicians, but
mathematicians can't hire me!"
By such declarations in the time
of his success and world-wide fame
Thomas Alva Edison helped to paint his
own portrait as an authentic American
folk hero: the unlettered tinkerer and
trial-and-error inventor who achieved
his results by persistence and a na-
tive knack for things. He is said, for ex-
ample, to have tried more than 1,600
lcinds of material ("paper and cloth,
thread, fishline, fiber, celluloid, box-
wood, coconut-shells, spruce, hickory,
hay, maple shavings, rosewood, punk,
cork, flax, bamboo and the hair out of a
red-headed Scotchman's beard") until
he hit upon the loop of carbonized cot-
ton thread that glowed in a vacuum for
more than half a day on October 21,
1879. Today, in a world that relies for
its artificial illumination largely on his
incandescent lamp, this invention is not
regarded as an especially profound con-
tribution to technology. It rates rather as
a lucky contrivance of Edison's cut-and-
try methods— of a piece with his stock
ticker, mimeograph machine, phono-
graph and alkaline storage-battery— in
the esteem of a public that has come to
appreciate the enormous practical signif-
icance of higher mathematics and ab-
struse physical theory.

If Edison's contribution to the light
of the world consisted solely in the se-
lection of a filament, this estimate of his
person and achievements might be al-
lowed to stand. But the history that is
so obscured by legend tells quite an-
other story. Edison's electric light was
not merely a lamp but a system of elec-
tric lighting. His invention was an idea
rather than a thing. It involved not only
technology but also sociology and eco-
nomics. Edison was indisputably the
first to recognize that electric lighting

would require that electricity be gen-
erated and distributed at high voltage
in order to subdivide it among a great
many high-resistance "burners," each
converting current at low amperage
(that is, in small volume) with great
efficiency into light.

In the 15 months between the time
he conceived his invention and the date
on which he demonstrated it to the pub-
lic, Edison and his associates designed
and built a new type of electric genera-
tor, successfully adapted the then much-
scorned parallel or "multiple-arc" circuit
that would permit individual lights to
be turned on or off separately and, last
of all, fashioned a lamp to meet the
specifications of his system. The labora-
tory notebooks of those months of fran-
tic labor show the Wizard of Menlo Park
endowed with all the prodigious capaci-
ties attributed to him by contemporary
legend. They show in addition that this
self-taught technologist was possessed of
a profound grasp of the nature of elec-
tricity and an intuitive command of its
logic and power.

It was on September 8, 1878, that
Edison was inspired to devote his talents
full time to the challenge of electric
lighting. On that day he went to An-
sonia, Conn., to visit the brass-manufac-
turing plant of William Wallace, co-
inventor with Moses G. Farmer of the
first practical electric dynamo in the
U. S. Wallace showed Edison eight bril-
liant carbon-arc lights of 500 candle-
power each, powered by a dynamo of
eight horsepower. It was with such a
system that Wallace and Farmer, as well
as Charles Brush of Cleveland, were
then beginning to introduce the electric
light on a commercial scale, for street-
lighting and for illuminating factories
and shops. Farmer had made the first
demonstration of arc-lighting in this

country two years earlier, at the Cen-
tennial Exposition in Philadelphia, and
John Wanamaker's store in that city was
already illuminated with arc lights.

Carbon arcs are still employed in
searchlights and in theater floodlights
and projectors to produce light of high
intensity. The current crossing a small
gap between the electrodes creates an
arc. Ionization and oxidation of the car-
bon in the heat of the arc generate a
brilliant blue-white light.

In the 1870's Europe was a decade
ahead of the U. S. in the technology of
arc-lighting. Stores, railway stations,
streets and lighthouses in Britain and
France were equipped with arc lights.
Shedding an almost blinding glare, they
bumed in open globes that emitted nox-
ious gases, and they could be employed
only high overhead on streets or in pub-
lic buildings. Since they consumed large
amounts of current, they had to be wired
in series, that is, connected one to an-
other in a single continuous circuit so
that all had to be turned on or off to-
gether. The multiple-arc circuit, with the
lights connected as in the rungs of a lad-
der between the main leads of the cir-
cuit, was not adapted to such systems
and was considered prohibitive in cost.

Edison himself had experimented
with arc lights, using carbon strips as
burners. He had also investigated the

Editor's Note

The author has based this article
on material in his biography Edi-
son, just published by the McGraw-
Hill Book Company. Copyright ©
1959 by Matthew Josephson.

163

incandescent light, as had many inven-
tors before him. But the slender rod or
pencil of carbon or metal would always
burn up, sooner rather than later, upon
being heated to incandescence by the
current. It would do so though substan-
tially all of the air had been pumped out
of the glass envelope in which it was
contained. Edison had abandoned the
effort to devote himself to a more prom-
ising invention: the phonograph.

Now at Wallace's establishment, con-
fronted with the achievements of others
in the field, he regained his earlier en-
thusiasm. As an eyewitness recalled,
"Edison was enraptured. ... He fairly
gloated. He ran from the instruments
[the dynamos] to the lights, and then
again from the lights back to the electric
instruments. He sprawled over a table
and made all sorts of calculations. He cal-
culated the power of the instruments
and the lights, the probable loss of power
in transmission, the amount of coal the
instrument would use in a day, a week,
a month, a year."

To William Wallace he said challeng-
ingly: "I believe I can beat you making
the electric light. I do not think you are
working in the right direction." They
shook hands in friendly fashion, and
with a diamond-pointed stylus Edison
signed his name and the date on a goblet
provided by his host at dinner.

From Edison's own complete and ex-
plicit notebooks and from the buoyant
interviews that he gave to the press at
this time we know what made him feel
in such fine fettle as he left Wallace's
plant. "I saw for the first time everything
in practical operation," he said. "I saw
the thing had not gone so far but that I
had a chance. The intense light had not
been subdivided so that it could be
brought into private houses. In all elec-
tric lights theretofore obtained the light
was very great, and the quantity [of
lights] very low. I came home and made
experiments two nights in succession. I
discovered the necessary secret, so sim-
ple that a bootblack might understand
it. . . . The subdivision of light is all
right."

The Subdivision of Light

At this time there flashed into Edison's
mind the image of the urban gas-lighting
system, with its central gashouse and gas
mains running to smaller branch pipes
and leading into many dwelling places at
last to gas jets that could be turned on
or off at will. During the past half-cen-
tury gas-lighting had reached the stature
of a major industry in the U. S. It was

restricted, of course, to the cities; three
fourths of the U. S. population still lived
in rural areas by the dim glow of kero-
sene lamps or candles. Ruminating in
solitude, Edison sought to give a clear
statement to his objective. In his note-
book, under the title "Electricity versus
Cas as a General Illuminant," he wrote:

"Object: E. ... to effect exact imita-
tion of all done by gas, to replace light-
ing by gas by lighting by electricity. To
improve the illumination to such an ex-
tent as to meet all requirements of nat-
ural, artificial and commercial condi-
tions. . . . Edison's great effort— not to
make a large light or a blinding light,
but a small light having the mildness of
gas."

To a reporter for one of the leading
New York dailies who had shadowed
him to Ansonia, Edison described a vi-
sion of a central station for electric light-
ing that he would create for all of New
York City. A network of electric wire
would deliver current for a myriad of
small household lights, unlike the daz-
zling arc lights made by Farmer and
Brush. In some way electric current
would be metered and sold. Edison said
he hoped to have his electric-light in-
vention ready in six weeks! At Menlo
Park, N.J., where his already famous
workshop was located, he would wire all
the residences for light and hold a "grand
exhibition."

Thus from the beginning Edison riv-
eted his attention not so much upon the
search for an improved type of incan-
descent filament as upon the analysis of
the social and economic conditions for
which his invention was intended. As he
turned with immense energy to expand-
ing the facilities at Menlo Park and se-
curing the essential financing, he con-
tinued his studies of the gas-lighting in-
dustry. In parallel he projected the eco-
nomics of the electric-lighting system he
envisioned.

Cas had its inconvenience and dan-
gers. "So unpleasant . . . that in the new
Madison Square theater every gas jet is
ventilated by small tubes to cany away
the products of combustion." But what-
ever is to replace gas must have "a gen-
eral system of distribution— the onlv pos-
sible means of economical illumination."
Gathering all the back files of the gas
industry's journals and scores of volumes
bearing on gas illumination, he studied
the operations and habits of the indus-
try, its seasonal curves and the layout of
its distribution systems. In his mind he
mapped out a network of electric-light
lines for an entire city, making the
shrewd judgment: "Poorest district for

light, best for power— thus evening up
whole city." He meant that in slum dis-
tricts there would be higher demand for
small industrial motors. Against tables
for the cost of converting coal to gas he
calculated the cost of converting coal
and steam into electric energy. An ex-
pert gas engineer, whose services Edison
engaged at this time, observed that few
men knew more about the world's gas
business than did Edison.

Edison had a homo oeconomicus with-
in him, a well-developed social and com-
mercial sense, though he was careless of
money and was not an accountant of the
type exemplified by his contemporary
John D. Rockefeller. Before the experi-
mental work on his invention was under
way, he had formed a clear notion,
stated in economic terms, of what its ob-
ject must be This concept guided his
search and determined the pattern of his
technical decisions, so that the result
would be no scientific toy but a product
useful to people everywhere. By his ini-
tial calculation of the capital investment
in machinery and copper for a whole
system of light distribution he was led
to define the kind of light he sought and
the kind of generating and distributing
system he needed.

Backers of the Electric Light

In the crucial matter of financing his
inventive work Edison had the generous
and imaginative aid of Crosvenor Low-
rey, a patent and corporation lawyer
well established in the financial com-
munity of Wall Street. Lowrey had fall-
en completely under Edison's spell and
regarded him much as a collector of
paintings regards a great artist whose
works he believes are destined for im-
mortality. Using his extensive connec-
tions and the favorable press-notices that
he encouraged Edison to secure during
late September and early October, 1878,
Lowrey assembled a sponsoring syndi-
cate of some of the most important fin-
anciers of the time. The underwriters
of the Edison Electric Light Company,
which was incorporated in mid-October,
included William H. Vanderbilt and
J. P. Morgan's partner Egisto Fabbri.
This was an unprecedented develop-
ment in U. S. business. Inventors had
been backed in the development of in-
ventions already achieved; Edison's fi-
nanciers were backing him in research
that was to lead to a hoped-for invention.
In many respects the venture marks the
beginning in this country of close rela-
tions between finance and technology.

"Their money," Edison said, "was in-

164

The Invention of the Electric Light

EDISON AND HIS PHONOGRAPH were photographed in 1878
by Mathew Brady. He had worked with electric lights but had

turned to the more promising phonograph. In the year that this
photograph was made, however, he resumed his work on lighting.

165

MENLO PARK was depicted in Frank Leslie's Illustrated News-
paper for January 10, 1880. The barnlike "tabernacle" of Edison's

laboratory is visible a! ihe far right. In its windows passengers on
the nearby railroad could see his experimental lights burning.

vested in confidence of my ability to
bring it back again." The 31-year-old
Edison was by now a well-known figure
in Wall Street. His quadruplex telegraph
system, by which four separate messages
could be transmitted over a single wire,
had furnished the pivotal issue in the vast
economic war waged between Western
Union and the rival telegraph empire of
the robber baron Jay Could. Edison's
carbon microphone had transformed the
telephone from an instrument of limited
usefulness to an efficient system of long-
range communication that was now ra-
diating across the country. The shares of
gas-lighting enterprises had tumbled on
the New York and London exchanges
upon Edison's announcement, in the
press campaign instigated by Lowrey,
that he was now about to displace gas
with electricity in the lighting of homes
and factories.

The alliance between Edison and his
sponsors was nonetheless an uneasy one.
The first rift appeared before the end of
October, when the rival inventor Wil-
liam Sawyer and his partner Albon Man
announced that they had "beaten" Edi-
son and applied for a patent on a carbon-
pencil light in a nitrogen-filled glass
tube. There was a flutter of panic in the
directorate of the Edison Electric Light
Company. The suggestion was made
that Edison should join forces with Saw-
yer and Man. Lowrey passed the sug-
gestion on to S. L. Criffin, a former
junior executive at Western Union whom
Lowrey had hired to help Edison with
his business affairs.

Criffin sent back a hasty "confiden-
tial" reply: "I spoke to Mr. Edison re-
garding the Sawyer-Man electric light.
... I was astonished at the manner in
which Mr. Edison received the informa-
tion. He was visibly agitated and said it
was the old story, that is, lack of confi-
dence. . . . No combination, no consoli-

dation for him. I do not feel at liberty to
repeat all he said, but I do feel impelled
to suggest respectfully that as little be
said to him as possible with regard to
the matter."

In view of Edison's talent for candid
and salty language Griffin's reticence is
understandable. After that there was no
further talk of consolidation with Saw-
yer or any other inventor.

The Menlo Park Laboratory

In his belief that he would "get ahead
of the other fellows" Edison was sus-
tained by his unbounded confidence in
his laboratory, its superior equipment
and its staff. The Menlo Park laboratory
was still the only full-time industrial re-
search organization in the country, in
itself perhaps Edison's most important
invention. During this period the physi-
cal plant was greatly expanded; a sep-
arate office and library, a house for two
80-horsepower steam engines, and a
glass blower's shed were added to the
original barnlike "tabernacle." Even
more important, Edison had collected a
nucleus of talented engineers and skilled
craftsmen, who were of inestimable help
to him in working out his ideas.

The self-taught Edison thought pri-
marily in concrete, visual terms. When
he was at work on the quadruplex tele-
graph, he had even built a model made
up of pipes and valves corresponding to
the wires and relays of his system, and
with running water replacing the elec-
tric current, so that he could actually see
how it worked. But now he would have
to depend far more on theory and mathe-
matics.

One of the happiest effects of Gros-
venor Lowrey 's personal influence was
the hiring of Francis R. Upton, a young
electrical engineer who had worked for
a year in the Berlin laboratory of the

great physicist Hermann von Helmholtz.
Edison jocularly nicknamed Upton "Cul-
ture," and, according to an oft-told story,
put the "green" mathematician in his
place with one of his scientific practical
jokes. He brought out a pear-shaped
glass lamp-bulb and gave it to Upton,
asking him to calculate its content in
cubic centimeters. Upton drew the
shape of the bulb exactly on paper, and
derived from this an equation for the
bulb's volume. He was about to compute
the answer when Edison returned and
impatiently asked for the results. Upton
said he would need more time. "Why, '
said Edison, "I would simply take that
bulb, fill it with a liquid, and measure
its volume directly!"

When Upton joined the staff late in
October, Edison had already committed
himself to the incandescent light. This,
rather than the arc light, was the way to
imitate the mildness of gas. But the fila-
ment glowing in a vacuum had been
sought in vain by numerous inventors
for half a century. In choosing the in-
candescent light rather than the arc-
light he was "putting aside the technical
advance that had brought the arc light
to the commercial stage." No one, in-
cluding himself, had succeeded in mak-
ing an incandescent lamp that would
work for more than a few minutes.

Edison's first efforts in 1878 were not
notably more successful. Knowing that
carbon has the highest melting point of
all the elements, he first tried strips of
carbonized paper as "burners" and man-
aged to keep them incandescent for
"about eight minutes" before they
burned up in the partial vacuum of his
glass containers. Turning to the infusi-
ble metals, he tried spirals of platinum
wire; they gave a brilliant light but
melted in the heat. Edison accordingly
devised a feedback thermostat device
that switched off the current when the

166

heat approached the melting point. The
lamp now blinked instead of going out
entirely. Nonetheless, with his eye on
the problem of financing, Edison filed a
patent application on October 5 and in-
vited the press in for a demonstration.

As this discouraging work proceeded
in the weeks that followed, Edison
turned, with Upton's help, to calculating
the current that would be consumed by
a lighting system equipped with a cer-
tain number of such lamps. They as-
sumed that the lights would be con-
nected in parallel, so their imaginary
householder could turn one light in the
circuit on or off at will, as in a gas-light-
ing system. Thinking in round numbers,
they assumed that these lamps, when
perfected, might have a resistance of one
ohm and so would consume 10 amperes
of current at 10 volts. Allowing in addi-
tion for the energy losses in the distribu-
tion system, they found that it would
require a fabulous amount of copper to
light just a few city blocks. Such a sys-
tem of low-resistance lights was clearly
a commercial impossibility.

This was the gist of the objections
which had greeted Edison's first an-
nouncements that he would use an in-
candescent bulb in a parallel circuit.
Typical of the scorn heaped upon him
was the opinion expressed by a commit-
tee set up by the British Parliament to
investigate the crash of gas-lighting se-
curities. With the advice of British sci-

entists, the members of the committee
declared that though these plans seemed
"good enough for our transatlantic
friends," they were "unworthy of the at-
tention of practical or scientific men."
From Ohm's law, which governs the re-
lationship between voltage, amperage
and resistance in a circuit, the report
argued that if an electric light of 1,000
candlepower were divided into 10
smaller lights and connected in parallel,
each of the smaller lights would radiate
not one tenth but "one hundredth only of
the original light." In this judgment such
figures as Lord Kelvin and John Tyndall
concurred. Before the Royal Institution
in London the distinguished electrician
Sir William Preece declared: "Subdivi-
sion of the electric light is an absolute
tgnts fatuus."

Ohm's law does indeed show that the
amount of current (amperes) flowing in
a circuit is equal to the electromotive
force (volts) divided by the resistance
(ohms) in the circuit. Edison's contem-
poraries reasoned that an increase in the
number of lights in a circuit would in-
crease the resistance and therefore re-
duce the flow of current to each. It was
thought that the only way to provide
these lights with sufficient current was to
reduce the resistance in the distribution
system. In a parallel circuit this meant
increasing the thickness of the copper
conductors to an impractical degree.
Such were the limits on the operation

The Invention of the Electric Light

of arc lights, with their low resistance
and huge appetite for current. Upton's
calculations showed that this conclu-
sion also applied to Edison's first low-
resistance incandescent lamps.

Edison now confounded his collabora-
tor by proposing that he make the same
sort of estimates for an entirely different
kind of circuit. This time he would
assume lights of very high resistance,
supplied with current at high voltage
and low amperage. In November and
December Upton made calculations on
the basis of the same number of lights,
but lights with the high resistance of
100 ohms each. These lights were to
operate on the low current of only one
ampere. Their high resistance was to be
offset, in accord with Ohm's law, by the
high voltage of 100 volts in the circuit.
The result was astonishing: A high-
resistance system would require only
one hundredth of the weight of copper
conductor needed for a low-resistance
system. And copper was the most costly
element involved— the decisive eco-
nomic factor.

The High-Resistance System

Here was the crux of Edison's insight
at Ansonia. He had recognized there
that the subdivision of light called for
lamps of high resistance which would
consume but little current; to balance
the electrical equation it would be neces-

INTERIOR OF EDISON'S LABORATORY at Menlo Park was
also depicted in the January 10, 1880, issue of Frank Leslie's

Illustrated Newspaper. At the time of the work on the electrir
light the laboratory had expanded into several other buildings.

167

sary to supply the current at high volt-
age. This was the "necessary secret" that
was "so simple." Today every high-
school physics student learns that the
power lost in transmitting electric ener-
gy varies with the square of the current.
Thus a tenfold reduction in current
meant a decrease of a hundredfold in the
energy wasted (or a hundredfold de-
crease in the weight of the transmis-
sion line). It was a conception easily
reached by an elementary applica-
tion of Ohm's law, but it had not oc-
curred to any of Edison's contem-
poraries. Even Upton did not immedi-
ately grasp the full import of Edison's
idea. As he said later: "I cannot imagine
why I did not see the elementary facts
in 1878 and 1879 more clearly than I
did. I came to Mr. Edison a trained man,
with a year's experience in Helmholtz's

laboratory, ... a working knowledge of
calculus and a mathematical turn of
mind. Yet my eyes were blind in com-
parison with those of today; and ... I
want to say that I had company!"

With Upton's figures before him Edi-
son was convinced that a new and strate-
gic invention lay surely within his grasp.
It was clear what kind of distributing
system he wanted. And he knew what
form of incandescent burner would serve
his purpose. To offer the necessary re-
sistance to the passage of current it must
have a small cross section and so would
have a small radiating surface.

By January, 1879, Edison was testing
his first high-resistance lamp. It had a
spiral of very fine platinum wire set in
a globe that contained as high a vacuum
as could be achieved with an ordinary
air pump. The results were encourag-

ing; these lamps lasted "an hour or two."
He then attacked the dual problem of
getting a higher vacuum and improving
his incandescing element. After another
trial with carbon, he returned to metals:
platinum, iridium, boron, chromium,
molybdenum, osmium— virtually every
infusible metal. He thought of tungsten,
but could not work it with existing tools.
Discouraged by the problem, Edison
tried nitrogen in his globe and then re-
sumed his efforts to obtain a higher
vacuum. Hearing of the new and effi-
cient Sprengel vacuum pump, which
used mercury to trap and expel air, he
sent Upton to borrow one from the near-
by College of New Jersey (now Prince-
ton University). When Upton returned
with the pump late that night, Edison
kept him and the other men on the staff
up the rest of the night trying it out.

GENERATOR which Edison developed for the needs of electric
lighting appears at right in this engraving from Scientific Ameri-

can for October 18, 1879 (at that lime this magazine appeared
weekly I. The generator was railed the "long-w .listed Mary Ann."

168

The Invention of the Electric Light

At this stage Edison made a useful
finding: "I have discovered," he noted,
"that many metals which have gas with-
in their pores have a lower melting point
than when free of such gas." With the
aid of the Sprengel pump he devised a
method of expelling these occluded
gases, by heating the element while the
air was being exhausted from the bulb.
The platinum wire within the bulb
thereupon became extremely hard and
could endure far higher temperatures.
Edison later said that at this stage he
"had made the first real steps toward the
modern incandescent lamp."

Meanwhile the spirits of his financial
sponsors had begun to droop. Their bril-
liant inventor, far from having achieved
anything tangible, was hinting plainly
that he needed more monev. The first
Brush arc lights were ablaze over lower
Broadway, and more were being in-
stalled elsewhere with impressive effect.
Edison's backers began to have serious
doubts as to whether he had pursued the
right course. To shore up their morale
Lowrey arranged to have Edison give
them a private demonstration.

In April, as one of Edison's associates
recalled it, 'They came to Menlo Park
on a late afternoon train from New
York. It was already dark when they
were conducted into the machine shop
where we had several platinum lamps in-
stalled in series." The "boss" showed his
visitors pieces of platinum coil he was
using in the lamps, pointed out the
arrangement of the lights and described
the type of generator he hoped to build.
Then, the room having grown quite
dark, he told "Honest John" Kruesi to
"turn on the juice slowly."

"Today, I can still see those lamps
rising to a cherry-red . . . and hear Mr.
Edison saying 'A little more juice' and
the lamps began to glow. 'A little more,'
. . . and then one emits a light like a
star, after which there is an eruption
and a puff, and the machine shop is in
total darkness. . . . The operation was
repeated two or three times, with about
the same results."

The platinum coils still consumed a
lot of power for the light they gave, and
they were costly and short-lived. The
temporary Wallace-Farmer dynamos
heated up badly, and were not powerful
enough to enable Edison to connect his
lamps in parallel. Edison admitted that
the system was not yet "practical."

It was a gloomy gathering that broke
up on that raw April evening. All of
Lowrey's abounding faith would be nec-
essary to rally, the spirits and funds of
Edison's despondent backers. Some

VACUUM PUMP used to remove air from lamp bulbs (lop center) was of a new type about
which Edison had read in a scientific journal. The man is holding a vessel of mercury.

rumors of the disappointing demonstra-
tion leaked out; the price of Edison stock
fell sharply, while that of gas-lighting
securities rose. "After that demonstra-
tion," Edison's associate relates, "we
had a general house cleaning at the labo-
ratory, and the metallic lamps were
stored away."

Edison now rallied his staff to efforts
on a much broader area of the front
"under siege." He followed three main
lines of investigation. One group he
detailed to the task of developing the
dvnarno to supply the constant-voltage

current required by his high-resistance
system. He set another group to pulling
down a still higher vacuum in the glass
bulbs. The third team, under his watch-
ful eye, carried out the series of experi-
ments in which 1,600 different materials
were tested for their worth as incan-
descent elements.

The "Long-Waisted Mary Ann"

To subdivide the electric current for
numerous small lights in parallel Edison
needed a dynamo which would produce

169

a higher voltage than any dynamo in ex-
istence, and which would maintain that
voltage constant under varying demands
for current from the system. Existing
dynamos were designed around the fal-
lacious notion, held by most electrical
experts, that the internal resistance of
the dynamo must be equal to the ex-
ternal resistance of the circuit. Through
study of battery circuits they had proved
that a dynamo could attain a maximum
efficiency of only 50 per cent. In 1877 a
committee of scientists appointed by the
Franklin Institute in Philadelphia had
been impressed to discover that the most
successful European dynamo, designed
by Zenobe Theophile Cramme, con-
verted into electricity 38 to 41 per cent
of the mechanical energy supplied to
it. The efficiency of the Brush dynamo
was even lower: 31 per cent. These ma-
chines and their theoretically successful

contemporaries all produced current at
a relatively low voltage.

Edison had concluded, however, that
he must produce a dynamo of reduced
internal resistance capable of generating
current at a high voltage. Such a ma-
chine would not only meet the needs of
his lighting system but would also con-
vert mechanical energy to electrical en-
ergy with far greater efficiency. As his
associate Francis Jehl recalled, Edison
said that "he did not intend to build up
a system of distribution in which the ex-
ternal resistance would be equal to the
internal resistance. He said he was just
about going to do the opposite; he
wanted a large external resistance and
a low internal resistance. He said he
wanted to sell the energy outside the
station and not waste it in the dynamo
and the conductors, where it brought no
profits." Jehl, who carried out the tests

SERIES CIRCUIT (top) requires thai a number of electric lights (circles) be turned on
or off at the Mine time by a single switch (break in circuit). Parallel circuit (bottom),
which was adopted by Edison, makes it possible to turn lights on or off one at a time.

EDISON'S LIGHT.

IJie Great Inventor's Triumph in
Electric Illumination.

A SCRAP OF PAPER.

It Makes a Light, Without Gas or
Flame, Cheaper Than Oil.

TRANSFORMED IN THE FURNACE.

Complete Details of the Perfected
Carbon Lamp,

FIFTEEN MONTHS OF TOIL.

Siory of His Tireless Experiments with Lamps,
Barters acd Generators.

SUCCESS IN A COTTON THREAD.

The Wizard's Byplay, with Bodily Pain
and Gold "Tailings."

HISTORY OF ELECTRIC LIGHTING.

The oar approach of ine first puoltc exhibition of
Sduon's long looked for electric light, uooaued to
take place on New Vuri Eve at Menlo Pari, on
»UicU occasion that place will bo Illuminated with
the Dew light, has revived public lotereet In the
great inventor's work, and throughout tte mvlllsed
world scientists and people generally are anxiously
'•raiting the result. From the beginning of hie ex-
periments in electric lighting to the preeent lime
klr. Edison h.e kept his laboratory gaardedly
closed, and no authoritative account (except that
PubUahed lu the Uuild some months ago rotating,
to his first patent) of any of the important steps of
his progress has been made public — a course of pro-
cedure the Inreutor found absolutely necessary for
his own protection. The BxaiLO la now, however,
suabled to preeent to Its res dire a foil and accurate
account of his work from Its Inception to its oom-
pUilon.

a uoertZD nru.

EJitou's electric light, lucredible as It may appear.
Is produced from a little piece of paper — a tiny strip
or pauar that a breath would blow away. Through

FIRST NEWSPAPER ACCOUNT of Edi-
son's brilliant success appeared in The
/Vein York Herald for December 21, 1879.

170

The Invention of the Electric Light

of resistance, also remarked that the art
of constructing dynamos was then as
mysterious as air navigation. All elec-
t :cal testing was in the embryonic stage.
"There were no instruments for measur-
ing volts and amperes directly: it was
like a carpenter without his foot rule."

Upton himself had his difficulties in
this hirherto unexplored field: "I re-
member distinctly when Mr. Edison gave
me the problem of placing a motor in
circuit, in multiple arc, with a fixed re-
sistance; and I . . . could find no prior
solution. There was nothing I could find
bearing on the [effect of the] counter-
electro-motive force of the armature . . .
and the resistance of the armature on the
work given out by the armature. It was a
wonderful experience to have problems
given me by him based on enormous ex-
perience in practical work and applying
to new lines of progress."

The problem of a constant-voltage
dynamo was attacked with the usual
Edisonian elan. Seeking to visualize
every possible structural innovation for
his dynamo armature, he had his men
lay out numerous wooden dummies on
the floor and wind wire around them,
spurring them on in their task by laying
wagers as to who would finish first,.

After Edison had decided upon the
form of winding and type of electromag-
nets to be used, Upton made drawings
and tables from which the real armatures
were wound and attached to the com-
mutator. Edison eventually worked out
an armature made of thin sheets of iron
interleaved with insulating sheets of
mica; this armature developed fewer
eddy currents and so produced less heat
than the solid armature cores then used.
When the new cores were test-run, it
was Upton who made the mathematical
calculations from these tests and drew
up the final blueprints.

The self-effacing Upton can be given
principal credit for interpreting Edi-
son's ideas and translating them into
mathematical form. A careful student of
contemporary electrical knowledge, he
seems to have been conversant with, and
to have guided himself by, the design of
a German dynamo, made by the Siemens
works, that employed an auxiliary source
of current to excite its field magnets.

The new Menlo Park dynamo com-
prised many admirable features for that
period. With its great masses of iron and
large, heavy wires, it stood in bold con-
trast to its contemporary competitors.
Owing to the two upright columns of its
field electromagnets, it was nicknamed
"Edison's long-waisted Mary Ann."

When the dynamo was run at the cor-
rect speed, the voltage between its arma-

ture brushes was approximately 110,
and remained fairly constant, falling but
slightly when increasing amounts of cur-
rent were taken out of the machine.
Edison and Upton also contrived a sim-
ple but ingenious dynamometer by
which the torque of a drive belt was
used to measure the work output of the
steam engine that powered the dynamo.
When Kruesi completed the first oper-
ating machine, Upton carefully checked
the results. To his astonishment— and
quite as Edison had "guessed"— the new
dynamo, tested at full load, showed 90-
per-cent efficiency in converting steam
power into electrical energy.

Ldison was as jubilant as a small boy.
As was usual with him, the world was
soon told all about his "Faradic ma-
chine." It was described and depicted in
Scientific American for October 18,
1879, in an article written by Upton.

Once more there was scoffing at
Edison's "absurd claims." The hectoring
of Edison by some of the leading U. S.
electrical experts, among them Henry
Morton of the Stevens Institute of Tech-
nology, now seems traceable to their
ignorance. Reading Morton's predictions
of failure, Edison grimly promised that
once he had it all running "sure-fire,"
he would erect at Menlo Park a little
statue to his critic which would be eter-
nally illuminated by an Edison lamp.

As a matter of fact, this allegedly
ignorant "mechanic" was to be found
reading scientific journals and institu-
tional proceedings at all hours of the day
and night. It was thus that he had
learned about the Sprengel vacuum
pump. This device enabled him to
achieve an increasingly greater vacuum
and to test a broad variety of metals, rare
earths and carbon compounds under
hitherto unexplored conditions.

The globe itself was also much im-
proved, by the inventor's own design,
after he had brought to Menlo Park an
artistic German glass blower named
Ludwig Boehm. Edison one day drew a
sketch of a one-piece, all-glass globe
whose joint was completely sealed, and
late in April, 1879, Boehm, working skill-
fully with hand and mouth, fashioned
it in the small glass blower's shed in back
of the laboratory.

"There never has been a vacuum pro-
duced in this country that approached
anywhere near the vacuum which is
necessary for me," Edison wrote in his
notebook. After months of effort he could
say exultantly: "We succeeded in mak-
ing a pump by which we obtained a
vacuum of one-millionth part of an
atmosphere."

In the late summer of 1879 he realized

with growing excitement that a key posi-
tion had been won. He had a dynamo
supplying constant high voltage, and a
tight glass globe containing a high vacu-
um. In his mind's eye he saw what might
be done with an extremely fine, highly
resistant incandescing substance under
these conditions. His state of tension is
reflected in the laboratory notebooks by
such exclamations as: "S - - - ! Glass
busted by Boehm!" All that remained for
him was to discover a filament that
would endure.

The Carbon Filament

In late August or early September—
about a year after he first took up his
search— he turned back to experiment-
ing with carbon, this time for good. The
rods of carbon he had tried earlier had
been impossible to handle, as he now
understood, because carbon in its porous
state has a marked propensity for ab-
sorbing gases. But once he had a truly
high vacuum and a method for expelling
occluded gases he saw that he might
achieve better results with carbon than
with platinum.

In a shed in back of the laboratory
there was a line of kerosene lamps always
burning, and a laborer engaged in scrap-
ing the lampblack from the glass chim-
neys to make carbon cake. But lampblack
carbon by itself was not durable enough
to be made into fine lamp filaments. Edi-
son and Upton had an-ived at the conclu-
sion that, given a 100-volt multiple-arc
circuit, the resistance of the lamps should
be raised to about 200 ohms; this meant
that the filament could be no thicker
than a 64th of an inch.

Through the summer months Edison
and his staff worked at the tantalizing
task of making fine reeds of lampblack
carbon mixed with tar. His assistants
kept kneading away at this putty-like
substance for hours. It seemed impos-
sible to make threads out of it; as an
assistant complained one day, the stuff
crumbled.

"How long did you knead it?" Edison
asked.

"More than an hour."

"Well just keep on for a few hours
more and it will come out all right."

Before long they were able to make
filaments as thin as seven thousandths
of an inch. Edison then systematically
investigated the relations between the
electrical resistance, shape and heat
radiation of the filaments. On October
7, 1879, he entered in his notebook
a report on 24 hours of work. "A spiral
made of burnt lampblack was even bet-
ter than the Wallace (soft carbon) mix-

171

hire." This was indeed promising: the
threads lasted an hour or two before
they burned out. But it was not yet
good enough.

As he felt himself approaching the
goal Edison drove his co-workers harder
than ever. They held watches over cur-
rent tests around the clock, one man
getting a few hours' sleep while another
remained awake. One of the laboratory
assistants invented what was called a
"corpse-reviver," a sort of noise machine
that would be set going with horrible
effect to waken anyone who overslept.
Upton said that Edison "could never
understand the limitations of the
strength of other men because his own
mental and physical endurance seemed
to be without limit."

The laboratory notebooks for October,
1879, show Edison's mood of anticipation
pervading the whole staff. He pushed on
with hundreds of trials of fine filaments,
so attenuated that no one could conceive

how they could stand up under heat.
Finally he tried various methods of
treating cotton threads, hoping that their
fibrous texture might give strength to
the filament even after they had been
carbonized. Before heating them in the
furnace he packed them with powdered
carbon in an earthenware crucible
sealed with fire clay. After many failures
in the effort to clamp the delicate fila-
ment to platinum lead-in wires, Edison
learned to mold them together with
lampblack and then fuse the joint be-
tween them in the act of carbonization.
Then, as Edison later related, it was
necessary to take the filament to the
glass blower's shed in order to seal it
within a globe: "With the utmost pre-
caution Batchelor took up the precious
carbon, and I marched after him, as if
guarding a mighty treasure. To our con-
sternation, just as we reached the glass
blower's bench, the wretched carbon
broke. We turned back to the main
laboratory and set to work again. It was

late in the afternoon before we produced
another carbon, which was broken by
a jeweler's screwdriver falling against
it. But we turned back again and before
nightfall the carbon was completed and
inserted in the lamp. The bulb was ex-
hausted of air and sealed, the current
turned on, and the sight we had so long
desired to see met our eyes."

"Ordinary Thread"

The entries in the laboratory note-
books, although bare and impersonal,
nonetheless convey the drama and sense
of triumphant resolution pervading the
laboratory that night: "October 21—
No. 9 ordinary thread Coats Co. cord
No. 29, came up to one-half candle and
was put on 18 cells battery permanently

at 1:30 A.M No. 9 on from 1:30

A.M. till 3 P.M.-13X hours and was then
raised to 3 gas jets for one hour then
cracked glass and busted."

As the light went out the weary men

EARLY EXPERIMENTAL LAMP is de-
picted in one of Edison's notebooks. Thi>
lamp had a filament of platinum. It mehed.

FRANCIS R. UPTON made invaluable calculations for Edison's system. An electrical en-
gineer who had studied with Hermann von Helmholtz, he was named "Culture" by Edison.

172

The Invention of the Electric Light

waiting there jumped from their chairs
and shouted with joy. Edison, one of
them recalled, remained quiet and then
said: "If it can bum that number of hours
I know I can make it bum a hundred."
Yet all the workers at Menlo Park— Edi-
son, Upton, Kruesi, Boehm and the rest-
were completely astonished at their suc-
cess. They had become accustomed to
laboring without hope. "They never
dreamed," as one contemporary account
put it, "that their long months ... of
hard work could be ended thus abruptly,
and almost by accident. The suddenness
of it takes their breath away."

For once Edison tried to be discreet
and keep his momentous discoveries a
secret until he could improve upon his
lamp filament. At length, after experi-
menting with various cellulose fibers,
he found that paper, in the form of tough
Bristol cardboard, proved most endur-
ing when carbonized. Edison was ex-
ultant when this filament burned for 170
hours, and swore that he would perfect
his lamp so that it would withstand 400
to 1,000 hours of incandescence before
any news of it was published.

On November 1, 1879, he executed a
patent application for a carbon-filament
lamp. Its most significant passage was
the declaration: "The object of the in-
vention is to produce electric lamps giv-
ing light by incandescence, which lamps
shall have high resistance, so as to allow
the practical subdivision of the electric
light. . . . The invention consists in a
light-giving body of carbon wire ... to
offer great resistance to the passage of
the electric current, and at the same
time present but a slight surface from
which radiation can take place." The
specifications called for a distinctive
one-piece all-glass container, lead-in

wires of platinum that passed through
the glass base and were fused to the
carbon filament, and joints that were
sealed by fusing the glass.

Here were the essential features of
the basic Edison carbon-filament lamp,
in the form that was to be known to the
world during the next half century. It
was not the "first" electric light, nor
even the first incandescent electric
lamp. It was, however, the first practical
and economical electric light for uni-
versal domestic use.

Edison had spent more than $42,000
on his experiments-far more than he
had been advanced by his backers. Now
he asked for more money so that he
might complete a pilot light-and-power
station at Menlo Park: But the directors
were still uncertain about the future of
the invention. Was it "only a laboratory
toy," as one of them charged? Would
it not need a good deal of work before it ,
became marketable? Crosvenor Lowrey
stoutly defended his protege\ He got no
results until he prematurely, and over
Edison's objections, made the secret of
the electric lamp public.

Rumors had been spreading for sev-
eral weeks. New Jersey neighbors told
of brilliant lights blazing all night at
Menlo Park, and railroad passengers be-
tween New York and Philadelphia also
saw the bright lights with astonishment
from their train windows. In Wall Street
there was a flurry of speculation in
Edison stock; the price rose briefly to
$3,500 a share.

Then came a front-page story in The
New York Herald on Sunday, December
21, 1879. There followed an exclusive
article about the inventor's struggles for
the past 14 months, told to the world,
con amore, by Marshall Fox, who had

written much of Edison before. The de-
tailed treatment of such an adventure
in applied science as a feature story was
something of an innovation. Also some-
what unusual in the journalism of the
time was its relative accuracy of detail,
owing to help provided by Upton, who
also supplied drawings for the Herald's
Sunday supplement. The writer did his
best to explain how this light was pro-
duced from a "tiny strip of paper that
a breath would blow away"; why the
paper filament did not burn up but be-
came as hard as granite; and how the
light-without-flame could be ignited—
without a match— when an electric cur-
rent passed through it, giving a "bright,
beautiful light, like the mellow sunset
of an Italian autumn."

In the week following Christmas hun-
dreds of visitors made their way to the
New Jersey hamlet. Edison hurried with
his preparations for an announced New
Year's Eve display as best he could, but
was forced to use his whole staff of 60
persons to handle the crowds. He could
do no more than put on an improvised
exhibition, with only one dynamo and
a few dozen lights.

The closing nights of the year 1879
turned into a spontaneous festival that
reached its climax on New Year's Eve,
when a mob of 3,000 sight-seers flooded
the place. The visitors never seemed to
tire of turning those lights on and off.

The inventor promised the sight-seers
that this was but a token of what was
in store. He was awaiting the completion
of a new generator, he said, and intended
to illuminate the surroundings of Menlo
Park, for a square mile, with 800 lights.
After that he would light up the dark-
ness of the neighboring towns, and even
the cities of Newark and New York.

173

Hi-fi is a field in which erroneous ideas abound.
Both human and electronic factors are involved in
the accurate reproduction of sound.

11 High Fidelity

Edgar Villchur

Two chapters from his book Reproduction of Sound published in 1962.

It might appear that following a dis-
cussion of the nature of sound, the
logical subject to consider would be
the criteria for reproducing this sound
with "high fidelity" to the original. One
other element, however, should be cov-
ered first— the way in which we hear.

Perception of Sound

We have already seen, in examining
units of measurement for pitch and
power— the octave and the decibel— that
our perception of sound does not neces-
sarily correspond directly to the objec-
tive reality. The illusion is consistent,
however, so that a given sound always
has the same effect on a normal ear.

An important element in the percep-
tion of sound was discovered by Fletcher
and Munson in 1933. These investigators
demonstrated that our impression of
loudness did not depend solely on the
amplitude of the sound wave, but on
other things as well. Specifically, they
showed that sound in the lower treble
range of the frequency spectrum-the
3500-cps region— appeared to be much
louder than sound of the same amplitude

at any other part of the spectrum. Thus,
if the frequency scale was swept by a
tone which continuously rose in fre-
quency but kept exactly the same ampli-
tude, the loudness, or apparent ampli-
tude, would increase to a maximum at
about 3500 cps and then fall off again.

This fact does not have much practical
interest for the person listening to re-
produced music, except as it describes
the relative nuisance value of different
types of noise. No matter how lop-sided
our interpretation of acoustic reality, we
make the same interpretation in the con-
cert hall as in our living room, and the
craftsmen who designed musical instru-
ments (who worked to satisfy their ears,
not sound-level meters) perceived sound
in the same way.

Fletcher and Munson made a second
discovery, however, that does bear di-
rectly on the reproduction of sound.
They found that the effect described
above took place in varying degree, de-
pending on the over-all level of the
sound. For very high amplitude sound
the drop in loudness with frequency
below 3500 cps hardly occurred at all,

175

while for very soft sound the effect was
maximum. Above 3500 cps the effect re-
mained constant, within 2 or 3 db, no
matter what the over-all sound level.

The well-known "equal loudness con-
tours," also referred to as the Fletcher-
Munson curves, are reproduced in Fig.
2—1. Each curve plots the sound ampli-
tude required to produce the same per-
ceived loudness at different frequencies
of the scale. It can be seen that normal
hearing losses in the bass end become
progressively greater as the over-all
sound level is decreased.

This means that if an orchestra plays
a musical passage at the sound level rep-
resented by 90 db, and if this music is
reproduced at the 60 db level, we will
hear the bass with less relative loudness
than we would have heard it at the con-
cert itself. If you follow the 90- and
60-db curves, shown superimposed in
Fig. 2—2, you will see that there is ap-
proximately a 14 db perceived loss at
50 cps— it takes 14 db more of actual
amplitude, in the lower curve, to pro-
duce the same relative loudness at 50
cps as it does in the upper curve.

In order to re-create the original bal-
ance of perceived frequencies at low vol-

ume levels, it has become customary to
introduce bass boost which is related to
the setting of the volume control, either
automatically or otherwise.

A volume control tied to automatic
bass boost is called a loudness control.
(Some loudness controls also boost the
treble spectrum appreciably at low vol-
ume settings. There is no justification
for this in the Fletcher-Munson curves. )

High Fidelity to What?

The assumption will be made here
that the purpose of high fidelity equip-
ment is to reproduce as closely as possi-
ble the experience of the concert hall,
not to transcend or improve it.

I remember an exhibition at New
York's Museum of Modern Art, during
the late thirties, of "high fidelity" repro-
ductions of water color paintings. Life-
size reproductions were hung side by
side with the originals, and it was often
difficult or impossible to tell them apart.
There was no question in anyone's mind
about how to judge the quality of these
prints. The only criterion was accuracy.
The public that visited the exhibit was
used to looking at paintings, and was
able to make an immediate comparison

Fig. 2-1. The Fletcher-
Munton equal loud-
ness contours. For
•ach curvo, the
height at any point

repre»enf» the found
amplitude required to
produce the •am*
• ubjective loudness
as at 1000 cps. (After
Fletcher and Munson)

FEELING

-'z.

^^c

ai 60

s^s

s^\

F-^.

>— —

■^~-

■J

-1 ll

500 WOO 2000

IN CrCLES PER SECOND

5000 10,000 20,000

176

High Fidelity

•X

* .20
> S «!0

£ z

i! »

z
o-'o

20 DB

1 H—

3D6 «o

-3

I '

-*3

20 ' ' ' • •

100 iooo 10

FREQUENCY IN CYCLES PER SECOND

2001

Fig. 2-2. The 60 and
90 db Fletcher-Mun-
ton curvet superim-
posed. The shaded
area represents the
difference in normal
hearing loss from one
sound level to the
other.

between the copy and the original. No.
one thought of the prints as entities in
themselves, with qualities independent
of the qualities of the originals.

This point of view does not always
hold in the field of high fidelity musical
reproduction. Only a minority of today's
high fidelity public are concert-goers.
Many have never attended a live con-
cert; they know the sound of the orches-
tra or of individual musical instruments
only as it is reported by amplifiers and
loudspeakers. They may know what they
like in reproduced sound, but they have
no way of evaluating the realism of
reproduction.

This partly explains why so much vari-
ation is tolerated in audio equipment.
The same record may sound very dif-
ferent when played through different
brands of equipment, each brand equally
acceptable in the market place. The
evaluation of high fidelity components
is popularly thought of as an entirely
subjective matter, like comparing the
tone of one violin to that of another
rather than like holding a facsimile up to
its original.

For similar reasons high fidelity dem-
onstrations such as the annual Hi-Fi
shows can get away with a lot of sound
that is startling but essentially non-mu-
sical. Some of the "reproduced" sound
that greets the show visitor is necessarily
unfamiliar because it has no live coun-
terpart. A harmonica blown up in vol-
ume to the dimensions of a theatre organ
is a new and different instrument. A

crooner whispering into a microphone
an inch away invents a new sound; his
unamplified voice is never heard in pub-
lic. A combination of Bongo drum,
chimes and electric guitar creates a tutti
which one may like or dislike, but for
which there is no equivalent in one's
memory to serve as a live standard.

Such sound can only be accepted as
a self-sufficient entity, like an old calen-
dar chromo. Any resemblance to five
music or to painting is purely coinci-
dental, and the science and /or art of
reproduction is not really involved.

High fidelity has undoubtedly in-
creased rather than decreased the ranks
of music lovers, and there are probably
more people than ever who are unim-
pressed with gimmick sound. Many de-
signers and manufacturers in the field
work only for naturalness of reproduc-
tion. The designer of integrity avoids
like the plague those exaggerations that
sometimes attract the novice— over-em-
phasized bass for "depth," over-em-
phasized mid-range for "presence,"
over-emphasized treble for "brilliance."
These distortions are more properly
called, respectively, boominess, nasality
or "honkiness," and harshness.

Many demonstrations are not, fortu-
nately, of the gimmick type, and use
musical material played at musical lev-
els. There have also been concerts staged
with live musicians, in which direct com-
parisons of reproduced sound to the
sound of the live instruments could be
made, in the same way that direct com-

177

parisons of prints to original paintings
were made at the Museum of Modern
Art. The live vs. recorded public concert
is one method of giving direction to
equipment designers and perspective to
high fidelity consumers. Although trans-
ferring concert hall atmosphere to the
home has special problems of its own,
success in creating an identity of sound
in the concert hall itself solves the major
part of the problem. Even more vital to
maintaining balance and perspective in
the high fidelity world is live concert
attendance.

We are now prepared to discuss the
technical standards of quality that may
be applied to a sound reproducing sys-
tem. There will be no dividing lines pro-
posed, at which low fidelity becomes
medium, high, or super.

Frequency Response

The frequency response of a sound re-
producing system, or of one of its com-
ponents, describes its relative handling
of parts of the input signal which differ
in frequency. "Handling" may refer to
electrical amplification, as in an ampli-
fier, to conversion of mechanical to elec-
trical energy, as in a pickup, or to con-
version from electrical to acoustical
energy, as in a loudspeaker.

There are two aspects of frequency
response: the range of frequencies han-
dled, and the uniformity with which the
unit or system responds to different fre-
quencies. Knowledge of the first of these
is useless without knowledge of the sec-
ond. Let us therefore pass over the ques-
tion of range for the moment, and deter-
mine what uniformity will be required
for the range we finally decide on.

Uniformity of Response

Although the trained ear can usually
perceive a change of sound level of a
db or less in test signals, the average
observer is probably less sensitive to a
change of sound level in a particular
frequency range of a musical passage.

Reproduction which remains constant
over its frequency range within one or
two db would thus probably be ade-
quate for perfect apparent fidelity, other
things being equal.

This standard can be met in amplifiers
without much difficulty, even at high
power levels. The best pickups are also
able to conform, but loudspeakers are
laggard in this respect.

The results of non-uniform reproduc-
tion are several. Undue volume in a par-
ticular section of the sound spectrum
can produce stridency or boominess as
opposed to natural musical sound. More
particularly, the existence of sharp peaks
in the response curve, usually repre-
senting a resonant condition, mean that
hangover or ringing may be present—
the speaker cone or section of cone will
continue to vibrate after the signal has
stopped. This is perceived as a "rain-
barrel" effect, a muddying up of the
sound and impairment of the distinct-
ness of the different instrumental voices.
Such an effect is also indicated when the
listener is unable to distinguish clearly
the pitch of low-frequency tones.

Another important effect of peaked
frequency response is the exaggeration
of unwanted noise components such
as turntable rumble or record surface
scratch. This effect was not given its due
recognition in the earlier days of high
fidelity, when the existence of rumble
and surface noise was proudly displayed
as evidence of extended frequency range.

The amount of surface noise in a
good quality modern LP record and the
amount of rumble from a good record
player are such that there will not be
much significant noise produced in a
system with uniform frequency response,
even though the frequency range be ex-
tended to the limits of the present state
of the art. In a comparison test con-
ducted recently between two tweeters,
the one which was able to reproduce
almost an octave more of treble (into the
inaudible region) showed a dramatic

178

High Fidelity

decrease of surface noise, due to its ex-
treme evenness of response. There was
no selective reproduction of discrete fre-
quency regions, and the switch to the
superior speaker produced a fuller, more
natural treble simultaneously with the
reduction in surface noise.

A similar situation exists with regard
to turntable rumble. A peaked system
whose response falls off rapidly below
60 cps may exhibit more turntable
rumble than a smooth system whose
full response extends an octave lower.

Tell-tale evidence of the existence of
peaked reproduction in the bass may be
gathered from listening to the reproduc-
tion of speech. The male speaking voice
ordinarily contains no sound compo-
nents whose frequency is below 100 cps,
and the reproducing system should give
no hint (by a boomy, resonant quality
in the voice) that it is also capable of
speaking in the tones of the double bass.

Range of Response

It is generally agreed among acoustics
authorities that the range of 40 to 15,000
cps is sufficient for perfect or near-per-
fect apparent fidelity in the reproduction
of orchestral music. The phrase "near-
perfect" is meant to imply that when
such a range has been achieved the de-
signer should direct his attention to inac-
curacies of reproduction more gross than
are associated with the frequency limita-
tions indicated.

For the pipe organ enthusiast, how-
ever, there is significant intelligence
(significant, that is, from the point of
view of the emotional impact of the
music) down to 32 cps or lower. 32.7
cps is three octaves below middle C rela-
tive to A-440, and is the lowest note of
the average pipe organ, although many
larger organs reach down an octave
lower. These low organ tones are distin-
guished by the fact that they contain
a strong fundamental component. The
lowest tones of the piano, on the other
hand, contain no fundamental energy

that significantly affects the quality of
the sound. Even though the lowest key
on the piano strikes 27.5 cps, response
down to this frequency is not required
for the reproduction of piano music.

Probably no characteristic of audio
components is so freely booted about
by advertising copywriters as frequency
range. Any numerical range of frequen-
cies listed is totally meaningless unless
accompanied by a description of the
decibel tolerance above or below refer-
ence that is being used, and, for a loud-
speaker, by a description of off-axis re-
sponse as well. A 3-in. speaker made
for portable radios will "respond" when
stimulated by a 30-cps signal— perhaps
by having its cone tear loose and fly out
into the air— and almost any speaker,
even a woofer, will make some kind of
sound when stimulated by a high-pow-
ered 15,000-cps signal. A frequency re-
sponse rating must mean something
more than that a signal of given fre-
quency makes a speaker move audibly,
or that it makes an amplifier show an
electrical output of some sort at its ter-
minals. It must mean that within a stated
frequency range, and, for power devices,
within a stated range of power, the fun-
damental output of a given device is
uniform to a stated degree.

Treble Dispersion

The on-axis response of a loudspeaker
may be very deceiving, because the
higher frequencies tend to be directed
in a beam which continually narrows as
the frequency is raised. Good sound dis-
persion must therefore be a qualifying
factor for any treble response curve.

A speaker which has relatively uni-
form treble output both on-axis and off-
axis (over a reasonably large solid angle
—perhaps 45 degrees in any direction
from the axis) will reproduce music with
a "spaciousness" that does not exist
when there is more concentrated beam-
ing of the treble. Furthermore, severely
attenuated off-axis response in the treble

179

means that the total sound power radi-
ated at treble frequencies is considerably
less than that implied by the on-axis
response curve. It is this total radiated
power, rather than the on-axis pressure,
that determines whether a speaker will
sound dull, natural, or over-bright in a
normally reverberant room.

Transient Response

Transient response refers to the ac-
curacy of reproduction of the wave
envelope, and is concerned with the
reproduction of attack and decay char-
acteristics of the sound. We have seen
that uniform frequency response predicts
the absence of ringing; if the steady-
state frequency response curve does not
have peaks, the reproduced sound will
die away just as in the original.

Consider, for example, the tone repre-
sented in (A) of Fig. 2—3. Perfect re-
production would produce an identical
wave form, differing perhaps only in
amplitude, while poor transient response
would be indicated by the hangover that
is apparent in (B). The continuation of
the reproduced signal after the original

END OF REPRO-
DUCED TONE
SHOWING
HANGOVER

Fig. 2-3. Poor transient response.

has ended may be compared to a color
smear on a reproduced painting.

Attack time involves the reproduction
of frequencies higher than the funda-
mental. Although a percussive tone may
have a low fundamental pitch, the fre-
quency components associated with its
steep attack characteristic may be very
high. Natural reproduction of a drum

beat through a two-way speaker sys-
tem may thus be accomplished by the
"woofer" handling the fundamental tone
and its proper decay, while the "tweeter"
contributes the sound components that
make up the sharp attack.

Harmonic and Intermodulatlon
Distortion

Reproducing devices have a charac-
teristic way of performing with less than
perfect accuracy. In addition to the fre-
quencies at which they are asked to
vibrate mechanically (or alternate elec-
trically) they introduce new modes of
oscillation of their own— and these new
frequencies are harmonics, integral mul-
tiples of the original frequency. This
inaccuracy is called harmonic distor-
tion. It is measured as the ratio of the
amplitude of the spurious harmonics to
the true signal, in per cent.

We have seen that harmonics of fun-
damental frequencies are produced in
any case by musical instruments. Yet
small amounts of harmonic distortion
produce very unpleasant effects. The
sound becomes harsh, unmusical; the
bass is wooden and the treble painful.

The primary reason for this is that
with harmonic distortion comes an at-
tendant evil— intermodulation distortion.
Intermodulation distortion can be de-
scribed as the introduction of new sound
components, at sum and difference fre-
quencies, when tones of two or more fre-
quencies are passed through a non-linear
system— that is, a system which creates
harmonic distortion. These sum and dif-
ference frequencies are harmonically un-
related to the original musical tones.
They are musically discordant, and they
serve to create raucous, unmusical sound
in a degree proportional to their relative
strength. The formation of intermodula-
tion products is illustrated in Fig. 2—4.

The primary importance of low dis-
tortion has always been recognized by
audio authorities. It has also become in-

180

NON-DISTORTING

REPRODUCING

DEVICE

SOLE COMPONENTS

ARE 50 CPS AND

1000 CPS

WWIMAM

50 CPS

REPRODUCING
DEVICE WITH
DISTORTION

WMAft/vwi

COMPONENTS

INCLUDE 950 CPS

AND 1050 CPS

1000 CPS

Fig. 2-4. Intermodulation distortion as a result of harmonic distortion of the low-frequency wave
form. Note that the wave envelope of the high-frequency tone is "modulated."

High Fidelity

creasingly recognized by the high fidel-
ity public in recent years, after the first
flush of excitement over reproducing
regions of the frequency spectrum pre-
viously untouched. Amplifier manufac-
turers now feature distortion data over
frequency response data; unfortunately
it is very rare for loudspeaker specifi-
cations to make any quantitative refer-
ence to distortion at all. The reason lies
in the fact that while both harmonic dis-
tortion and intermodulation distortion
(the latter is usually greater by a factor
of 3 or 4 ) can be kept to extremely low
values in high quality amplifiers— a small
fraction of one per cent at rated power—
the corresponding values for loudspeak-
ers are much higher. In the octave below
60 cps it is a rare speaker indeed which
can hold harmonic distortion, at any
appreciable sound level, below the 5 per
cent mark over the entire octave, and
many speakers produce percentages of
distortion in this frequency region ten

times as great. But the listening results
are not as bad as might appear at first
glance: speaker response is normally
severely attenuated in this lower range,
which helps, and there is comparatively
little musical material of such low fre-
quency to be distorted.

When the reproducing system has a
minimum of low frequency distortion,
very low bass tones of high power, such
as might be produced by organ pedal
pipes, not only remain pure in timbre
themselves but do not create intermodu-
lation with the rest of the music; they
do not destroy the purity of the treble
by introducing false tones.

Power Capability

The power capability of a high-quality
reproducing system should be such as
to be able to establish an intensity level
of sound in the living room equal to the
level at a good seat in the original con-
cert hall. The electrical power required

181

of the amplifier for achieving this goal
depends upon the efficiency of the
speaker, and the sound power required
of the speaker depends on the size and
other acoustical characteristics of the
room. Concert-hall level can be estab-
lished in a living room with a tiny
fraction of the acoustical power of a
symphony orchestra, because the lower
power is concentrated in a much smaller
area.

"Concert-hall level" is sometimes mis-
interpreted to mean the sound level
which would be created if the orchestra
were somehow jammed into the living
room itself. The writer has yet to ex-
perience at a live concert, even during
fortissimo passages, an assault on his
ears that compares to hi-fi assaults he
has weathered. It is interesting to note
that certain hi-fi demonstrations pre-
clude intelligible conversation which is
not shouted, while whispered conver-
sations in a concert hall are liable to
prove extremely distracting and annoy-
ing to one's neighbors. It is the sound
intensity level at the ear, not the power
of the orchestra, that we are trying to
reproduce.

Noise Level

Any sound component not present in
the original program material, other
than distortion products, is referred to
as noise, even though it may be periodic
and not conform to our strictly scientific
definition. Hum, rumble, surface scratch,
tube hiss or other circuit noise and sim-
ilar disturbances tend to destroy the
auditory illusion, and must be kept to a
minimum.

A standard for satisfactorily low noise
has been established by the FCC for FM
broadcast stations. It is that the power
ratio of the maximum signal to the noise
must always be at least 60 db; this rep-
resents a ratio of one million to one.

Dynamic Range

The dynamic range, or range of ampli-

tude of the reproduced sound from soft-
est to loudest, is determined by the two
factors just discussed, noise level and
power capability.

Soft musical passages can be masked
by any of the types of noise referred to,
and therefore the lowest sound levels
that can be used must be much louder
than the noise level. The maximum sound
levels that can be used, of course, are
limited by the power capability of the
system.

A dynamic range of 60 db, or a mil-
lion to one power ratio between highest
and lowest sound levels, is generally
considered adequate for reproduction
of the largest symphony orchestra.

Stereo

All of the above considerations apply
equally to monaural and to stereophonic
reproducing systems. These objective
elements of equipment fidelity— low dis-
tortion, adequate frequency response,
dynamic range, etc.— are able, in stereo,
to contribute more to the subjective illu-
sion of musical reality than in a mon-
aural system.

A stereo record-reproduce system
has in effect two parallel and complete
monaural systems. The work of each
component along the way is done twice.
The sound is picked up by two separate
microphones; the output of each micro-
phone is recorded on a separate track of
the tape; the record groove, although
not doubled, is cut in such a way as to
independently contain the record of
each signal channel; the pickup con-
tains two separate generating elements
which independently sense and trans-
mit each signal channel; the two signal
outputs of the pickup are sent through
independent amplifiers and fed to two
independent loudspeakers. There are
variations on this ideal scheme, but the
above describes the basic concept of
stereo.

The purpose of this dual-channel re-
production is, in the simplest terms, to

182

High Fidelity

help recreate the acoustical atmosphere
of the concert hall. In the old-fashioned
stereopticon each visual channel gave a
slightly different perspective view of the
subject. Similarly, in stereo recording,
each microphone gets a slightly differ-
ent auditory perspective. It is important
to note that this auditory perspective is
of the orchestra or soloists in the hall in
which they are performing, not merely
of the musical performers in the ab-
stract. This is important because a good
part of the sound that reaches our ears
at a concert does not come directly from
the orchestra, but is reflected from the
walls and ceiling of the concert hall.

The channels of a stereo system are
identified as "right and "left." This does
not mean that one microphone picks up
the sound of the right section of the
orchestra only, and that the other micro-
phone picks up the sound from the left
section of the orchestra. It does mean
that one microphone has a right-
oriented perspective of the total sound
in the recording hall, and that the other
microphone has a left-oriented perspec-
tive of the total sound. When these two
recorded channels (which, like the two
photos on a stereopticon card, are very
similar to each other) are reproduced
through two separate loudspeakers they
create, although not perfectly, the illu-
sion of the acoustical environment and
sense of space of the concert hall. There
is an increased awareness of the phys-
ical position of different instruments,
but this is very much less important

than the general increase in realism and
the consequent increase of clarity, par-
ticularly from the point of view of the
distinctness of the different musical
voices.

There is an approach to stereo
recording, commonly referred to as
"ping-pong" stereo, which provides an
exaggerated separation between the
right and left channels. If only the left
side of the orchestra were playing dur-
ing a particular passage, there would be
practically no sound from the right re-
cording channel. The left-right orienta-
tion of the different instruments is the
primary goal in this case, rathe; than
reproduction of the original acoustical
environment. The degree to which one's
attention is directed to the physical
position of the instruments in "ping-
pong" stereo is often much greater than
that at the live concert itself.

The greatest benefit of good stereo
recording and reproduction is that it
frees us, to a greater extent than was
possible previously, from the acoustical
environment of the listening room, and
transports us to some extent to the
acoustical environment of the hall in
which the recording was made. The
normal living room does not provide the
proper acoustical atmosphere for a
musical concert, particularly of a large
orchestra. Musical instrument designers
worked in terms of the tonal qualities
that would be produced in the type of
concert hall with which they were
familiar.

183

THE SOUND REPRODUCING SYSTEM

The phonograph is a classic example
of an invention that cannot be cred-
ited wholly to one man. In 1877 Edison
directed his assistant, John Kruesi, to
construct the first complete record-
reproduce system, but sound recorders
were sold on a commercial b?sis as early
as 1860, and Thomas Young's "A Course
of Lectures on Natural Philosophy" de-
scribed and illustrated a crude but prac-
tical sound recorder in 1807.

Young's recorder consisted of a sharp
metal stylus held by spring tension
against a revolving cylinder, the cylinder
coated with wax and turned by a gov-
ernor-controlled gravity motor. When
a vibrating body such as a tuning fork
was held against the stylus, a wavy
line was cut into the wax. This line rep-
resented the wave form of the vibra-
tions, and it could be studied and ana-
lyzed at leisure. The recorder was a
mechanical draftsman, that could sense
very small motions and record pressure
changes that took place within a period
of a very small fraction of a second.

By 1856 Leon Scott de Martinville
had constructed the "phonautograph"

(self-writer of sound) illustrated in
Fig. 3—1. The sound wave form was
scratched by a hog-bristle stylus on the
surface of a cylinder coated with lamp-
black, but the big advance over Young's
machine was the fact that the phonauto-
graph could record directly from the
air. The force of the acoustical vibrations

Fig. 3-1. The phonautograph of lion Scott do
Martinville — a commercial sound recorder of
the eighteen sixties. (Courtesy Smithsonian
Institution)

184

High Fidelity

was concentrated by a horn onto a dia-
phragm, and the stylus was attached to
the diaphragm, so that the recording
needle did not have to actually touch
the vibrating source of sound. This de-
vice, which corresponds in function to
the modern oscilloscope, was a catalogue
item of the Paris firm of Koenig, and was
sold as a measuring instrument to acous-
tical laboratories.

The phonautograph which is at the
Smithsonian Institution at Washington
would undoubtedly reproduce music if
a proper record were placed on its re-
volving cylinder. The theoretical possi-
bility of playback was understood then,
too, but the lampblack records were use-
less for playback, as their grooves were
not rigid enough to direct the vibrations
of a playback needle. About half a year
before Edison got his brainstorm Charles
Cros conceived a method for bringing
the groove sinuosities back to life as

sound. The lampblack recording was to
be photo-engraved on a metal cylinder,
and running a needle through the hard
groove would then cause the needle to
vibrate from side to side, in the same
time pattern as the hog bristle stylus
that first inscribed the line.

For reasons which may be related to
nineteenth century differences in tradi-
tion between the scholar and the indus-
trial engineer, Cros didn't even construct
a working model, but merely filed a com-
plete, sealed description of his system
with the Academie des Sciences. On the
other hand, less than a month after
Edison first conceived of a reproducing
phonograph the country was reading
about a working unit in newspaper head-
lines. There was a great stir of excite-
ment over this amazing tonal imitator,
(see Fig. 3-2) with public demonstra-
tions, lectures before august scientific
bodies, and a visit to the White House.

Rg. 3-2. Edit on with his tin-foil phonograph. (Photograph by Brady — courtesy Smithsonian Insti-
tution)

185

The excitement soon died down, as
the Edison machine was an impractical
toy, with neither permanent records nor
usable fidelity. The recorded groove was
indented into a semi-hard material, tin
foil; it was only able to retain its shape
partially, and that for very few play-
ings. Subsequent technical improve-
ments, however, made the phonograph
a popular device by the turn of the cen-
tury. It is curious that our modem re-
cording system, in which the record is a
mechanical copy of the original master,
is more closely related to Cros' system
than to Edison's. Emil Berliner, the
father of the moulded or cast record,
began his research work by successfully
carrying out Cros' proposals.

The Mechanical or "Acoustic"
Phonograph

It would be useful to consider the de-
sign of the non-electric phonograph, as
illustrated in (A) of Fig. 3-3. A better
insight can thereby be gained into the

L_ 1 O Q O

Fig. 3-3. (A) The mechanical phonograph. (B)
The electric phonograph.

function of the various components of
a modern electronic system.

The wave forms frozen into the record
groove control the vibrations of the play-
back stylus when the groove is dragged
past the stylus by a revolving turntable.
These stylus vibrations, although they
contain a fairly large amount of me-
chanical energy, engage practically no
air, like the revolutions of a bladeless
electric fan. The needle is therefore
attached to a diaphragm, which vibrates
in sympathy with the stylus and has a
much larger surface area in contact with
the air of the room.

But even the reproducing diaphragm
doesn't get a sufficient bite of the air
for practical purposes. Therefore the dia-
phragm is placed at the narrow throat
of an acoustical horn, and the actual
usable sound emerges into the room
from the much larger mouth of the horn.
The system works somewhat as though
the diaphragm area were really that of
the horn's mouth.

It can be seen that all of the energy
radiated by the horn is taken from the
mechanical vibrations of the needle, and
the forces between needle and record
groove are necessarily great. This has
obvious implications for record wear,
but perhaps more important, the de-
mands for power placed on the "sound
box" or "speaker" (old-fashioned terms
for the needle-diaphragm-head assem-
bly) place a severe limitation on musi-
cal fidelity. High distortion and peaked
and severely limited frequency response
are to be expected.

The Phonograph Amplifier

The solution to this problem lies in
changing the function of the phono-
graph pickup, from the primary genera-
tor of sound power to a device which
controls an outside source of power. If
the power from the outside source is
made to oscillate in imitation of the
needle vibrations, two benefits can result:

1. The final output sound derived

186

High Fidelity

from the record groove can be much
louder.

2. The power demands on the
pickup itself are no longer heavy. The
pickup can be designed for quality
rather than loudness; the problems
of achieving uniform, extended fre-
quency response and low distortion
are considerably lessened. So, inci-
dentally, is the required weight on
the pickup and the grinding away of
the record groove.

The control of an outside source of
power to conform to given oscillations
is called amplification. The first phono-
graph amplifier was pneumatic: the
needle was made to actuate an air valve,
which periodically throttled a flow of
compressed air. Most of the work of ra-
diating sound power was thus performed
by the air compressor, and the stylus
was relieved of part of its burden.

All modern sound reproducing sys-
tems use amplifiers, but unlike the first
pneumatic systems these amplifiers are
electronic. The phonograph pickup is no
longer a sound generator but an elec-
tric generator. It produces small alter-
nating voltages at its terminals, whose
wave forms conform to those of the
groove and of the recorded sound. The
pickup has to generate very little power,
because the output voltage can be ampli-
fied to almost any desired degree. The
amplified electrical power must finally,
of course, be converted back into sound
by a loudspeaker. The two types of re-
producing system, electrical and purely
mechanical, are shown in Fig. 3—3.

The Modern Sound Reproducing
System

The purpose of the historical approach
used above has been to furnish the
reader with an appreciation of the rea-
son for the modern audio system being
designed as it is. With the electronic
amplifier supplying the brute force, so
to speak, the mechanical components-
pickup and loudspeaker— can be built

in such a way as to suppress the natural
resonant tendencies inherent in mechani-
cal vibratory systems.

Before discussing each of the audio
components in detail, it would be useful
to make a brief survey of the entire re-
producing system. A complete monaural
system is illustrated in Fig. 3—4.

First of all the disc record must be
revolved by a motor and turntable. The
chief operational requirements of this
part of the system are that it revolve at
the correct speed, that the speed be con-
stant, and that extraneous vibrations
do not communicate themselves to the
pickup.

The first of these requirements is for
the purpose of keeping the reproduced
music at the same absolute pitch at
which it was recorded: too fast a turn-
table speed will make the pitch sharp,
and too low a speed will make it flat.
The second condition listed, constant
speed, is required in order to avoid pitch
variations, or "wow." The third require-
ment, lack of extraneous vibrations,
keeps low-frequency noise called "rum-
ble" out of the final sound.

The groove variations are sensed by
the needle, or stylus, which in high-
quality systems is jewel tipped; it is
usually diamond. The needle must have
an unmarred, smooth surfaced, hard tip,
normally of spherical shape.

The pickup is an electric generator
(usually either of the piezo-electric,
variable reluctance, or moving-coil type)
whose function is to translate the me-
chanical vibrations of the needle into
electrical oscillations of the same wave
form. It must do this with minimum
distortion of the wave form, and must
not allow resonances of its own to in-
fluence its output voltage significantly.
It is also an advantage for the pickup
to impose as little work as possible on
the needle. The greater the force re-
quired for the groove to displace the
needle from side to side, the greater the
vertical bearing force will have to be to

187

TAPE MECHANISM

PICKUP
STYLUS

TONE ARM

1ST

MOTOR

a a a — [

itHnnQQ

CONTROL UNIT

POWER AMPLIFIER

SPEAKER
SYSTEM

Fig. 3-4. Diagram of a complete monaural •ound reproducing system.

maintain proper and constant stylus-
groove contact, and the greater the
wear of both record and needle.

The tone arm holds the pickup in
place over the groove, and must pro-
vide sufficient freedom of motion so
that the pressure of the groove walls
alone can make the needle move across
the record, following the recorded spiral.
It must also be free enough to follow
warp and eccentricity of the disc easily.
The tone arm must hold the pickup ap-
proximately tangent to the groove being
played, must provide the proper vertical
force for the pickup, and must not allow
its own resonant behavior to influence
the system.

The electrical output of one type of
pickup, the piezo-electric, is usually fed
directly to the amplifier. It is of the
order of V2 volt or more, and is a fairly
accurate replica of the recorded sound.
This is so because the characteristic fre-
quency response of the pickup is more
or less the inverse image of the frequency
characteristics "built in" to the record.
(This last subject will be taken up in
detail later.)

The reluctance and moving-coil pick-
ups, however, produce a much smaller
amount of electrical energy. The output

voltage of these pickups (which are
classed together as magnetic types) may
be as low as a few thousandths of a
volt. Furthermore the characteristic fre-
quency response of the magnetic pickup
does not compensate for the way in
which the frequency characteristics of
the recorded sound has been doctored.
Therefore the pickup output must be
passed through a preamplifier before it
enters the amplifier proper.

The preamplifier is normally com-
bined with the main amplifier control
sections (volume and tone controls).
Its functions are to increase the output
voltage of the pickup, and to compensate
accurately for the frequency character-
istics of the record so that the sound is
not deficient in bass and heavy in the
treble. Since different record companies
have made records with different char-
acteristics the preamplifier may allow
the operator to choose between several
types of frequency compensation. The
need for such control, which is called
variable record equalization, has disap-
peared with modem records, which are
standardized on the RIAA recording
characteristic.

The control section of the amplifier
allows the operator to regulate the vol-

188

High Fidelity

ume, and, in most cases, to either ac-
centuate or attenuate ("boost" or "cut")
the bass and treble portions of the repro-
duced sound independently. The pri-
mary function of tone control is to com-
pensate for deficiencies in associated
equipment or program material, and to
compensate for acoustical conditions of
the room in which the music is heard.
When the control section and phono-
graph preamplifier are combined on one
chassis, the entire unit is commonly re-
ferred to as a preamplifier.

The power amplifier receives the elec-
trical signal as it is finally shaped, and
releases another signal, ideally identical
in all respects except power. The power
amplification may be tens of millions
of times, from a fraction of a micro-
watt (one millionth of a watt) to dozens
of watts.

Although the demands on the ampli-
fier are very great, and although it
appears to be the most complicated of
the system components, it is the least
imperfect of these components. The per-
centages of harmonic and intermodula-
tion distortion, the irregularities of fre-
quency response, and the extraneous
noise introduced by an amplifier built
according to the best current design
practice, and without regard for cost,

are such that they are not limiting fac-
tors in the fidelity of the reproduced
sound.

The final component of the sound
system is the loudspeaker system, which
consists of the speaker mechanism itself
and the speaker enclosure. The loud-
speaker converts the alternating elec-
trical output of the amplifier into me-
chanical vibrations of a cone or dia-
phragm. But the cone vibrating by itself
cannot, for reasons that will be discussed
further on, produce adequate bass en-
ergy. It must be mounted in an enclo-
sure or baffle of some sort, which gives
the vibrating surface the "bite" of air
that it needs to radiate low-frequency
sound.

The speaker and its enclosure, like the
amplifier, should introduce as little dis-
tortion and frequency irregularity into
the signal as possible. Typical speaker
deficiencies are irregular frequency re-
sponse, poor transient response (hang-
over), and harmonic and intermodula-
tion distortion.

Two other components are shown in
Fig. 3—4. The tuner is a device which
converts AM or FM radio signals to
audio signals that can be handled by the
audio amplifier; the tape transport
mechanism, with its associated pream-

MUITIPLEX FM TUNER

Fig. 3-5. A stereo reproducing system.

189

plifier, provides a signal of the same cated); the stereo tuner receives the

nature as that coming from the tuner "multiplex" FM stereo signal and sepa-

or phonograph pickup. rates it into two separate channels,

Fig. 3-5 shows the basic elements of which it feeds independently to each of

a stereo reproducing system. The stereo the control units. Each control unit and

tape mechanism has two heads which each power output is shown duplicated,

independently reproduce each channel The two control units and power ampli-

that is recorded in parallel on the tape; fiers may be separate, or they may be

the stereo pickup provides two separate combined on one chassis, or all four

output signals from the two channels units may be combined on one chassis,

recorded in the groove (the turntable but in any case they must provide inde-

and pickup arm do not have to be dupli- pendent amplification for each channel.

190

Since the Niagara power plant was built, commercial
electric power has been almost entirely alternating
current. Now new consideration is being given to
the advantages of direct current for long distance
power transmission.

12 The Future of Direct Current Power Transm

ission

N. L Allen

A popular article published in 1967.

The history of technology provides many examples of
unexpected turns of fortune, and electrical technology is
no exception. It frequently happens that a principle or
technique, originally the basis of a well-established
system, is superseded by a device making a significant
advance, only to reappear in a different guise as the 'last
word' in the state of the art. An obvious example is the
crystal of the early radio receiver. This was superseded
by the thermionic valve, but it has now developed into
the more sophisticated form of the transistor. Not many
years before the era of the crystal receiver, an appreciable
proportion of electrical energy was generated, trans-
mitted, and used in the form of direct current. At that
time, generation and consumption usually took place in
the same locality, distribution was simple, and the
quantities of energy transmitted were small by modern
standards. However, serious limitations appeared as it
became necessary to distribute electrical energy more
widely, and direct current as the distributing medium
gave way to alternating current.

In many countries, the economic advantages of being
able to concentrate power generation in large stations
have led to the adoption of a comprehensive network of
power lines that interconnect generating plant and the
areas where the power is used. As the length of a power
line increases, the current passed, for minimum power
loss, decreases: the economic operating voltage for trans-
mission of a given power therefore increases. The trans-
mission of larger quantities of energy at high voltages
and low currents is greatly facilitated by the ease with
which alternating current can be transformed to the
voltage most appropriate for the power lines. In the
receiving areas of the system, the voltage can equally
easily be transformed to lower values suitable for distri-
bution, and a system of far greater flexibility can be set
up than is the case with direct current. Fur .her, it is
difficult to switch and, particularly, to interrupt direct
current. The interruption of an alternating current by
circuit breakers is relatively easy because the current
passes through zero twice in every cycle.

This combination of circumstances made alternating
current the natural choice as power systems increased in
size. The main links operated initially at 132 kilovolts,
but the need for increased power during the post-war
years has led to the adoption of 275 kilovolts and, more
recently, 400 kilovolts as the operating voltages of the
principal links in Britain. The power is distributed locally
at lower voltages. During this period, the remaining
direct current distribution systems have been reduced or
eliminated.

Transmission over long distances

What, then, is the place of direct current? There is
certainly no good reason for turning away completely
from alternating current distribution. But there have
always been some situations in power distribution prac-
tice in which direct current has distinct advantages over
alternating current, and it is worth while considering
what these situations are.

One basic factor in power system design is the need to
find the simplest and most efficient means of transferring
power from one point to another. Figure 1 (a) shows the
basic three-phase alternating current system and figure
1 (b) a favoured direct current system, which has positive
and negative polarities on the two lines, and is linked by
convenors to alternating current for generation at one
end and distribution at the other. In both cases, the
maximum voltage to earth is E, but for alternating
current, it is the root-mean-square value Ejy/ '2 that
determines the power transmitted. This is lEIA cos 9/^2,
where lA is the current in each conductor, lagging behind
the voltage in phase by 9 degrees. In the direct current
system, the power transmitted by each line is E/D, where
ID is the current. For transmission of equal power by the
two systems, therefore, it can be shown that each
alternating current line has 4/(3 cos* 9) times the cross
sectional area of the corresponding direct current line, a
factor which is always greater than 133. Moreover, the

191

alternating current system requires three cables rather
than two, so that the amount of copper required is
2/cos2 <f times that in the direct current system, a factor
which is always greater than 2.

Direct current, then, reduces the cost of the cables.
This may appear trivial compared with the other capital
costs in electrical systems, but over great distances, as in
the United States and the Soviet Union, the saving in
cable, and in the means of supporting the cable, becomes
a very significant factor that can outweigh the cost of
providing the convenor stations at each end of the
system.

Great distances bring further problems in alternating
current transmission that do not occur with direct
current. These problems arise from the relationship be-
tween the wavelength of the oscillation and the dimen-
sions of the system. The quarter-wavelength of a 50
cycles per second wave in air is about 900 miles, and the
transmission of energy through a conductor can be re-
garded as due to an influx of energy along its length from
the electromagnetic field that surrounds it. Over short
distances, this field is very nearly the same at all points,
since electromagnetic energy is conveyed with the

_4.._

(b)

Figure 1 Simplified distribution systems: (a) alternating
current, (b) direct current.

velocity of light. But at distances greater than 900 miles,
the fact that the velocity of light is finite results in
significant differences, at any instant, in the phase of the
current at the two ends.

This situation leads to difficulties where two parts of a
power circuit, joined by a long alternating current link,
are out of phase and where a loop is formed through
another part of the network of different length. Large
circulating currents will be set up unless some form of
compensation is applied. A direct current link obviates
these difficulties; as a corollary, it may be noted also
that if a direct current line is used to link two alternating
current systems, they need not be synchronized with
each other.

Transmission over short distances

For long-distance transmission, overhead lines, supported
by towers, are used. The virtues of direct current are
most clearly shown when the current is carried by under-
ground or underwater cables. Here, the central core of
the cable, which is at the transmission voltage, is sur-
rounded by an insulant, the exterior of which is at earth
potential. This constitutes a coaxial capacitor, and the
capacitance per mile of a cable rated at 200 kV is
typically about 03 microfarads. In an alternating current
circuit, this capacitance is charged and discharged,
through the inductance and resistance of the cable itself,
once every half-cycle. Additional generating capacity is
needed to supply this charging current. In the example
quoted, at 200 kV, the charging current requires about
5000 ikilovolt-amperes per mile of cable ; at 400 kV
the figure is about 15 000 kilovolt-amperes per mile. For
appreciable lengths of cable, the losses become such that
the charging currents must be supplied at intermediate
points. At 200 kV, these points are about 25 miles apart
for 50-cycle alternating current; at 400 kV, only 15
miles. Thus, alternating current transmission becomes
impracticable in cables over long distances. Further, the
cost of the generating capacity needed to supply the
charging current is significant. Taking a rough figure of
£50 per kilowatt of installed capacity at the generating
station, this extra cost is £250 000 per mile for a 200
kilovolt cable. By contrast, with direct current in the
steady state, there is no charging current. It may well be
worthwhile, therefore, to accept the cost of converting
to direct current to avoid having to provide this charg-
ing current. Direct current is also advantageous in that
there are no dielectric losses due to reversal of the elec-
tric stress in the insulant.

The balance between the two systems

To summarize, direct current has significant advantages
for the transmission of bulk power over great distances
by overhead lines, and over short or long distances by
cable. In addition to the technical advantages already
examined, direct current may be valuable in linking two
alternating current systems that need not then be
synchronized. Alternatively, a very large alternating
current system mav be divided by direct current links

192

The Future of Direct Current Power Transmission

into two or more smaller systems: this is a possible future
development as power systems continue to increase in
size. It is necessary, however, to examine some disad-
vantages of direct current, and some relevant non-
technical factors, to demonstrate the balance affecting
the final choice of system.

The most obvious drawback to the use of direct
current is the need for conversion at each end of the link
in order to integrate it with established alternating
current systems. The technical details are outlined later,
but it may be mentioned here that the cost of the con-
version equipment is about twice that of the alternating
current equipment required for the termination of a
power line of corresponding size and output . These
costs must be set against the savings inherent in the
direct current system. There is therefore, a limit to the
length of a line, below which the capital outlay on a
direct current system is higher than that of an alternating
current system. Estimates of the critical length for a long
overhead line naturally vary, depending mainly on the
power to be transmitted and the voltage to be employed,
but figures of more than 300 miles have frequently been
quoted. This approach is unlikely to be favoured,

therefore, in the British Isles, but such systems are being
developed in the United States and in the Soviet Union.
For underground or submarine cables, where dielectric
losses and charging currents are so important, the
'critical length' is reduced to about 30 miles, and it is in
short submarine links and in urban transmission lines
that direct current finds its second important application.
Indeed, where large amounts of power have to be intro-
duced into large cities, legal and social considerations
may predominate over technical and economic factors.
It is frequently extremely difficult to obtain permission
to erect overhead lines in urban areas, and the distur-
bance to local amenities caused by the towers for high-
tension cables may not be justifiable. Underground
cables become necessary, and it is preferable to use
direct current for distances greater than about 30
miles.

In choosing between the systems, the fact that there
can be no direct current transformer and that there is no
satisfactory circuit breaker ensures that alternating
current maintains its general superiority for distribution
purposes. The use of direct current is thus confined to
the bulk transmission of high power between discrete
parts of a system or between two separate systems.

193

The Reader for Unit 3 contained the first part of
Newman's biography of this outstanding mathematician
and physicist. This final part covers primarily his
work on electromagnetic theory.

James Clerk Maxwell, Part II

James R. Newman

A biographical essay published in 1955.

In February, 1858, Maxwell wrote a letter to his aunt, Miss
Cay, beginning, "This comes to tell you that I am going to have
a wife." "Don't be afraid," he added, "she is not mathematical,
but there are other things besides that, and she certainly won't
stop mathematics." His engagement to Katherine Mary Dewar,
daughter of the principal of Marischal College, was formally
announced the same month, and in June they were married.

195

Their union became very close: they enjoyed doing things
together — horseback riding, reading aloud to each other,
traveling — and he even found useful tasks for her in his
experimental work. The marriage was childless, but this very
fact increased the couple's dependency and devotion. Maxwell
regarded the marriage tie in an "almost mystical manner."
The published letters to his wife overflow with religiosity.*

The Aberdeen appointment terminated in 1860 when the
two colleges, King's and Marischal, were fused into a new
university and Maxwell's chair in physics at Marischal was
eliminated. He was not long at liberty. In the summer of the
same year he became professor of natural philosophy at
King's College, London, a post he retained until 1865. The
teaching schedule at King's was long and arduous; in the
evenings there were lectures to be given to "artisans" as part
of his regular duties. Living in London offered him the oppor-
tunity to see something of Faraday, with whom, up to this time,
Maxwell had had only correspondence, to make the acquaint-
ance of other scientific men and to renew old friendships. He
was no solitary. "Work is good, and reading is good, but
friends are better," he wrote to his friend Litchfield.

Yet despite academic duties and social distractions, the five
years in London were the most productive of his life. The
paper "On the Theory of Three Primary Colors," the two
articles in the Philosophical Magazine on "Physical Lines of
Force" and the culminating electrical memoir "A Dynamical
Theory of the Electromagnetic Field," the Bakerian lecture
"On the Viscosity or Internal Friction of Air and other Gases,"
and the celebrated paper "On the Dynamical Theory of Gases,"
all belong to this period. He also performed important experi-
mental work during these years. At his house in Kensington,

* He did not write in this vein to others and it is a little puzzling why he found
it necessary in corresponding with her to quote Scriptures, to express the fer-
vent hope that the Lord would protect her from evil, and that she would get
her eyes off "things seen and temporal and be refreshed with things eternal."

196

James Clerk Maxwell, Part II

in a large garret, he measured the viscosity of gases and ob-
tained practical confirmation of the theoretical work I have
described. (For example, he found that the viscosity of air at
12 millimeters of mercury measured the same as at normal
pressure of 760 millimeters, thus proving that viscosity is in-
dependent of density.) To maintain the necessary temperature,
a fire had to be kept up in the midst of very hot weather and
kettles kept boiling to produce steam, which would be allowed
to flow into the room. Mrs. Maxwell acted as stoker. Another
investigation dealt with the ratio of the electromagnetic to the
electrostatic unit of electricity and led to one of Maxwell's
greatest discoveries. But I must postpone explaining this work,
even though to do so means abandoning the strict chronology
of events in Maxwell's life, until I have sketched the develop-
ment of his ideas on electricity.

To gain an appreciation of Maxwell's stupendous contribu-
tion to this branch of science it is necessary first to describe
very briefly the position of electrical theory when he embarked
on his studies.

In the eighteenth century, Charles Augustin de Coulomb
established the fundamental facts of electrostatic attraction
and repulsion. He showed that an inverse-square law, resem-
bling that of gravitational forces, applied to electric charges:
attraction or repulsion between charged bodies is directly
proportional to the product of the charges and inversely pro-
portional to the square of the distance between them.* (The
same discoveries, and others going beyond them, were made
earlier by the brilliant English recluse Henry Cavendish, but
his researches remained unpublished until 1879.) The next
major advance was that of Hans Oersted, who in 1819 found
that the flow of electric current through a wire parallel to a
magnetic needle makes the needle swing to a position at right

* F = k-^jr-, where F equals the force; k, a constant; q and q', the charges;

r2
r, the separating distance.

197

angles to the current. In other words, a current produces a
magnetic field.

A complementary series of advances was made early in the
same century by the French physicist and mathematician
Andre Ampere, whom Maxwell called the Newton of electric-
ity. The accolade was not undeserved, but there is a special
reason for Maxwell's conferring it: Ampere was the first to
explain the relationship of electric currents in terms of me-
chanical action,* an approach later perfected by Maxwell
himself. By experiment Ampere learned that a coil of wire
carrying an electric current behaves like a magnet, and he
suggested that a magnet owes its property to tiny electrical
currents inside the steel molecules. Thus a great conceptual
link was forged; for magnetism was shown to be not distinct
from electricity, but rather a name we give to some of the
effects of moving electric currents.

The crown of these fundamental researches was the im-
mortal work of Michael Faraday. He found that an electric
current flowing in one circuit can cause ("induce") a current
to flow in another circuit; that there is a magnetic field between
two currents; that a current can also be induced to flow in a
wire by use of a magnet — in other words, as a symmetric
counterpart to the phenomena discovered by Oersted and
Ampere, that changes in a magnetic field produce an electric
current.

Faraday's explanation of these phenomena is of central
importance to understanding Maxwell's work. He imagined
lines of force running through space as the instrumentality of
electric and magnetic actions.

These lines, it should be emphasized, were not conceived as
mere mathematical makeshifts, but as entities possessing phys-
ical properties. The lines spread out in every direction from
an electric charge or magnetic pole; every electric line of force

* He showed how to calculate the mechanical forces between circuits carrying
currents, from an assumed law of force between each pair of elements of the
circuit.

198

James Clerk Maxwell, Part II

starts from a positive charge and ends on a negative charge;
the more powerful the source, the more lines emanate from it.
Along the lines there is tension, a kind of pull, so that each
line behaves like an elastic thread trying to shorten itself; lines
of force repel each other sideways; the ends of a line of force,
representing charges, can move freely over the surface of a
conductor but are anchored on an insulator.

This hypothetical system, for which Faraday was convinced
he had found experimental evidence, was the starting point of
Maxwell's studies. He believed in it; he sought to develop it.

However, it must not be supposed that everyone accepted
Faraday's hypothesis. In fact, the majority of electricians — I
use the term in its older sense — regarded lines of force as a
concept much inferior to that of "action at a distance." They
likened electricity to gravitation. They imagined a charge (or
mass) situated at one point in space mysteriously influencing
a charge (or mass) at another point, with no linkage or con-
nection of any kind, however tenuous, bridging the distance
between the charges (or masses). Where Faraday sought to
assimilate the behavior of electricity to that of a mechanical
system, in which all parts are joined by levers, pulleys, ropes
and so on, the others held electricity to be a special case, to
which mechanical analogies were inapplicable. Maxwell ad-
mirably summarized the cleavage between the two views:
"Faraday, in his mind's eye, saw lines of force traversing all
space, where the mathematicians saw centres of force attract-
ing at a distance; Faraday saw a medium where they saw noth-
ing but distance; Faraday sought the seat of the phenomena in
real actions going on in the medium, they were satisfied that
they had found it in a power of action at a distance impressed
on the electric fluids."

Maxwell's first electrical paper "On Faraday's Lines of
Force" was delivered at Cambridge in 1855, within a few
months after he had finished reading Faraday's Experimental
Researches. What he tried to do was imagine a physical model
embodying Faraday's lines, whose behavior, like that of any

199

machine, could be reduced to formulae and numbers. He did
not suggest that the model represented the actual state of things;
on the other hand, he had no confidence in what mathematical
manipulations alone would reveal about the actual state of
things. It was important, he said, so to balance the method of
investigation that the mind at every step is permitted "to lay
hold of a clear physical conception, without being committed
to any theory founded on the physical science from which that
conception is borrowed."* Such a method will neither lead

* The opening paragraph of the paper is worth giving in full. "The present
state of electrical science seems peculiarly unfavorable to speculation. The laws
of the distribution of electricity on the surface of conductors have been analyt-
ically deduced from experiment; some parts of the mathematical theory of
magnetism are established, while in other parts the experimental data are want-
ing; the theory of the conduction of galvanism and that of the mutual attrac-
tion of conductors have been reduced to mathematical formulae, but have not
fallen into relation with the other parts of the science. No electrical theory can
now be put forth, unless it shows the connection not .only between electricity at
rest and current electricity, but between the attractions and inductive effects of
electricity in both states. Such a theory must accurately satisfy those laws the
mathematical form of which is known, and must afford the means of calculat-
ing the effects in the limiting cases where the known formulae are inapplicable.
In order therefore to appreciate the requirements of the science, the student
must make himself familiar with a considerable body of most intricate mathe-
matics, the mere attention of which in the memory materially interferes with
further progress. The first process therefore in the effectual study of the science,
must be one of simplification and reduction of the results of previous investiga-
tion to a form in which the mind can grasp them. The results of this simplifica-
tion may take the form of a purely mathematical formula or of a physical hypoth-
esis. In the first case we entirely lose sight of the phenomena to be explained;
and though we may trace out the consequences of given laws, we can never ob-
tain more extended views of the connections of the subject. If, on the other
hand, we adopt a physical hypothesis, we see the phenomena only through a
medium, and are liable to that blindness to facts and rashness in assumption
which a partial explanation encourages. We must therefore discover some meth-
od of investigation which allows the mind at every step to lay hold of a clear
physical conception, without being committed to any theory founded on the
physical science from which that conception is borrowed, so that it is neither
drawn aside from the subject in pursuit of analytical subtleties, nor carried be-
yond the truth by a favorite hypothesis. In order to obtain physical ideas with-
out adopting a physical theory we must make ourselves familiar with the exist-
ence of physical analogies. By a physical analogy I mean that partial similarity
between the laws of one science and those of another which makes each of them
illustrate the other. Thus all the mathematical sciences are founded on rela-
tions between physical laws and laws of numbers, so that the aim of exact sci-
ence is to reduce the problems of nature to the determination of quantities by
operations with numbers."

200

James Clerk Maxwell Part

into a blind alley of abstractions, nor permit the investigator
to be "carried beyond the truth by a favorite hypothesis."

Analogies are, of course, the lifeblood of scientific specula-
tion. Maxwell gives a number of examples, among them the
illuminating suggestion of William Thomson comparing the
formulae of the motion of heat with those of attractions (such
as gravitation and electricity) varying inversely as the square
of the distance. To be sure, the quantities entering into heat
formulae — temperature, flow of heat, conductivity — are
distinct from a quantity such as force entering into the formu-
lae of inverse-square attraction. Yet the mathematical laws of
both classes of phenomena are identical in form. "We have
only to substitute source of heat for center of attraction, flow
of heat for accelerating effect of attraction at any point, and
temperature for potential, and the solution of a problem in
attractions is transformed into that of a problem of heat."*

Maxwell proposed a hydrodynamical analogy to bring be-
fore the mind in "convenient and manageable form those math-
ematical ideas which are necessary to the study of the phe-
nomenon of electricity. "t The analogy was combined with
Faraday's lines of force, so that they were converted from
lines into "tubes of flow" carrying an incompressible fluid
such as water. He was then able to show that the steady flow of
particles of this fluid would give rise to tensions and pressures
corresponding to electrical effects. The fluid moving through a
system of such tubes represented electricity in motion; the
form and diameter of the tubes gave information as to strength
and direction of fluid (electric) flow. The velocity of the fluid
was the equivalent of electrical force; differences of fluid pres-
sure were analogous to differences of electrical pressure or
potential. Since the tubes were flexible and elastic, and ar-

* "On Faraday's Lines of Force," Transactions of the Cambridge Philosophical
Society, vol. X, part I, included in The Scientific Papers of James Clerk Max-
well, op. cit.

t Ibid.

201

ranged so as to form surfaces — each tube being in contact
with its neighbors — pressure transmitted from tube to tube
furnished an analogy to electrical induction.

One of Faraday's key concepts deals with the effect on space
of lines of magnetic force. A wire introduced into ordinary
space remains inert; but if magnetic lines of force are intro-
duced into the space, a current flows through the wire. Faraday
explained this by saying that the introduction of the magnet
threw the space into an "electro-tonic state." This concept
could not be fitted into the hydrodynamical analogy; Maxwell
admitted that while he could handle Faraday's conjecture
mathematically, the electro-tonic state at any point of space be-
ing defined "as a quantity determinate in magnitude and direc-
tion," his representation involved no physical theory — "it is
only a kind of artificial notation."*

It was a wonderful paper, and Faraday, to whom Maxwell
sent a copy, appreciated how much it advanced the "interests
of philosophical truth." "I was at first almost frightened," he
wrote Maxwell, "when I saw such mathematical force made to
bear upon the subject, and then wondered to see that the sub-
ject stood it so well."t Other students, however, thought the
subject stood it not at all well. Electricity was mysterious
enough without adding tubes and surfaces and incompressible
fluids. But Maxwell, who had good training in being consid-
ered queer, went on with the task of extending Faraday's ideas.

The second great memoir, On Physical Lines of Force, a
series of three papers published in the Philosophical Magazine
in 1861 and 1862, was an attempt to describe a more elaborate
mechanism that would not only account for electrostatic effects
but also explain magnetic attraction and Faraday's concept of

* For a discussion of Maxwell's use of physical analogy, see Joseph Turner.
"Maxwell on the Method of Physical Analogy," The British Journal for the
Philosophy of Science, vol. VI, no. 23, November, 1955.

t Campbell and Garnett, op. cit., p. 519.

202

James Clerk Maxwell, Part II

electromagnetic induction. Again, Maxwell used a concrete,
mechanical image to exhibit and develop his theory.* For, as
he said, "scientific truth should be regarded as equally scien-
tific whether it appears in the robust form and vivid colouring
of a physical illustration or in the tenuity and paleness of a
symbolic expression."

In the new model a magnetic field is produced by the rota-
tion in space of what Maxwell called "molecular vortices."
These may be thought of as slender cylinders (Maxwell him-
self had a disconcerting way of modifying the image as he
went along) that rotate round the lines of magnetic force. The
lines, traced by the pattern of iron filings about a magnet, are
the axes of rotation of the cylinders; the velocity of rotation
depends on the intensity of the magnetic force. Two mechan-
ical effects are associated with the cylinders: tension in the
direction of the lines of force, and pressure, exerted in the
"equatorial" direction (i.e., lateral pressure), arising from
the centrifugal force produced by the rotating cylinders. Com-
bined, these effects mechanically reproduce magnetic phe-
nomena: magnetism is a force exerted both along the axis and
outward from the axis.

It may now be asked how this curious arrangement fitted in
with the known facts that an electric current produces a mag-
netic field, and changing magnetic forces produce an electric
current. Step by step Maxwell answers this question.

The first point to clarify is the structure of a uniform mag-
netic field. Maxwell supposed this to consist of a portion of
space filled with cylinders rotating at the same velocity and in
the same direction "about axes nearly parallel." But immedi-
ately a puzzle confronted him. Since the cylinders are in con-
tact, how can they possibly rotate in the same direction? For

* As Turner top. cit.) points out. Maxwell employed two analogies. One
bridged a stationary field and a solid under stress. The other is between elec-
tricity and fluid motion, "with its suggestion that Ampere's laws be modified to
satisfy the equation of continuity."

203

Model of an electromagnetic field used by Maxwell visualized "Molecular
vortices" rotating in space. In this illustration the vortices are slender
cylinders seen from the end. (Maxwell gave the cylinders a hexagonal cross
section to simplify the geometry of the model.) Between the vortices are
small "idle wheels." If a row of the idle wheels is moved from A toward B,
they cause the adjacent vortices to rotate in the opposite direction. ( Scientific
American)

as everyone knows, a revolving wheel or cylinder causes its
neighbor to revolve in the opposite direction; thus one would
expect the rotation of the cylinders to alternate in direction
from one to the next. Maxwell hit upon a pretty idea. He sup-
posed the cylinders to be separated by rows of small spheres,
like layers of ball bearings, which acted as gears (in Max-
well's words, "idle wheels"). This arrangement, resembling a
device envisaged a century earlier by John Bernoulli, the

204

James Clerk Maxwell, Part II

younger, fulfilled the requirement. The spheres rotate in an
opposite sense to that of each of the cylinders with which they
are in contact, and so the cylinders all rotate in the same direc-
tion.

And now, as just reward for his ingenuity, Maxwell found
that the spheres could be made to serve another, even more
valuable, purpose. Think of them as particles of electricity.
Then by purely mechanical reasoning it can be shown that
their motions in the machine of which they are a part serve to
explain many electrical phenomena.

Consider these examples. In an unchanging magnetic field
the cylinders all rotate at the same constant rate; thus they
maintain a constant magnetic field. The little rotating spheres
keep their position; there is no flow of particles, hence no elec-
tric current, a result that tallies with the properties of a uni-
form magnetic field. Now suppose a change in the magnetic
force. This means a change in the velocity of rotation of the
cylinders. As each cylinder is speeded up, it transmits the
change in velocity to its neighbors. But since a cylinder now
rotates at a slightly different speed from its neighbor, the
spheres between them are torn from their positions by a kind
of shearing action. In other words, they begin to move from
their centers of rotation, in addition to rotating. This motion of
translation is an electric current; again, a result that tallies
with the properties of a changing magnetic field.

Observe now how the model begins to live a life of its own.
It was designed, as J. J. Thomson has pointed out,* to exhibit
Faraday's great discovery that magnetic changes produce elec-
tric currents. It suggested to Maxwell the no less striking con-
verse phenomenon that changes in electric force might produce
magnetism. t Assume the spheres and cylinders are at rest. If

* Sir J. J. Thompson, "James Clerk Maxwell." in James Clerk Maxwell, A
Commemoration Volume, op. cit.

t Ampere, of course, had already demonstrated that currents in wires produced
accompanying magnetic fields.

205

a force is applied to the spheres of electricity, they begin to
rotate, causing the cylinders of magnetism with which they are
in contact to rotate in the opposite direction. The rotation of the
cylinders indicates a magnetic force. Moreover, the model
holds up even as to details. Take a single illustration. Mag-
netism acts at right angles to the direction of flow of current. If
you will examine the diagram of Maxwell's model, you will
see that the cylinders will rotate in the direction perpendicular
to the motion of the spheres, thus bearing out the observation
that a magnetic force acts at right angles to the flow of a cur-
rent.

"I do not bring it forward," Maxwell wrote of his system,
"as a mode of connection existing in Nature. ... It is, how-
ever, a mode of connection which is mechanically conceivable
and easily investigated, and it serves to bring out the actual
mechanical connection between the known electromagnetic
phenomena.* Certain aspects of these "mechanical connec-
tions" have already been discussed — rotations, pressures,
tensions — which account for the reciprocal relations between
currents and magnetic forces. t The connections also serve to
explain the repulsion between two parallel wires carrying cur-
rents in opposite directions, an effect produced by the centrifu-
gal pressures of the revolving cylinders acting on the electrical
particles between them. The induction of currents is similarly
elucidated: this phenomenon, says Maxwell, is simply "part of
the process of communicating the rotary velocity of the vor-
tices [cylinders] from one part of the field to another." In
other words, whenever electricity (Maxwell's particles) "yields
to an electromotive force," induced currents result. His dia-
gram and the accompanying text make this beautifully clear.

Maxwell was not done with his model. It had helped in the

* "On Physical Lines of Force," op. cit.

t The model explained, for example, why a current of electricity generated heat:
for as the particles (or spheres) move from one cylinder to another, "they
experience resistance, and generate irregular motions, which constitute heat."

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James Clerk Maxwell. Part II

interpretation of magnetism, the behavior of electric currents,
the phenomenon of induction; it had yet to pass the supreme
test: that is, to supply a mechanical explanation of the origin
of electromagnetic waves. To orient ourselves in this matter we
must examine briefly the question of condensers and insulators.
An electric condenser is a device for storing electricity. In
its simplest form it consists of two conducting plates separated
by an insulating material, or dielectric as it is called. The
plates can be charged, after which the charges attract each
other through the dielectric and are thus said to be "bound" in
place. Faraday in his experiments had come upon a curious
fact. He found that two condensers of the same size, fed by the
same electric source and with insulation of equal thickness,
differed markedly in their capacity to take or to hold a charge
if the insulating material (dielectric) was different. This was
difficult to understand if all dielectrics were equally imperme-
able to an electric current. Moreover, if it were true, as Max-
well already was beginning to suspect, that light itself is an
electrical phenomenon, how could light pass through certain
dielectrics, empty space among them? With the help of his
model, Maxwell advanced a bold hypothesis. Conductors, he
said, pass a current when the electrical particles they contain
are acted upon by an electric force. Under such an impulsion,
the little particles move more or less freely from cylinder to
cylinder, and the current flows as long as the force persists.
Not so in a dielectric. The particles are present but an easy
passage from cylinder to cylinder is impossible. This fact may-
be taken as the characteristic attribute of a dielectric, having
to do with its physical structure. Yet it was known that "local-
ized electric phenomena do occur in dielectrics." Maxwell sug-
gested that these phenomena also are currents — but of a
special kind. When an electric force acts on a dielectric, the
particles of electricity are "displaced," but not entirely torn
loose; that is, they behave like a ship riding at anchor in a
storm. The medium in which they are located, the magnetic

207

cylinders, is elastic ; under pressure the particles move, a lim-
ited distance, until the force pushing them is balanced by the
stresses due to the elastic reaction of the medium. Thus a state
of equilibrium is attained. But as soon as the impelling force
ceases to act, the particles snap back to their original positions.
The net effect of these mechanical actions is twofold. First, the
initial displacement of the electric particles constitutes a cur-
rent that passes through the dielectric. A current of this type is
called a displacement current to distinguish it from currents
that flow through conductors and are therefore known as con-
duction currents.* Wherever there is an electric force, said
Maxwell, there is displacement; wherever there is displace-
ment, there is a current.

Second, whenever the pressure displacing the particles is re-
leased, and they snap back, they overshoot and oscillate briefly
about their fixed positions. The oscillation is transmitted
through the magnetic medium (the insulator) as a wave. This
wave is the return phase of the displacement current.t (Max-
well suggested this disturbance on analogy to the displacement
of an elastic solid under stress.)

Maxwell next arrived at an epoch-making conclusion. The
velocity of the displacement wave, or current, depends on the
electrical properties of the medium in which it moves. More-
over, this velocity, as he showed, was "within the limits of
experimental error, the same as that of light." Hence, he in-

* The contrast between displacement currents and currents through conductors
was vividly expressed by Henri Poincare. A displacement current, he said, is
an elastic reaction like the compression of a spring: it can only be effected by
pressure against resistance. Equilibrium is reached when resistance balances
pressure. When the pressure is removed the spring regains its original form. A
conduction current, on the other hand, is like a viscous reaction such as is en-
countered in moving a body immersed in water. It can be effected only by pres-
sure; the resistance depends on velocity; the motion continues as long as the
motive force acts, and equilibrium will never be established. "The body does not
return to the starting point, and the energy expended in moving it cannot be
restored, having been completely transformed into heat through the viscosity of
the water." (Maxwell's Theory and Wireless Telegraphy, New York, 1904.)

t If the electric force applied to the insulator is varied continually, it will pro-
duce a continually varying displacement wave: in other words, a continuing
current.

208

James Clerk Maxwell, Part

Electromagnetic wave as visualized by Maxwell is a moving disturbance
which tends to separate positive (plus sign) and negative (dot) charges. In
the drawing at the top, magnetic lines of force (arrows) lie at right angles
to the direction in which the disturbance is moving. The drawing at the bot-
tom depicts the two components of the electromagnetic wave. The electrical
component is shown in black, the magnetic component in color. (Scientific
American)

ferred, "the elasticity of the magnetic medium in air is the
same as that of the luminiferous medium, if these two coex-
istent, coextensive and equally elastic media are not rather
one medium."

209

More must be said as to how Maxwell actually arrived at
this conclusion. In the 1850s the German physicists Wilhelm
Weber and Friedrich Kohlrausch had investigated an impor-
tant relationship, namely, the ratios of electrostatic to electro-
dynamic action. The electrostatic unit of charge was defined
as the repulsion between two (like) unit charges at unit dis-
tance apart. The electrodynamic unit was defined as the repul-
sion between two definite lengths of wire carrying currents
"which may be specified by the amount of charge which travels
past any point in unit time." In order to compare the repulsion
between static charges with that between moving charges, a
factor of proportionality must be introduced, since the units
are different for static and dynamic phenomena. That is, one
must determine how many positive units of electricity flowing
in one wire, and negative units flowing in the other, are re-
quired to produce between the wires a repulsion quantitatively
equal to that between two static units. The factor turns out to
be a velocity; for since the length of the wires is fixed, and the
number of units of electricity passing a given point in a given
time can be measured, what the investigator must consider is
the dimension length divided by time or velocity. Weber and
Kohlrausch had found that the velocity of propagation of an
electric disturbance along a perfectly conducting wire is close
to 3 x 1010 centimeters per second. This was an astonishing
coincidence, for the figure was about the same as the velocity
of light as it had been determined a few years earlier by the
French physicist Hippolyte Fizeau.

Kirchhoff remarked the coincidence, but did not pursue it;
Maxwell did. In 1860 he attacked the problem experimentally,
using an ingenious torsion balance to compare the repulsion
between two static charges and two wires carrying currents.
The Weber-Kohlrausch results were roughly confirmed. Also,
at about the same time (he said, in fact, that the pencil and
paper work was done before seeing Weber's memoir), he cal-
culated the velocity of displacement currents in empty space
or in any other dielectric. The resulting values tallied closely.

210

James Clerk Maxwell, Part II

In other words, currents in a wire, displacement currents in a
dielectric, and light in empty space (which of course is a
dielectric) all traveled with the same velocity. With this evi-
dence at hand, which he communicated in a letter to Faraday
in 1861, Maxwell did not hesitate to assert the identity of the
two phenomena — electrical disturbances and light. "We can
scarcely avoid the inference," he said, "that light consists in
the transverse undulations of the same medium which is the
cause of electric and magnetic phenomena."

"On Physical Lines of Force," despite its cogwheels and
other gross mechanical adjuncts, may be regarded as the most
brilliant of Maxwell's electrical papers. If it did not claim to
give a picture of the true state of things, it was at least enor-
mously enlightening as to how electricity and magnetism could
interact in a purely mechanical relationship. Maxwell himself
summarized the achievements of the theory as follows. It ex-
plained magnetic forces as the effect of the centrifugal force
of the cylinders; induction as the effect of the forces called into
play when there is a change of angular velocity of the cylin-
ders; electromotive force as an effect produced by stress on the
connecting mechanism; electric displacement as a result of the
elastic yielding of the mechanism; electromagnetic waves as
an accompaniment of displacement. The paper is one of the
rare examples of scientific literature in which one may glimpse
the play of imagination, the actual exercise of inductive power,
the cultivation of nascent ideas.

None of the basic concepts unfolded in this memoir was
discarded in the more mathematical writings that followed.
But Maxwell now had to outgrow his model. In "A Dynamical
Theory of the Electromagnetic Field," published in 1864,*
Maxwell, in Sir Edmund Whittaker's words, displayed the
architecture of his system "stripped of the scaffolding by aid
of which it had first been erected."t The particles and cylinders

* Royal Society Transactions, vol. CLV.

t History of the Theories of Aether and Electricity: The Classical Theories,
London, 1951.

211

are gone; in their place is the field — "the space in the neigh-
borhood of the electric or magnetic bodies" — and the aether,
a special kind of "matter in motion by which the observed
electromagnetic phenomena are produced." The matter com-
posing the aether has marvelous properties. It is very fine and
capable of permeating bodies; it fills space, is elastic and is
the vehicle of "the undulations of light and heat." Yet for all
its refinements and subtleties, the medium is no less a mechan-
ical rig than the cylinders and spheres of its predecessor. It
can move, transmit motions, undergo elastic deformations,
store potential (mechanical) energy and release it when the
deforming pressures are removed. Though susceptible to the
action of electric currents and magnets, it is nonetheless a
mechanism that, as Maxwell said, "must be subject to the gen-
eral laws of Dynamics, and we ought to be able to work out all
the consequences of its motion, provided we know the form of
the relation between the motions of the parts." In the preceding
paper Maxwell already had devised a set of equations that
described the possible mechanical basis of electrical and mag-
netic phenomena, and, in particular, how certain changes in
electric and magnetic forces could produce electrical waves.
He now elaborated the hypothesis of displacement currents and
obtained the expressions that are in substance the famous Max-
wellian equations of the electromagnetic field.

In their most finished form the equations appear in the
Treatise on Electricity and Magnetism (1873), the culmina-
tion of Maxwell's researches, which he wrote at Glenlair in the
years following his resignation from King's College. This
celebrated work deals with every branch of electric and mag-
netic science and presents the results of twenty years of thought
and experiment. Maxwell remained faithful to Faraday, whose
point of view is emphasized throughout the Treatise. Charac-
terizing his own part as that of an "advocate," Maxwell makes
no attempt to describe the hypotheses propounded by Weber,
Gauss, Riemann, Carl and Franz Neumann, or Ludwig Lorenz,

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James Clerk Maxwell, Part II

the foremost cultivators of the theory of action at a distance.

The task Maxwell set himself was, first, to formulate mathe-
matically electromagnetic phenomena as observed experi-
mentally, and, second, to show that these mathematical
relationships could be deduced from the fundamental science
of dynamics; or to put it another way, that the laws of elec-
tricity in motion could be derived from the laws applicable to
any system of moving bodies. As always, Maxwell was very
cautious in expressing himself about the nature of electricity.
It behaves, he said, like an incompressible fluid; "wherever
there is electric force there is electric displacement." These,
as J. J. Thomson observed, are the only definite statements
about electricity to be found in the treatise, which led Hertz
to say that Maxwell's theory is Maxwell's equations, and
caused Helmholtz to comment that "he would be puzzled to
explain what an electric charge was on Maxwell's theory be-
yond being the recipient of a symbol."

What are the Maxwellian equations? I cannot hope to give
an easy answer to this question, but at the cost of deliberate
oversimplification I must try summarily to explain them, for
they are the heart of the theory.

Maxwell based the equations on four principles: (1) that
an electric force acting on a conductor produces a current
proportional to the force; (2) that an electric force acting on
a dielectric produces displacement proportional to the force;
(3) that a current produces a magnetic force (i.e., a moving
electric charge is surrounded by a magnetic field) at right
angles to the current's lines of flow and proportional to its
intensity; (4) that a changing magnetic force (or field) pro-
duces a current proportional to the intensity of the force. The
third and fourth principles exhibit a striking symmetry. The
third is Faraday's law of electromagnetic induction, according
to which "the rate of alteration in the number of lines of mag-
netic induction passing through a circuit is equal to the work
done in taking unit electric charge round the circuit." Max-

213

MJL1_____.

Hgffl---

sliw

214

James Clerk Maxwell, Part

Lines of force appear in Electricity and Magnetism, left: "Uniform magnetic
field disturbed by an electric current in a straight conductor." above: "Two
circular currents." (Scientific American)

well's complementary law, the fourth principle, is that "the
rate of alteration in the number of lines of electric force pass-
ing through a circuit is equal to the work done in taking a unit
magnetic pole round it."

On this foundation two sets of symmetrical equations can be
erected. One set expresses the continuous nature of electric
and magnetic fields; the second set tells how changes in one
field produce changes in the other. In these formulations the
mechanical aspects of the theory are retained, perfect conti-
nuity is preserved by treating electricity as if it were an in-
compressible fluid, and wave phenomena are deduced as the
consequences of displacement in a dielectric.

How does the concept of the field enter the theory? We have

215

followed Maxwell as he stripped his model of its particles and
cylinders and reduced it to an aetherial medium. In the
Treatise, while not abandoning the medium altogether, he robs
it of almost all its attributes other than form. The matter of the
medium, as Poincare says, is left only with purely geometric
properties, the atoms dwindle to mathematical points, subject
to the laws of dynamics alone. The grin is left but the cat is
gone. It is a perfect example of mathematical abstraction.*

The aether is a thing that wiggles when it is prodded,
but does nothing on its own. An electromagnetic field con-
sists of two kinds of energy, electrostatic or potential en-
ergy, and electrodynamic or kinetic energy. The aether, like

* Einstein made an interesting comment about Maxwell's equations and his use
of the concept of the field. "He showed that the whole of what was then known
about light and electromagnetic phenomena was expressed in his well-known
double system of differential equations, in which the electric and the magnetic
fields appear as the dependent variables. Maxwell did, indeed, try to explain,
or justify, these equations by intellectual constructions. But he made use of
several such constructions at the same time and took none of them really seri-
ously, so that the equations alone appeared as the essential thing and the
strength of the fields as the ultimate entities, not to be reduced to anything
else. By the turn of the century the conception of the electromagnetic field as
an ultimate entity had been generally accepted and serious thinkers had aban-
doned the belief in the justification, or the possibility, of a mechanical explana-
tion of Clerk Maxwell's equations. Before long they were, on the contrary,
actually trying to explain material points and their inertia on field theory lines
with the help of Maxwell's theory, an attempt which did not, however, meet
with complete success. Neglecting the important individual results which Clerk
Maxwell's life work produced in important departments of physics, and con-
centrating on the changes wrought by him in our conception of the nature of
physical reality, we may say this: — before Clerk Maxwell people conceived of
physical reality — insofar as it is supposed to represent events in nature — as
material points, whose changes consist exclusively of motions, which are sub-
ject to partial differential equations. After Maxwell they conceived physical
reality as represented by continuous fields, not mechanically explicable, which
are subject to partial differential equations. This change in the conception of
reality is the most profound and fruitful one that has come to physics since
Newton; but it has at the same time to be admitted that the program has by
no means been completely carried out yet."

I am puzzled as to what Einstein meant in saying that Maxwell's equation
eliminated the notion of mechanism in explaining electromagnetic phenomena.
Similar views have been expressed by many other physicists and philosophers.
Maxwell himself would not have agreed with this position. His writings refute
it. The inference was drawn by his successors. But there is a more important

216

James Clerk Maxwell, Part II

a universal condenser, may be conceived as storing energy —
in which case, being elastic, it is deformed. Since the aether
fills all space and therefore penetrates conductors as well as
dielectrics, it no longer makes any difference whether we deal
with a conduction current or a displacement current; in either
case the aether is set in motion. This motion is communicated
mechanically from one part of the medium to the next and is
apprehended by us as heat, or light, or mechanical force (as
in the repulsion between wires) or other phenomena of mag-
netism and electricity. The ruling principle of all such phe-
nomena, it should be observed, is that of least action. This is
the grand overriding law of the parsimony of nature: every

point that requires clarification; namely, do the equations justify the inference?
It is true that a field is not the same as a material particle, and that the motion
of a particle is not the same as a change in a field. It is true also that the con-
cept "material particle" was long held to he intuitively clear, while the concept
"field" has never heen so regarded. This makes it easier to say mysterious
things about fields, which no one would dream of saying about particles. But a
more careful definition of these concepts, as physicists actually use them, raises
serious question as to whether a field is any less suited to a "mechanistic" ex-
planation than a system of material particles; indeed, whether a mechanistic
explanation fits either or neither case. In modern physics material particles are
not what they once were. They are pale abstractions, quite incapable of any-
thing so robust as a collision. But then what is a collision? One thinks of bil-
liard balls knocking together, as a pristine example. This, however, is a plain
man's way of thinking. The modern physicist has rid his mind of such seductive
images. (As far back as the eighteenth century, the Italian physicist Boscovich
proposed the idea that the heart of an atom is not solid substance but a mere
center of immaterial force.) As particles fade, the field becomes more substan-
tial. Properties are now ascribed to it that make it seem more real and more
potent than a billiard ball or a boulder. Of course the field is hard to describe
in homely terms. Yet it is quite capable, as physicists tell us, of doing homely
things. It produces and undergoes changes — now as if it were a cloud, now an
engine, now an ocean. In short it has mechanical effects. By this I mean effects
of a kind produced by what used to be called material particles. Moreover, it
has mechanical properties. By this I mean properties of a kind produced by
what we call a machine. The field can do things no system of particles or
machine yet conceived can do. Since it can also do all they can do, it is a super-
machine. Is there any point in saving the name? I think there is, to keep our
thinking straight. We ought to keep it to describe both fields and particles or
we ought to discard it entirely. If the word "mechanism" has any meaning in the
universe of refined observation, it has as much meaning in relation to fields as
to particles. At the same time I am quite prepared to believe that it has as little
meaning in one case as the other; for that matter, no meaning in either.

217

action within a system is executed with the least possible ex-
penditure of energy. It was of the first importance to Maxwell
that electrical phenomena should satisfy the principle, for
otherwise his mechanical explanation of the phenomena would
not have been possible.

With these points in mind, we may examine a set of Max-
well's equations in a form that describes the behavior of an
electromagnetic field under the most general conditions, i.e., a
field moving in empty space. No conductors are present, no
free charges, and the medium is a vacuum. The equations then
read

1) divE = 0

2) divH = 0

. _ 1 dH

3) curlE-- - -^

1 dE

4) curlH= - ^

The meaning of the symbols is as follows: E and H represent
electric and magnetic field strength; since they vary in time,
and from place to place, they are functions of the space co-
ordinates x, y, z (not shown) and of the time coordinate, t.
C is the velocity of light and enters the equations as the rate
of propagation; div (an abbreviation for divergence) and curl
(an abbreviation for rotation) represent mathematical opera-
tions whose physical meaning is explained below.

Divergence is essentially a measure of rate of change. In
words, then, equation 1

div E = 0

says that in a moving field the electric intensity is the same at
every point, i.e., the rate of change is zero at every point. More
loosely, this equation extends to the field the classical principle
that electric lines of force can be neither created nor de-
stroyed. Thus the equation says that the number of electric
lines of force, representing the field strength, that enter any

218

James Clerk Maxwell, Part II

tiny volume of space must equal the number leaving it. Mak-
ing use of still another analogy, if one conceives of electricity
in Maxwell's idiom, as an incompressible fluid, equation 1
states that as much fluid flows out of a tiny volume of space in
a given time as flows in.*

* For the reader interested in a little more detail, the following explanation
may be helpful. Equation 1 states that the divergence of the electric field inten-
sity is zero at any point in space and at any instant of time. The meaning of the
equation may be visualized as follows. It is customary to represent £ at a given
instant of time by a series of lines whose relative density in space is propor-
tional to E. These lines have direction because £ is a vector. Consider a point
P and a sphere surrounding P. Let us suppose that the intensity of the electric
field on the left hemispherical surface of the sphere is uniform over the surface
and is directed at each point perpendicular to the surface.

Suppose further that some change takes place in the electric field intensity E
in the region occupied by the sphere but such that on the right hemispherical
surface the field E is again uniform and perpendicular to the surface but strong-
er than on the left portion. We would indicate this increase in the intensity of
E by having more lines leave the sphere on the right than enter on the left.
Using the number of lines as a measure of E, we count the lines entering the
spherical surface and multiply this number by the area of the hemisphere, and
regard this product as negative. Let us next form the analogous product of the
area and the number of lines leaving the surface, and regard this product as
positive. The algebraic sum of these two products, that is, the positive plus the
negative, is called the net electric flux through the spherical surface. This net
flux is the divergence of E over the volume of the sphere. In our illustration
the net flux of E has increased as E passes through the sphere. Hence we
should say in this case that the divergence of E through the sphere is positive.
If we now divide this net flux through the sphere by the volume of the sphere,
we obtain the next net flux per unit volume. We now imagine that the sphere
becomes smaller and smaller and contracts to the point P. Of course the net
flux per unit volume changes and approaches some limiting value. This limiting
value, which is a mathematical abstraction, is div E at the point P. Thus div E
is essentially a measure of the spatial rate of change of E at the point P. Since
equation 1 says that for electric fields div E = 0 at each point P, we may say
that the net spatial rate of change of E is zero in empty space. More loosely
stated, this equation says that electric field lines are neither created nor de-
stroyed at the point P. It is to be noted that the phrase "spatial rate of change"
is intended to emphasize that the divergence is concerned with the way in
which E changes from point to point in space at the same instant of time. This
spatial rate must be distinguished from the rate at which some quantity, for
example, E itself in equation 4, may change during some interval of time.

219

Equation 2

div H = 0

makes the same assertion for magnetic lines as equation 1
makes for electric lines.
Equation 3

curl E — -55—

is Maxwell's way of stating Faraday's law of induction. The
equation describes what happens in a changing magnetic field.

The right side expresses rate of change,—^ — , multiplied by a

very small factor, (the negative sign before the fraction

is purely a matter of algebraic convenience) ; the left side ex-
presses the fact that an electric field is created by a changing
magnetic field. But the equation is more than analytic; thanks
to the sign curl, it actually gives a picture of the event. A simple
diagram may help make this clear. Suppose the existence of a
magnetic field uniform over a region of space. We draw a
circle

_ H

surrounding a bundle of parallel lines, which represent the
intensity and direction of the magnetic field. The circle lies in
a plane perpendicular to the lines. If the field is changed (by

220

James Clerk Maxwell. Part II

motion or by increase or reduction of strength), it produces
an electric field that acts in a circle around the lines of mag-
netic force (though it may also act in other directions). By
summing the work done in moving unit electric charge around
the circle, we obtain what is called the net electromotive force
around the circle.* If the circle were made of wire, the chang-
ing magnetic lines would of course induce the flow of a cur-
rent; but even without a wire — and therefore no current — a
force would be induced. Dividing this force by the area en-
closed by the circle gives the net electromotive force (per unit
area) which "curls" around the circle. Now imagine the circle
growing smaller and smaller and shrinking finally to the point
P. By this limiting process we obtain a limiting value of the
net electromotive force per unit area : this is curl E at P. Thus
equation 3 says that the limiting value of electromotive force
per unit area equals the rate of change of H at the point P,

multiplied by the tiny negative fraction, J Or, again,

more loosely stated, a changing magnetic field creates an
electric field whose electromotive force per unit area at any
given point and instant of time equals the time rate of change
of the magnetic field at that point and instant.

Equation 4

curl H — — -^r
c Ot

says that, except for the change in algebraic sign (which has
to do with the directions of the fields), the roles of E and H in

* In physical terms, we obtain the net capacity of the electric field to move
current along the circle.

t The symbol c, which here stands for the ratio of the electrostatic to the elec-
tromagnetic units of electricity, is required to translate E (an electrostatic phe-
nomenon) and H (an electromagnetic phenomenon) into the same system of
units. The equation explains how Maxwell was able to connect electrical and
magnetic phenomena with the velocity of light, for c is in fact that velocity.

221

equation 3 may be reversed. At any given point and instant the
magnetomotive force (the analogue for magnetic fields of
electromotive force) per unit of area created by a changing
electric field is equal to the time rate of change of the electric

field multiplied by the tiny positive fraction — . Now, the

reader who has followed this discussion will perceive that the

time rate of change of E, -«— , is none other than Maxwell's

displacement current. For since the changes are taking place
in the dielectric known as empty space, the only currents that
can flow are displacement currents.* Prior to Maxwell, it was
thought that the magnetic field H could be produced only by
currents that flowed in wires passing through the circle. If no
wires were present, the law thought to be applicable was
curl H = 0. It was Maxwell's great discovery, deduced me-
chanically from his model and expressed mathematically in
this equation, that a time-varying electric field produces (or
must be accompanied by) a net "curled" magnetic force even
in an insulator or empty space. t

According to Maxwell's theory, the introduction of a time-
varying electric force in a dielectric produces displacement
waves with the velocity of light. To put it another way, it is the
surge and ebbing of the force that produces the periodic dis-
placement waves; a static charge would merely create an in-
stantaneous displacement, which would be fixed, but not a

* Equation 4 assumes the existence of this current and relates it quantitatively
to the magnetomotive force generated by the existent magnetic field. Physically
we may regard the magnetic field as creating the displacement current or, con-
versely, regard the displacement current as creating the accompanying magnetic
field and magnetomotive force.

t Maxwell called -=- the displacement current, the term "displacement" mean-
ing that the electric field intensity E was being altered or displaced as time

■qe
varies, and the term "current" suggesting that — had the properties of a cur-

a ■ &E

rent Mowing in a wire even though — existed in empty space.

222

James Clerk Maxwell, Part II

wave. Now, an electric current, as we have seen, whether in a
dielectric or in a conductor, is accompanied by a magnetic
force; and similarly a periodic wave of electric displacement
is accompanied by a periodic magnetic force. The wave front
itself, as Maxwell showed, comprises electric vibrations at
right angles to the direction of propagation and a magnetic
force at right angles to the electric displacement. The com-
pound disturbance is therefore called an electromagnetic wave.
A light wave (which is a displacement wave) is, as Henri
Poincare later elaborated, "a series of alternating currents,
flowing in a dielectric, in the air, or in interplanetary space,
changing their direction 1,000,000,000,000,000 times a sec-
ond. The enormous inductive effect of these rapid alternations
produces other currents in the neighboring portions of the
dielectric, and thus the light waves are propagated from place
to place."

The electromagnetic theory of light was testable experi-
mentally, and indeed stood up remarkably well in laboratory
trials. But this was only a limited confirmation of Maxwell's
system, for if his reasoning was correct, there must be other
electrical waves produced by initial disturbances of differing
intensity. These waves would differ from light in wave length
and would therefore not be visible, yet it should be possible to
detect them with appropriate instruments. How to find them,
not to say generate them, was now the crucial problem. Max-
well did not live to see it solved. Not until ten years after his
death were his prophecies fulfilled and the skepticism of his
most distinguished contemporaries refuted. As late as 1888
Lord Kelvin referred to Maxwell's waves as a "curious and
ingenious, but not wholly tenable hypothesis" ; but a year later
Helmholtz's greatest pupil, Heinrich Hertz, nosed out Oliver
Lodge in the race to demonstrate their existence. In a series of
brilliant experiments he showed how electric waves could be
"excited" (i.e., generated) by oscillation and detected by
a circular conductor provided with a small gap; and how they
could be polarized, reflected, refracted, made to form shadows

223

and to interfere with each other. The connection, he said, "be-
tween light and electricity ... of which there were hints and
suspicions and even predictions in the theory, is now estab-
lished. . . . Optics is no longer restricted to minute aether
waves, a small fraction of a millimetre in length; its domain is
extended to waves that are measured in decimetres, metres and
kilometres. And in spite of this extension, it appears merely
... as a small appendage of the great domain of electricity.
We see that this latter has become a mighty kingdom."

The Treatise, written while Maxwell was "in retirement" at
Glenlair, drew only part of his energy. As a "by-work" during
the same period he wrote a textbook on heat, which appeared
in 1870, and a number of papers of considerable importance
on mathematics, color vision and topics of physics. He main-
tained a heavy scientific and social correspondence, enlarged
his house, studied theology, composed stanzas of execrable
verse, rode his horse, went on long walks with his dogs, visited
his r ghbors and played with their children, and made fre-
quent trips to Cambridge to serve as moderator and examiner
in the mathematical tripos.

In 1871 a chair in experimental physics was founded at
Cambridge. It is hard to realize that at the time no courses in
heat, electricity and magnetism were being taught there, and
no laboratory was available for the pursuit of these arcane
matters. The University, as a contemporary scholar delicately
observed, "had lost touch with the great scientific movements
going on outside her walls." A committee of the faculty began
to bestir itself, a report was issued, and the lamentable facts
fell under the gaze of the Duke of Devonshire, Chancellor of
the University. He offered the money for the building and
furnishing of the famous Cavendish Laboratory. Thomson, it
was known, would not leave his post at Glasgow to take the
new chair, and Maxwell, though at first reluctant to leave
Glenlair, yielded to the urging of his friends to offer himself
as a candidate. He was promptly elected.

224

James Clerk Maxwell, Part II

He now devoted himself to the task of designing and super-
intending the erection of the laboratory. His aim was to make
it the best institution of its kind, with the latest apparatus and
the most effective arrangements for research. He inspected
Thomson's laboratory at Glasgow and Clifton's at Oxford to
learn the desirable features of both and embody them in the
Cavendish. He presented to the laboratory all the apparatus in
his own possession and supplemented the Duke's gift by gen-
erous money contributions. With so many details to be taken
care of, the structure and its appointments were not completed
until 1874. The delay, while inevitable, was inconvenient. "I
have no place," wrote Maxwell, "to erect my chair, but move
about like the cuckoo, depositing my notions in the Chemical
Lecture Room in the first term, in the Botannical in Lent and
in the Comparative Anatomy in Easter." His "notions" were
the courses he gave, beginning in 1871, on heat, electricity and
electromagnetism, a schedule maintained throughout the ten-
ure of his chair. And though the audiences were often small,
some of the best students were soon attracted to his lectures,
which contained much important original work. The renais-
sance that followed in physical science at Cambridge was the
direct result of his influence.

Maxwell's classic Matter and Motion, "a small book on a
great subject," was published in 1876. About this time he
contributed articles on various subjects — "Atom," "Aether,"
"Attraction," "Faraday," among others — to the famous ninth
edition of the Encyclopaedia Britannica. His public lectures
include a charming discourse "On the Telephone," which,
though delivered when he was already very ill, is not only as
clear as his best expositions but filled with gay, amusing
asides. Speaking, for example, of "Professor Bell's inven-
tion," he comments on "the perfect symmetry of the whole
apparatus — the wire in the middle, the two telephones at the
ends of the wire, and the two gossips at the ends of the tele-
phones "A task that occupied him for five years, almost to

the very end of his life, was editing twenty packets of unpub-

225

lished scientific papers of Henry Cavendish, who was great-
uncle to the Duke of Devonshire. This splendid two-volume
work, published in 1879, did much to fix the reputation of an
immensely gifted investigator, whose important work on elec-
tricity was unknown to his contemporaries because the results
were confided only to his manuscripts. Maxwell repeated
Cavendish's experiments and showed that he had anticipated
major discoveries in electricity, including electrostatic capac-
ity, specific inductive capacity and Ohm's law.

As Maxwell grew older, friends remarked on his "ever-in-
creasing soberness" of spirit. This must not be taken to mean he
was invariably melancholy or withdrawn or that his nice sense
of fun — about himself no less than about others — had van-
ished. He continued to see his many friends, to write light
verse and parodies, to promenade with his dog Toby, who was
at Maxwell's side even in the laboratory, to play small prac-
tical, but never mean, jokes, to engage in what was called
"humorous mystification" by advancing preposterous scien-
tific ideas in conversation while keeping a straight face. All
things, he once remarked, are "full of jokes," though they are
also "quite full of solemn matters," and he was as likely to
stress their light as their grave aspect.

But it is true he became somewhat more reticent with the
passing years, and more and more concealed his feelings and
reflections beneath an ironical shell. The tough, rational,
Scotch common-sense cord of his nature had always been inter-
twined with threads of mysticism. Often plain, even blunt, in
his address, he also had an allusive way of speaking and
showed a fondness for parables. He had faith in science, yet
he was at bottom skeptical as to how much could be learned
from science alone about nature and meaning. It was all very
well, he felt, to have "ideal aspirations"; on the other hand,
"It's no use thinking of the chap ye might have been." His
contemporaries remember him as both modest and intellectu-
ally scornful, tentative in his scientific opinions and dogmatic
when others seemed to him to be immoderately self-assured.

226

James Clerk Maxwell. Part II

"No one knows what is meant by" so-and-so was his way of
answering a cocksure formulation of a scientific "truth."

The most striking of Maxwell's traits was his gentleness.
"His tenderness for all living things was deep and instinctive;
from earliest childhood he could not hurt a fly." An extraordi-
nary selflessness characterized his relationship to those close
to him. When his brother-in-law came to London to undergo
an operation, Maxwell gave up the ground floor of his house
to patient and nurse and left himself with a room so small that
he frequently breakfasted on his knees because there was no
room for a chair at the table. Mrs. Maxwell had a serious and
prolonged illness in the last years of Maxwell's life, and he
insisted on nursing her. On one occasion it is reported that he
did not sleep in a bed for three weeks. But his work went on
as usual, and he was as cheerful as if he enjoyed the ordeal —
which may indeed have been the case. Nor did he give the
slightest sign of being downcast or show self-pity when his own
fatal illness seized him.

In the spring of 1877 he began to be troubled with pain and
a choking sensation on swallowing. For some strange reason he
consulted no one about his symptoms for almost two years,
though his condition grew steadily worse. His friends at Cam-
bridge observed that he was failing, that the spring had gone
out of his step. When he went home to Glenlair for the sum-
mer of 1879, he was so obviously weakening that he called for
medical help. He was in terrible pain, "hardly able to lie still
for a minute together, sleepless, and with no appetite for the
food which he so required." He understood thoroughly that his
case was hopeless, yet his main concern seemed to be about the
health of his wife. In October he was told he had only a month
to live. On November 5 he died. "No man," wrote his physi-
cian, Dr. Paget, "ever met death more consciously or more
calmly." When Maxwell was buried in Parton Churchyard at
Glenlair, the world had not yet caught up with his ideas. Even
today it has not fully explored the kingdom created by his
imagination.

227

Oersted established a connection between electric
currents and magnetism; Faraday found the connection
between magnetic fields and induced electric cur-
rents. But it was Maxwell who synthesized and ex-
tended these two results.

14 On the Induction of Electric Currents

James Clerk Maxwell

An excerpt from his Treatise on Electricity and Magnetism
published in 1873.

528.] The discovery by Orsted of the magnetic action of an
electric current led by a direct process of reasoning to that of
magnetization by electric currents, and of the mechanical action
between electric currents. It was not, however, till 1831 that
Faraday, who had been for some time endeavouring to produce
electric currents by magnetic or electric action, discovered the con-
ditions of magneto-electric induction. The method which Faraday
employed in his researches consisted in a constant appeal to ex-
periment as a means of testing the truth of his ideas, and a constant
cultivation of ideas under the direct influence of experiment. In
his published researches we find these ideas expressed in language
which is all the better fitted for a nascent science, because it is
somewhat alien from the style of physicists who have been accus-
tomed to established mathematical forms of thought.

The experimental investigation by which Ampere established the
laws of the mechanical action between electric currents is one of
the most brilliant achievements in science.

The whole, theory and experiment, seems as if it had leaped,
full grown and full armed, from the brain of the 'Newton of elec-
tricity.' It is perfect in form, and unassailable in accuracy, and
it is summed up in a formula from which all the phenomena may
be deduced, and which must always remain the cardinal formula of
electro-dynamics.

The method of Ampere, however, though cast into an inductive
form, does not allow us to trace the formation of the ideas which
o-uided it. We can scarcely believe that Ampere really discovered
the law of action by means of the experiments which he describes.
We are led to suspect, what, indeed, he tells us himself*, that he

* Thdorie da rherwminet Electrodynamiqiut, p. 9.

229

discovered the law by some process which he has not shewn us,
and that when he had afterwards built up a perfect demon-
stration he removed all traces of the scaffolding by which he had
raised it.

Faraday, on the other hand, shews us his unsuccessful as well
as his successful experiments, and his crude ideas as well as his
developed ones, and the reader, however inferior to him in inductive
power, feels sympathy even more than admiration, and is tempted
to believe that, if he had the opportunity, he too would be a dis-
coverer. Every student therefore should read Ampere's research
as a splendid example of scientific style in the statement of a dis-
covery, but he should also study Faraday for the cultivation of a
scientific spirit, by means of the action and reaction which will
take place between the newly discovered facts as introduced to him
by Faraday and the nascent ideas in his own mind.

It was perhaps for the advantage of science that Faraday, though
thoroughly conscious of the fundamental forms of space, time, and
force, was not a professed mathematician. He was not tempted
to enter into the many interesting researches in pure mathematics
which his discoveries would have suggested if they had been
exhibited in a mathematical form, and he did not feel called upon
either to force his results into a shape acceptable to the mathe-
matical taste of the time, or to express them in a form which
mathematicians might attack. He was thus left at leisure to
do his proper work, to coordinate his ideas with his facts, and to
express them in natural, untechnical language.

It is mainly with the hope of making these ideas the basis of a
mathematical method that I have undertaken this treatise.

529.] We are accustomed to consider the universe as made up of
parts, and mathematicians usually begin by considering a single
particle, and then conceiving its relation to another particle, and so
on. This has generally been supposed the most natural method.
To conceive of a particle, however, requires a process of abstraction,
since all our perceptions are related to extended bodies, so that
the idea of the all that is in our consciousness at a given instant
is perhaps as primitive an idea as that of any individual thing.
Hence there may be a mathematical method in which we proceed
from the whole to the parts instead of from the parts to the whole.
For example, Euclid, in his first book, conceives a line as traced
out by a point, a surface as swept out by a line, and a solid as
generated by a surface. But he also defines a surface as the

230

On the Induction of Electric Currents

boundary of a solid, a line as the edge of a surface, and a point
as the extremity of a line.

In like manner we may conceive the potential of a material
system as a function found by a certain process of integration with
respect to the masses of the bodies in the field, or we may suppose
these masses themselves to have no other mathematical meaning

than the volume-integrals of — V2*, where * is the potential.

In electrical investigations we may use formulae in which the
quantities involved are the distances of certain bodies, and the
electrifications or currents in these bodies, or we may use formulae
which involve other quantities, each of which is continuous through

all space.

The mathematical process employed in the first method is in-
tegration along lines, over surfaces, and throughout finite spaces,
those employed in the second method are partial differential equa-
tions and integrations throughout all space.

The method of Faraday seems to be intimately related to the
second of these modes of treatment. He never considers bodies
as existing with nothing between them but their distance, and
acting on one another according to some function of that distance.
He conceives all space as a field of force, the lines of force being
in general curved, and those due to any body extending from it on
all sides, their directions being modified by the presence of other
bodies He even speaks of the lines of force belonging to a body
as in some sense part of itself, so that in its action on distant
bodies it cannot be said to act where it is not. This, however,
is not a dominant idea with Faraday. I think he would rather
have said that the field of space is full of lines of force, whose
arrangement depends on that of the bodies in the field, and that
the mechanical and electrical action on each body is determined by
the lines which abut on it.

231

The magnetic properties of certain materials and the
electric effects produced by friction were both known
in ancient days. Oersted's experiment with electric
current and a compass showed that electricity and
magnetism are related. Maxwell found the connec-
tion between the two phenomena in his electromag-
netic equations.

15 The Relationship of Electricity and Magnetism

D. K. C. MacDonald

Excerpt from his book, Faraday, Maxwell, and Kelvin, published in 1964.

We know that an electric current can produce forces
on a magnet in its vicinity, or, in other words, an elec-
tric current produces a magnetic "field." Faraday had
shown, moreover, that a changing magnetic field (pro-
duced either by moving a magnet or by varying an elec-
tric current in a coil) could induce an electric current
in a neighboring, but separate, coil of wire. Thus,
through these fundamental experiments of Oersted,
Ampere, and particularly Faraday, various vital facts
had been discovered about how electric currents and
magnets could interact with one another and, as we
have said earlier, these discoveries were already lead-
ing to exciting practical developments such as the elec-
tric telegraph and the submarine cables. But, in broad
terms, what James Clerk Maxwell tried to do was to
build up a more general picture of these interactions
between electric and magnetic effects (or "fields")

233

without worrying so much about actual coils of wire
with electric currents in them, or about how in practice
one actually produced the magnetic fields. Following
Faraday's general lead in concentrating on the "lines
of force" or the "fields," Maxwell tried to work out
directly and quantitatively the interaction in space of
the electric field on the magnetic field, and vice versa,
wherever they might exist. In his mind Maxwell in-
vented, or designed, various semi-mechanical models
to build up his theory, but in the end he could discard
this mental scaffolding and give a complete mathemati-
cal description of electromagnetic behavior which holds
good to this day.

Consider the production of a magnetic field by a cur-
rent of electricity in a coil. We know that such a cur-
rent always involves a movement of electric charge,
so from the electrical point of view we may say that
something is changing all the time. One of the things
Maxwell did was to generalize this discovery boldly,
saying in essence: [I] "A Changing Electric Field Will
Always Produce a Magnetic Field."

But, on the other hand, Faraday had shown that
the movement of a magnet could produce an electric
current, as we have already seen; so on the same lines
this can be generalized to say: [II] "A Changing
Magnetic Field Can Produce an Electric Field"

The ultimate result of James Clerk Maxwell's work
was, in effect, that he expressed these two basic ideas
in precise, quantitative terms, and he came out finally
with what are now known as Maxwell's Equations,
which, as I already have said, remain today the stand-
ard method of predicting how electricity and magnetism
will behave under any given conditions. The acme of
Maxwell's work, however, was his discovery that when
applied in free, empty space his equations took on a
form which is equally descriptive of any undamped

234

The Relationship of Electricity and Magnetism

wave motion propagating itself freely from place to
place. Thus, if you drop a stone into a large pond of
water a ripple or wave will proceed out from that
place, and some of the energy from the falling stone
will radiate outward in the wave from the splash. If
you shout to somebody else some distance away, then it
is a vibration or wave in the air around you which car-
ries the sound to the distant person; or if you rig up a
long, tight rope or string between two points, and then
"twang" the rope, you can see a wave running along
the rope, and this wave carries some of the energy that
you put in the "twang." Again, if there is a violent
storm at sea, the energy from this storm gets carried
over long distances by waves in the ocean; the waves
which smash on the rocks of Newfoundland may well
be getting their energy from a storm a thousand miles
or more out in the Atlantic Ocean. In each of these lat-
ter examples the waves will be damped to some degree
or other. For example, waves traveling on the surface
of the sea lose some energy by dragging deeper layers
of water, by the very fact that water is not entirely free
to move by itself, but has a viscosity or "stickiness,"
which means that the waves ultimately suffer losses by
friction.

The particularly remarkable, and unique, feature of
electromagnetic waves is the fact that they can propa-
gate themselves quite freely without damping through
empty space where no matter whatsoever is present,
but it is not difficult to see from the two italicized state-
ments above that a self-propelled wave motion of the
electromagnetic field might be possible.

Imagine that we have electric and magnetic fields
present in a small region of space, and that the fields
are changing suitably with time. As the electric field
changes at some point in space it will produce a mag-
netic field in the neighborhood, and if things are right

235

this magnetic field will then reinforce the magnetic
field in some regions, and in turn the over-all changing
magnetic field will produce again a fresh electric field
in its neighborhood. What Maxwell's equations showed
was that this process, perhaps somewhat reminiscent of
an endless game of leapfrog, could indeed be self-
maintained, with the energy constantly radiating out-
ward from where the waves started.

But this was not all. Maxwell was able to predict
from this theory, moreover, the speed with which such
an electromagnetic wave should travel in space. This
speed was simply determined by the ratio of two meas-
urements which could be made on electric and mag-
netic quantities in the laboratory, and it turned out
that the speed predicted in this way was very close to
the already known speed of light (about 300,000
km/sec «=* 186,000 miles/sec). Furthermore, it is also
a well-known characteristic of light that it too can
propagate through empty space, as witness the light of
day which reaches us unfailingly from the sun across
about a hundred million miles of empty space. So Max-
well could finally say with confidence that, physically
speaking, light must be a form of electromagnetic
radiation.

Some years after Maxwell's death, Heinrich Hertz
(1857-94) was able to show experimentally, using
electrical apparatus, the direct generation and detection
of the electromagnetic waves predicted by Maxwell.
These "Hertzian waves" are the great-grandfather of
the waves which carry all our radio and television
broadcasts today, and in fact radio waves, television
waves, light waves, X-rays, and gamma rays, are all
members of one and the same family— electromagnetic
waves. In free space they all travel with identically the
same speed, which for convenience we always refer to
as "the velocity of light." What distinguishes one type

236

The Relationship of Electricity and Magnetism

of wave from another is simply its rate of vibration, or
the corresponding wave length (i.e., the distance be-
tween two successive "crests" or "troughs" of a wave).
A typical radio wave vibrates at, or has a frequency
(/) of, about a million times a second (/ = 10G cy-
cles/sec = 1 M c/s), and has a wave length (X) of
about 300 meters. For those who do not mind an equa-
tion, the relationship is very simple, namely f\ = c,
where c denotes, as always in physical science, the
velocity of light. At the other end of the scale, a gamma
ray might have a wave length of only about one ten-
billionth part of a centimeter (\ = 10-10 cm), and a
corresponding frequency of vibration of about three
hundred billion billion cycles/sec (/ = 3 X 1020 c/s).

Electromagnetic Waves

Maxwell's electromagnetic theory also led to intense
discussion later about the fundamental nature of the
electromagnetic waves involved. Many physicists felt
that in order to have a wave at all there had to be
"something" to do the waving or vibrating, and they in-
vented a sort of all-pervading, universal, thin soup or
consomme which they called the "aether." But whether
it is more reasonable to talk about electromagnetic
waves in free space (which still worries some people
for the same sort of reason that "action at a distance"
worried people), or whether it is better to try to think
about an all-permeating, vibrating "aether" is not a
very burning issue today. What matters now is that
Maxwell's Equations are a generally accepted founda-
tion for discussing electromagnetic behavior under the
widest range of possible situations, and also that Max-
well's lead in analyzing electromagnetism by means of
the electric and magnetic fields has led more generally
to the concept of discussing other forms of interaction

237

through some appropriate "field." Indeed, Maxwell
himself was at first very inclined to believe that gravita-
tional attraction must also be propagated in this way,
but he ran up against difficulties with the energy in-
volved which seemed to him then insurmountable.

We have seen that, starting from the picture of "ac-
tion at a distance" between charges of electricity, Max-
well, following Faraday's lead, could reformulate the
problem in terms of a field acting through, and at all
points of, space of which the charged particles are, so
to speak, now just the "terminals" or "end points." The
discovery that this electromagnetic field would vibrate
in free space was a great step toward identifying light
as an electromagnetic wave, since the wave phenome-
non of light (interference, diffraction, etc.) had been
known for a long time. At the same time there had al-
ways been some persistent reasons for regarding light
alternatively as a corpuscular phenomenon, and Ein-
stein was to show, half a century later, that Maxwell's
vibrating electromagnetic aether, when coupled with
Planck's quantum theory first proposed around 1900,
could also then be regarded in a more or less corpuscu-
lar manner. What Planck and Einstein showed was
that the energy in the electromagnetic field could only
exist in certain minimum-sized bundles or "quanta"
dependent in magnitude on the frequency of vibration
and the newly discovered Planck's constant. These
"bundles" of light, or more technically "quanta" of the
electromagnetic field, are generally known today as
photons. So now we can think of electromagnetic in-
teractions as either conveyed by the vibrating aether
or equivalently as conveyed by streams of photons
which will to some extent behave like particles. In deal-
ing with many kinds of interactions, including those
which hold an atomic nucleus together, modern physics
finds it most valuable to be able to think in both these

238

The Relationship of Electricity and Magnetism

terms without being bound to regard one picture as
more necessarily "real" than the other.

239

The formulation of Maxwell's equations opened the
new area of science called electromagnetism, with
far-reaching consequences.

16 The Electromagnetic Field

Albert Einstein and Leopold Infeld

Excerpt from their book entitled the Evolution of Physics published
in 1938 and 1961.

THE REALITY OF THE FIELD

The quantitative, mathematical description of the
laws of the field is summed up in what are called Max-
well's equations. The facts mentioned so far led to the
formulation of these equations but their content is
much richer than we have been able to indicate. Their
simple form conceals a depth revealed only by careful
study.

The formulation of these equations is the most im-
portant event in physics since Newton's time, not only
because of their wealth of content, but also because
they form a pattern for a new type of law.

The characteristic features of Maxwell's equations,
appearing in all other equations of modern physics, are
summarized in one sentence. Maxwell's equations are
laws representing the structure of the field.

Why do Maxwell's equations differ in form and
character from the equations of classical mechanics?
What does it mean that these equations describe the
structure of the field? How is it possible that, from the
results of Oersted's and Faraday's experiments, we can
form a new type of law, which proves so important for
the further development of physics?

241

We have already seen, from Oersted's experiment,
how a magnetic field coils itself around a changing
electric field. We have seen, from Faraday's experi-
ment, how an electric field coils itself around a chang-
ing magnetic field. To outline some of the characteris-
tic features of Maxwell's theory, let us, for the moment,
focus all our attention on one of these experiments,
say, on that of Faraday. We repeat the drawing in
which an electric current is induced by a changing mag-
netic field. We already know that an induced current
appears if the number of lines of force, passing the sur-
face bounded by the wire, changes. Then the current
will appear if the magnetic field changes or the circuit
is deformed or moved: if the number of magnetic lines
passing through the surface is changed, no matter how
this change is caused. To take into account all these
various possibilities, to discuss their particular influ-
ences, would necessarily lead to a very complicated
theory. But can we not simplify our problem? Let us
try to eliminate from our considerations everything
which refers to the shape of the circuit, to its length,
to the surface enclosed by the wire. Let us imagine
that the circuit in our last drawing becomes smaller and

242

The Electromagnetic Field

smaller, shrinking gradually to a very small circuit en-
closing a certain point in space. Then everything con-
cerning shape and size is quite irrelevant. In this limit-
ing process where the closed curve shrinks to a point,
size and shape automatically vanish from our consid-
erations and we obtain laws connecting changes of
magnetic and electric field at an arbitrary point in
space at an arbitrary instant.

Thus, this is one of the principal steps leading to
Maxwell's equations. It is again an idealized experiment
performed in imagination by repeating Faraday's ex-
periment with a circuit shrinking to a point.

We should really call it half a step rather than a
whole one. So far our attention has been focused on
Faraday's experiment. But the other pillar of the field
theory, based on Oersted's experiment, must be consid-
ered just as carefully and in a similar manner. In this
experiment the magnetic lines of force coil themselves
around the current. By shrinking the circular magnetic
lines of force to a point, the second half-step is per-
formed and the whole step yields a connection be-
tween the changes of the magnetic and electric fields
at an arbitrary point in space and at an arbitrary instant.

But still another essential step is necessary. Accord-
ing to Faraday's experiment, there must be a wire test-
ing the existence of the electric field, just as there must
be a magnetic pole, or needle, testing the existence of
a magnetic field in Oersted's experiment. But Maxwell's
new theoretical idea goes beyond these experimental
facts. The electric and magnetic field, or in short, the
electromagnetic field is, in Maxwell's theory, some-
thing real. The electric field is produced by a changing
magnetic field, quite independently, whether or not

243

there is a wire to test its existence; a magnetic field is
produced by a changing electric field, whether or not
there is a magnetic pole to test its existence.

Thus two essential steps led to Maxwell's equations.
The first: in considering Oersted's and Rowland's ex-
periments, the circular line of the magnetic field coil-
ing itself around the current and the changing electric
field, had to be shrunk to a point; in considering.Fara-
day's experiment, the circular line of the electric field
coiling itself around the changing magnetic field had to
be shrunk to a point. The second step consists of the
realization of the field as something real; the electro-
magnetic field once created exists, acts, and changes
according to Maxwell's laws.

Maxwell's equations describe the structure of the
electromagnetic field. All space is the scene of these
laws and not, as for mechanical laws, only points in
which matter or charges are present.

We remember how it was in mechanics. By knowing
the position and velocity of a panicle at one single
instant, by knowing the acting forces, the whole future
path of the particle could be forseen. In Maxwell's
theory, if we know the field at one instant only, we
can deduce from the equations of the theory how the
whole field will change in space and time. Maxwell's
equations enable us to follow the history of the field,
just as the mechanical equations enabled us to follow
the history of material particles.

But there is still one essential difference between me-
chanical laws and Maxwell's laws. A comparison of
Newton's gravitational laws and Maxwell's field laws

244

The Electromagnetic Field

will emphasize some of the characteristic features ex-
pressed by these equations.

With the help of Newton's laws we can deduce the
motion of the earth from the force acting between the
sun and the earth. The laws connect the motion of the
earth with the action of the far-off sun. The earth and
the sun, though so far apart, are both actors in the play
of forces.

In Maxwell's theory there are no material actors.
The mathematical equations of this theory express the
laws governing the electromagnetic field. They do not,
as in Newton's laws, connect two widely separated
events; they do not connect the happenings here with
the conditions there. The field here and novo depends
on the field in the immediate neighborhood at a time
just past. The equations allow us to predict what will
happen a little further in space and a little later in time,
if we know what happens here and now. They allow
us to increase our knowledge of the field by small steps.
We can deduce what happens here from that which
happened far away by the summation of these very
small steps. In Newton's theory, on the contrary, only
big steps connecting distant events are permissible. The
experiments of Oersted and Faraday can be regained
from Maxwell's theory, but only by the summation of
small steps each of which is governed by Maxwell's
equations.

A more thorough mathematical study of Maxwell's
equations shows that new and really unexpected con-
clusions can be drawn and the whole theory submitted
to a test on a much higher level, because the theoretical
consequences are now of a quantitative character and
arc revealed by a whole chain of logical arguments.

245

Let us again imagine an idealized experiment. A small
sphere with an electric charge is forced, by some ex-
ternal influence, to oscillate rapidly and in a rhythmical
way, like a pendulum. With the knowledge we already
have of the changes of the field, how shall we describe
everything that is going on here, in the field language?

The oscillation of the charge produces a changing
electric field. This is always accompanied by a chang-
ing magnetic field. If a wire forming a closed circuit is
placed in the vicinity, then again the changing mag-
netic field will be accompanied by an electric current
in the circuit. All this is merely a repetition of known
facts, but the study of Maxwell's equations gives a
much deeper insight into the problem of the oscillating
electric charge. By mathematical deduction from Max-
well's equations we can detect the character of the
field surrounding an oscillating charge, its structure
near and far from the source and its change with time.
The outcome of such deduction is the electromagnetic
'wave. Energy radiates from the oscillating charge trav-
eling with a definite speed through space; but a trans-
ference of energy, the motion of a state, is character-
istic of all wave phenomena.

Different types of waves have already been consid-
ered. There was the longitudinal wave caused by the
pulsating sphere, where the changes of density were
propagated through the medium. There was the jelly-
like medium in which the transverse wave spread. A
deformation of the jelly, caused by the rotation of the
sphere, moved through the medium. What kind of
changes are now spreading in the case of an electro-
magnetic wave? Just the changes of an electromagnetic
field! Every change of an electric field produces a mag-

246

The Electromagnetic Field

netic field; every change of this magnetic field pro-
duces an electric field; every change of ... , and so
on. As field represents energy, all these changes spread-
ing out in space, with a definite velocity, produce a
wave. The electric and magnetic lines of force always
lie, as deduced from the theory, on planes perpendicu-
lar to the direction of propagation. The wave pro-
duced is, therefore, transverse. The original features of
the picture of the field we formed from Oersted's and
Faraday's experiments are still preserved, but we now
recognize that it has a deeper meaning.

The electromagnetic wave spreads in empty space.
This, again, is a consequence of the theory. If the oscil-
lating charge suddenly ceases to move, then, its field
becomes electrostatic. But the series of waves created
by the oscillation continues to spread. The waves lead
an independent existence and the history of their
changes can be followed just as that of any other ma-
terial object.

We understand that our picture of an electromag-
netic wave, spreading with a certain velocity in space
and changing in time, follows from Maxwell's equa-
tions only because they describe the structure of the
electromagnetic field at any point in space and for any
instant.

There is another very important question. With
what speed does the electromagnetic wave spread in
empty space? The theory, with the support of some
data from simple experiments having nothing to do
with the actual propagation of waves, gives a clear an-
swer: the velocity of an electromagnetic wave is equal
to the velocity of light.

247

Oersted's and Faraday's experiments formed the
basis on which Maxwell's laws were built. All our re-
sults so far have come from a careful study of these
laws, expressed in the field language. The theoretical
discovery of an electromagnetic wave spreading with
the speed of light is one of the greatest achievements in
the history of science.

Experiment has confirmed the prediction of theory.
Fifty years ago, Hertz proved, for the first time, the
existence of electromagnetic waves and confirmed ex-
perimentally that their velocity is equal to that of light.
Nowadays, millions of people demonstrate that elec-
tromagnetic waves are sent and received. Their ap-
paratus is far more complicated than that used by
Hertz and detects the presence of waves thousands of
miles from their sources instead of only a few yards.

248

Instruments borne aloft by artificial satellites and
probes report that our planet is encircled by two zones
containing high-energy radiation against which space
travelers will have to shield themselves.

Radiation Belts Around the Earth

James Van Allen

An article published in Scientific American in 1959.

So far, the most interesting and least
expected result of man's explora-
tion of the immediate vicinity of
the earth is the discovery that our planet
is ringed by a region— to be exact, two re-
gions—of high-energy radiation extend-
ing many thousands of miles into space.
The discovery is of course troubling to
astronauts; somehow the human body
will have to be shielded from this radia-
tion, even on a rapid transit through the
region. But geophysicists, astrophysi-
cists, solar astronomers and cosmic-ray
physicists are enthralled by the fresh im-
plications of these findings. The configu-
ration of the region and the radiation it
contains bespeak a major physical phe-
nomenon involving cosmic rays and solar
corpuscles in the vicinity of the earth.
This enormous reservoir of charged par-
ticles plays a still-unexplained role as
middleman in the interaction of earth
and sun which is reflected in magnetic
storms, in the airglow and in the beauti-
ful displays of the aurora.

The story of the investigation goes
back to 1952 and 1953, before any of
us could think realistically about the use
of earth satellites to explore the environ-
ment of the earth. Parties from our lab-
oratory at the State University of Iowa
spent the summers of those years aboard
Coast Guard and naval vessels, cruising
along a 1,500-mile line from the waters
of Baffin Bay, near the magnetic pole in
the far northwestern corner of Green-
land, southward to the North Atlantic
off the coast of Newfoundland. Along
the way we launched a series of rocket-

carrying balloons— "rockoons." (The bal-
loon lifts a small rocket to an altitude of
12 to 15 miles, whence the rocket car-
ries a modest payload of instruments to
a height of 60 to 70 miles.) Our objec-
tive was to develop a profile of the cos-
mic-ray intensities at high altitudes and
latitudes, and thus to learn the nature of
the low-energy cosmic rays which at
lower altitudes and latitudes are de-
flected by the earth's magnetic field or
absorbed in the atmosphere.

Most of the readings radioed down
from the rockets were in accord with
plausible expectations. Two rockoons
sent aloft in 1953, however, provided us
with a puzzle. Launched near New-
foundland by Melvin Gottlieb and Les-
lie Meredith, they encountered a zone
of radiation beginning at an altitude of
30 miles that was far stronger than we
had expected. At first we were uneasy
about the proper operation of our in-
struments. But critical examination of
the data convinced us that we had un-
questionably encountered something
new in the upper atmosphere.

Significantly these measurements were
made in the northern auroral zone. In
this zone, which forms a ring some 23
degrees south of the north geomagnetic
pole, the incidence of visible auroras
reaches its maximum. Since rockets fired
north and south of the zone had revealed
nothing unusual, we speculated that the
strong radiation played some part in the
aurora. Showers of particles from the
sun, it was thought, come plunging into
the atmosphere along magnetic lines of

force and set off these displays [see "Au-
rora and Airglow," by C. T. Elvey and
Franklin E. Roach; Scientific Ameri-
can, September, 1955]. But the theory
underlying this explanation did not ex-
plain satisfactorily why the aurora and
the high-intensity radiation we had de-
tected should occur in the auroral zone
and not in the vicinity of the geomag-
netic pole itself. Nor could it account
for the high energies required to carry
the solar particles through the atmos-
phere to such relatively low altitudes.

The mystery deepened when we
found in later studies that the radiation
persists almost continuously in the zone
above 30 miles, irrespective of visible
auroral displays and other known high-
altitude disturbances. More discriminat-
ing detectors established that the radia-
tion contains large numbers of electrons.
Our original observations had detected
X-rays only; now it turned out that the
X-rays had been generated by the im-
pact of electrons on the skin of the in-
strument package ( as if it had been the
"target" in an X-ray tube) and on the
sparse atoms of the upper atmosphere
itself. Sydney Chapman and Gordon
Little at the University of Alaska sug-
gested that such a process might well
account for the attenuation of radio sig-
nals in the lower ionosphere of the auro-
ral zones.

he International Geophysical Year
gave us our first opportunity to in-
vestigate the "auroral soft radiation" on
a more comprehensive scale. During the

249

STRUCTURE OF RADIATION BELTS revealed by contours of
radiation intensity (black lines) is shown schematically by shading

(left); dots {right) suggest distribution of particles in the two
belts. Contour numbers give counts per second; horizontal scale

summer and fall of 1957 Laurence Ca-
hill and I launched a number of rockoons
off the coast of Greenland and also got
off one successful flight in Antarctica.
The latter flight established that the ra-
diation exists in the southern as well as
the northern auroral zone. In February,
1958, Carl Mclhvain fired a series of
two-stage rockets through visible auro-
ras above Fort Churchill in Canada, and
discovered that the radiation includes

energetic protons (hvdrogen nuclei) as
well as electrons.

Meanwhile all of us had been pushing
a new development that greatly expand-
ed the possibilities for high-altitude re-
search. During the summer of 1955 the
President and other Government author-
ities were finally persuaded that it
might be feasible to place artificial satel-
lites in orbit, and authorized an I. G. Y.
project for this purpose. In January,

1956, a long-standing group of high-
altitude experimentalists, called the
Rocket and Satellite Research Panel,
held a symposium to consider how the
satellites could be most fruitfully em-
ployed. At that meeting our group pro-
posed two projects. One was to put a
satellite into an orbit nearly pole-to-pole
to survey the auroral radiation in both
the north and south auroral zones. Such
orbits, however, did not appear to be

250

Radiation Belts Around the Earth

shows distance in earth radii (about 4,000 miles) from the center
of the earth. Particles in the inner belt may originate with the

radioactive decay of neutrons liberated in the upper atmosphere by
cosmic rays; those in the outer belt probably originate in the sun.

technically feasible in the immediate
future. For the time being we were
forced to abandon the use of a satellite
to probe farther into the auroral soft
radiation. We also suggested that a satel-
lite orbiting over the lower latitudes of
the earth might usefully be employed in
a comprehensive survey of cosmic-ray
intensities over those regions.- This proj-
ect was adopted, and we were author-
ized to prepare suitable experimental

apparatus [see "The Artificial Satellite
as a Research Instrument," by James A.
Van Allen; Scientific American, No-
vember, 1956]. It was planned to place
this apparatus on one of the early Van-
guard vehicles.

The difficulties and failures of the
Vanguard are now history. Sputnik I
stimulated some high government offi-
cials to accept a proposal that a num-
ber of us had been urging for more than

a year: to use the proven Jupiter C
rocket as a satellite-launching vehicle.
As a result on January 31, 1958, Ex-
plorer I went into orbit carrying our
simple cosmic-ray detector and a radio
to broadcast its readings.

In the first reports from stations locat-
ed in the U. S. the intensity of radiation
increased with altitude along the expect-
ed curve. Several weeks later, however,
we began to get tapes from stations in

251

EXPLORER IV AND PIONEER III gave the first detailed picture of the radiation belts.
The Explorer IV satellite (short ellipse) monitored radiation levels for nearly two months
at altitudes up to 1,300 miles. The Pioneer III lunar probe (long ellipse) provided data out
to 65,000 miles. Its orbit is shown distorted because of the earth's rotation during flight.

EXPLORER IV ORBIT covered the entire region 51 degrees north and south of the equator;
the black curve shows a small part of its trace on the earth's surface. More than 25 observa-
tion stations (colored dots) recorded data from several thousand of the satellite's passes.

100.000

/ w

^^^^

10,000 20.000 30,000 40,000

RADIAl DISTANCE FROM CENTER OF EARTH IMIIESI

PIONEER III DATA gave the first confirmation of two distinct rings of particles. Counting
rates on both the outbound (black curve) and the inbound (gray curve) legs of the flight
showed two peaks. The two curves differ because they cover different sections of the belts.

South America and South Africa which
gave us counting rates for much higher
altitudes, due to the eccentricity of the
satellite's orbit. These records brought us
a new surprise. At high altitudes over the
equatorial region the apparent counting
rate was very low; in some passes it
dropped to zero for several minutes. Yet
at lower altitudes the rate had quite
"reasonable" values— from 30 to 50
counts a second. Again we were uneasy
about the trustworthiness of the instru-
ments. The only alternative seemed to
be that cosmic rays do not strike the
uppermost layers of the atmosphere over
the tropics, and we were quite unable
to accept this conclusion.

Our uneasiness was increased bv the
incompleteness of our early data. The
Explorer I apparatus broadcast its obser-
vations continuously, but its signals
could be picked up only intermittently,
when the satellite came within range of
a ground station. Our original apparatus,
designed and developed by George Lud-
wig for the Vanguard satellites, included
a magnetic-tape recorder which could
store its observations for a complete orbit
around the earth and then report them in
a "burst" on radio command from the
ground.

T)y early February, working with the
*-* Jet Propulsion Laboratory, we had
convertea this apparatus for use in the
Explorer II satellite. The first attempt to
get it into orbit failed. A second rocket
placed Explorer III, carrying identical
apparatus, in orbit on March 26. This
satellite fully confirmed the anomalous
results of Explorer I. At altitudes of 200
to 300 miles the counting rate was low.
When the satellite went out to 500 to
600 miles, the apparent rate ascended
rapidly and then dropped almost to zero.
One dav, as we were puzzling over the
first tapes from Explorer III, Mcllwain
suggested the first plausible explanation
for their peculiar readings. He had just
been calibrating his rocket instruments,
and called our attention to something
that we all knew but had temporarily
forgotten: A sufficiently high level of
radiation can jam the counter and send
the apparent counting rate to zero. We
had discovered an enormously high level
of radiation, not a lack of it. As Ernest
Ray, a member of our group, inaccu-
rately but graphically exclaimed: "Space
is radioactive!"

During the next two months Explorer
III produced a large number of playback
records, every one of which showed the
same effect. At low altitudes the count-
ing rate was reasonably attributable to

252

Radiation Belts Around the Earth

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LXTLUKt-K IV inaiKUJncn 19 "....* Plastic scin. mbes could be compared to estimate the penetrability of the radia-

Dicture of the nature and intensity of the radiation, riasuc sun luuoa r

picture o. me nature a a » energies; two tion. Radio signals suggested by the red curves in upper drawing

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different scaling factors adapted i, to both high and low counting were recorded by S">undj.a -s and a ler pi ,e ihroug •

rates. Cesium-iodide scintillator measured the total energy input multichannel oscillograph to y.eld record, hke that shown below.

253

MILES
1,500 1,000 5C0

MUES
500 1,000 1,500

TWO SETS OF CONTOURS from readings on opposite sides of
the earth Hell and center) show the northern and southern "horns"

of radiation, which point toward the auroral zones; the contour
numbers show radiation intensity in counts per second. The "tipped"

cosmic rays. At higher altitudes— the pre-
cise height depended on both latitude
and longitude— the count increased to
very high values. Up to the points at
which the counter jammed, it showed
counting rates more than 1,000 times
the theoretical expectation for cosmic
rays. From the rate of increase and the
length of the periods of jamming we
judged that the maximum count prob-
ably went to several times this level.
Since the radiation appeared to resem-
ble the auroral soft radiation, we would
not have been surprised to find it in the
auroral zone or along the magnetic lines
of force that connect these zones. But in
the equatorial latitudes these lines of
force lie much farther out in space than
the altitudes attained by the satellites.

On May 1 of last year we were able
to report with confidence to the National
Academy of Sciences and the American
Physical Society that Explorers I and
III had discovered a major new phenom-
enon: a very great intensity of radiation
above altitudes of some 500 miles over
the entire region of their traverse, some
34 degrees north and south of the equa-
tor. At the same time we advanced the
idea that the radiation consists of
charged particles— presumably protons
and electrons— trapped in the magnetic
field of the earth.

We could rule out uncharged particles
and gamma and X-rays because they
would not be confined by the magnetic
field, and so would be observed at lower
altitudes. The possibility that the earth's

magnetic field might act as a trap for
charged particles was first suggested by
the Norwegian physicist Carl Stormer
in a classical series of papers beginning
some 50 years ago, and there was a
considerable body of evidence for the
existence of low-energy charged parti-
cles throughout our solar system and
specifically in the vicinity of the earth.
But there had been no indication that
these particles would possess the high
energies we had detected.

From Stormer's theoretical discussion
and our own observations we evolved a
rough picture of the trapping mechan-
ism. When a fast-moving charged parti-
cle is injected into the earth's magnetic
field, it describes a corkscrew-shaped
trajectory, the center line of which lies
along a magnetic line of force. The turns
of the helical path are quite open over
the equator but become tighter as the
particle reaches the stronger magnetic
field toward the poles [see illustration at
bottom of opposite page]. At the lower
end of its trajectory the particle goes into
a flat spiral and then winds back along
a similar path to the other hemisphere,
making the transit from one hemisphere
to the other in a second or so. During
this time its line of travel shifts slightly,
SO that the particle drifts slowly around
the earth as it corkscrews from hemi-
sphere to hemisphere. An electron drifts
from west to east; a proton, in the op-
posite direction. At each end of its path
the particle descends into regions of
higher atmospheric density; collisions

with the atoms of atmospheric gases
cause it gradually to change its trajectory
and to lose energy. After a period of days
or weeks the particle is lost into the lower
atmosphere.

r 1 1here was obviously an urgent scien-
-*- tific need to extend these observa-
tions with equipment of greater dynamic
range and discrimination. In April of
1958 we persuaded several Federal
agencies to support further satellite
flights of our radiation equipment as an
adjunct to the I. G. Y. program, and we
received the enthusiastic support of the
National Academy of Sciences for the
continuation of our work. We also per-
suaded the Army Ballistic Missile Agen-
cy and the Cape Canaveral Air Force
Base to try to place the satellite in an
orbit more steeply inclined to the equa-
tor; at an inclination of about 50 degrees
to the equator it would cover a much
greater area of earth and skim the edges
of both auroral zones.

Working night and dav, we set out at
once to build new apparatus of a more
discriminating nature. We retained the
Geiger tube, which we had used in pre-
vious satellites, as a basic "simple-mind-
ed" detector. To be ready for the highest
intensities of radiation, however, we
used a much smaller tube that would
yield a lower count in a given flux of
radiation, and we hooked it into a circuit
that would scale down its count by a
much larger factor. To obtain a better
idea of the penetrability of the radiation

254

Radiation Belts Around the Earth

MAGNETIC AXIS

MAGNETIC EQUATOR

drawing al right shows the essential symmetry
axis. The structure of the radiation zone was

we shielded a similar Geiger tube with a
millimeter of lead. As a more discriminat-
ing particle detector we adopted a plas-
tic scintillator and photomultiplier tube
to respond to electrons with an energy
of more than 650,000 electron volts and
to protons of more than 10 million elec-
tron volts. Finally we glued a thin cesi-
um-iodide crystal to the window of an-
other photomultiplier tube; the light
emitted by the crystal when it was ir-
radiated would measure the over-all in-
put of energy rather than the arrival of
individual particles. To keep out light
when the crystal faced the sun, we
shielded it with thin, opaque nickel foil.
A special amplifier gave this detector a
large dynamic range extending from
about .1 erg per second to 100,000 ergs
per second.

Explorer IV carried this apparatus in-
to orbit on July 26, and sent down data
for almost two months. Magnetic tapes
from some 25 observing stations flowed
in steadily from late July to late Septem-
ber; altogether we obtained some 3,600
recorded passes of the satellite. A typical
pass was readable for several minutes;
some of the best were readable for up to
20 minutes, a large fraction of the time
required for the satellite to make a turn
around the earth. We are still analyzing
this mass of data, but the preliminary
results have already proved to be en-
lightening.

The readings have confirmed our ear-
lier estimates of the maximum levels of
radiation. Moreover, we have extended

of the radiation around the earlh*s magnetic
built up from hundreds of observed points.

our observations to more than 50 degrees
north and south of the equator and have
been able to plot the intensity of the
radiation at various latitudes and longi-
tudes for altitudes up to 1,300 miles.
The intensity contours follow the shape
of the earth in the equatorial region, but
as they approach high northern and
southern latitudes they swing outward,
then inward and sharplv outward again
to form "horns" reaching down toward

the earth near the auroral zones [see
illustrations at the top oj these two
pages]. The entire picture so far is com-
pletely consistent with the magnetic-
trapping theory.

It was clear from the contours that
Explorers I, III and IV penetrated onlv
the lower portion of the radiation belt.
As early as last spring we began to make
hypothetical extensions of the observed
contours out to a distance of several
thousand miles. One of these speculative
diagrams showed a single, doughnut-
shaped belt of radiation with a ridge
around the northern and southern edges
of its inner circumference, correspond-
ing to the horns of the contours. Another
showed two belts— an outer region with
a banana-shaped cross section that ex-
tended from the northern to the southern
auroral zone and an inner belt over the
equator with a bean-shaped cross section
[see illustration on pages 40 and 41].
The latter diagram seemed to fit the con-
tours better. In our seminars and after-
hour discussions Mcllwain held out for
the two-belt theory. The rest of us tend-
ed to agree with him but preferred to
stay with the single "doughnut" because
of its simplicity.

T^o take the question out of the realm
■*- of speculation we had to secure
measurements through the entire region
of radiation. In May, therefore, I ar-
ranged to have one of our radiation de-
tectors carried aboard the lunar probes
planned for the fall of 1958. On October

mm&**

TRAPPED PARTICLES spiral rapidly back and forth along a corkscrew shaped path
whose center is a magnetic line of force. At the same time they drift slowly around the earth
{broken arrows). Electrons I negative) and protons I positive* drift in opposite directions.

255

11, 12 and 13 Pioneer I, the first lunar
probe, carried our instruments nearly
70,000 miles out from the earth. Though
its readings were spotty, they confirmed
our belief that the radiation extended
outward for many thousands of miles,
with its maximum intensity no more than
10,000 miles above the earth.

The next attempted moon shot, Pio-
neer II, was a fizzle. Pioneer III, how-
ever, went off beautifully on December
6. Although this rocket was intended to
reach the vicinity of the moon, we were
almost as pleased when it failed to do
so, for it gave us excellent data on both
the upward and downward legs of its
flight, cutting through the radiation re-
gion for 65,000 miles in two places.

The observations on both legs showed
a double peak in intensity [see illustra-
tion at bottom of page 42], establishing
that there are indeed two belts rather
than one. The inner belt reaches its
peak at about 2,000 miles from the earth,
the outer one at about 10,000 miles.
Bevond 10,000 miles the radiation in-
tensity diminishes steadily; it disappears
almost completely beyond 40,000 miles.
The maximum intensity of radiation in
each belt is about 25,000 counts per sec-
ond, equivalent to some 40,000 parti-

cles per square centimeter per second.

Most of us believe that this great
reservoir of particles originates largely
in the sun. The particles are somehow
injected into the earth's magnetic field,
where they are deflected into corkscrew
trajectories around lines of force and
trapped. In this theoretical scheme the
radiation belts resemble a sort of leaky
bucket, constantly refilled from the sun
and draining away into the atmosphere.
A particularly large influx of solar par-
ticles causes the bucket to "slop over,"
mainly in the auroral zone, generating
visible auroras, magnetic storms and re-
lated disturbances. The normal leakage
may be responsible for the airglow which
faintly illuminates the night sky and may
also account for some of the unexplained
high temperatures which have been ob-
served in the upper atmosphere.

This solar-origin theory, while attrac-
tive, presents two problems, neither of
which is yet solved. In the first place
the energy of many of the particles we
have observed is far greater than the pre-
sumed energy of solar corpuscles. The
kinetic energy of solar corpuscles has
not been measured directly, but the
time-lag between a solar outburst and
the consequent magnetic disturbances

HEAD OF EXPLORER IV includes nose rone (left), instrument "payload" (center) and
protective shell i right). Payload includes four detectors, two radio transmitters, batteries
and associated electronic circuity. The outer shell is approximately six inches in diameter.

on earth indicates that the particles are
slow-moving and thus of relatively low
energy. It may be that the earth's mag-
netic field traps only a high-energy frac-
tion of the particles. Alternatively, some
unknown magnetohydrodynamic effect
of the earth's field may accelerate the
sluggish particles to higher velocities.
Some such process in our galaxv has
been suggested as responsible for the
great energies of cosmic rays. The second
problem in the solar-origin theory is that
it is difficult to explain how charged
particles can get into the earth's mag-
netic field in the first place. We believe
that neither problem is unsolvable.

Nicholas Christofilos of the University
of California and the Soviet physicist
S. N. Vernov have suggested an entirelv
different theory of how the radiation
originates. They note that neutrons are
released in large numbers in the earth's
upper atmosphere by the impact of cos-
mic rays. These neutrons, being un-
charged, can travel through the mag-
netic field without deflection. In due
course some of them decav there into
electrons and protons, which are trapped.

Our group agrees that particle-injec-
tion of this sort is going on, and at a rate
which can be easily calculated; but we
feel for a number of reasons that it can-
not be the main source of radiation-belt
particles. If we are right in supposing
that the radiation belts provide the "res-
ervoir" for the aurora, the neutron hy-
pothesis cannot account for more than
one 10,000th of the auroral energy out-
put. Even if the association between
the radiation belts and the aurora turns
out to be fortuitous, preliminary indica-
tions both from our work and from the
Russian experience with Sputnik III
suggest that most of the particles in the
radiation belt have much lower energies
than those of particles that would be
produced by neutron decay. A full
knowledge of the energy distribution of
the particles will aid greatly in clarifying
their origin.

Neither theory explains why there
should be two belts rather than one. It is
tempting to combine the two theories
and suppose that the inner belt orig-
inates with "internal injection"— i.e., neu-
tron-decav products— and the outer one
with "external injection" of solar cor-
puscles. The two-belt configuration may
of course be a transitory phenomenon,
though the data from Explorer IV and
Pioneer III indicate that the separate
belts persisted in essentially the same
form for at least five months. We should
bear in mind, however, that 1958 was
a \ ear of great solar activity. Three years

256

Radiation Belts Around the Earth

FOUR-STAGE ROCKET launched the Pioneer III moon probe on
December 6, 1958. Though the flight failed to reach the moon, its

outbound leg gave a continuous record of radiation out to 65,000
miles; the inbound leg gave data between 30,000 and 10,000 miles.

from now we may well find a much
lower over-all intensity and perhaps a
different structure altogether.

In addition to these possible long-term
changes, there may be short-term fluc-
tuations in the belts. While we feel sure
that the influx and leakage of particles
must balance in the long run, a major
solar outbreak may temporarily increase
the intensity of the radiation many-fold.
If we were to detect such fluctuations
and were to find that they coincide with
solar outbursts on the one hand and
with terrestrial magnetic disturbances
on the other, we would have a plain
lead to the origin of the particles. Be-
fore long we hope to launch a satellite

that will monitor radiation levels for
at least a year.

/"\ur measurements show that the max-
^-^ imum radiation level as of 1958 is
equivalent to between 10 and 100 roent-
gens per hour, depending on the still-
undetermined proportion of protons to
electrons. Since a human being exposed
for two days to even 10 roentgens would
have onlv an even chance of survival, the
radiation belts obviously present an ob-
stacle to space flight. Unless some prac-
tical way can be found to shield space-
travelers against the effects of the radia-
tion, manned space rockets can best take
off through the radiation-free zone over

the poles. A "space station" must orbit
below 400 miles or beyond 30,000 miles
from the earth. We are now planning a
satellite flight that will test the efficacy
of various methods of shielding.

The hazard to space-travelers may not
end even when they have passed the
terrestrial radiation belts. According to
present knowledge the other planets of
our solar system mav have magnetic
fields comparable to the earth's and thus
may possess radiation belts of their own.
The moon, however, probablv has no
belt, because its magnetic field appears
to be feeble. Lunar probes should give
us more definite information on this
point before long.

257

How does the brain work? Part of the answer lies in
electrophysiology, the study of the relation between
electricity and nervous stimulation.

18 A Mirror for the Brain

W. Grey Walter

A chapter from his book The Living Brain published in 1963.

The Greeks had no word for it. To them the
brain was merely "the thing in the head," and completely
negligible. Concerned as so many of them were about man's
possession of a mind, a soul, a spiritual endowment of the
gods, it is strange they did not anticipate our much less enter-
prising philosophers of some score of centuries later, and in-
vent at least a pocket in the head, a sensorium, to contain it.
But no, the Greeks, seeking a habitation for the mind, could
find no better place for it than the midriff, whose rhythmic
movements seemed so closely linked with what went on in
the mind.

The Hebrews also attributed special dignity to that part of
the body; thence Jehovah plucked man's other self. Old ideas
are not always as wide of the mark as they seem. The rhythm
of breathing is closely related to mental states. The Greek
word for diaphragm, phren, appears in such everyday words
as frenzy and frantic, as well as in the discredited phrenology
and the erudite schizophrenia.

259

Above the midriff the classical philosophers found the
vapours of the mind; below it, the humours of the feelings.
Some of these ideas persisted in physiological thought until
the last century and survive in the common speech of today.
Hysteric refers by derivation to the womb. The four basic
human temperaments were: choleric, referring to the gall
bladder; phlegmatic, related to inflammation; melancholic,
black bile; and sanguine, from the blood. This classification
of temperaments was revived by a modern physiologist, Pav-
lov, to systematize his observations of learning.

As in nearly all notions that survive as long as these fossils
of language have survived, there is an element of truth, of
observation, in them. States of mind are certainly related to
the organs and liquors designated, and may even be said in
a sense to originate in them. The philosopher, William James,
was responsible with Lange for a complete theory of emotion
which invoked activity in the viscera as the essential precursor
of deep feeling. Some of the most primitive and finest phrases
in English imply this dependence of sincere or deep emotion
on heart or bowels. But communication of thought is so rapid
that the Greeks overlooked the existence or need of a relay
station. And no doubt it is for the same reason that we all
seem particularly given to the same error of over-simplification
when we first begin, or refuse to begin, to consider how the
mind works. We know what makes us happy or unhappy.
Who, in the throes of sea-sickness, would think of dragging
in the brain to account for his melancholy state?

More curious still is Greek negligence of the brain, con-
sidering their famous oracular behest, "Know thyself." Here
indeed was speculation, the demand for a mirror, insistence
upon a mirror. But for whom, for what? Was there, among

260

A Mirror for the Brain

the mysteries behind the altar, concealed perhaps in the
Minerva myth, a suspicion of something more in the head
than a thing, and that the organ which had to do the knowing
of itself must be an organ of reflection?

The brain remained for more than two thousand years in
the dark after its coming of age. When it was discovered by
the anatomist, he explored it as a substance in which might
be found the secret dwelling of intelligence; for by that time
the mind had moved from the diaphragm to the upper story,
and Shakespeare had written of the brain, "which some sup-
pose the soul's frail dwelling-house." Dissection was high
adventure in those days. Most people believed what an
ironical writer today was "astonished to leam," that "it is
possible for anger, envy, hatred, malice, jealousy, fear and
pride, to be confined in the same highly perishable form of
matter with life, intelligence, honesty, charity, patience and
truth.*' The search for such prize packets of evil and virtue
in the brain tissue, dead or alive, could only lead to disap-
pointment. The anatomist had to be satisfied with weighing
the "grey matter" — about 50 ounces for man and 5 less for
woman — and making sketches of the very complicated and
indeed perishable organisation of nerves and cells which his
knife revealed. He could do little more. It should enlighten
us at once as to the essential character of brain activity, that
there was no possible understanding of ihe mechanism of
the brain until the key to it, the electrical key, was in our
hands.

There were some flashes of foresight, sparks in the scien-
tific dark, before Galvani put his hand on the key. What gen-
erated all the speculations of the day was a new notion in

261

science, the conception of physical motion which began to
acquire importance with Galileo and continued with Newton
and into our own times with Rutherford and Einstein. First
among these imaginative flashes may be mentioned the novel
proposal made by the 16th Century philosopher, Hobbes,
when disputing the dualist theory of Descartes. The French
philosopher contemplated a non-spatial mind influencing the
body through the brain, and suggested the pineal gland as
the rendezvous for mind and matter. The proposal advanced
by Hobbes, in rejecting this popular theory, was that thought
should be regarded as being produced by bodies in motion.
Hobbes was born in the year of the Spanish Armada; the
Royal Society had received its charter seventeen years before
he died in 1679.

The controversy about ihe residential status of the mind
is almost as much out of date as that in which the non-
existence of motion seemed to be proved by the hare and
tortoise fable. But the value of Hobbes' speculation was en-
during; the observation and correlation of mental and phys-
ical phenomena are today a routine of physiological research.

More specific than the speculation of Hobbes was that of
Dr. David Hartley about a century later. Hartley in 1749
anticipated by two hundred years the kind of theory of mental
function for which evidence has been found in the last year
or two. His "Observations on Man, his Frame, his Duty and
his Expectations" is a milestone in the history of English
thought. Hartley, a contemporary of Newton and Hume, was
a pioneer of what he termed the "doctrine of mechanism."
According to this, he suggested, mental phenomena are de-
rived from rhythmic movements in the brain — vibrations, he
called them; upon these is superimposed a fine structure of

262

A Mirror for the Brain

"vibratiuncles" which give thought and personality their
subtle shades and variations. Hartley realised quite well the
value of the plastic and compact virtues such a system might
have. He was also the first to develop the theory of "associa-
tion of ideas" in a rigorous form, relating this to his "vibra-
tiuncles" in a manner which we should now consider strictly
scientific in the sense that it is susceptible to experimental
test. It is difficult for us to appreciate the originality of his
notions, the gist of which is now a commonplace of electro-
physiology.

Hartley wrote nearly half a century before Galvani ( 1737-
1798 ) and with him we might say farewell to fancy. But to
pass over the famous Galvani- Volta controversy with the
bald statement that the one claimed to have discovered elec-
tricity in animals and the other its generation by metals, would
be unfair to any reader who may not know how strangely
truth came out of that maze of error.

The incident began with an experiment made by Luigi and
Lucia Galvani in the course of their long and patient study
of that still fresh mystery, electricity. The word had been in
use since William Gilbert coined it in the 16th century from
elektron, meaning amber, another pretty semantic shift; and
Henry Cavendish had already, eight years before the inci-
dent, determined the identity of its dynamic laws with those
of gravitation. Everybody in high society was familiar with
the effects of discharges from Leyden jars upon the lifeless
muscles of executed criminals; and Louis XV had, in the
words of Silvanus Thomson, "caused an electric shock from a
battery of Leyden jars to be administered to 700 Carthusian
monks joined hand to hand, with prodigious effect." But in
Bologna in 1790 the professor of anatomy had a notion that

263

it was atmospheric electricity which acted upon the muscle
tissues of animals. On a stormy evening, one version of the
story goes, he and his wife had the curious idea of testing
this point by tying a dead frog to the top of the iron balustrade
of the court-yard, apparently using copper wire to hold it
by the leg. They expected that, as the storm approached, the
frog would be convulsed by electric shocks. And, as they
watched the thunder cloud come near, so indeed it happened;
the dead frog, hanging against the iron grill, twitched in re-
peated convulsions.

Further experiments convinced the Galvani that they had
witnessed a form of electricity derived from living processes,
not merely from the atmosphere. He published a famous ac-
count of his experiments on the relation of animal tissue to
electricity: De viribus Electricitatis in Motu Musculari Com-
mentarius (1791). Volta seized upon this to refute the whole
of Galvani's thesis, repeating his experiment not only with-
out the storm but without the frog, proving that the elec-
tricity in question could be generated by copper and zinc
sheets. This "current electricity" as it was called, was there-
fore metallic, and no nonsense about any animal variety. So
ended a controversy and a friendship. So began the science
of electrical engineering.

Eppur, the Galvani might have repeated, si muove. For
their discredited experiment had truly revealed, not indeed
what they supposed, but something more wonderful. What
had happened was that, swaying in the wind, the suspended
frog had come into contact with the iron bars, between which
and the copper wire a current had been generated, activating
its muscles. The Galvani had demonstrated the electrical
aspect of nervous stimulation.

264

A Mirror for the Brain

This was an event as important to the physiologist as its
counter-event was to the physicist; it was the starting-point
of that branch of the science with which we are concerned
here, electrophysiology.

Volta's counter-demonstration led directly to the invention
of the electric battery, and economic opportunity evoked
electrical engineering from the Voltaic pile. There was no
such incentive for research when, a generation later, the
existence of animal electricity was proved. Instead, the dis-
covery was exploited by the academic dilettante and the
quack. The Aristotelian doctors of the period, assuming that
where there is electricity there is magnetism, saw in it proof
also of Mesmer's "Propositions" which had been published
in his "Memoire sur la Decouverte du Magnetisme Animal"
in 1779, floundering deeper into mystification than Dr. Mes-
mer himself, who had at least declared in his "Memoire" that
he used the term analogically, and that he "made no further
use of electricity or the magnet from 1776 onwards."

There is still controversy about the origin and nature of
animal electricity. Nobody who has handled an electric eel
will question the ability of an animal to generate a formidable
voltage; and the current is demonstrably similar in effect to
that of a mineral dry cell. On the other hand, there is no evi-
dence that the electric energy in nerve cells is generated by
electro-magnetic induction or by the accumulation of static
charge. The bio-chemist finds a complicated substance, acetyl-
choline, associated with electric changes; it would be reason-
able to anticipate the presence of some such substance having
a role at least as important as that of the chemicals in a Le-
clanche cell.

We know that living tissue has the capacity to concentrate

265

potassium and distinguish it from sodium, and that neural
electricity results from the differential permeability of an
inter-face, or cell-partition, to these elements, the inside of
a cell being negatively charged, the outside positively.
Whether we call this a chemical or an electrical phenomenon
is rather beside the point. There would be little profit in argu-
ing whether a flash-lamp is an electrical or chemical device;
it is more electrical than an oil lamp, more chemical than a
lightning flash. We shall frequently refer to changes of po-
tential as electrical rhythms, cycles of polar changes, more
explicitly electro-chemical changes. We shall be near the truth
if we keep in mind that electrical changes in living tissue,
the phenomena of animal electricity, are signs of chemical
events, and that there is no way of distinguishing one from
the other in the animal cell or in the mineral cell. The current
of a nerve impulse is a sort of electro-chemical smoke-ring
about two inches long travelling along the nerve at a speed
of as much as 300 feet per second.

The neglect and mystification which obscured Galvani's
discovery, more sterile than any controversy, forced electro-
physiology into an academic backwater for some decades. A
few experiments were made; for example, by Biedermann,
who published a 2-volume treatise called Electrophysiology,
and by Dubois-Reymond, who introduced Michael Fara-
day's induction coil into the physiological laboratory and the
term faradisation as an alternative to galvanisation into the
physiotherapist's vocabulary. Faraday's electrical and elec-
trifying research began in 1831, the date also of the foun-
dation of the British Association for the Advancement of
Science; but physiology long remained a backward child of
the family.

266

A Mirror for the Brain

Hampered though these experimenters were by lack of
trustworthy equipment — they had to construct their own
galvanometers from first principles — they gradually accumu-
lated enough facts to show that all living tissue is sensitive
in some degree to electric currents and, what is perhaps more
important, all living tissue generates small voltages which
change dramatically when the tissue is injured or becomes
active.

These experiments were not concerned with the brain; they
were made on frog's legs, fish eggs, electric eels and flayed
vermin. Nor could the brain be explored in that way.

Following life through creatures you dissect,
You lose it in the moment you detect

It took a war to bring the opportunity of devising a tech-
nique for exploring the human brain — and two more wars to
perfect it Two medical officers of the Prussian army, wan-
dering through the stricken field of Sedan, had the brilliant if
ghoulish notion to test the effect of the Galvanic current on
the exposed brains of some of the casualties. These pioneers
of 1870, Fritsch and Hitzig, found that when certain areas at
the side of the brain were stimulated by the current, move-
ments took place in the opposite side of the body.

That the brain itself produces electric currents was the dis-
covery of an English physician, R. Caton, in 1875.

This growing nucleus of knowledge was elaborated and
carried further by Ferrier in experiments with the "Faradic
current.'* Toward the end of the century there was a spate of
information which suggested that the brain of animals pos-
sessed electrical properties related to those found in nerve and
muscle. Prawdwicz-Neminski in 1913 produced what he

267

called the "electro-cerebrogranT of a dog, and was the first to
attempt to classify such observations.

The electrical changes in the brain, however, are minute.
The experiments of all these workers were made on the ex-
posed brains of animals. There were no means of amplifica-
tion in those days, whereby the impulses reaching the exterior
of the cranium could be observed or recorded, even if their
presence had been suspected. On the other hand, the grosser
electrical currents generated by the rhythmically contracting
muscles of the heart were perceptible without amplification.
Electro-cardiography became a routine clinical aid a gen-
eration before the invention of the thermionic tube made it
possible to study the electrical activity of the intact human
brain.

From an unexpected quarter, at the turn of the century,
came an entirely new development. Turn up the section on
the brain in a pre-war textbook of physiology and you will
find gleanings from clinical neuro-anatomy and — Pavlov. Al-
most as if recapitulating the history of physiological ideas,
Pavlov's work began below the midriff. He found that the
process of digestion could not be understood without refer-
ence to the nervous system, and so commenced his laborious
study of learning in animals.

In the gospel according to Stalin, Pavlov founded not
merely a branch of physiology as Galvani had done, but a
whole new science — Soviet physiology. His work indeed was
original; it owed nothing to Galvani, lying quite outside elec-
trophysiology, to which it was nevertheless eventually, though
not in Pavlov's day, to contribute so much in the way of under-
standing.

A Mirror for the Brain

For nearly two generations Pavlov's experiments were the
major source of information on brain physiology. Workers in
the English laboratories had not permitted themselves to ex-
plore further than the top of the spinal cord. One took an
anatomical glance at the brain, and turned away in despair.
This was not accountable to any peculiar weakness of physio-
logical tradition but to the exigencies of scientific method
itself. A discipline had been building up through the cen-
turies which demanded that in any experiment there should
be only one variable and its variations should be measurable
against a controlled background. In physiology this meant
that in any experiment there should be only one thing at a
time under investigation — one single function, say, of an
organ — and that the changes of material or function should
be measurable. There seemed to be no possibility of isolating
one single variable, one single mode of activity, among the
myriad functions of the brain. Thus there was something like
a taboo against the study of the brain. The success of Pavlov
in breaking this taboo early in the century was due to his
contrivance for isolating his experimental animals from all
but two stimuli; his fame rests on his measurement of re-
sponses to the stimuli.

There was no easy way through the academic undergrowth
of traditional electrophysiology to the electrical mechanisms
underlying brain functions. The Cambridge school of electro-
physiology, under a succession of dexterous and original ex-
perimenters beginning toward the end of the last century,
developed its own techniques in special fields of research, par-
ticularly in the electrical signs of activity in muscles, nerves
and sense organs. At the same time, the Oxford school under
the leadership of Sherrington was beginning to unravel some

269

of the problems of reflex function of the spinal cord. In both
these schools the procedure adopted, to comply with the
traditional requirements of scientific method, was to dissect
out or isolate the organ or part of an organ to be studied. This
was often carried to the extreme of isolating a single nerve
fibre only a few thousandths of a millimetre in diameter, so
as to eliminate all but a single functional unit.

Imagine, then, how refreshing and tantalizing were the
reports from Pavlov's laboratory in Leningrad to those en-
gaged on the meticulous dissection of invisible nerve tendrils
and the analysis of the impulses which we induced them to
transmit After four years spent working literally in a cage
and chained by the ankle — not for punishment but for elec-
trical screening — enlargement came when my professor of
that date, the late Sir Joseph Barcroft, assigned me to estab-
lishing a laboratory in association with a visiting pupil of
Pavlov, Rosenthal. We spent a year or so on mastering the
technique and improving it by the introduction of certain
electronic devices. The Russian results were confirmed. To
do more than this would have required staff and equipment
far beyond the resources of the Cambridge laboratory.

Meanwhile, another major event in the history of physiology
had taken place. Berger, in 1928, at last brought Hartley's
vibrations into the laboratory and with them a method which
seemed to hold out the promise of an investigation of elec-
trical brain activity as precise as were the reflex measure-
ments of Pavlov. When Pavlov visited England some time
after we heard of this, as the English exponent of his work
I had the privilege of discussing it with him on familiar terms.
Among other things, I asked him if he saw any relation be-
tween the two methods of observing cerebral activity, his

270

A Mirror for the Brain

method and Berger's. The latter, I was even then beginning
to suspect, might in some way provide a clue to how the con-
ditioning of a reflex was effected in the brain. But Pavlov
showed no desire to look behind the scenes. He was not in
the least interested in the mechanism of cerebral events; they
just happened, and it was the happening and its consequence
that interested him, not how they happened. Soviet physiology
embalmed the body of this limited doctrine as mystically as
the body of Lenin, for the foundations of their science. The
process of conditioning reflexes has a specious affinity with
the Marxian syllogism. Others have found in the phenomena
sufficient substantiation for a gospel of Behaviourism.

Pavlov was before his time. He would have been a greater
man, his work would have been more fertile in his lifetime,
and Russian science might have been spared a labyrinthine
deviation, had the work of Berger come to acknowledgement
and fruition in his day. But again there was delay; Berger
waved the fairy wand in 1928; the transformation of Cinder-
ella was a process of years.

There were reasons for this delay. For one thing, Berger
was not a physiologist and his reports were vitiated by the
vagueness and variety of his claims and the desultory nature
of his technique. He was indeed a surprisingly unscientific
scientist, as personal acquaintance with him later confirmed.

The first occasion on which the possibilities of clinical elec-
troencephalography were discussed in England was quite an
informal one. It was in the old Central Pathological Labora-
tory at the Maudsley Hospital in London, in 1929. The team
there under Professor Golla was in some difficulty about
electrical apparatus; they were trying to get some records of

the "Berger rhythm," using amplifiers with an old galvanom-
eter that fused every time they switched on the current. Golla
was anxious to use the Matthews oscillograph, then the last
word in robust accuracy, to measure peripheral and central
conduction times. I was still working at Cambridge under the
watchful eye of Adrian and Matthews and was pleased to
introduce this novelty to him and at the same time, with
undergraduate superiority, put him right on a few other
points. When, at lunch around the laboratory table, he re-
ferred to the recent publication of Berger's claims, I readily
declared that anybody could record a wobbly line, it was a
string of artefacts, even if there were anything significant in
it there was nothing you could measure, and so on. Golla
agreed with milder scepticism, but added: "If this new ap-
paratus is as good as you say, it should be easy to find out
whether Berger's rhythm is only artefact; and if it isn't, the
frequency seems remarkably constant; surely one could meas-
ure that quite accurately." And he surmised that there would
be variations of the rhythm in disease.

Cambridge still could not accept the brain as a proper study
for the physiologist. The wobbly line did not convince us or
anybody else at that time. Berger's "elektrenkephalograms"
were almost completely disregarded. His entirely original and
painstaking work received little recognition until in May,
1934, Adrian and Matthews gave the first convincing demon-
stration of the "Berger rhythm" to an English audience, a
meeting of the Physiological Society at Cambridge.

Meanwhile, Golla was reorganising his laboratory, and his
confidence in the possibilities of the Berger method was
growing. When he invited me to join his research team as
physiologist at the Central Pathological Laboratory, my first

272

A Mirror for the Brain

task was to visit the German laboratories, including particu-
larly that of Hans Berger.

Berger, in 1935, was not regarded by his associates as in
the front rank of German psychiatrists, having rather the
reputation of being a crank. He seemed to me to be a modest
and dignified person, full of good humour, and as unperturbed
by lack of recognition as he was later by the fame it even-
tually brought him. But he had one fatal weakness: he was
completely ignorant of the technical and physical basis of
his method. He knew nothing about mechanics or electricity.
This handicap made it impossible for him to correct serious
shortcomings in his experiments. His method was a simple
adaptation of the electrocardiographic technique by which
the electrical impulses generated by the heart are recorded.
At first he inserted silver wires under the subject's scalp; later
he used silver foil bound to the head with a rubber bandage.
Nearly always he put one electrode over the forehead and
one over the back of the head; leads were taken from these to
an Edelmann galvanometer, a light and sensitive "string" type
of instrument, and records were taken by an assistant photog-
rapher. A potential change of one-ten-thousandth of a volt —
a very modest sensitivity by present standards — could just be
detected by this apparatus. Each record laboriously produced
was equivalent to that of two or three seconds of modern con-
tinuous pen recording. The line did show a wobble at about
10 cycles per second. ( See Figure 3. ) He had lately acquired
a tube amplifier to drive his galvanometer, and his pride and
pleasure in the sweeping excursions of line obtained by its
use were endearing.

Berger carried the matter as far as his technical handicap
permitted. He had observed that the larger and more regular

273

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274

A Mirror for the Brain

rhythms tended to stop when the subject opened his eyes or
solved some problem in mental arithmetic. This was con-
firmed by Adrian and Matthews with leads from electrodes
on Adrian's head attached to a Matthews amplifier and ink-
writing oscillograph. This superior apparatus, and a more
careful location of electrodes, enabled them to go a step fur-
ther and prove that the 10 cycles per second rhythm arises in
the visual association areas in the occiput and not, as Berger
supposed, from the whole brain.

Only some years later was it realised what an important
step this was. Its significance could not be recognised while
so little was known about the components of the "wobbly
line," the electroencephalogram or, abbreviated, EEC Un-
avoidably at the time, the significance of the salient character
of the normal EEG was overlooked; it was found, in Adrian's
phrase, "disappointingly constant." The attention of many
early workers in electroencephalography therefore turned
from normal research to the study of nervous disease. In im-
mediate rewards this has always been a rich field. In this in-
stance, a surprising state was soon reached wherein what
might be called the electropathology of the brain was further
advanced than its electrophysiology.

In the pathological laboratory, Golla's earlier surmise, that
there would be variations of the rhythmic oscillation in
disease, was soon verified. A technique was developed there
by which the central point of the disturbance in the tissue
could be accurately determined. For surgery, the immediate
result of perfecting this technique was important; it made
possible the location of tumours, brain injuries, or other phys-
ical damage to the brain. It was helpful in many head cases
during the war as well as in daily surgical practice.

275

The study of epilepsy and mental disorders also began to
occupy the attention of many EEG workers. The difficulties
encountered in these subjects threw into prominent relief
the essential complexity of the problem as compared with
those of classical physiology. The hope of isolating single func-
tions had now been abandoned; those who entered this field
were committed to studying the brain as a whole organ and
through it the body as a whole organism. They were therefore
forced to multiply their sources of information.

It is now the general EEG practice, not only for clinical
purposes, but in research, to use a number of electrodes si-
multaneously, indeed as many as possible and convenient.
The standard make of EEG recorder has eight channels.
Eight pens are simultaneously tracing lines in which the
recordist, after long experience, can recognise the main com-
ponents of a complex graph. The graphs can also be auto-
matically analysed into their component frequencies. A more
satisfactory method of watching the electrical changes in all
the main areas, as in a moving picture, a much more informa-
tive convention than the drawing of lines, has been devised
at the Burden Neurological Institute. This will be described
after a simple explanation of what is meant by the rhythmic
composition of the normal EEG; for its nature, rather than the
methods of recording and analysing it, is of first importance
for understanding what follows.

If you move a pencil amply but regularly up and down on
a paper that is being drawn steadily from right to left, the
result will be a regular series of curves. If at the same time
the paper is moving up and down, another series of curves
will be added to the line drawn. If the table is shaking, the
vibration will be added to the line as a ripple. There will then

276

A Mirror for the Brain

be three components integrated in the one wavy line, which
will begin to look something like an EEG record. The line
gives a coded or conventional record of the various fre-
quencies and amplitudes of different physical movements. In
similar coded or integrated fashion the EEG line reports the
frequencies and amplitudes of the electrical changes in the
different parts of the brain tapped by the electrodes on the
scalp, their minute currents being relayed by an amplifier
to the oscillograph which activates the pens.

All EEG records contain many more components than this;
some may show as many as 20 or 30 at a time in significant
sizes. Actually there may be tens of thousands of impulses
woven together in such a manner that only the grosser com-
binations are discernible.

A compound curve is of course more easily put together
than taken apart. ( See Figure 4. ) The adequate analysis of a
few inches of EEG records would require the painstaking com-
putation of a mathematician — it might take him a week or so.
The modern automatic analyser in use in most laboratories
writes out the values of 24 components every 10 seconds, as
well as any averaging needed over longer periods.

The electrical changes which give rise to the alternating
currents of variable frequency and amplitude thus recorded
arise in the cells of the brain itself; there is no question of
any other power supply. The brain must be pictured as a
vast aggregation of electrical cells, numerous as the stars of
the Galaxy, some 10 thousand million of them, through which
surge the restless tides of our electrical being relatively thou-
sands of times more potent than the force of gravity. It is
when a million or so of these cells repeatedly fire together

277

that the rhythm of their discharge becomes measureable in
frequency and amplitude.

What makes these million cells act together — or indeed
what causes a single cell to discharge — is not known. We are
still a long way from any explanation of these basic mechanics
of the brain. Future research may well carry us, as it has car-

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taken apart." (a) A compound curve in which the three components
can be detected by visual inspection, ratios 1:2 and 2:3. (b) The three
components (ratios 8:9, 9:10) of this compound curve cannot be
determined at sight The bottom line shows their frequencies auto-
matically recorded every 10 seconds. Note the accidental similarity of
this curve to the EEG record of alpha rhythms in Figure 3 (b).

278

A Mirror for the Brain

ried the physicist in his attempt to understand the compo-
sition of our atomic being, into vistas of ever increasing
enchantment but describable only in the convention of mathe-
matical language. Today, as we travel from one fresh vista
to another, the propriety of the language we use, the con-
vention we adopt, becomes increasingly important. Arith-
metic is an adequate language for describing the height and
time of the tides, but if we want to predict their rise and fall
we have to use a different language, an algebra, with its spe-
cial notation and theorems. In similar fashion, the electrical
waves and tides in the brain can be described adequately by
counting, by arithmetic; but there are many unknown quan-
tities when we come to the more ambitious purposes of under-
standing and predicting brain behaviour — many x's and y's;
so it will have to have its algebra. The word is forbidding
to some people; but, after all, it means no more than "the
putting together of broken pieces."

EEG records may be considered, then, as the bits and
pieces of a mirror for the brain, itself speculum speculorum.
They must be carefully sorted before even trying to fit them
together with bits from other sources. Their information
comes as a conventional message, coded. You may crack the
code, but that does not imply that the information will neces-
sarily be of high significance. Supposing, for instance, you
pick up a coded message which you think may be about a mo-
mentous political secret. In the first stage of decoding it you
might ascertain that the order of frequency of the letters was
ETAONI. This does not sound very useful information; but
reference to the letter-frequency tables would assure you at
least that it was a message in English and possibly intelligible.
Likewise, we watch the frequencies as well as the amplitude
and origin of the brain rhythms, knowing that many earnest
seekers for the truth have spent lifetimes trying to decipher

279

what they thought were real messages, only to find that their
horoscopes and alembics contained gibberish. The scientist
is used to such hazards of research; it is only the ignorant
and superstitious who regard him, or think he regards him-
self, as a magician or priest who is right about everything all
the time.

Brain research has just about reached the stage where the
letter frequencies of the code indicate intelligibility and their
grouping significance. But there is this complication. The
ordinary coded message is a sequence in time; events in the
brain are not a single sequence in time — they occur in three-
dimensional space, in that one bit of space which is more
crowded with events than any other we can conceive. We
may tap a greater number of sectors of the brain and set more
pens scribbling; but the effect of this will only be to multiply
the number of code signals, to the increasing embarrassment
of the observer, unless the order and inter-relation of the
signals can be clarified and emphasised. Redundancy is al-
ready a serious problem of the laboratory.

The function of a nervous system is to receive, correlate,
store and generate many signals. A human brain is a mecha-
nism not only far more intricate than any other but one that
has a long individual history. To study such a problem in
terms of frequency and amplitude as a limited function of
time — in wavy lines — is at the best over-simplification. And
the redundancy is indeed enormous. Information at the rate
of about 3,600 amplitudes per minute may be coming through
each of the eight channels during the average recording pe-
riod of 20 minutes; so the total information in a routine record
may be represented by more than half a million numbers; yet
the usual description of a record consists only of a few sen-
tences. Only rarely does an observer use more than one-
hundredth of one per cent of the available information.

280

A Mirror for the Brain

"What's in a brain that ink may character . . . ?"
For combining greater clarity with greater economy, many
elaborations of methods have been adopted in clinic and
laboratory. They still do not overcome the fundamental em-
barrassment of redundancy and the error of over-simphfi ca-
tion, both due to the limitations of a time scale. A promising
alternative is a machine that draws a snapshot map instead
of a long history, projecting the electrical data visually on a
spatial co-ordinate system which can be laid out so as to repre-
sent a simple map or model of the head. This moving pano-
rama of the brain rhythms does approximate to Sherrington's
"enchanted loom where millions of flashing shuttles weave a
dissolving pattern, always a meaningful pattern though never
an abiding one." ( Figure 5. )

We have called the apparatus which achieves this sort of
effect at the Burden Institute a toposcope, by reason of its
display of topographic detail. The equipment was developed
by Harold Shipton, whose imaginative engineering trans-
formed the early models from entertainment to education.
Two of its 24 channels are for monitoring the stimuli; the
others, instead of being connected with pens, lead the elec-
trical activity of the brain tapped by the electrodes for display
on the screens of small cathode-ray tubes. So instead of wavy
lines on a moving paper, the observer sees, to quote Sherring-
ton again, "a sparkling field of rhythmic flashing points with
trains of travelling sparks hurrying hither and thither." As-
sembled in the display console, 22 of the tubes give a kind
of Mercator's projection of the brain. Frequency, phase and
time relations of the rhythms are shown in what at first ap-
pears to be a completely bewildering variety of patterns in
each tube and in their ensemble. Then, as the practised eye
gains familiarity with the scene, many details of brain ac-
tivity are seen for the first time. A conventional pen machine

281

is simultaneously at the disposal of the observer, synchronised
so that, by turning a switch, a written record of the activity
seen in any five of the tubes can be made. Another attachment
is a camera with which at the same time permanent snapshot
records of the display can be obtained. ( Figure 6. )

Thus, from Berger's crude galvanometer to this elaborate
apparatus requiring a whole room of its own, electroenceph-
alography has progressed from a technique to a science. Its
clinical benefits, by-products of free research, are acknowl-
edged; they can be gauged by the vast multiplication of EEG
laboratories. From Berger's lone clinic have sprung several
hundred EEG centres — more than 50 in England alone. Lit-
erally millions of yards of paper have been covered with fran-
tic scribblings. In every civilized country there is a special
learned society devoted to the discussion of the records and
to disputation on technique and theory. These societies are
banded together in an International Federation, which pub-
lishes a quarterly Journal and organises international con-
gresses.

For a science born, as it were, bastard and neglected in
infancy, this is a long way to have travelled in its first quarter
of a century. If it is to provide the mirror which the brain
requires to see itself steadily and whole, there is still a long
road ahead. The following chapters give the prospect as seen
from the present milestone, assuming that such studies are
allowed to continue. Looking back, we realise that the present
scale of work as compared with previous physiological re-
search is elaborate and expensive. But our annual cost of con-
ducting planned investigations of a fundamental nature into
man's supreme faculties is less than half that of one medium
tank, and the money spent on brain research in all England
is barely one-tenth of one per cent of the cost of the national
mental health services.

282

A Mirror for the Brain

Figure 5. ". . . a moving panorama of the brain rhvthms." The Toposcope Laboratory. The subject's couch and
triggered stroboscope (flicker) reflector at extreme left be\ond desk of 6-channel pen recorder with remote control
panel. The 22-channeI toposcope amplifier is in the background, the display panel at right centre, camera and pro-
jector at extreme right.

Figure 6. ". . . always a meaningful pattern though never an abiding one."
Snapshots of the "sparkling field of rhythmic flashing points." Each of the tube
screens, which form a chart oi the head seen from above with nose at top.
shows bv the flashing sectors of its disc the activity of the corresponding area
of the brain. (Top left) Resting alpha rhythms, (fop right) Theta rhythms in
anger. (Bottom left) Wide response to double flashes of light. (Bottom right)
Spread of response to triple flashes.

283

Physics is full of concepts of which we cannot form
simple pictures. Therefore the authors, like most
modern scientists, recommend taking a "mathematical
view. "

19 Scientific Imagination

Richard P. Feynman, Robert B. Leighton, and Matthew Sands
Excerpt trom The Feynman Lectures on Physics, Volume II, 1964.

I have asked you to imagine these electric and magnetic fields. What do you
do? Do you know how? How do /imagine the electric and magnetic field? What
do / actually see? What are the demands of scientific imagination? Is it any
different from trying to imagine that the room is full of invisible angels? No, it is
not like imagining invisible angels. It requires a much higher degree of imagination
to understand the electromagnetic field than to understand invisible angels. Why?
Because to make invisible angels understandable, all I have to do is to alter their
properties a little bit— I make them slightly visible, and then I can see the shapes
of their wings, and bodies, and halos. Once I succeed in imagining a visible angel,
the abstraction required — which is to take almost invisible angels and imagine
them completely invisible— is relatively easy. So you say, "Professor, please give
me an approximate description of the electromagnetic waves, even though it may
be slightly inaccurate, so that I too can see them as well as I can see almost invisible
angels. Then I will modify the picture to the necessary abstraction."

I'm sorry I can't do that for you. I don't know how. I have no picture of this
electromagnetic field that is in any sense accurate. I have known about the electro-
magnetic field a long time— I was in the same position 25 years ago that you are
now, and I have had 25 years more of experience thinking about these wiggling
waves. When I start describing the magnetic field moving through space, I speak
of the E- and # fields and wave my arms and you may imagine that I can see them.

285

I'll tell you what I see. I see some kind of vague shadowy, wiggling lines — here
and there is an E and B written on them somehow, and perhaps some of the lines
have arrows on them — an arrow here or there which disappears when I look too
closely at it. When I talk about the fields swishing through space, I have a terrible
confusion between the symbols I use to describe the objects and the objects them-
selves. I cannot really make a picture that is even nearly like the true waves. So
if you have some difficulty in making such a picture, you should not be worried
that your difficulty is unusual.

Our science makes terrific demands on the imagination. The degree of
imagination that is required is much more extreme than that required for some of
the ancient ideas. The modern ideas are much harder to imagine. We use a lot
of tools, though. We use mathematical equations and rules, and make a lot of
pictures. What I realize now is that when I talk about the electromagnetic field in
space, I see some kind of a superposition of all of the diagrams which I've ever
seen drawn about them. I don't see little bundles of field lines running about be-
cause it worries me that if I ran at a different speed the bundles would disappear.
I don't even always see the electric and magnetic fields because sometimes I think
I should have made a picture with the vector potential and the scalar potential,
for those were perhaps the more physically significant things that were wiggling.

Perhaps the only hope, you say, is to take a mathematical view. Now what is
a mathematical view? From a mathematical view, there is an electric field vector
and a magnetic field vector at every point in space; that is, there are six numbers
associated with every point. Can you imagine six numbers associated with each
point in space? That's too hard. Can you imagine even one number associated
with every point? I cannot! I can imagine such a thing as the temperature at every
point in space. That seems to be understandable. There is a hotness and coldness
that varies from place to place. But I honestly do not understand the idea of a
number at every point.

So perhaps we should put the question: Can we represent the electric field by
something more like a temperature, say like the displacement of a piece of jello?
Suppose that we were to begin by imagining that the world was filled with thin
jello and that the fields represented some distortion — say a stretching or twisting —
of the jello. Then we could visualize the field. After we "see" what it is like we
could abstract the jello away. For many years that's what people tried to do.
Maxwell, Ampere, Faraday, and others tried to understand electromagnetism
this way. (Sometimes they called the abstract jello "ether.") But it turned out that
the attempt to imagine the electromagnetic field in that way was really standing in
the way of progress. We are unfortunately limited to abstractions, to using in-
struments to detect the field, to using mathematical symbols to describe the field,
etc. But nevertheless, in some sense the fields are real, because after we are all
finished fiddling around with mathematical equations— with or without making
pictures and drawings or trying to visualize the thing— we can still make the instru-
ments detect the signals from Mariner II and find out about galaxies a billion miles
away, and so on.

286

Scientific Imagination

The whole question of imagination in science is often misunderstood by people
in other disciplines. They try to test our imagination in the following way. They
say, "Here is a picture of some people in a situation. What do you imagine will
happen next?" When we say, "I can't imagine," they may think we have a weak
imagination. They overlook the fact that whatever we are allowed to imagine in
science must be consistent with everything else we know: that the electric fields and
the waves we talk about are not just some happy thoughts which we are free to
make as we wish, but ideas which must be consistent with all the laws of physics
we know. We can't allow ourselves to seriously imagine things which are obviously
in contradiction to the known laws of nature. And so our kind of imagination is
quite a difficult game. One has to have the imagination to think of something that
has never been seen before, never been heard of before. At the same time the
thoughts are restricted in a strait jacket, so to speak, limited by the conditions that
come from our knowledge of the way nature really is. The problem of creating
something which is new, but which is consistent with everything which has been
seen before, is one of extreme difficulty.

While I'm on this subject I want to talk about whether it will ever be possible
to imagine beauty that we can't sec. It is an interesting question. When we look
at a rainbow, it looks beautiful to us. Everybody says, "Ooh, a rainbow." (You
see how scientific I am. I am afraid to say something is beautiful unless I have an
experimental way of defining it.) But how would we describe a rainbow if we were
blind? We are blind when we measure the infrared reflection coefficient of sodium
chloride, or when we talk about the frequency of the waves that are coming from
some galaxy that we can't see — we make a diagram, we make a plot. For instance,
for the rainbow, such a plot would be the intensity of radiation vs. wavelength
measured with a spectrophotometer for each direction in the sky. Generally, such
measurements would give a curve that was rather flat. Then some day, someone
would discover that for certain conditions of the weather, and at certain angles in
the sky, the spectrum of intensity as a function of wavelength would behave
strangely; it would have a bump. As the angle of the instrument was varied only a
little bit, the maximum of the bump would move from one wavelength to another.
Then one day the physical review of the blind men might publish a technical article
with the title "The Intensity of Radiation as a Function of Angle under Certain
Conditions of the Weather." In this article there might appear a graph such as
the one in Fig. 20-5. The author would perhaps remark that at the larger angles
there was more radiation at long wavelengths, whereas for the smaller angles the
maximum in the radiation came at shorter wavelengths. (From our point of view,
we would say that the light at 40° is predominantly green and the light at 42° is
predominantly red.)

287

Wavelength

Fig. 20-5. The intensity of electro-
magnetic waves as a function of wave-
length for three angles (measured from
the direction opposite the sun), observed
only with certain meteorological con-
ditions.

Now do we find the graph of Fig. 20-5 beautiful? It contains much more de-
tail than we apprehend when we look at a rainbow, because our eyes cannot see
the exact details in the shape of a spectrum. The eye, however, finds the rainbow
beautiful. Do we have enough imagination to see in the spectral curves the same
beauty we see when we look directly at the rainbow? I don't know.

But suppose I have a graph of the reflection coefficient of a sodium chloride
crystal as a function of wavelength in the infrared, and also as a function of angle.
I would have a representation of how it would look to my eyes if they could see
in the infrared — perhaps some glowing, shiny "green," mixed with reflections from
the surface in a "metallic red." That would be a beautiful thing, but I don't know
whether I can ever look at a graph of the reflection coefficient of NaCl measured
with some instrument and say that it has the same beauty.

On the other hand, even if we cannot see beauty in particular measured results,
we can already claim to see a certain beauty in the equations which describe general
physical laws. For example, in the wave equation (20.9), there's something nice
about the regularity of the appearance of the x, the y, the z, and the /. And this
nice symmetry in appearance of the x, y, z, and / suggests to the mind still a greater
beauty which has to do with the four dimensions, the possibility that space has
four-dimensional symmetry, the possibility of analyzing that and the developments
of the special theory of relativity. So there is plenty of intellectual beauty asso-
ciated with the equations.

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(20.9)

288

Magnifying glasses, spectacles, cameras, projectors, eyes,
microscopes, telescopes— they all work on the same simple
principles.

20 Lenses and Optical Instruments

Physical Science Study Committee

From the textbook Physics by Physical Science Study Committee, 1 962.

Optical instruments — cameras, projectors, tele-
scopes, and microscopes — usually are built with
lenses ; that is, with pieces of refractive materials
to converge or diverge light according to our
design. A whole industry is devoted to the design
and production of such instruments or their
components. All these instruments are under-
stood and designed in terms of Snell's law. The
whole field of applications rests on the simple sum-
mary of refraction that we reached in the last
chapter, nx sin 6X = n2 sin d2. Most optical tech-
nology stems from this little bit of physics.

In this chapter, we want to learn how the laws
of refraction are related to the construction of
lenses and optical systems. An extensive treat-
ment of the design of optical systems is, however,
beyond the purpose of this chapter.

14-1. The Convergence of Light by a Set
of Prisms

We found in Chapter 12 that we could control
and redirect light beams by the use of curved
mirrors. Devices that can accomplish similar
purposes through refraction, instead of reflection,
are called lenses. To understand how a lens
operates, let us examine the behavior of light in
passing through the combination of a plate of
glass with parallel sides and the two triangular
prisms shown in Fig. 14-1 (a). If a parallel beam
of light falls on this system from the left, so that
it is normally incident on the plate of glass, it will
behave as indicated by the rays shown in the

figure. The light that passes through the plate
in the center will continue along its original
direction, since the angle of incidence is 0°.
Light striking the upper prism will be deviated
downward by an amount depending on the open-
ing angle of the prism and on its index of refrac-

14-1. Construction of a lens by the process of subdividing prismatic
sections.

289

tion. Similarly, light striking the lower prism
will be deviated upward. As a result, there is a
region, shown shaded in the figure, through
which passes almost all of the light that falls on
the plate and the prisms.

The convergence of a parallel beam of light into
a limited region by this system resembles the
convergence of a similar beam by a set of mirrors.
(See Section 12-6.) While working with mirrors,
we decreased the size of the region into which
the light was converged by using an increased
number of mirrors, each smaller than the original
one. Let us try the same scheme here. Fig.
14-1 (b) shows parts of the central plate and of
the two prisms cut away and replaced by pieces
of new prisms. The size of the shaded region is
clearly smaller than it was before.

If we continue the process of removing parts
of the prisms and replacing them by sections
having smaller opening angles, we come closer
and closer to a piece of glass with the smoothly
curved surface shown in Fig. 14-1 (c). This
device is the limit that is approached as we
increase the number of prisms indefinitely, just as
the parabolic mirror of Fig. 12-16 was the limit
approached as we used more and more plane
mirrors to converge parallel light. In Fig. 14-2
we have actually carried out the construction
indicated in Fig. 14-1. The lens produced by
the process that we have outlined converges all
of the parallel light that strikes it to a line as
shown in Fig. 14-3.

14-2. The experiments diagramed in Fig. 14—1.

14—3. Convergence of light by a cylindrical lens like the one
shown in Fig. 14—1. Note that the light is brought to a focus
along a line.

14-2. Lenses

The device we have just constructed is called a
cylindrical lens. Notice that we have not given
any definition of the surfaces of the lens, except
that they are obtained by increasing indefinitely
the number of sections of prisms that are used to
converge the light. It is possible to show that
these surfaces are approximated very closely by
circular cylinders. In other words, the lines
representing the surfaces in Fig. 14-1 (c) are arcs
of circles. The differences between the ideal
surfaces and those of circular cylinders are very
slight whenever both the width of the lens and its
maximum thickness are considerably smaller
than the distance from the lens to the line at which
parallel light is converged.

Cylindrical lenses bring the light from a distant
point source of light to a focus along a line. For
most purposes we prefer that the light from a point
source should be focused at a point. This focus-
ing can be accomplished by constructing a lens
whose surfaces curve equally in all directions.
Such surfaces are portions of spheres. Almost
all lenses are bounded by two spherical surfaces.

The line passing through the center of the lens
and on which the centers of the two spheres are
located is called the axis of the lens. The point
on this axis at which incident parallel rays focus
or converge is the principal focus, F. The distance
of the principal focus from the center of the lens
is known as the focal length, f

The two surfaces of a lens do not always have
the same radius. For example, the lens shown in
Fig. 14-4 has a spherical surface of much larger

290

Lenses and Optical Instruments

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radius at its right-hand boundary than it has at
the left.

If a lens is thin compared to its focal length,
it makes no difference which side of the lens the
light enters, the focal length is always the same.
This symmetry is obvious if the lens is itself
symmetric. That it is true for all thin lenses can
easily be shown by an experiment in which a lens
is used to focus the parallel rays of the sun to a
point on a piece of paper or cardboard. If the
lens is then flipped over, the focus occurs at the
same distance from the lens (Fig. 14-5).

This result is also predicted by a detailed
application of Snell's law from which we find

H»-<-4>

where R^ and R2 are the radii of the opposing
spherical surfaces.* We see that interchanging
Ri and R2, which is equivalent to turning the lens
aver, does not change the calculated value of/.

From this equation, we can also see that when
Ri and R2 are small, the lens will have a short
focal length. This is illustrated in Fig. 14-6 where
ive see that the paths of light rays through the
[ens in (b) are bent more sharply, so that the
focal length is shorter than in (a).

14-3. Real Images Formed by Lenses

We have thus far concentrated our attention
>n the focusing of light by a lens when the light
x>mes from a very distant object. In the practical
lse of lenses, we are commonly interested in the

'We shall not give the proof of this "lens maker's" formula
here. Although no new physics is involved, the proof is a
long-winded application of trigonometry and Snell's law.
Later, however, we can use the results of further study to
get the formula more easily. It is therefore discussed at
the end of Part II (see pages 302-303).

14—5. The principal foci of a lens. For thin lenses the focal
distance is the same for parallel light entering either the side with
a small radius (a) or the side with a larger radius (b).

light coming from near-by objects and we all
know that lenses do form images of such objects.
We can locate the images with the help of the
knowledge that we have gained about the be-
havior of initially parallel rays.

Fig. 14-7 shows a lens, an object H», and its
image Ht. To find the location of this image, we
draw the two principal rays from the top of the
object, one ray parallel to the axis and the other
through the principal focus F2. The ray parallel
to the axis is bent by the lens so as to pass through
the principal focus Fv We also know that rays
coming from the right and parallel to the axis
would be deviated to pass through the other
principal focus F2. It follows from the reversi-
bility of light paths that the ray from the top of
H0 that passes through F2 from the left must travel
parallel to the axis after it has passed through the
lens. All rays starting from the top of H0 will
converge very close to the point at which these
two bent rays intersect. This point is therefore
the real image of the top of H0.

We could have chosen any other point on the
object and located its image in the same way.
Had we done so for a number of points, we would
have found that the image, //;, falls along the
line that is shown in the figure.

291

14—6. The shorter the radius of the surface of a lens, the shorter
the focal length.

You probably have noticed that, in constructing
the two principal rays, we have not considered the
exact path of the ray within the lens, but have
broken it sharply. This approximate construction
is good enough for our present purposes because
our location of the two principal foci is accurate
only if the lens thickness (at its center) is small
compared with the focal length. The only lenses
to which our construction accurately applies are
therefore thin lenses. For the purposes of ray
diagrams, we may consider such lenses to be
circular plates perpendicular to the axis.

Convex lenses, like parabolic mirrors, focus
parallel rays to a point. Lenses, therefore, obey
the same equation relating image distance, focal
length, and object distance as do mirrors :

The proof of this equation in the case of convex
lenses is the same as for mirrors (Section 12-9).
As there, we use the shaded similar triangles
formed by the principal rays shown in Fig. 14-7.
Considering first the shaded similar triangles to
the left of the lens, we see that H-JH0 =//50-
The shaded triangles to the right of the lens give
HJH0 = SJf- Combining the two equations, we
have

S0S{ =p.

14-4. Camera, Projector, and Eye

Produce an image of the sun with a convex lens.
Since the sun is far away, the image is formed
practically at the principal focus and you can see
it there on a piece of paper. Images of closer
objects lie beyond the principal focus; and, in
order to capture them on paper or on a photo-
graphic film, we have to change the distance
between lens and film. To make a photographic
camera, then, we usually make a light-tight box
with a bellows that allows us to move the lens.
By adjusting the length of the bellows, we can
place a sharp image on the photographic film.
With some cameras we can place a piece of
ground glass where the film is later inserted.

14-7. The formation of a real image by a converging lens.

292

Lenses and Optical Instruments

14-8. A camera. The ray* of light that form the image of the
head of the arrow are indicated.

We can then view the image directly and focus
sharply on the particular object we want to
photograph (Fig. 14-8).

As long as the object is more than twice the
focal distance from the lens, so that S0 is longer
than/, the image size is smaller than the object,
as Hi/H0 =f/S0 shows. When a small object is
brought closer to the principal focus, the image
moves to distances behind the lens that are large

retina

optic nerve

retina

optic nerve

14—9. The lens of an eye adjusted to focus the light from a dis-
tant object (a) and from one near by.

compared with the focal length; also, the image
becomes bigger than the object. Consequently,
to photograph small objects, a lens of short focal
length is useful.

A projector is just a camera worked backwards.
You can make one by taking the back off a
camera, mounting the slides or film where the
film usually goes, and shining a bright light
through the film and out through the lens. The
lens then forms an enlarged image well in front
of the camera, where you can place a screen.

In cameras, projectors, and other man-made
optical instruments, images are always brought
into focus by changing the position of a lens with
respect to the object. The eye, on the other hand,
is unusual: it focuses images on the retina by
changing its curvature and hence the focal length
of its lens. When an object is at a very large
distance from the eye, the rays entering the eye
are nearly parallel and an image is formed at the
principal focus as shown in Fig. 14-9 (a). When
a close-by object is viewed, the image is formed
beyond the focal point, and eye muscles form
the elastic eye lens into a sharper curve, de-
creasing its focal length so that a real image
will form on the retina [Fig. 14-9 (b)].

14-5. The Magnifier or Simple Microscope

Let us go back to the small object that we
brought close to the principal focus of a lens.
As the object is moved through the principal
focus the real image moves infinitely far away
on the other side of the lens ; and when the object
is between the lens and the principal focus a virtual
image is formed behind the object just as in the
case of a concave mirror that we discussed in

293

Section 12-10. The situation is illustrated in
Fig. 14-10. As in the case of the concave mirror,
the convex lens always forms an enlarged virtual
image.

What is the maximum magnification that we
can obtain in this way? If we wish to see the
greatest possible detail in an object, we get it as
close to the eye as possible, thus giving a large
real image on the retina of the eye. But there is
a limit to how close we can view an object. As
the object gets closer to the eye, the eye muscles
must change the shape of the eye lens so that its
radius of curvature becomes smaller and smaller
in order to form a sharply focused real image on
the retina. Soon a limit is reached; the adult
eye cannot accommodate to an object closer than
about 25 cm. This object distance is called the
distance of most distinct vision. Try bringing
a pencil closer and closer to your eye. You will
see more and more detail until finally, with a great
straining of your eye muscles, you can no longer
keep a sharp image. Is your distance of most
distinct vision greater or less than the average
of 25 cm?

A convex lens helps us to see more detail by
forming an enlarged virtual image which we can
place at a comfortable distance from the eye.
We notice in Fig. 14-10 that no matter where
the object is placed between the lens and F2, the
top of the image always lies on the line FYD, and

Hi = — Si as usual.

Consequently, to make the image look as large
as possible we should bring our eye right up to
the lens as in Fig. 14-11; and in addition we
should move the object (or the lens and our eye)
until the image gets as close as we can clearly
accommodate. This is the way to get the largest
angle between the rays entering our eye from the
top and from the bottom of the object; and since
this light is what the eye works with, it is the
way to make the object (or its virtual image)
look largest.

Now for our own comfort we place the image
at the distance of most distinct vision d, so the
image distance S, (measured from Fx) is approxi-
mately given by Si = d +f. Therefore

Hi -5?S, - y°(</+/) = H0(j+ l)-
Furthermore, since we are looking at this image

14-10. Formation of a virtual image by a converging lens .

from the distance of most distinct vision just as
we could best look at the object without the aid
of the lens, the magnification of the image we
see is Hi/H0. That is, maximum magnification is

This equation tells us the greatest magnification
of a simple microscope. What, then, determines
how great a magnification we can get? The focal
length, /, of the convex lens is the determining
factor; the smaller it is, the greater the magnifica-
tion. In order to get a small/we use glass of high
refractive index to produce sharper bending of
the light for a given curvature of the lens surfaces.
Also we need surfaces of small radius (sharp
curvature). But a small radius of curvature means
a small lens size, since the lens diameter cannot

distance of
most distinct vision

14-11. A converging lens used as a magnifier. The image is
placed at the distance of closest distinct vision. Since the eye
is very close to the lens, the distance from the image to the lens
is about the same as that to the eye.

294

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14—13. Distortion by a lens. These three photographs were
made by looking through the same lens. At left, the lens was
held so that the page of the telephone book is slightly below

the focal region; in the middle picture, the page is in the focal
region; at right, the focal region lies below the page. Note
the geometrical distortions.

14-7. Limitations of Optical Instruments

If you hold a magnifying glass close to this
page, you can see a clear, undistorted and slightly
magnified image of the print. Now slowly raise
the glass from the paper and at the same time
increase the distance between your eyes and the
lens. At some positions the image appears
distorted. If your eyes are far enough from the
glass, you may also detect some rainbow colors
when looking at a corner of the page. In Figure
14-13 we see three pictures. They were made
by looking through the same lens. In the first
picture the lens was held so that the page of the
telephone book lies entirely (but slightly) below
the focal region; in the second picture the page
is in the focal region; and in the last the focal
region lies below the page. Clearly, in each
case the image of the page looks quite different
from the page itself. Part of the game of design-
ing really good optical instruments is to minimize
the geometrical distortions so apparent in these
pictures.

What are the origins of these defects in images?
First, we know even for mirrors (Chapter 12)
that a surface designed to bring light from one
small object to a sharp focus is not the correct
surface to bring light to an exact focus from an
object at a different place. The same is true for
lens surfaces. Some blurring of the image there-
fore results. In addition, when we look through
different parts of a lens the images are at different
positions (and the magnification is different).

The image therefore is distorted. In photography
distortion and blurring are often cut down by
using a "stop," a barrier with a small hole in it
so that we use only a selected portion of the lens.
The colored edges of images usually arise
because of the dispersion of the light that passes
through a lens. The focal length of a lens is
slightly longer for red light than it is for blue
light, because the blue light is refracted more
strongly than the red. This undesirable effect is
called chromatic aberration. It can be greatly
reduced by using a weakly diverging lens made of
glass for which the index of refraction changes
greatly with color, in conjunction with a strongly

14-14. A lens built of two pieces to minimize the different
focal properties of different colors. Such doublets are often made
with one common surface and glued together. They are called
achromatic lenses.

196

Lenses and Optical Instruments

converging lens of glass for which the index of
refraction changes less with color (Fig. 14-14).
This trick makes the focal properties of the whole
system of lenses nearly the same for all colors.

The problem of designing a system of lenses
with the smallest amount of distortions and
aberrations is a very complicated one. But the
complications arise only in the detailed applica-
tions of the laws of refraction; they involve no
new principle. Disentangling these complica-
tions will not enrich our understanding of basic

optical phenomena, and therefore we shall not
do it here.

There is one limiting factor affecting optical
magnifiers which causes a blur in the image and
is of a fundamental nature. This is the inevitable
diffraction which results from the limited size
of the objective lens through which the light
must pass. At high magnification it is this
blurring that prevents us from seeing finer and
finer detail. We shall learn more about diffrac-
tion in Chapter 19.

FOR HOME, DESK, AND LAB

14-15. For Problem 1.

1. A crude converging lens can be constructed by
placing two 30°-60°-90° glass prisms together
with a glass block as shown in Fig. 14-15.

(a) What is the focal length of this "lens" to
one significant figure?

(b) Would such a lens form a clear image?
Explain.

2. If two 45° prisms of glass (index = 1.50) are ar-
ranged as in Fig. 14—16 they will not converge
parallel light. Why not? What will happen to
the light?

3. Some lighthouses and light buoys mark the posi-
tions of dangerous rocks and shoals. The light
must be concentrated at a low angle with respect
to the horizon (light directed upward is wasted)
and must be equally visible from all points of the
compass.

(a) Can you design a "lens" which will do this?

(b) Instead of using a continuous curved sur-
face, such lights often use a lens made of sections
of prisms. Can you draw a diagram of such a
lens? It is called a Fresnel lens after the French
physicist who first devised such a lens.

(c) Automobile headlights are constructed to
give a wide, flat, horizontal beam. Parabolic
reflectors are made to give a narrow beam which
passes through a Fresnel lens in the front of the
headlight. Examine an automobile headlight and
see if you can understand how it gives broad,
horizontal beams.

14-16. For Problem 2.

4. Use the Lens Maker's Formula

}--»ft+fi

to find the focal length of a glass iens (n = 1.50)
with one flat surface and one with a radius of 10
cm. (Such a lens is called a plano-convex lens.)

(a) What are the focal lengths of the two lenses
shown in Fig. 14-17? (Index of glass = 1.50.)
(b) How does the focal length of (b) compare
with a flat block of glass?

A lens (index = 1.50) has a focal length in air of
20.0 cm.

(a) Is its focal length in water greater or less
than in air?

(b) What is its focal length in water?

Hint: Notice that every individual refraction
depends on the relative index of refraction.

297

7. A lens whose focal length is 10 cm is used in a
slide projector to give a real image on a screen at a
distance of 6.0 meters.

(a) What will be the magnification?

(b) How far is the lens placed from the slide?

8. Prove that if two identical converging lenses of
focal length 10 cm are placed 40 cm apart, the
combination will form an upright image of an
object that is 20 cm away from the first lens and
the magnification will be 1.

9. (a) Prove that the size of the image of the sun
produced by a convex lens is proportional to the
focal length. What is the constant of pro-
portionality?

(b) How large an image of the sun (diameter
1.4 X 109 m) will be formed by a lens of focal
length 1.0 meter?

(c) What will be the ratio of the size of the
images of the sun formed by a lens of 10 cm focal
length and a lens of 10 m focal length?

10. How large an image will be formed of an artifi-
cial satellite (53 cm in diameter) passing at an
altitude of 500 miles, if it is photographed with a
camera whose focal length is 10 cm? Would you
expect an actual photograph to show a larger or
smaller image than the size you have calculated?

14-17. For Problem 5.

11. (a) What is the focal length of the lens in Fig.
14-18? (Index of the glass is 1.50.)

(b) By sketching the paths of some light rays,
show what the lens does to incident light parallel
to its axis.

(d) What happens as you move the object to-
ward the lens? Can S; ever get bigger than S0?
Is the image ever bigger than the object?

(e) How would you find (experimentally) the
focal length of a diverging lens?

12. Assume your distance of most distinct vision is
1 5 cm. What is the maximum magnification that
can be obtained with each of the following convex
lenses when used as a magnifying glass or simple
microscope?

(a) / = 30 cm,

(b) / = 10 cm,

(d) / = 1 mm.

(e) Graph the
a function of "/."

maximum magnification as

13. Assume your distance of most distinct vision is
25 cm. A compound microscope has an eyepiece
of 2.0 cm focal length and an objective of 4.0 mm
focal length. The distance between objective and
eyepiece is 22.3 cm. What is its magnification to
two significant figures?

14. Using the microscope of Problem 13, with the
same adjustment, we see an amoeba. With a
ruler, we measure the size of the virtual image by
looking at it with one eye and at the ruler with
the other. On the ruler the amoeba appears to be
about 10 cm long. About how big is it really?

15. For the maximum magnification of an eyepiece, we

d
found - + 1 where d is taken as the distance of

most distinct (or closest distinct) vision. If your

eyes can accommodate to see distinctly at 15 cm,

15 cm , ._

we should write — - — + 1 as the magnification

of a simple magnifier for you. Also, if you can

14-18. For Problem 11.

298

Lenses and Optical Instruments

object

5 cm

10 cm

14-19. For Problem 19.

accommodate to images no closer than 35 cm,
— j h 1 would apply. Why does the magnifi-
cation go up for someone who accommodates
poorly at small distances? Does he see more
detail than someone who can accommodate
closer? Be prepared to discuss this question in
class.

16. Two lenses both have a focal length of 20 cm, but
one has a diameter four times that of the other.
Draw sketches of the two lenses and tell how the
images they form differ.

17. (a) What is the ratio of the focal lengths of a
crown-glass lens for violet light and for red light?
(The index of refraction for various colors is
given in Table 4, Chapter 13.)

(b) Is the ratio the same for all kinds of glass?

18. A lens of focal length 20 cm is placed 30 cm from
a plane mirror and an object is placed on the axis
10 cm from the mirror. Where will the image of
the object be found?

19. Where are the images of the object in Fig. 14-19?
Can you see all the images if you look through the
lens

(a) with your eye near the lens?

(b) with your eye far from the lens?

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