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{{Literatur
|Autor=Heaviside, Oliver;
|Jahr=1893
|Titel=Electromagnetic theory
|Stichworte=electromagnetic theory; magnetism; electricity; theory; vector analysis; electric waves;
|Band=1
|Verlag=“The Electrician” printing and publishing company, limited
|Ort=London
|Seiten=1-466
|Originalsprache=en
|Zusammenfassung=Chapter I. Introduction. Chapter II. Outline of the electromagnetic connections. Appendix A: The rotational ether in its application to electromagnetism. Chapter III. The elements of vectorial algebra and analysis. Chapter IV. Theory of plane electromagnetic waves. Appendix B: A gravitational and electromagnetic analogy.

''(OCR text)''
PREFACE.

THIS work was originally meant to be a continuation of the
series "Electromagnetic Induction and its Propagation,"
published in The Electrician in 1885-6-7, but left unfinished.
Owing, however, to the necessity of much introductory
repetition, this plan was at once found to be impracticable,
and was, by request, greatly modified. The result is some-
thing approaching a connected treatise on electrical theory,
though without the strict formality usually associated with
a treatise. As critics cannot always find time to read more
than the preface, the following remarks may serve to direct
their attention to some of the leading points in this volume.

The first chapter will, I believe, be found easy to read,
and may perhaps be useful to many men who are accustomed
to show that they are practical by exhibiting their ignorance
of the real meaning of scientific and mathematical methods
of enquiry.

The second chapter, pp. 20 to 131, consists of an outline
scheme of the fundamentals of electromagnetic theory from
the Faraday-Maxwell point of view, with some small modifi-
cations and extensions upon Maxwell's equations. It is done
in terms of my rational units, which furnish the only way ot
carrying out the idea of lines and tubes of force in a con-
sistent and intelligible manner. It is also done mainly in
terms of vectors, for the sufficient reason that vectors are
the main subject of investigation. It is also done in the
duplex form I introduced in 1885, whereby the electric and
magnetic sides of electromagnetism are symmetrically ex-
hibited and connected, whilst the "forces" and "fluxes"
are the objects of immediate attention, instead of the
potential functions which are such powerful aids to obscuring
and complicating the subject, and hiding from view useful
and sometimes important relations.

The third chapter, pp. 132 to 305, is devoted to vector
algebra and analysis, in the form used by me in my former
papers. As I have at the beginning and end of this chapter
stated my views concerning the unsuitability of quaternions
for physical requirements, and my preference for a vector
algebra which is based upon the vector and is dominated by
vectorial ideas instead of quaternionic, it is needless to say
more on the point here. But I must add that it has been
gratifying to discover among mathematical physicists a con-
siderable and rapidly growing appreciation of vector algebra
on these lines; and moreover, that students who had found
quaternions quite hopeless could understand my vectors very
well. Regarded as a treatise on vectorial algebra, this chap-
ter has manifest shortcomings. It is only the first rudiments
of the subject. Nevertheless, as the reader may see from the
applications made, it is fully sufficient for ordinary use in
the mathematical sciences where the Cartesian mathematics
is usually employed, and we need not trouble about more
advanced developments before the elements are taken up.
Now, there are no treatises on vector algebra in existence yet,
suitable for mathematical physics, and in harmony with the
Cartesian mathematics (a matter to which I attach the
greatest importance). I believe, therefore, that this chapter
may be useful as a stopgap.

The fourth chapter, pp. 306 to 466, is devoted to the
theory of plane electromagnetic waves, and, being mainly
descriptive, may perhaps be read with profit by many who
are unable to tackle the mathematical theory comprehen-
sively. It may be also useful to have results of mathematical
reasoning expanded into ordinary language for the benefit of
mathematicians themselves, who are sometimes too apt to
work out results without a sufficient statement of their
meaning and effect. But it is only introductory to plane
waves. Some examples in illustration thereof have been
crowded out, and will probably be given in the next volume.
I have, however, included in the present volume the applica-
tion of the theory (in duplex form) to straight wires, and
also an account of the effects of self-induction and leakage,
which are of some significance in present practice as well
as in possible future developments. There have been some
very queer views promulgated officially in this country con-
cerning the speed of the current, the impotence of self-
induction, and other material points concerned. No matter
how eminent they may be in their departments, officials need
not be scientific men. It is not expected of them. But
should they profess to be, and lay down the law outside their
knowledge, and obstruct the spreading of views they cannot
understand, their official weight imparts a fictitious impor-
tance to their views, and acts most deleteriously in propagating
error, especially when their official position is held up as a
screen to protect them from criticism. But in other countries
there is, I find, considerable agreement with my views.

Having thus gone briefly through the book, it is desirable
to say a few words regarding the outline sketch of electro-
magnetics in the second chapter. Two diverse opinions have
been expressed about it. On the one hand, it has been said
to be too complicated. This probably came from a simple-
minded man. On the other hand, it has been said to be too
simple. This objection, coming from a wise man, is of
weight, and demands some notice.

Whether a theory can be rightly described as too simple
depends materially upon what it professes to be. The pheno-
mena involving electromagnetism may be roughly divided
into two classes, primary and secondary. Besides the main
primary phenomena, there is a large number of secondary
ones, partly or even mainly electromagnetic, but also trenching
upon other physical sciences. Now the question arises whether
it is either practicable or useful to attempt to construct a
theory of such comprehensiveness as to include the secondary
phenomena, and to call it the theory of electromagnetism. I
think not, at least at present. It might perhaps be done ii
the secondary phenomena were thoroughly known ; but their
theory is so much more debatable than that of the primary
phenomena that it would be an injustice to the latter to too
closely amalgamate them. Then again, the expression of the
theory would be so unwieldy as to be practically useless ; the
major phenomena would be apparently swamped by the minor.
It would, therefore, seem best not to attempt too much, but
to have a sort of abstract electromagnetic scheme for the
primary phenomena only, and have subsidiary extensions
thereof for the secondary. The theory of electromagnetism
is then a primary theory, a skeleton framework corresponding
to a possible state of things simpler than the real in innu-
merable details, but suitable for the primary effects, and
furnishing a guide to special extensions. From this point of
view, the theory cannot be expressed too simply, provided it
be a consistent scheme, and be sufficiently comprehensive to
serve for a framework. I believe the form of theory in the
second chapter will answer the purpose. It is especially
useful in the duplex way of exhibiting the relations, which is
clarifying in complicated cases as well as in simple ones. It
is essentially Maxwell's theory, but there are some differences.
Some are changes of form only ; for instance, the rationalisa-
tion effected by changing the units, and the substitution ol
the second circuital law for Maxwell's equation of electro-
motive force involving the potentials, etc. But there is one
change in particular which raises a fresh question. What is
Maxwell's theory? or, What should we agree to understand
by Maxwell's theory ?

PREFACE. vii.

The first approximation to the answer is to say, There is
Maxwell's book as he wrote it ; there is his text, and there
are his equations : together they make his theory. But when
we come to examine it closely, we find that this answer is
unsatisfactory. To begin with, it is sufficient to refer to
papers by physicists, written say during the twelve years
following the first publication of Maxwell's treatise, to see
that there may be much difference of opinion as to what his
theory is. It may be, and has been, differently interpreted by
different men, which is a sign that it is not set forth in a per-
fectly clear and unmistakeable form. There are many obscuri-
ties and some inconsistencies. Speaking for myself, it was
only by changing its form of presentation that I was able to
see it clearly, and so as to avoid the inconsistencies. Now
there is no finality in a growing science. It is, therefore,
impossible to adhere strictly to Maxwell's theory as he gave it
to the world, if only on account of its inconvenient form.
But it is clearly not admissible to make arbitrary changes in
it and still call it his. He might have repudiated them
utterly. But if we have good reason to believe that the
theory as stated in his treatise does require modification to
make it self-consistent, and to believe that he would have
admitted the necessity of the change when pointed out to him,
then I think the resulting modified theory may well be called
Maxwell's.

Now this state of things is exemplified by his celebrated
circuital law defining the electric current in terms of magnetic
force. For although he did not employ the other, or second
circuital law, yet it may be readily derived from his equation
of electromotive force ; and when this is done, and the law
made a fundamental one, we readily see that the change it
suffers in passing from the case of a stationary to that of a
moving medium should be necessarily accompanied by a
similar change in the first, or Maxwell's circuital law. An
independent formal proof is unnecessary ; the similarity of

Vlll. PREFACE.

form and of the conditions of motion show that Maxwell's
auxiliary term in the electromotive force, viz., VqB (the
motional electric force), where q is the velocity of the medium
and B the induction, requires the use of a similar auxiliary
term in the first circuital law, viz., VDq, the motional
magnetic force, D being the displacement. And there is yet
another change sometimes needed. For whilst B is circuital,
so that a convective magnetic current does not appear in
the second circuital equation, D is not always circuital, and
convective electric current must therefore appear in the first
circuital equation. For the reason just mentioned, it is the
theory as thus modified that I consider to represent the true
Maxwellian theory, with the other small changes required to
make a fit. But further than this I should not like to go,
because, having made a fit, it is not necessary, and because it
would be taking too great a liberty to make additions without
the strongest reason to consider them essential.

The following example, which has been suggested to me
by remarks in Prof. Lodge's recent paper on " Aberration
Problems," referring to a previous investigation of Prof. J. J.
Thomson, will illustrate the matter in question. It is known
that if V be the speed of light through ether, the speed
through a stationary transparent body, say water, is V//A, if p
is the refractive index. Now what is the speed when the
water is itself moving in the same direction as the light
waves ? This is a very old problem. Fresnel considered that
the external ether was stationary, and that the ether was /a 2
times as dense in the water as outside, and that, when
moving, the water only carried forward with it the extra ether
it contained (or equivalently). This makes the speed of
light referred to the external ether be V//* + v(l -ft~ 2 ), if v
is the speed of the water. The experiments of Fizeau and
Michelson have shown that this result is at least approxi-
mately true, and there is other evidence to support FresnePs
hypothesis, at least in a generalised form. But, in the case

PREFACE. is.

of water, the additional speed of light due to the motion of
the water might be ^v instead of (1 - fir 2 ) v, without much
disagreement. Now suppose we examine the matter electro-
magnetically, and enquire what the increased speed through
a moving dielectric should be. If we follow Maxwell's
equations literally, we shall find that the extra speed is |r,
provided i?/V is small. This actually seems to corroborate
the experimental results. But the argument is entirely a
deceptive one. Maxwell's theory is a theory of propagation
through a simple medium. Fundamentally it is the ether,
but when we pass to a solid or liquid dielectric it is still to be
regarded as a simple medium in the same sense, because the
only change occurring in the equations is in the value of one
or both ethereal constants, the permittivity and inductivity
practically only the first. Consequently, if we find, as above,
that when the medium is itself moved, its velocity is not
superimposed upon that of the velocity of waves through the
medium at rest, the true inference is that there is something
wrong with the theory. For all motion is relative, and it is
an axiomatic truth that there should be superimposition of
velocities, so that V//* + v should be the velocity in the above
case according to any rational theory of propagation through
a simple medium, the extra velocity being the full v t instead
of Jv. And, as a matter of fact, if we employ the modified
or corrected circuital law above referred to, we do obtain full
superimposition of velocities.

This example shows the importance of having a simply
expressed and sound primary theory. For if the auxiliary
hypotheses required to explain outstanding or secondary phe-
nomena be conjoined to an imperfect primary theory we shall
surely be led to wrong results. Whereas if the primary theory
be good, there is at least a chance of its extension by auxiliary
hypotheses being also good. The true conclusion from Fizeau
and Michelson's results is that a transparent medium like
water cannot be regarded as (in the electromagnetic theory)

X. PREFACE.

a simple medium like the ether, at least for waves of light,
and that a secondary theory is necessary. Fresnel's sagacious
speculation is justified, except indeed as regards its form of
expression. The ether, for example, may be identical inside
and outside the body, and the matter slip through it without
sensibly affecting it. At any rate the evidence that this is the
case preponderates, the latest being Prof. Lodge's experiments
with whirling discs, though on the other hand must not be
forgotten the contrary conclusion arrived at by Michelson as
to the absence of relative motion between the earth and sur-
rounding ether. But if the ether be stationary, Fresnel's
speculation is roughly equivalent to supposing that the mole-'
cules of transparent matter act like little condensers in increas-
ing the permittivity, and that the matter, when in motion,
only carries forward the increased permittivity. But however
this matter may be finally interpreted, we must have a clear
primary theory that can be trusted within its limits. Whether
Maxwell's theory will last, as a sufficient and satisfactory
primary theory upon which the numerous secondary deve-
lopments required may be grafted, is a matter for the future
to determine. Let it not be forgotten that Maxwell's theory
is only the first step towards a full theory of the .ether ; and,
moreover, that no theory of the ether can be complete that
does not fully account for the omnipresent force of gravi-
tation.

There is one other matter that demands notice in conclu-
sion. It is not long since it was taken for granted that the
common electrical units were correct. That curious and
obtrusive constant 4?r was considered by some to be a sort of
blessed dispensation, without which all electrical theory would
fall to pieces. I believe that this view is now nearly extinct,
and that it is well recognised that the 4?r was an unfortunate
and mischievous mistake, the source of many evils. In plain
English, the common system of electrical units involves an
irrationality of the same kind as would be brought into the

PREFACE. X i.

metric system of weights and measures, were we to define
the unit area to be the area, not of a square with unit side,
but of a circle of unit diameter. The constant TT would then
obtrude itself into the area of a rectangle, and everywhere
it should not be, and be a source of great confusion and
inconvenience. So it is in the common electrical units,
which are truly irrational. Now, to make a mistake is easy
and natural to man. But that is not enough. The next
thing is to correct it. When a mistake has once been started,
it is not necessary to go on repeating it for ever and ever
with cumulative inconvenience.

The B. A. Committee on Electrical Standards had to do
two kinds of work. There was the practical work of making
standards from the experimentally found properties of matter
(and ether). This has been done at great length, and with
much labour and success. But there was also the theoretical
work of fixing the relations of the units in a convenient,
rational, and harmonious manner. This work has not yet
been done. To say that they ought to do it is almost a
platitude. Who else should do it ? To say that there is
not at present sufficient popular demand for the change does
not seem very satisfactory. Is it not for leaders to lead ?
And who should lead but the men of light and leading who
have practical influence in the matter ?

Whilst, on the one hand, the immense benefit to be gained
by rationalising the units requires some consideration to fully
appreciate, it is, on the other hand, very easy to overestimate
the difficulty of making the change. Some temporary incon-
venience is necessary, of course. For a time there would be
two sorts of ohms, &c., the old style and the new (or rational).
But it is not a novelty to have two sorts of ohms. There
have been several already. Eemember that the number of
standards in present existence is as nothing to the number
going to be made, and with ever increasing rapidity, by reason
of the enormously rapid extension of electrical industries.

XII. PREFACE.

Old style instruments would very soon be in a minority, and
then disappear, like the pins. I do not know that there is a
more important practical question than this one of rational-
ising the units, on account of its far-reaching effect, and
think that whilst the change could be made now with ease
(with a will, of course), it will be far more troublesome if
put off until the general British units are reformed; even
though that period be not so distant as it is customary to
believe. Electricians should set a good example.

The reform which I advocate is somewhat similar to the
important improvement made by chemists in their units
about a quarter of a century ago. One day our respected
master informed us that it had been found out that water
was not HO, as he had taught us before, but something
else. It was henceforward to be H 2 0. This was strange
at first, and inconvenient, for so many other formulae had
to be altered, and new books written. But no one questions
the wisdom of the change. Now observe, here, that the
chemists, when they found that their atomic weights were
wrong, and their formulae irrational, did not cry " Too late,"
ignore the matter, and ask Parliament to legalise the old
erroneous weights ! They went and set the matter right.
Verb. sap.

DECEMBER 16, 1893.
|Online=https://archive.org/stream/electromagnetict01heavrich#page/n5/mode/2up
|Zugriff=6. Juli 2018
}}

@@ Zeile 208: / Zeile 208: @@
 disagreement. Now suppose we examine the matter electromagnetically, and enquire what the increased speed through
 a moving dielectric should be. If we follow Maxwell's
-equations literally, we shall find that the extra speed is <math>\frac{1}{2}\nu</math>,
+equations literally, we shall find that the extra speed is 1/2ν,
 provided i?/V is small. This actually seems to corroborate
 the experimental results. But the argument is entirely a

@@ Zeile 3: / Zeile 3: @@
 |Jahr=1893
 |Titel=Electromagnetic theory
-|Stichworte=electromagnetic theory; magnetism; electricity; theory; vector analysis; electric waves;
+|Stichworte=electromagnetic theory; magnetism; electricity; theory; vector analysis; electric waves; english;
 |Band=1
 |Verlag=“The Electrician” printing and publishing company, limited

@@ Zeile 8: / Zeile 8: @@
 |Ort=London
 |Seiten=1-466
 |Originalsprache=en
 |Zusammenfassung=Chapter I. Introduction.<br/>Chapter II. Outline of the electromagnetic connections.<br/>Appendix A: The rotational ether in its application to electromagnetism.<br/>Chapter III. The elements of vectorial algebra and analysis.<br/>Chapter IV. Theory of plane electromagnetic waves.<br/>Appendix B: A gravitational and electromagnetic analogy.

Heaviside 1893 - Versionsgeschichte

Andreas Plank: Stichworte

Andreas Plank: +Deutsche Übersetzung

Andreas Plank am 6. Juli 2018 um 02:36 Uhr

Andreas Plank am 6. Juli 2018 um 02:35 Uhr

Andreas Plank: Die Seite wurde neu angelegt: „{{Literatur |Autor=Heaviside, Oliver; |Jahr=1893 |Titel=Electromagnetic theory |Stichworte=electromagnetic theory; magnetism; electricity; theory; vector analy…“