IN MEMORIAM
FLOR1AN CAJOR1
ELEMENTARY LESSONS
ELECTRICITY & MAGNETISM
MAP OF ENGLAND, SHOWING
LINES OF EQUAL MAGNETIC DECLINATION
FOR THE YEAR 1888.
ELEMENTARY LESSONS
IN
ELECTRICITY & MAGNETISM
BY
SILVANUS P. THOMPSON, B.A., D.Sc., F.R.A.S.
PROFESSOR OF EXPERIMENTAL PHYSICS IN
UNIVERSITY COLLEGE, BRISTOL
Hontoon
MACMILLAN AND CO.
1884
M304869
\The right of translation is reserved.}
STEREOTYPED EDITION.
PREFACE.
THESE Lessons in Electricity and Magnetism are in-
tended to afford to beginners a clear and accurate
knowledge of the experiments upon which the Sciences
of Electricity and Magnetism are based, and of the
exact laws which have been thereby discovered. The
difficulties which beginners find in studying many
modern text -books arise partly from the very wide
range of the subject, and partly from want of famili-
arity with the simple fundamental experiments. We
have, at the outset, three distinct sets of phenomena
to observe, viz. those of Frictional Electricity, of
Current Electricity, and of Magnetism ; and yet it is
impossible to study any one of these rightly without
knowing something of them all. Accordingly, the first
three Chapters of this work are devoted to a simple
exposition of the prominent experimental facts of these
three branches of the subject, reserving until the later
Chapters the points of connection between them, and
such parts of electrical theory as are admissible in a
strictly elementary work. No knowledge of algebra
beyond simple equations, or of geometry beyond the
first book of Euclid, is assumed.
A series of Exercises and Problems has been added
at the end of the Book in order that students, who
viii PREFACE.
so desire, may test their power of applying thought to
what they read, and of ascertaining, by answering the
questions or working the problems, how far they have
digested what they have read and made it their own.
Wherever it has been necessary to state electrical
quantities numerically, the practical system of electrical
units (employing the volt, the ohm, and the ampere, as
units of electromotive -force, resistance, and current,
respectively) has been resorted to in preference to any
other system. The Author has adopted this course
purposely, because he has found by experience that
these units gradually acquire, in the minds of students
of .electricity, a concreteness and reality not possessed
by any mere abstract units, and because it is hoped
that the Lessons will be thereby rendered more useful
to young telegraphists to whom these units are already
familiar, and who may desire to learn something of the
Science of Electricity beyond the narrow limits of their
own practical work.
Students" should remember that this little work is but
the introduction to a very widely-extended science, and
those who desire not to stop short at the first step should
consult the larger treatises of Faraday, Maxwell, Thom-
son, Wiedemann, and Mascart, as well as the more
special works which deal with the various technical
Applications of the Science of Electricity to the Arts
and Manufactures. Though the Author does not think
it well in an elementary text-book to emphasize particular
theories on the nature of Electricity upon which the
highest authorities are not yet agreed, he believes that
it will add to a clear understanding of the matter if he
states .his own views on the subject.
PREFACE.
The theory of Electricity adopted throughout these
Lessons is, that Electricity, whatever its true nature, is
one, not two: that this Electricity, whatever it may
prove to be, is not matter ', and is not energy / that it
resembles both matter and energy in one respect, how-
ever, in that it can neither be created nor destroyed.
The doctrine of the Conservation of Matter, established
a century ago by Lavoisier, teaches us that we can
neither destroy nor create matter, though we can alter
its distribution, and its forms and combinations, in
innumerable ways. The doctrine of the Conservation
of Energy, which has been built up during the past
half-century by Helmholtz, Thomson, Joule, and Mayer,
teaches us that we can neither create nor destroy energy,
though we may change it from one form to another,
causing it to appear as the energy of moving bodies, or
as the energy of heat, or as the static energy of a body
which 'has been lifted against gravity, or some .other
attracting force, into a position whence it can run down,
and where it has the potentiality of doing work. , So
also the doctrine of the Conservation of Electricity, now
growing into shape, 1 but here first enunciated under
this name, teaches us that we can neither create. nor
destroy Electricity though we may alter its distribution,
may cause more to appear at one place and less at
another, may change it from the condition of rest to
that of motion, or may cause it to spin round in whirl-
pools or vortices, which themselves can attract or repel
1 This is undoubtedly the outcome of the ideas of Maxwell and of
Faraday as to the nature of Electricity. Since the above was written an
elegant analytical statement of the "Doctrine of the Conservation of Elec-
tricity " has been published by Mons. G. Lippmann, who had independently,
and at an earlier date, arrived at the same view.
x PREFACE.
other vortices. According to this view all our electrical
machines and batteries are merely instruments for alter-
ing the distribution of Electricity by moving some of it
from one place to another, or for causing Electricity,
when accumulated or heaped together in one place, to
do work in returning to its former level distribution.
Throughout these Lessons the attempt has been made
to state the facts of the Science in language consonant
with this view, but at the same time rather to lead the
student to this as the result of his study than to insist
upon it dogmatically at the outset.
PREFACE TO FIFTH EDITION.
THE chief additions which have been made in the text
of this work since its first appearance relate to such
modern applications of .electricity as dynamo -electric
machines, electric lamps, and telephones. A few
changes in phraseology have been made in order to
avoid possible ambiguity of meaning. The names of
the now universally recognised units have been adopted
throughout. The determinations of the value of the
British Association unit of resistance (in terms of the
true ohm), and of Siemens' mercurial unit, made recently
by Lord Rayleigh, are inserted at page 326.
S. P. T.
UNIVERSITY COLLEGE, BRISTOL,
October 1883.
CONTENTS.
Jttst
CHAPTER I.
FRICTIONAL ELECTRICITY.
LESSON PAGE
I. Electrical Attraction and Repulsion . . i
II. Electroscopes . . . . . . . n
III. Electrification by Induction . . . . 18
IV. Conduction and Distribution of Electricity . . 28
V. Electrical Machines ...... 40
VI. The Leyden Jar and other Accumulators . . 53
VII. Other Sources of Electricity .... 62
CHAPTER II.
MAGNETISM.
VIII. Magnetic Attraction and Repulsion 72
IX. Methods of Making Magnets .... 82
X. Distribution of Magnetism . . . . .87
XI. Laws of Magnetic Force ..... 95
Note on Ways of Reckoning Angles and Solid-Angles . 108
Table of Natural Sines and Tangents . . , .III
XII. Terrestrial Magnetism ..... 112
xii CONTENTS.
CHAPTER III.
CURRENT ELECTRICITY.
LESSON PAGE
XIII. Simple Voltaic Cells . . . . ,122
XIV. Chemical Actions in the Cell . . . 131
XV. Voltaic Batteries 137
XVI. Magnetic Actions of the Current . . . 1 50
XVII. Galvanometers 161
XVIII. Chemical Actions of the Current. Voltameters. 171
XIX. Physical and Physiological Effects of the Current 180
Second
CHAPTER IV.
ELECTROSTATICS.
XX. Theory of Potential 190
Note on Fundamental and Derived Units . . 208
XXI. Electrometers 211
XXII. Specific Inductive Capacity, etc. . . 220
XXIII. Phenomena of Discharge .... 235
XXIV. Atmospheric Electricity 253
CHAPTER V.
ELECTROMAGNETICS.
XXV. Theory of Magnetic Potential . . .265
Note on Magnetic and Electromagnetic Units . 278
Note on Measurement of Earth's Magnetic Force in
Absolute Units . . . . . .281
Note on Index Notation ..... 282
XXVI. Electromagnets 283
XXVII. Electrodynamics . . . . . 290
XXVIII. Diamagnetism -..-.. 300
CONTENTS.
CHAPTER VI.
MEASUREMENT OF CURRENTS, ETC.
LESSON PAGE
XXIX. Ohm's Law and its Consequences . . . 307
XXX. Electrical Measurements . . . . . 316
Note on the Ratio of the Electrostatic to the Electro-
magnetic Units . . . . . 326
CHAPTER VII.
HEAT, LIGHT, AND WORK, FROM ELECTRIC CURRENTS.
XXXI. Heating effects of Currents .... 328
XXXII. The Electric Light 333
XXXIII. Electromotors (Electromagnetic Engines) . 340
CHAPTER VIII.
THERMO-ELECTRICITY.
XXXIV. Thermo-Electric Currents .... 346
CHAPTER IX.
ELECTRO-OPTICS.
XXXV. General Relations between Light and Electricity 353
CONTENTS.
CHAPTER X.
INDUCTION CURRENTS (MAGNETO-ELECTRICITY).
LESSON PAGE
XXXVI. Currents produced by Induction . . 361
XXXVII. Magneto-electric and Dynamo-electric Genera-
tors 375
CHAPTER XL
ELECTRO-CHEMISTRY.
XXXVIII. Electrolysis and Electrometallurgy . . 387
CHAPTER XII.
TELEGRAPHS AND TELEPHONES.
XXXIX. Electric Telegraphs 401
XL. Electric Bells, Clocks, and Telephones . 4H
APPENDIX.
PROBLEMS AND EXERCISES ,421
INDEX ^ 3
MAGNETIC MAP OF ENGLAND AND WALES Frontispiece.
ELEMENTARY LESSONS
ON
ELECTRICITY & MAGNETISM,
^art ftrgt.
CHAPTER I.
FRICTIONAL ELECTRICITY.
LESSON I. Electrical Attraction and Repulsion.
1. Electrical Attraction. If you take a piece of
sealing-wax, or of resin, or a glass rod, and rub it upon
a piece of flannel or silk, it will be found to have ac-
quired a property which it did not previously possess :
namely, the power of attracting to itself such light
bodies as chaff, or dust, or bits of paper (Fig. i). This
curious power was originally discovered to be a property
of amber, or, as the Greeks called it, ^Ae/crpov, which
is mentioned by Thales of Miletus (B.C. 600), and by
Theophrastus in his treatise on Gems, as attracting light
bodies when rubbed. Although an enormous number of
substances possess this property, amber and jet were the
only two in which its existence had been recognised by
the ancients, or even down to so late a date as the time
of Queen Elizabeth. About the year 1600, Dr. Gilbert
of Colchester discovered by experiment that not only
S> B
ELEMENTARY LESSONS ON [CHAP. i.
amber and jet, but a very large number of substances,
such as diamond, sapphire, rock-crystal, glass, sulphur,
sealing-wax, resin, etc., which he styled electrics?-
possess the same property. Ever since his time the
name electricity has been employed to denote the
agency at work in producing these phenomena. Gilbert
also remarked that these experiments are spoiled by the
presence of moisture.
Fig. i.
2. A better way of observing the attracting force is
to employ a small ball of elder pith, or of cork, hung by
a fine thread from a support, as shown in Fig. 2. A
dry warm glass tube, excited by rubbing it briskly with
a silk handkerchief, will attract the pith ball strongly,
showing that it is highly electrified. The most suitable
rubber, if a stick of sealing-wax is used, will be found to
1 " Electrica ; quse attrahunt eadem ratione ut electrum." (Gilbert).
CHAP, i.] ELECTRICITY AND MAGNETISM.
be flannel, woollen cloth, or, best of all, fur. Boyle
discovered that an electri-
fied body is itself at-
tracted by one that has
not been electrified. This
may be verified (see Fig.
3) by rubbing a stick of
sealing-wax, or a glass rod,
and hanging it in a wire
loop at the end of a silk
thread. If, then, the hand
be held out towards the
suspended electrified body,
it will turn round and ap-
proach the hand. So,
again, a piece of silk rib-
bon, if rubbed with warm
indiarubber, or even if drawn between two pieces of
warm flannel, and then held up by one end, will be
found to be attracted
by objects presented to
it. If held near the
wall of the room it will
fly to it and stick to it.
With proper precau-
tions it can be shown
that both the rubber
and the thing rubbed
are in an electrified
state, for both will
attract light bodies ;
Fig. 2.
Fig. 3-
but to show this, care
must be taken not to
handle the rubber too much. Thus, if it is desired to
show that when a piece of rabbit's fur is rubbed upon
sealing-wax, the fur becomes also electrified, it is better
not to take the fur in the hand, but to fasten it to the
ELEMENTARY LESSONS ON [CHAP. I.
end of a glass rod as a handle. The reason of this
precaution will be explained toward the close of this
lesson, and more fully in Lesson IV.
A large number of substances, including iron, gold,
brass, and all the metals, when held in the hand and
rubbed, exhibit no sign of electrification, that is to say,
do not attract light bodies as rubbed amber and rubbed
glass do. Gilbert mentions also pearls, marble, agate,
and the lodestone, as substances not excited electrically
by rubbing them. Such bodies were, on that account,
formerly termed non - electrics j but the term is erro-
neous, for if they are fastened to glass handles and then
rubbed with silk or fur, they behave as electrics.
3. Electrical Repulsion. When experimenting,
as in Fig. i , with a rubbed glass rod and bits of chopped
paper, or straw, or bran, it will be noticed that these
little bits are first attracted
and fly up towards the ex-
cited rod, but that, having
touched it, they are
speedily repelled and fly
back to the table. To
show this repulsion better,
let a small piece of feather
or down be hung by a silk
thread to a support, and
let an electrified glass rod
be held near it. It will
dart towards the rod and
stick to it, and a moment
later will dart away from
it, repelled by an invisible
force (Fig. 4), nor will it
again dart towards the rod. If the experiment be
repeated with another feather and a stick of sealing-wax
rubbed on flannel the same effects will occur. But, if
now the hand be held towards the feather, it will rush
Fig. 4.
CHAP, i.] ELECTRICITY AND MAGNETISM.
5
toward the hand, as the rubbed body in Fig. 3 did.
This proves that the feather, though it has not itself
been rubbed, possesses the property originally imparted to
the rod by rubbing it. In fact, it has become electrified,
by having touched an electrified body which has given
part of its electricity to it. It would appear then that
two bodies electrified with the same electricity repel one
another. This may be confirmed by a further experi-
ment. A rubbed glass rod, hung up as in Fig. 3, is
repelled by a similar rubbed glass rod ; while a rubbed
stick of sealing-wax is repelled by a second rubbed stick
of sealing-wax. Another way of showing the repulsion
between two simi-
larly electrified bodies
is to hang a couple
of small pith -balls,
by thin linen threads
to a glass support,
as in Fig. 5, and
then touch them both
with a rubbed glass
rod. They repel one
another and fly apart,
instead of hanging
down side by side,
while the near pre-
sence of the glass rod will make them open out still
wider, for now it repels them both. The self-repulsion
of the parts of an electrified body is beautifully illustrated
by the experiment of electrifying a soap-bubble, which
expands when electrified.
4. Two kinds of Electrification. - Electrified
bodies do not, however, always repel one another. The
feather which (see Fig. 4) has been touched by a rubbed
glass rod, and which in consequence is repelled from
the rubbed glass, will be attracted if a stick of rubbed
sealing-wax be presented to it ; and conversely, if the
Fig. 5-
6 ELEMENTARY LESSONS ON [CHAP. i.
feather has been first electrified by touching it with the
rubbed sealing-wax, it will be attracted to a rubbed glass
rod, though repelled by the rubbed wax. So, again, a
rubbed glass rod suspended as in Fig. 3 will be attracted
by a rubbed piece of sealing-wax, or resin, or amber,
though repelled by a rubbed piece of glass. The two
pith -balls touched (as in Fig. 5) with a rubbed glass
rod fly from one another by repulsion, and, as we have
seen, fly wider asunder when the excited glass rod is
held near them; yet they fall nearer together when a
rubbed piece of sealing-wax is held under them, being
attracted by it. Symmer first observed such phenomena
as these, and they were independently discovered by Du
Fay, who suggested in explanation of them that there
were two different kinds of electricity which attracted
one another while each repelled itself. The electricity
produced on glass by rubbing it with silk he called
vitreous electricity, supposing, though erroneously, that
glass could yield no other kind ; and the electricity
excited in such substances as sealing-wax, resin, shellac,
indiarubber, and amber, by rubbing them on wool or
flannel, he termed resinous electricity. The kind of
electricity produced is, however, found to depend not only
on the tiling rubbed but on the rubber also ; for glass
yields " resinous " electricity when rubbed with a cat's
skin, and resin yields " vitreous " electricity if rubbed
with a soft amalgam of tin and mercury spread on
leather. Hence these names have been abandoned in
favour of the more appropriate terms introduced by
Franklin, who called the electricity excited upon glass by
rubbing it with silk positive electricity, and that produced
on resinous bodies by friction with wool or fur, negative
electricity. The observations of Symmer and Du Fay may
therefore be stated as follows : Two positively electrified
bodies repel one another: two negatively electrified bodies
repel one another : but a positively electrified body and
a negatively electrified body attract one another.
CHAP, i.] ELECTRICITY AND MAGNETISM. 7
5. Simultaneous production of both Electrical
States. Neither kind of electrification is produced
alone ; there is always an equal quantity of both kinds
produced ; one kind appearing on the thing rubbed
and an equal amount of the other kind on the rubber.
The clearest proof that these amounts are equal can be
given in some cases. For it is found that if both the
electricity of the rubber and the + electricity of the thing
rubbed be imparted to a third body, that third body will
show no electrification at all, the two equal and opposite
electrifications having exactly neutralised each other.
In the following list the bodies are arranged in such
an order that if any two be rubbed together the one
which stands earlier in the series becomes positively
electrified, and the one that stands later negatively
electrified : Fur, wool, ivory, glass, silk, metals, sul-
phur, indiarubber, guttapercha, collodion.
6. Theories of Electricity. Several theories, have
been advanced to account for these phenomena, but all
are more or less unsatisfactory. Symmer proposed a
" two-fluid " theory, according to which there are two
imponderable electric fluids of opposite kinds, which
neutralise one another when they combine, and which
exist combined in equal quantities in all bodies until
their condition is disturbed by friction. A modification
of this theory was made by Franklin, who proposed
instead a "one-fluid" theory, according to which
there is a single electric fluid distributed usually uniformly
in all bodies, but which, when they are subjected to friction,
distributes itself unequally between" the rubber and the
thing rubbed, one having more of the fluid, the other
less, than the average. Hence the terms positive and
negative, which are still retained; that body which is
supposed to have an excess being said to be charged
with positive electricity (usually denoted by the plus sign
4- ), while that which is supposed to have less is said to
be charged with negative electricity (and is denoted by
8 ELEMENTARY LESSONS ON [CHAP, i,
the minus sign ). These terms are, however, purely
arbitrary, for in the present state of science we do not
know which of these two states really means more and
which means less. It is, however, quite certain that
electricity is not a material fluid, whatever else it
may be. For while it resembles a fluid in its property
of apparently flowing from one point to another, it differs
from every known fluid in almost every other respect.
It possesses no weight ; it repels itself. It is, moreover,
quite impossible to conceive of two fluids whose proper-
ties should in every respect be the precise opposites of
one another. For these reasons it is clearly misleading
to speak of an electric fluid or fluids, however convenient
the term may seem to be. Another theory, usually known
as the molecular theory of electricity, and first dis-
tinctly upheld by Faraday, supposes that electrical states
are the result of certain peculiar conditions of the mole-
cules of the bodies that have been rubbed, or of the
"aether" which is believed to surround the molecules.
There is much to be said in favour of this hypothesis,
but it has not yet been proven. In these lessons, there-
fore, we shall avoid as far as possible all theories, and
shall be content to use the term electricity.
7. Charge. The quantity of electrification of either
kind produced by friction or other means upon the surface
of a body is spoken of as a charge, and a body when
electrified is said to be charged. It is clear that there
may be charges of different values as well as of either
kind. When the charge of electricity is removed from
a charged body it is said to be discharged. Good
conductors of electricity are instantaneously discharged
if touched by the hand or by any conductor in contact
with the ground, the charge thus finding a means of
escaping to earth. A body that is not a good conductor
may be readily discharged by passing it rapidly through the
flame of a spirit-lamp or a candle ; for the flame instantly
carries off the electricity and dissipates it in the air.
CHAP, i.] ELECTRICITY AND MAGNETISM. 9
Electricity may either reside upon the surface of bodies
as a charge, or flow through their substance as a
current. That branch of the science which treats of
the laws of the charges upon the surface of bodies is
termed electrostatics, and is dealt with in Chapter
IV. The branch of the subject which treats of the flow
of electricity in currents is dealt with in Chapter III., and
other later portions of this book.
8. Conductors and Insulators. The term " con-
ductors," used above, is applied to those bodies which
readily allow electricity to flow through them. Roughly
speaking bodies may be divided into two classes those
which conduct and those which do not; though very
many substances are partial conductors, and cannot well
be classed in either category. All the metals conduct
well ; the human body conducts, and so does water.
On the other hand glass, sealing-wax, silk, shellac, gutta-
percha, indiarubber, resin, fatty substances generally,
and the air, are " non-conductors." On this account
these substances are used to make supports and handles
for electrical apparatus where it is important that the
electricity should not leak away ; hence they are some-
times called insulators or isolators. Faraday termed
them dielectrics. We have remarked above that Gil-
bert gave the name of non-electrics to those substances
which, like the metals, yield no sign of electrification when
held in the hand and rubbed. We now know the reason
why they show no electrification ; for, being good conduct-
ors, the electricity flows away as fast as it is generated.
The observation of Gilbert that electrical experiments
fail in damp weather is also explained by the knowledge
that water is a conductor, the film of moisture on the
surface of damp bodies causing the electricity produced
by friction to leak away as fast as it is generated.
9. Other electrical effects. The production of
electricity by friction is attested by other effects than
those of attraction and repulsion, which hitherto we have
io ELEMENTARY LESSONS ON [CHAP. i.
assumed to be the test of the presence of electricity.
Otto von Guericke first observed that sparks and flashes
of light could be obtained from highly electrified bodies at
the moment when they were discharged. Such sparks are
usually accompanied by a snapping sound, suggesting on a
small scale the thunder accompanying the lightning spark,
as was remarked by Newton and other early observers.
Pale flashes of light are also produced by the discharge
of electricity through tubes partially exhausted of air by
the air-pump. Other effects will be noticed in due course.
IO. Other Sources of Electrification. The stu-
dent must be reminded that friction is by no means the
only source of electricity. The other sources, per-
cussion, compression, heat, chemical action, physiological
action, contact of metals, etc., will be treated of in Lesson
VII. We will simply remark here that friction between
two different substances always produces electrical
separation, no matter what the substances may be.
Symmer observed the production of electricity when a
silk stocking was drawn over a woollen one, though
woollen rubbed upon woollen, or silk rubbed upon silk,
produces no electrical effect. If, however, a piece of
rough glass "be rubbed on a piece of smooth glass,
electrification is observed ; and indeed the conditions of
the surface play a very important part in the production
of electricity by friction. In general, of two bodies
thus rubbed together, that one becomes negatively
electrical whose particles are the more easily removed
by friction. Differences of temperature also affect the
electrical conditions of bodies, a warm body being usually
negative when rubbed on a cold piece of the same sub-
stance. Peclet found the degree of electrification produced
by rubbing two substances together to be independent of
the pressure and of the size of the surfaces in contact,
but depended on the materials and on the velocity with
which they moved over one another. Rolling friction
and sliding friction produced equal effects. The quantity
CHAP, i.] ELECTRICITY AND MAGNETISM. u
of electrification produced is, however, not proportional
to the amount of the actual mechanical friction ; hence
it appears doubtful whether friction is truly the cause of
the electrification. Indeed, it is probable that the true
cause is the contact of dissimilar substances (see Art.
73), and that when on contact two particles have
assumed opposite electrical states, one being + the
other , it is necessary to draw them apart before their
respective electrifications can be observed. Electrical
machines are therefore machines for bringing dissimilar
substances into intimate contact, and then drawing apart
the particles that have touched one another and become
electrical.
LESSON 1 1 . Electroscopes.
11. Simple Electroscopes. An instrument for
detecting whether a body is electrified or not, and
whether the electrification is positive or negative, is
termed an Electroscope. The feather which was
attracted or repelled, and the two pith balls which flew
apart, as we found in Lesson I., are in reality simple
electroscopes. There are, however, a number of pieces
of apparatus better adapted for this particular purpose,
some of which we will describe.
12. Straw -Needle Electroscope. The earliest
electroscope was that devised by Dr. Gilbert, and shown
in Fig. 6, which consists of a stiff straw balanced lightly
Fig. 6.
upon a sharp point. A thin strip of brass or wood, or
even a goose quill, balanced upon a sewing needle, will
ELEMENTARY LESSONS ON [CHAP. i.
serve equally well. When an electrified body is held near
the electroscope it is attracted and turned round, and will
thus indicate the presence of quantities of electricity far
too small to attract bits of paper from a table.
13. G-old-Leaf Electroscope. A still more sensi-
tive instrument is the G-old-Leaf Electroscope in-
vented by Bennet, and shown in Fig. 7. We have
seen how two pith -balls when similarly electrified repel
one another and stand apart, the force of gravity being
partly overcome by the force of the electric repulsion.
Fig. 7.
A couple of narrow strips of the thinnest tissue paper,
hung upon a support, will behave similarly when electri-
fied. But the best results are obtained with two strips
of gold-leaf, which, being excessively thin, is much
lighter than the thinnest pape/. The Gold-Leaf Electro-
scope is conveniently made by suspending the two leaves
within a wide-mouthed glass jar, which both serves to
CHAP, i.] ELECTRICITY AND MAGNETISM. 13
protect them from draughts of air and to support them
from contact with the ground. Through the cork, which
should be varnished with shellac or with paraffin wax, is
pushed a bit of glass tube, also varnished. Through this
passes a stiff brass wire, the lower end of which is bent
at a right angle to receive the two strips of gold-leaf,
while the upper supports a flat plate of metal, or may be
furnished with a brass knob. When kept dry and free
from dust it will indicate excessively small quantities of
electricity. A rubbed glass rod, even while two or three
feet from the instrument, will cause the leaves to repel
one another. The chips produced by sharpening a pencil,
falling on the electroscope top, are seen to be electrified.
If the knob be even brushed with a small camel's hair
brush, the slight friction produces a perceptible effect.
With this instrument all kinds of friction can be shown
to produce electrification. Let a person, standing upon
an insulating support, such as a stool with glass legs,
or a board supported on four glass tumblers, be briskly
struck with a silk handkerchief, or with a fox's tail, or
even brushed with a clothes' brush, he will be electrified,
as will be indicated by the electroscope if he place one
hand on the knob at the top of it. The Gold-Leaf
Electroscope can further be used to indicate the kind of
electricity on an excited body. Thus, suppose we rubbed
a piece of brown paper with a piece of indiarubber and
desired to find out whether the electrification excited on
the paper was + or , we should proceed as follows :
First charge the gold leaves of the electroscope by
touching the knob with a glass rod rubbed on silk.
The leaves diverge, being electrified with + electrifi-
cation. When they are thus charged' the approach of
a body which is positively electrified will cause them to
diverge still more widely ; while, on the approach of one
negatively electrified, they will tend to close together.
If now the brown paper be brought near the electroscope,
the leaves will be seen to diverge more, proving the
14 ELEMENTARY LESSONS ON [CHAP. i.
electrification of the paper to be of the same kind as
that with which the electroscope is charged, or positive.
The Gold-Leaf Electroscope will also indicate roughly
the amount of electricity on a body placed in contact
with it, for the gold leaves open out more widely when
the quantity of electricity thus imparted to them is greater.
For exact measurement, however, of the amounts of
electricity thus present, recourse must be had to the instru-
ments known as Electrometers, described in Lesson XXI.
In another form of electroscope (Bohnenberger's) a
single gold leaf is used, and is suspended between two
metallic plates, one of which can be positively, the other
negatively electrified, by placing them in communication
with the poles of a "dry pile" (Art. 182). If the gold
leaf be charged positively or negatively it will be
attracted to one side and repelled from the other,
according to the law of attraction and repulsion men-
tioned in Art. 4.
14. Henley's Quadrant Electroscope. The
Quadrant Electroscope is sometimes employed as an
indicator for large charges of electricity. It consists of
a pith ball at the end of a light
arm fixed on a pivot to an upright.
When the whole is electrified the
pith-ball is repelled from the up-
right and flies out at an angle,
indicated on a graduated scale or
quadrant behind it. Its usual form
is shown in Fig. 8. This little
electroscope, which is seldom
used except to show whether an
electric machine or a Leyden
battery is charged, must on no
account be confused with the deli-
cate "Quadrant Electrometer" described in Lesson
XXL, whose object is to measure very small charges
of electricity not to indicate large ones.
CHAP, i.] ELECTRICITY AND MAGNETISM.
15. The Torsion Balance. Although more pro-
perly an Electrometer than a mere Electroscope, it
will be most convenient to describe here the instrument
known as the Torsion
Balance. (Fig. 9.) This
instrument serves to
measure the force of the
repulsion between two
similarly electrified
bodies, by balancing the
force of this repulsion
against the force exerted
by a fine wire in untwist-
ing itself after it has been
twisted. The torsion
balance consists of a
light arm or lever of
shellac suspended within
a cylindrical glass case gt 9 *
by means of a fine silver wire. At one end this lever is
furnished with a gilt pith-ball, n. The upper end of the
silver wire is fastened to a brass top, upon which a circle,
divided into degrees, is cut. This top can be turned
round in the tube which supports it, and is known as the
torsion-head. Through an aperture in the cover there
can be introduced a second gilt pith -ball m, fixed to
the end of a vertical glass rod a. Round the glass case,
at the level of the pith-balls, a circle is drawn, and
divided also into degrees.
In using the torsion balance to measure the amount
of a charge of electricity, the following method is
adopted : First, the torsion-head is turned round until
the two pith -balls m and n just touch one another.
Then the glass rod a is taken out, and the charge of
electricity to be measured is imparted to the ball m,
which is then replaced in the balance. As soon as m
and n touch one another, part of the charge passes from
16, ELEMENTARY LESSONS ON [CHAP. i.
m to H, and they repel one another because they are
then similarly electrified. The ball , therefore, is driven
round and twists the wire up to a certain extent. The
force of repulsion becomes less and less as n gets
farther and farther from m ; but the force of the twist
gets greater and greater the more the string is twisted.
Hence these two forces will balance one another when
the balls are separated by a certain distance, and it is
clear that a large charge of electricity will repel the ball
n with a greater force than a lesser charge would.
The distance through which the ball is repelled is read
off not in inches but in angular degrees of the scale.
When a wire is twisted, the force with which it tends to
untwist is precisely proportional to the amount of the
twist. The force required to twist the wire ten degrees
is just ten times as great as the force required to twist
it one degree. In other words, the force of torsion is
proportional to the angle of torsion. The angular
distance between the two balls is, when they are not
very widely separated, very nearly proportional to the
actual straight distance between them, and represents
the force exerted between electrified balls at that
distance apart. The student must, however, carefully
distinguish between the measurement of the force and
the measurement of the actual quantity of electricity
with which the instrument is charged. For the force
exerted between the electrified balls will vary at different
distances according to a particular law known as the
" law of inverse squares," which requires to be carefully
explained.
16. The Law of Inverse Squares. Coulomb
proved, by means of the Torsion Balance, that the force
exerted between two small electrified bodies varies
inversely as the square of the distance between them
when the distance is varied. Thus, suppose two electri-
fied bodies one inch apart repel one another with a
certain force, at a distance of two inches the force will
CHAP, i.] ELECTRICITY AND MAGNETISM. 17
be found to be only one quarter as great as the force
at one inch ; and at ten inches it will be only jy- th
part as great as at one inch. This law is proved by the
following experiment with the torsion balance. The
two scales were adjusted to o, and a certain charge was
then imparted to the balls. The ball n was repelled
round to a distance of 36. The twist on the wire
between its upper and lower ends was also 36, or the
force of the repulsion was thirty-six times as great as the
force required to twist the wire by i. The torsion-head
was now turned round so as to twist the thread at the
top and force the ball n nearer to m, and was turned
round until the distance between n and m was halved.
To bring down this distance from 36 to 18, it was
found needful to twist the torsion -head through 126.
The total twist between the upper and lower ends of the
wire was now 126 + 18, or 144; and the force was
144 times as great as that force which would twist the
wire i. But 144 is four times as great as 36 ; hence
we see that while the distance had been reduced to one
half) the force between the balls had become four
times as great. Had we reduced the distance to one
quarter, or 9, the total torsion would have been found
to be 576, or sixteen times as great; proving the
force to vary inversely as the square of- the
distance.
In practice it requires great experience and skill to
obtain results as exact as this, for there are many
sources of inaccuracy in the instrument. The balls
must be very small, in proportion to the distances between
them. The charges of electricity on the balls are found,
moreover, to become gradually less and less, as if the
electricity leaked away into the air. This loss is less
if the apparatus be quite dry. It is therefore usual to
dry the interior by placing inside the case a cup con-
taining either chloride of calcium, or pumice stone
soaked with strong sulphuric acid, to absorb the moisture,
C
i8 ELEMENTARY LESSONS ON [CHAP. i.
Before leaving the subject of electric forces, it may be
well to mention that the force of attraction between
two oppositely electrified bodies varies also inversely as
the square of the distance between them. And in every
case, whether of attraction or repulsion, the force at any
given distance is proportional to the product of the
two quantities of electricity on the bodies. Thus, if
we had separately given a charge of 2 to the ball m and
a charge of 3 to the ball n, the force between them will
be 3x2 = 6 times as great as if each had had a
charge of i given to it.
17. Unit quantity of Electricity. In conse-
quence of these laws of attraction and repulsion, it is
found most convenient to adopt the following definition
for that quantity of electricity which we take for a unit or
standard by which to measure other quantities of elec-
tricity. One Unit of Electricity is that quantity which,
when placed at a distance of one centimetre from a
similar and equal quantity, repels it with a force of
one dyne. Further information about the measure-
ment of electrical quantities is given in Lessons XX.
and XXI.
"LESSON III. Electrification by Induction.
18. We have now learned how two charged bodies
may attract or repel one another. It is sometimes said
that it is the electricities in the bodies which attract or
repel one another ; but as electricity is not known to
exist except in or on material bodies, the proof that it
is the electricities themselves which are attracted is only
indirect. Nevertheless there are certain matters which
support this view, one of these being the electric influ-
ence exerted by an electrified body upon one not
electrified.
Suppose we rub a ball of glass with silk to electrify it,
CHAP, i.] ELECTRICITY AND MAGNETISM. 19
and hold it near to a body that has not been electrified,
what will occur? We take for this experiment the
apparatus shown in Fig. 10, consisting of a long
sausage -shaped piece of metal, either hollow or solid,
held upon a glass support. This "conductor," so called
because it is made of metal which permits electricity to
pass freely through it or over its surface, is supported on
glass to prevent the escape of electricity to the earth,
gla*ss being a non-conductor. The presence of the
positive electricity of the glass ball near this conductor
is found to induce electricity on the conductor, which,
Fig. 10.
although it has not been rubbed itself, will be found to
behave at its two ends as an electrified body. The
ends of the conductor will attract little bits of paper ;
and if pith -balls be hung to the ends they are found
to be repelled. It will, however, be found that the
middle region of the long -shaped conductor will give
no sign of any electrification. Further examination will
show that the two electrifications on the ends of the con-
ductor are of opposite kinds, that nearest the excited
glass ball being a negative charge, and that at the
farthest end being an equal charge, but of positive
20 ELEMENTARY LESSONS ON [CHAP. i.
sign. It appears then that a positive charge attracts
negative and repels positive, and that this influence can
be exerted at a distance from a body. If we had begun
with a charge of negative electrification upon a stick of
sealing-wax, the presence of the negative charge near the
conductor would have induced a positive charge on the
near end, and negative on the far end. This action,
discovered in 1753 by John Canton, is spoken of as
electric induction, or influence. It will take place
across a considerable distance. Even if a large sheet
of glass be placed between, the same effect will be
produced. When the electrified body is removed both
the charges disappear and leave no trace behind, and
the glass ball is found to be just as much electrified as
before ; it has parted with none of its own charge. It
will be remembered that on one theory a body charged
positively is regarded as having more electricity than
the things round it, while one with . a negative charge
is regarded as having less. According to this view
it would appear that when a body (such as the +
electrified glass ball) having more electricity than
things around it is placed near an insulated conductor,
the uniform distribution of electricity in that conductor
is disturbed, the electricity flowing away from that end
which is near the + body, leaving less than usual at
that end, and producing more than usual at the other
end. This view of things will account for the disappear-
ance of all signs of electrification when the electrified
body is removed, for then the conductor returns to its
former condition ; and being neither more nor less elec-
trified than all the objects around on the surface of the
earth, will show neither positive nor negative charge.
19. If the conductor be made in two parts, so that
while under the inductive influence of the electrified
body they can be separated, then on the removal of the
electrified body the two charges can no longer return
to neutralise one another, but remain each on their own
CHAP, i.] ELECTRICITY AND MAGNETISM. 21
portion of the conductor, and may be examined at
leisure.
If the conductor be not insulated on glass supports,
but placed in contact with the ground, that end only
which is nearest the electrified body will be found to be
electrified. The repelled electricity is indeed repelled
as far as possible into the earth. One kind of elec-
trification only is under these circumstances to be found,
namely, the opposite kind to that of the excited body,
whichever this may be. The same effect occurs in this
case as if an electrified body had the power of attracting
up the opposite kind of charge out of the earth, though
the former way of regarding matters is more correct.
The quantity of the two charges thus separated by
induction on such a conductor in the presence of a
charge of electricity, depends upon the amount of the
charge, and upon the distance of the charged body from
the conductor. A highly electrified glass rod will
produce a greater inductive effect than a less highly
electrified one ; and it produces a greater effect as it is
brought nearer and nearer. The utmost it can do will
be to induce on the near end a negative charge equal
in amount to its own positive charge, and a similar
amount of positive electricity at the far end ; but usually,
before the electrified body can be brought so near as to
do this, something else occurs which entirely alters the
condition of things. As the electrified body is brought
nearer and nearer, the charges of opposite sign on the
two opposed surfaces attract one another more and
more strongly and accumulate more and more densely,
until, as the electrified body approaches very near, a spark
is seen to dart across, the two charges thus rushing
together to neutralise one another, leaving the induced
charge of positive electricity, which was formerly repelled
to the other end of the conductor, as a permanent charge
after the electrified body has been removed.
2O. We are now able to apply the principle of
22 ELEMENTARY LESSONS ON [CHAP. I.
induction to explain why an electrified body should
attract things that have not been electrified at all. Let
a light ball be suspended by a silk thread (Fig. 1 i), and
a rubbed glass rod held near it. The positive charge
of the glass will induce a negative charge on the near side,
and an equal amount of posi-
tive electrification on the farther
side, of the ball. The nearer
half of the ball will therefore
be attracted, and the farther
half repelled ; but the attraction
Fi IT will be stronger than the repul-
sion, because the attracted elec-
tricity is nearer than the repelled. Hence on the whole
the ball will be attracted. It can easily be observed
that if a ball of non-conducting substance, such as wax,
be employed, it is not attracted so much as a ball of
conducting material. This in itself 'proves that induction
really precedes attraction.
21. Inductive capacity. We have assumed up to
this point that electricity could act at a distance, and
could produce these effects of induction without any
intervening means of communication. This, however,
is not the case, for Faraday discovered that the air in
between the electrified body and the conductor played a
very important part in the production of these actions.
Had some other substance, such as paraffin oil, or solid
sulphur, occupied the intervening space, the effect pro-
duced by the presence of the electrified body at the
same distance would have been greater. The power of
a body thus to allow the inductive influence of an
electrified body to act across it is called its inductive
capacity (see Article 49 and Lesson XXII.)
22. The Electrophorus. We are now prepared
to explain the operation of a simple and ingenious
instrument, devised by Volta in 1775, for the purpose
of procuring, by the principle of induction, an unlimited
CHAP, i.j ELECTRICITY AND MAGNETISM.
number of charges of electricity from one single charge.
This instrument is the Electrophorus (Fig. 12). It
consists of two parts, a round cake of resinous material
cast in a metal dish or "sole," about 12 inches in
diameter, and a round disc of slightly smaller diameter
made of metal, or of wood covered with tinfoil, and
Fig. 72
provided with a glass handle. Shellac, or sealing-wax,
or a mixture of resin, shellac, and Venice turpentine, may
be used to make the cake. A slab of sulphur will
also answer, but it is liable to crack. Sheets of hard
ebonised indiarubber are excellent ; but the surface of
this substance recfuires occasional washing with ammonia
and rubbing with paraffin oil, as the sulphur contained
24 ELEMENTARY LESSONS ON [CHAP. I.
in it is liable to oxidise and to attract moisture. To -use
the electrophorus the resinous cake must be beaten or
rubbed with a warm piece of woollen cloth, or, better
still, with a cat's skin. The disc or " cover" is then
placed upon the cake, touched momentarily with the
finger, then removed by taking it up by the glass handle,
when it is found to be powerfully electrified with a posi-
tive charge, so much so indeed as to yield a spark when
the knuckle is presented to it. The " cover " may be
replaced, touched, and once more removed, and will
thus yield any number of sparks, the original charge on
the resinous plate meanwhile remaining practically as
strong as before.
i i i i
Fig. 13. Fig. 14.
The theory of the electrophorus is very simple, pro-
vided the student has clearly grasped the principle of
induction explained above. When the resinous cake
is first beaten with the cat's skin its surface is negatively
electrified, as indicated in Fig. 13. When the metal
disc is placed down upon it, it rests really only on three
or four points of the surface, and may be regarded as an
insulated conductor in the presence of an electrified
body. The negative electrification of the disc therefore
acts inductively on the metallic disc or " cover," attract-
ing a positive charge to its under side, and repelling
a negative charge to its upper surface. This state
of things is shown in Fig. 14. If now, the cover be
tottched for an instant with the finger, the negative
charge of the upper surface (which is upon the upper
CHAP. i.J ELECTRICITY AND MAGNETISM. 25
surface being repelled by the negative charge on the cake)
will be neutralised by electricity flowing in from the
earth through the hand and body of the experimenter.
The attracted positive charge will, however, remain, beirrg
bound as it were by its attraction towards the negative
charge on the cake. Fig. 1 5 shows the condition of
things after the cover has been touched. If, finally, the
cover be lifted by its handle, the remaining positive
charge will be no longer " bound " on the lower surface
by attraction, but will distribute itself on both sides of
I
the cover, and may be used to give a spark, as already
said. It is clear that no part of the original charge has
been consumed in the process, which may be repeated
as often as desired. As a matter of fact, the charge on
the cake slowly dissipates especially if the air be damp.
Hence it is needful sometimes to renew the original
charge by afresh beating the cake with the cat's skin.
The labour of touching the cover with the finger at each
operation may be saved by having a pin of brass or a
strip of tinfoil projecting from the metallic " sole " on to
the top of the cake, so that it touches the plate each
time, and thus neutralises the negative charge by allow-
ing electricity to flow in from the earth.
Since the electricity thus yielded by the electrophorus
26 ELEMENTARY LESSONS ON [CHAP. i.
is not obtained at the expense of any part of the original
charge, it is a matter of some interest to inquire what
the source is from which the energy of this apparently
unlimited supply is drawn ; for it cannot be called
into existence without the expenditure of some other
form of energy, any more than a steam-engine can work
without fuel. As a matter of fact it is found that it
is a little harder work to lift up the cover when it
is charged with the + electricity than if it were not
charged ; for, when charged, there is the force of the
electric attraction to be overcome as well as the force
of gravity. Slightly harder work is done at the ex-
pense of the muscular energies of the operator ; and this
is the real origin of the energy stored up in the separate
charges.
23. Continuous Electrophori. The purely me-
chanical actions of putting down the disc on to the
cake, touching it, and lifting it up, can be performed
automatically by suitable mechanical arrangements,
which render the production of these inductive charges
practically continuous. The earliest of such contin-
uous electrophori was Bennet's " Doubler," the latest
is Holtz's machine, described in Lesson V.
24. "Free" and "Bound" Electricity. We
have spoken of a charge of electricity on the surface of
a conductor, as being " bound " when it is attracted by
the presence of a neighbouring charge of the opposite
kind. The converse term " free " is sometimes applied
to the ordinary state of electricity upon a charged con-
ductor, not in the presence of a charge of an opposite
kind. A "free" charge upon an insulated conductor
flows away instantaneously to the earth, if a conducting
channel be provided, as will be explained in the next
lesson. It is immaterial what point of the conductor be
touched. Thus, in the case represented in Fig. 10,
wherein a + electrified body induces electrification at
the near end, and 4- electrification at the far end of an
CHAP. I.] ELECTRICITY AND MAGNETISM. 27
insulated conductor, the charge is " bound," being
attracted, while the + charge at the other end, being
repelled, is "free"; and if the insulated conductor be
touched by a person standing on the ground, the "free"
electricity will flow away to the earth through his body,
while the " bound " electricity will remain, no matter
whether he touch the conductor at the far end, or at the
near end, or at the middle.
25. Inductive method of charging the Gold-
leaf Electroscope. The student will now be prepared
to understand the method by which a Gold-Leaf Electro-
scope can be charged with the opposite kind of charge to
that of the electrified body used to charge it. In Lesson
II. it was assumed that the way to charge an electro-
scope was to place the excited body in contact with the
knob, and thus permit, as it were, a small portion of the
charge to flow into the gold leaves. A rod of glass
rubbed on silk being + would thus obviously impart +
electrification to the gold leaves.
Suppose, however, the rubbed glass rod to be held a
few inches above the knob of the electroscope, as is
indeed shown in Fig. 7. Even at this distance the gold
leaves diverge, and the effect is due to induction. The
gold leaves, and the brass wire and knob, form one con-
tinuous conductor, insulated from the ground by the
glass jar. The presence of the + electricity of the
glass acts inductively on this " insulated conductor,"
inducing electrification on the near end or knob, and
inducing + at the far end, i.e., on the gold leaves,
which diverge. Of these two induced charges, the
on the knob is "bound," while the + on the leaves is
" free." If now, while the excited rod is still held above
the electroscope, the knob be touched by a person
standing on the ground, one of these two induced charges
flows to the ground, namely the free charge not that
on the knob itself, for it was " bound," but that on the
gold leaves which was " free " and the gold leaves
28 ELEMENTARY LESSONS ON [CHAP. i.
instantly drop down straight. There now remains only
the charge on the knob, " bound " so long as the
-f- charge of the glass rod is near to attract it. But
if, finally, the glass rod be taken right away, the -
charge is no longer " bound " on the knob, but is
" free " to flow into the leaves, which once more diverge
but this time with a negative electrification.
26. " The Return-Shock." It is sometimes noticed
that, when a charged conductor is suddenly discharged,
a discharge is felt by persons standing near, or may
even affect electroscopes, or yield sparks. This action,
known as the " return-shock," is due to induction. For
in the presence of a charged conductor a charge of
opposite sign will be induced in neighbouring bodies,
and on the discharge of the conductor these neighbour-
ing bodies may also suddenly discharge their induced
charge into the earth, or into other conducting bodies.
A " return-shock " is sometimes felt by persons standing
on the ground at the moment when a flash of lightning
has struck an object some distance away.
LESSON IV. Conduction and Distribution of Electricity.
27. Conduction. Toward the close of Lesson I.
we explained how certain bodies, such as the metals,
conduct electricity, while others are non-conductors or
insulators. This discovery is due to Stephen Gray ;
who, in 1729, found that a cork, inserted into the end
of a rubbed glass tube, and even a rod of wood stuck
into the cork, possessed the power of attracting light
bodies. He found, similarly, that metallic wire and pack-
thread conducted electricity, while silk did not.
We may repeat these experiments by taking (as in
Fig. 17) a glass rod, fitted with a cork and a piece of
wood. If "a bullet or a brass knob be hung to the end of
this by a linen thread or a wire, it is found that when the
CHAP, i.] ELECTRICITY AND MAGNETISM. 29
glass tube is rubbed the bullet acquires the property of
attracting light bodies. If a dry silk thread is used,
however, no electricity will flow down to the bullet.
Gray even succeeded in transmitting a charge of
electricity through a hempen thread over 700 feet lon^,,
suspended on silken loops. A little later Du r'ay
succeeded in sending electricity to no less ? distance
than 1256 feet through a moistened thread, thus proving
the conducting power of moisture. From that time the
classification of bodies into conductors and insulators
has been observed.
Fig. 17.
This distinction cannot, however, be entirely main-
tained, as a large class of substances occupy an inter-
mediate ground as partial conductors. For example, dry-
wood is a bad conductor and also a bad insulator ; it
is a good enough conductor to conduct away the high-
potential electricity obtained by friction ; but it v is a
bad conductor for the relatively low-potential electricity
of small voltaic batteries. Substances that are very bad
conductors are said to offer a great resistance to the
ELEMENTARY LESSONS ON [CHAP, i
flow of electricity through them. There is indeed no
substance so good a conductor as to be devoid of resist-
ance. There is no substance of so high a resistance as
not to conduct a little. Even silver, which conducts best
of all known substances, resists the flow of electricity to
a small extent ; and, on the other hand, such a non-con-
ducting substance as glass, though its resistance is many
million times greater than any metal, does allow a very
small quantity of electricity to pass through it. In the
following list, the substances named are placed in order,
each conducting better than those lower down on the list.
Silver
r Good Conductors.
Partial Conductors,
Oliver .
Copper .
Other metals
Charcoal .
|
Water .
j
The body
1
Cotton .
|
Dry Wood
i
Marble .
I
Paper
j
Oils
>
Porcelain
Wool .
Silk
Resin
Guttapercha
SheUac .
Ebonite .
Paraffin .
Glass
Dry air ,,,.
-
Non-Conductors or
Insulators.
A simple way of observing experimentally whether a
body is a conductor or not, is to take a charged gold-
leaf electroscope, and, holding the substance to be
examined in the hand, touch the knob of the electro-
scope with it. If the substance is a conductor the
electricity will flow away through it and through the
body to the earth, and the electroscope will be discharged.
Through good conductors the rapidity of the flow is so
CHAP, i.] ELECTRICITY AND MAGNETISM. 31
great that the discharge is practically instantaneous.
Further information on this question is given in Lesson
XXIII.
28. Distribution of Electricity on Bodies. If
electricity is produced at one part of a non-conducting
body, it remains at that point and does not flow over
the surface, or at most flows over it excessively slowly.
Thus if a glass tube is rubbed at one end, only that one
end is electrified. If a warm cake of resin be rubbed at
one part with a piece of cloth, only the portion rubbed
will attract light bodies. The case is, however, wholly
different when a charge of electricity is imparted to any
part of a conducting body placed on an insulating
support, for it instantly distributes itself all over the
surface, though in general not uniformly over all points
of the surface.
29. The Charge resides on the surface. A
charge of electricity resides only on the surface of
conducting bodies. This is proved by the fact that it
is found to be immaterial to the distribution what the
interior of a conductor is made of; it may be solid metal,
or hollow, or even consist of wood covered with tinfoil
or gilt, but, if the shape be the same, the charge will
distribute itself precisely in the same manner over the
surface. There are also several ways of proving by
direct experiment this very important fact. Let a hollow
metal ball, having an aperture at the top, be taken (as in
Fig. 1 8), and set upon an insulating stem, and charged
by sending into it a few sparks from an electrophorus.
The absence of any charge in the interior may be shown
as follows : In order to observe the nature of the
electricity of a charged body, it is convenient to have
some means of removing a small quantity of the charge
as a sample for examination. To obtain such a sample,
a little instrument known as a proof-plane is employed.
It consists of a little disc of sheet copper or of gilt paper
fixed at the end of a small glass rod. If this disc is laid
32 ELEMENTARY LESSONS ON [CHAP. I.
on the surface of an electrified body at any point, part
of the electricity flows into it, and it may be then re-
moved, and the sample thus obtained may be examined
with a Gold-leaf Electroscope in the ordinary way. For
some purposes a metallic bead, fastened to the end of a
glass rod, is more convenient than a flat disc. If such
Fig. 1 8.
a proof-plane be applied to the outside of our electrified
hollow ball, and then touched on the knob of an electro-
scope, the gold leaves will diverge, showing the presence
of a charge. But if the proof-plane be carefully inserted
through the opening, and touched against the inside of
CHAP, i.] ELECTRICITY AND MAGNETISM.
33
the globe and then withdrawn, it will be found that the
inside is destitute of electricity. An electrified pewter
mug will show a similar result, and so will even a
cylinder of gauze wire.
3O. Blot's experiment. Biot proved the same fact
in another way. A copper ball was electrified and
insulated. Two hollow hemispheres of copper, of a
larger size, and furnished with glass handles, were then
placed together outside it (Fig. 19). So long as they
did not come into contact the charge remained on the
Fig. 19.
inner sphere ; but if the outer shell touched the inner
sphere for but an instant, the whole of the electricity
passed to the exterior ; and when the hemispheres were
separated and removed the inner globe was found to be
completely discharged.
31. Further explanation. Doubtless the explana-
tion of this behaviour of electricity is to be found in
the property previously noticed as possessed by either
kind of electricity, namely, that of repelling itself ; hence
it retreats as far as can be from the centre and remains
D
34
ELEMENTARY LESSONS ON [CHAP. i.
upon the surface. An important proposition concerning
the absence of electric force within a closed conductor is
proved in Lesson XX. ; meanwhile it must be noted that
the proofs, so far, are directed to demonstrate the
absence of a free charge of electricity in the interior
of hollow conductors. Many other experiments have
been devised in proof. Thus, Terquem showed that
a pair of gold leaves hung inside a wire cage could
not be made to diverge when the cage was elec-
trified. Faraday constructed a conical bag of linen-
Fig. 20.
gauze, supported as in Fig. 20, upon an insulating
stand, and to which silk strings were attached, by which
it could be turned inside out. It was charged, and
the charge was shown by the proof- plane and electro-
scope to be on the outside of the bag. On turning it
inside out the electricity was once more found outside.
Faraday's most striking experiment was made with a
hollow cube, measuring 12 feet each way, built of wood,
covered with tinfoil, insulated, and charged with a
powerful machine, so that large sparks and brushes
CHAP, i.] ELECTRICITY AND MAGNETISM. 35
were darting off from every part of its outer surface.
Into this cube Faraday took his most delicate electro-
scopes ; but once within he failed to detect the least
influence upon them.
32. Applications. Advantage is taken of this in
the construction of delicate electrometers and other
instruments, which can be effectually screened from
the influence of electrified bodies by enclosing them
in a thin metal cover, closed all round, except where
apertures must be made for purposes of observation. It
has also been proposed by the late Prof. Clerk Maxwell
to protect buildings from lightning by covering them
on the exterior with a network of wires.
33. Apparent Exceptions. There are two ap-
parent exceptions to the law that electricity resides only
on the outside of conductors, (i) If there are electrified
insulated bodies actually placed inside the hollow con-
ductor, the presence of these electrified bodies acts in-
ductively and attracts the opposite kind of electricity to
the inner side of the hollow conductor. (2) When
electricity flows in a current, it flows through the sub-
stance of the conductor. The law is limited therefore
to electricity at rest, that is, to statical charges.
34. Faraday's " Ice-pail " Experiment. One ex-
periment of Faraday deserves notice, as showing the
part played by induction in these phenomena. He
gradually lowered a charged metallic ball into a hollow
conductor connected by a wire to a gold-leaf electro-
scope (Fig. 21), and watched the effect. A pewter ice-
pail being convenient for his purpose, this experiment is
continually referred to by this name, though any other
hollow conductor a tin canister or a silver mug, placed
on a glass support would of course answer equally
well. The following effects are observed : Suppose
the ball to have a + charge : as it is lowered into the
hollow conductor the gold leaves begin to diverge, for
the presence of the charge acts inductively, and attracts
ELEMENTARY LESSONS ON [CHAP. i.
a charge into the interior and repels a + charge to the
exterior. The gold leaves diverge more and more until
the ball is right within the hollow conductor, after which
no greater divergence is obtained. On letting the ball
touch the inside the gold leaves still remain diverging
as before, and if now the ball is pulled out it is found
to have lost all its electricity. The fact that the gold
leaves diverge no wider
after the ball touched
than they did just
before, proves that
when the charged ball
is right inside the
hollow conductor the
induced charges are
each of them precisely
equal in amount to
its own charge, and the
interior negative charge
exactly neutralises the
charge on the ball at
^ the moment when they
touch, leaving the equal
exterior charge un-
changed. An electric
cage, such as this ice-pail, when connected with an
electroscope or electrometer, affords an excellent means
of examining the charge on a body small enough to be
hung inside it. For without using up any of the charge
of the body (which we are obliged to do when applying
the method of the proof-plane) we can examine the
induced charge repelled to the outside of the cage,
which is equal in amount and of the same sign.
35. Distribution of Charge. A charge of elec-
tricity is not usually distributed uniformly over the
surfaces of bodies. Experiment shows that there is
more electricity on the edges and corners of bodies than
CHAP. I.] ELECTRICITY AND MAGNETISM.
37
upon their flatter parts. This distribution can be de-
duced from the theory laid down in Lesson XX., but
meantime we will give some of the chief cases as they
can be shown to exist. The term Electric Density is
used to signify the amount of electricity at any point of
a surface ; the electric density at a point is the number
of units of electricity per unit of area (i.e. per square
inch, or per square centimetre), the distribution being
supposed uniform over this small surface.
(a) Sphere. The distribution of a charge over an
insulated sphere of conducting material is uniform,
provided the sphere is remote from the presence of all
other conductors and all other electrified bodies : or, in
d
Fig. 22.
other words, the density is uniform all over it. This is
symbolised by the dotted line round the sphere in Fig.
22, #, which is at an equal distance from the sphere all
round, suggesting an equal thickness of electricity at
every point of the surface. It must be remembered
that the charge is not really of any perceptible thickness
at all ; it resides on or at the surface, but cannot be
said to form a stratum upon it.
(b) Cylinder -with rounded ends. Upon an
elongated conductor, such as is frequently employed in
electrical apparatus, the density is greatest at the ends
where the curvature of the surface is the greatest.
38 ELEMENTARY LESSONS ON [CHAP. i.
(c) Two Spheres in contact. If two spheres in
contact with each other are insulated and charged, it is
found that the density is greatest at the parts farthest
from the point of contact, and least in the crevice
between them. If the spheres are of unequal sizes
the density is greater on the smaller sphere, which has
the surface more curved. On an egg-shaped or pear-
shaped conductor the density is greatest at the small
end. On a cone the density is greatest at the apex ;
and if the cone terminate in a sharp point the density
there is very much greater than at any other point. At
a point, indeed, the density of the collected electricity
may be so great as to electrify the neighbouring particles
of air, which then are repelled, thus producing a con-
tinual loss of charge. For this reason points and sharp
edges are always avoided on electrical apparatus, except
where it is specially desired to set up a discharge.
(d) Flat Disc. The density of a charge upon a
flat disc is greater, as we should expect, at the edges
than on the flat surfaces ; but over the flat surfaces the
distribution is fairly uniform.
These various facts are ascertained by applying a
small proof- plane successively at various points of the
electrified bodies and examining the amount taken up by
the proof-plane by means of an electroscope or electro-
meter. Coulomb, who investigated mathematically as
well as experimentally many of the important cases of
distribution, employed the torsion balance to verify his
calculations. He investigated thus the case of the
ellipsoid of revolution, and found the densities of the
charges at the extremities of the axis to be proportional
to the lengths of those axes. He also showed that the
density of the charge at any other point of the surface of
the ellipsoid was proportional to the length of the per-
pendicular drawn from the centre to the tangent at that
point. Riess also investigated several interesting cases
of distribution. He found the density at the middle of
CHAP. I.] ELECTRICITY AND MAGNETISM. 39
the edges of a cube to be nearly two and a half times
as great as the density at the middle of a face ; while
the density at a corner of the cube was more than four
times as great.
36. Redistribution of Charge. If any portion
of the charge of an insulated conductor be removed, the
remainder of the charge will immediately redistribute
itself over the surface in the same manner as the original
charge, provided it be also isolated^ i.e., that no other
conductors or charged bodies be near to perturb the
distribution by complicated effects of induction.
If a conductor be charged with any quantity of elec-
tricity, and another conductor of the same size and shape
(but uncharged) be brought into contact with it for an
instant and then separated, it will be found that the
charge has divided itself equally between them. In the
same way a charge may be divided equally into three or
more parts by being distributed simultaneously over three
or more equal and similar conductors brought into contact.
If two equal metal balls, suspended by silk strings,
charged with unequal quantities of electricity, are
brought for an instant into contact and then separated,
it will be found that the charge has redistributed itself
fairly, half the sum of the two charges being now the
charge of each. This may even be extended to the
case of charges of opposite signs. Thus, suppose two
similar conductors to be electrified, one with a positive
charge of 5 units and the other with 3 units of negative
charge, when these are made to touch and separated,
each will have a positive charge of i unit ; for the
algebraic sum of + 5 and 3 is + 2, which, shared
between the two equal conductors, leaves + i for each.
37. Capacity of Conductors. If the conductors
be unequal in size, or unlike in form, the shares taken
by each in this redistribution will not be equal, but
will be proportional to the electric capacities of the
conductors. The definition of capacity in its relation
40 ELEMENTARY LESSONS ON [CHAP. i.
to electric quantities is given in Lesson XX., Art. 246.
We may, however, make the remark, that two insulated
conductors of the same form, but of different sizes, differ
in their electrical capacity ; for the larger one must
have a larger amount of electricity imparted to it in
order to electrify its surface to the same degree. The
term potential is employed in this connection, in the
following way : A given quantity of electricity will
electrify an isolated body up to a certain " potential "
(or power of doing electric work) depending on its
capacity. A large quantity of electricity imparted to a
conductor of small capacity will electrify it up to a
very high potential; just as a large quantity of water
poured into a vessel of narrow capacity will raise the
surface of the water to a high level in the vessel. The
exact definition of Potential, in terms of energy spent
against the electrical forces, is given in the Lesson on
Electrostatics (Art. 237).
It will be found convenient to refer to a positively
electrified body as one electrified to a positive or high
potential; while a negatively electrified body may be
looked upon as one electrified to a low or negative
potential. And just as we take the level of the sea
as a zero level, and measure the heights of mountains
above it, and the depths of mines below it, using the
sea level as a convenient point of reference for differ-
ences of level, so we take the potential of the earth's
surface (for the surface of the earth is always electrified
to a certain degree) as zero potential, and use it as a
convenient point of reference from which to measure
differences of electric potential.
LESSON V. Electrical Machines.
38. For the purpose of procuring larger supplies of
electricity than can be obtained by the rubbing of a rod
of glass or shellac, electrical machines have been '
CHAP, i.] ELECTRICITY AND MAGNETISM. 41
devised. All electrical machines consist of two parts,
one for producing, the other for collecting, the electricity.
Experience has shown that the quantities of + and
electrification developed by friction upon the two surfaces
rubbed against one another depend on the amount of
friction, upon the extent of the surfaces rubbed, and also
upon the nature of the substances used. If the two
substances employed are near together on the list of
electrics given in Art. 5, the electrical effect of rubbing
them together will not be so great as if two substances
widely separated in the series are chosen. To obtain
the highest effect, the most positive and the most
negative of the substances convenient for the construc-
tion of a machine should be taken, and the greatest
available surface of them should be subjected to friction,
the moving parts having a sufficient pressure against one
another compatible with the required velocity.
The earliest form of electrical machine was devised
by Otto von Guericke of Magdeburg, and consisted of
a globe of sulphur fixed upon a spindle, and pressed
with the dry surface of the hands while being made to
rotate ; with this he discovered the existence of electric
sparks and the repulsion of similarly electrified bodies.
Sir Isaac Newton replaced Von Guericke's globe of
sulphur by a globe of glass. A little later the form of
the machine was improved by various German electri-
cians ; Von Bose added a collector or " prime con-
ductor," in the shape of an iron tube, supported by a
person standing on cakes of resin to insulate him, or
suspended by silken strings ; Winckler of Leipzig sub-
stituted a leathern cushion for the hand as a rubber ;
and Gordon of Erfurth rendered the machine more easy
of construction by using a glass cylinder instead of a
glass globe. The electricity was led from the excited
cylinder or globe to the prime conductor by a metallic
chain which hung over against the globe. A pointed
collector was not employed until after Franklin's famous
42 ELEMENTARY LESSONS ON [CHAP. i.
researches on the action of points. About 1760 De
la Fond, Planta, Ramsden, and Cuthbertson, constructed
machines having glass plates instead of cylinders. The
only important modifications introduced since their time
are the substitution of ebonite for glass, and the inven-
tion of machines depending on the principles of induc-
tion and convection.
39. The Cylinder Electrical Machine. The
Cylinder Electrical Machine, as usually constructed,
consists of a glass cylinder mounted on a horizontal axis
capable of being turned by a handle. Against it is
pressed from behind a cushion of leather stuffed with
horsehair, the surface of which is covered with a
powdered amalgam of zinc or tin. A flap of silk attached
to the cushion passes over the cylinder, covering its
Fig. 23.
upper half. In front of the cylinder stands the " prime
conductor," which is made of metal, and usually of the
form of an elongated cylinder with hemispherical ends,
mounted upon a glass stand. At the end of the prime
conductor nearest the cylinder is fixed a rod bearing a
row of fine metallic spikes, resembling in form a rake ;
the other end usually carries a rod terminated in a brass
CHAP, i.] ELECTRICITY AND MAGNETISM. 43
ball or knob. The general aspect of the machine is
shown in Fig. 23. When the handle is turned the
friction between the glass and the amalgam -coated
surface of the rubber produces a copious electrical
action, electricity appearing as a -f- charge on the glass,
leaving the rubber with a charge. The prime con-
ductor collects this charge by the following process :
The + charge being carried round on the glass acts
inductively on the long insulated conductor, repelling a
+ charge to the far end ; leaving the nearer end ly
charged. The effect of the row of points is to drive off
in a continuous discharge ly electrified air towards the
attracting + charge upon the glass, which is neutralised
thereby ; the glass thus arriving at the rubber in a
neutral condition ready to be again excited. This action
of the points is sometimes described, though less cor-
rectly, by saying that the points collect the + electricity
from the glass. If it is desired to collect also the
charge of the rubber, the cushion must be supported on
an insulating stem and provided at the back with a
metallic knob. This device, permitting either kind of
charge to be used at will, is due to Nairne. It is, how-
ever, more usual to use only the -f charge, and to
connect the rubber by a chain to " earth," so allowing
the charge to be, neutralised.
4O. The Plate Electrical Machine. The Plate
Machine, as its name implies, is constructed with a
circular plate of glass or of ebonite, and is usually pro-
vided with two pairs of rubbers formed of double
cushions, pressing the plate between them, placed at its
highest and lowest point, and provided with silk flaps,
each extending over a quadrant of the circle. The prime
conductor is either double or curved round to meet the
plate at the two ends of its horizontal diameter, and is
furnished with two sets of spikes, for the same purpose
as the row of points in the cylinder machine. A
common form of plate machine is shown in Fig. 24.
44
ELEMENTARY LESSONS ON [CHAP. i.
The action of the machine is, in all points of theoretical
interest, the same as that of the cylinder machine. Its
advantages are that a large glass plate is more easy to
construct than a large glass cylinder of perfect form, and
that the length along the surface of the glass between the
collecting row of points and the edge of the rubber
cushions is greater
in the plate than in
the cylinder for the
same amount of sur-
face exposed to fric-
tion ; for, be it re-
marked, when the
two electricities thus
separated have col-
lected to a certain
extent, a discharge
will take place along
this surface, the
length of which limits
therefore the power
of the machine. In
a more modern form,
due to Le Roy, and modified by Winter, there is but one
rubber and flap, occupying a little over a quadrant of the
plate, and one collector or double row of points. In
Winter's machine the prime conductor consists of a ring-
shaped body, for which the advantage is claimed of
collecting larger quantities of electricity than the more
usual sausage -shaped conductor. Whatever advantage
the form may have is probably due to the curvature of
its surface being on the whole greater than that of the
commoner form.
41. Electrical Amalgam. Canton, finding glass
to be highly electrified when dipped into dry mercury,
suggested the employment of an amalgam of tin with
mercury as a suitable substance wherewith to cover the
Fig. 24.
CHAP. I.] ELECTRICITY AND MAGNETISM. 45
surface of the rubbers. An amalgam of zinc is also
effective ; though still better is Kienmayer's amalgam,
consisting of equal parts of tin and zinc, mixed while
molten with twice their weight of mercury. Bisulphide
of tin (" mosaic gold ") may also be used. These
amalgams are applied to the cushions with a little stiff
grease. They serve the double purpose of conducting
away the negative charge separated upon the rubber
during the action of the machine, and of affording as a
rubber a substance which is more powerfully negative
(see list in Art. 5) than the leather or the silk of the
cushion itself. Powdered graphite is also good.
42. Precautions in using Electrical Machines.
Several precautions must be observed in the use of
electrical machines. Damp and dust must be scrupu-
lously avoided. The surface of glass is hygroscopic,
hence, except in the driest climates, it is necessary to
warm the glass surfaces and rubbers to dissipate the
film of moisture which collects. Glass stems for in-
sulation may be varnished with a thin coat of shellac
varnish, or with paraffin (solid). A few drops of
anhydrous paraffin (obtained by dropping a lump of
sodium into a bottle of paraffin oil), applied with a bit of
flannel to the previously warmed surfaces, hinders the
deposit of moisture. An electrical machine which has
not been used for some months will require a fresh coat
of amalgam on its rubbers. These should be cleaned
and warmed, a thin uniform layer of tallow or other stiff
grease is spread upon them, and the amalgam, previously
reduced to a fine powder, is sifted over the surface.
All points should be avoided in apparatus for
frictional electricity except where they are desired, like
the " collecting " spikes on the prime conductor, to let off
a charge of electricity. All the rods, etc., in frictional
apparatus are therefore made with knobs, so as to avoid
sharp edges and points.
43. Experiments -with the Electrical Machine.
ELEMENTARY LESSONS ON [CHAP. i.
With the abundant supply of electricity afforded by
the electrical machine, many pleasing and instructive
experiments are possible. The phenomena of attrac-
tion and repulsion can be
shown upon a large scale.
Fig. 25 represents a device
known as the electric
chimes, 1 in which two small
brass balls hung by silk strings
are set in motion and strike
against the bells between
which they are hung. The
two outer bells are hung by
metallic wires or chains to
the knob of the machine.
The third bell is hung by a
silk thread, but communi-
cates with the ground by a
brass chain. The balls are
Fig. 25.
first attracted to the electrified outer bells, then repelled,
and, having discharged themselves against the uninsul-
ated central bell, are again attracted, and so vibrate to
and fro.
By another arrangement small figures or dolls cut out
of pith can be made to dance up and down between a
metal plate hung horizontally from the knob of the
machine, and another flat plate an inch or two lower and
communicating with " earth."
The effect of points in discharging electricity from
the surface of a conductor may be readily proved by
numerous experiments. If the machine be in good
working order, and capable of giving, say, sparks four
inches long when the knuckle is presented to the knob,
it will be found that, on fastening a fine pointed needle
1 Invented in 1752 by Franklin, for the purpose of warning him of the
presence of atmospheric electricity, drawn from the air above his house by a
pointed iron rod.
CHAP, i.] ELECTRICITY AND MAGNETISM.
47
to the conductor, it discharges the electricity so effect-
ually at its point that only the shortest sparks can be
Fig. 26.
drawn at the knob, while a fine jet or brush of pale
blue light will appear at the point. If a lighted taper
be held in front of the point,
the flame will be visibly blown
aside (Fig. 26) by the streams
of electrified air repelled from
the point. These air-currents
can be felt with the hand.
They are due to a mutual re-
pulsion between the electrified
air-particles near the point and
the electricity collected on the
point itself. That this mutual
reaction exists is proved by
the electric fly or electric
reaction -mill of Hamilton
(Fig. 27), which consists of Fig - 2 7-
a light cross of brass or straw, suspended on a pivot,
48 ELEMENTARY LESSONS ON [CHAP. I.
and having the pointed ends bent round at right
angles. When placed on the prime conductor of the
machine, or joined to it by a chain, the force of
repulsion between the electricity of the points and that
on the air immediately in front of them drives the
mill round in the direction opposite to that in which the
points are bent.
Another favourite way of exhibiting electric repulsion
is by means of a doll with long hair placed on the
machine ; the individual hairs stand on end when the
machine is worked, being repelled from the head, and from
one another. A paper tassel will behave similarly if
hung to the prime conductor. The most striking way
of showing this phenomenon is to place a person upon
a glass -legged stool, making him touch the knob of
the machine ; when the machine is worked, his hair,
if dry, will stand on end. Sparks will pass freely
between a person thus electrified and one standing
upon the ground.
The sparks from the machine may be made to kindle
spirits of wine or ether, placed in a metallic spoon,
connected by a wire, with the nearest metallic conductor
that runs into the ground. A gas jet may be lit by
passing a spark to the burner from the finger of the per-
son standing, as just described, upon an insulating stool.
44. Armstrong's Hydro-Electrical Machine.
The friction of a jet of steam issuing from a boiler,
through a wooden nozzle, generates electricity. In
reality it is the particles of condensed water in the jet
which are directly concerned. Sir W. Armstrong, who
investigated this source of electricity, constructed a
powerful apparatus, known as the hydro -electrical
machine (Fig. 28), capable of producing enormous
quantities of electricity, and yielding sparks five or six
feet long. The collector consisted of a row of spikes,
placed in the path of the steam jets issuing from the
nozzles, and was supported, together with a brass ball
CHAP, i.] ELECTRICITY AND MAGNETISM.
49
which served as prime-conductor, upon a glass pillar.
The nozzles were made of wood, perforated with a
crooked passage in order to increase the friction of
the jet against the sides.
Fig. 28.
45. Convection - Induction Machines. There
is another class of electrical machine, differing entirely
from those we have been describing, and depending
upon the employment of a small initial charge which,
acting inductively, produces other charges, which are
then conveyed by the moving parts of the machine to
E
So ELEMENTARY LESSONS ON [CHAP. i.
___^ *
some other point where they can increase the initial
charge, or furnish a supply of electricity to a suitable
collector. Of such instruments the oldest is the Elec-
trophorus of Volta, explained fully in Lesson III.
Bennet, Nicholson, Darwin, and others, devised pieces
of apparatus for accomplishing by mechanism that which
the electrophorus accomplishes by hand. Nicholson's
"revolving doubler consists of a revolving apparatus,
in which an insulated carrier can be brought into the
presence of an electrified body, there touched for an
instant to remove its repelled electricity, then carried
forward with its acquired charge towards another body,
to which it imparts its charge, and which in turn acts
inductively on it, giving it an opposite charge which
it can convey to the first body, thus increasing its
initial charge at every rotation. Similar instruments
have been contrived by Varley, Sir W. Thomson (the "re-
plenisher"), Topler, Carre, and Holtz. The two latter
are perfectly continuous in their action, and have been
well described as continuous electrophori. The machine
of Holtz has come into such general use as to deserve
explanation.
46. Holtz's Electrical Machine. The action of
this machine is not altogether easy to grasp, though in
reality simple enough when carefully explained. The
machine consists (see Fig. 29) of two plates, one, A,
fixed by its edges ; the other, B, mounted on an axis, and
requiring to be rotated at a high speed by a band and
driving pulley. There are two holes or windows, P and
P', cut at opposite points of the fixed plate. Two pieces
varnished paper, f and f are fastened to the plate above
the window on the left and below the one on the right.
These pieces of paper or armatures are upon the side
of the fixed plate away from the movable disc, or, as
we may say, upon the back of the plate. They are
provided with narrow tongues which project forward
through the windows towards the movable disc, which
CHAP, i.j ELECTRICITY AND MAGNETISM.
they nearly touch with their blunt points. The disc
must rotate in the opposite direction to that in which
these tongues point. On the front side of the moving
disc and opposite the two armatures are two metal
combs, furnished with rows of points, and joined
behind by brass rods, terminated with brass balls, ;;/,
#, which, at first, must touch one another. To work
the machine, a small initial charge must be given by an
'Fig. 29.
electrophorus, or by a rubbed glass rod, to one of the
two armatures. The disc is then rotated rapidly ; and
it is found that after a few turns the exertion required
to keep up the rotation increases greatly ; at the same
moment pale blue brushes of light are seen to issue from
the points, and if the rod m be drawn back so as to
separate the brass balls, a torrent of brilliant sparks
darts across the intervening space. The action of the
52 ELEMENTARY LESSONS ON [CHAP. i
machine is as follows. Suppose a small + charge to
be imparted at the outset to the right armature f ; this
charge acts inductively across the discs upon the
metallic comb, repels electricity through it, and leaves
the points negatively electrified. They discharge nega-
tively electrified air upon the front surface of the movable
disc ; the repelled charge passes through the brass rods
and balls, and is discharged through the left comb upon
the front side of the movable disc. Here it acts induc-
tively upon the paper armature, causing that part of it
which is opposite itself to be negatively charged, and
repelling a + charge into its farthest part, viz., into the
tongue, which, being bluntly pointed, slowly discharges
a + charge upon the back of the movable disc. If now
the disc be turned round, this + charge on the back
comes over from the left to the right side, in the direction
indicated by the arrow, and, when it gets opposite the
comb, increases the inductive effect of the already ex-
isting + charge on the armature, and therefore repels
more electricity through the brass rods and knobs into
the left comb. Meantime the charge which we saw had
been induced in the left armature, has in turn acted on
the left comb, causing a + charge to be discharged by
the points upon the front of the disc ; and, drawing elec-
tricity through the brass rods and knobs, has made the
right comb still more highly , increasing the discharge
of ly electrified air upon the front of the disc, neutral-
ising the + charge which is being conveyed over from the
left. These actions result in causing the top half of the
moving disc to be + ly electrified on both sides and the
bottom half of the disc to be - ly electrified. The charges
on the front serve, as they are carried round, to neutralise
the electricities let off by the points of the combs, while
the charges on the back, induced respectively in the neigh-
bourhood of each of the armatures, serve, when the rota-
tion of the disc conveys them round, to increase the
inductive influence of the charge on the other armature.
CHAP, i.] ELECTRICITY AND MAGNETISM. 53
Hence a very small initial charge is speedily raised to a
maximum, the limit being reached when the electrification
of the armatures is so great that the loss of electricity at
their surface equals the gain by convection and induction.
In the latest Holtz machines, a number of rotating discs
fixed upon one common axis are employed, and the whole is
enclosed in a glass case to prevent the access of damp. A
small disc of ebonite is now usually fixed to the same axis, and
provided with a rubber, in order to keep up the initial charge.
Holtz has constructed a machine with thirty-two plates.
Voss has lately constructed a simple machine on Topler's
plan, having small metallic discs affixed to the front of the rotat-
ing plate, these discs being lightly touched, while rotating, by
small brushes fixed upon the combs, thus providing by friction
a minute initial charge. Mascart has shown the interesting fact
that the Holtz machine is reversible in its action ; that is to say,
that if a continuous supply of the two electricities (furnished by
another machine) be communicated to the armatures, the move-
able plate will be thereby set in rotation and will turn in an
opposite sense.
In the most recent influence-machine of Wimshurst's there are
two discs rotating in opposite directions, each having fixed on
its surface a series of metal plates which act both as carriers
and as inductors.
Righi has lately shown that a Holtz machine can yield a
continuous current like a voltaic battery, the strength of the
current being nearly proportional to the velocity of rotation. It
was found that the electromotive-force of a machine was equal
to that of 52,000 DanielPs cells, or nearly 53,000 volts, at all
speeds. The resistance when the machine made 120 revolutions
per minute We*s 2810 million ohms ; but only 646 million ohms
when making 450 revolutions per minute.
LESSON VI. The Ley den Jar and other Condensers.
47. It was shown in previous lessons that the opposite
charges of electricity attract one another ; that electricity
cannot flow through glass ; and that yet electricity can
act across glass by induction. Two suspended pith-
balls, one electrified positively and the other negatively,
will attract one another across the intervening .air. If
a plate of glass be put between them they will still
54 ELEMENTARY LESSONS ON [CHAP. i.
attract one another, though neither they themselves nor
the electric charges on them can pass through the glass.
If a pith-ball electrified with a charge be hung inside a
dry glass bottle, and a rubbed glass rod be held outside,
the pith-ball will rush to the side of the bottle nearest to
the glass rod, being attracted by the + charge thus
brought near it. If a pane of glass be taken, and a piece
of tinfoil be stuck upon the middle of each face of the
pane, and one piece of tinfoil be charged positively,
and the other negatively, the two charges will attract
one another across the glass, and will no longer be found
to be free. If the pane is set up on edge, so that neither
piece of tinfoil touches the table, it will be found that
hardly any electricity can be got by merely touching either
of the foils, for the charges are " bound," so to speak,
by each other's attractions ; each charge is inducing the
other. In fact it will be found that these two pieces of
tinfoil may be, in this manner, charged a great deal
more strongly than either of them could possibly be
if it were stuck to a piece of glass alone, and then elec-
trified. In other words, the capacity of a conductor is
greatly increased when it is placed near to a conductor
electrified with the opposite kind of charge. If its
capacity is increased, a greater quantity of electricity
may be put into it before it is charged to a high degree
of potential. Hence, such an arrangement for holding
a large quantity of electricity may be called a con-
denser or accumulator of electricity.
48. Condensers. Next, suppose that we have two
brass discs, A and B (Fig. 30), set upon insulating
stems, and that a glass plate is placed between them.
Let B be connected by a wire to the knob of an electrical
machine, and let A be joined by a wire to " earth." The
+ charge upon B will act inductively across the glass
plate on A, and will repel electricity into the earth,
leaving the nearest face of A negatively electrified.
This charge on A will attract the + charge of
CHAP. I.] ELECTRICITY AND MAGNETISM.
55
B to the side nearest the glass, and a fresh supply of
electricity will come from the machine. Thus this ar-
rangement will become an accumulator or condenser.
If the two brass discs are pushed up close to the glass
plate there will be a still stronger attraction between the
+ and charges, because they are now nearer one
another, and the inductive action will be greater ; hence
a still larger quantity can be accumulated in the plates.
We see then that the capacity of an accumulator is
increased by bringing the plates near together. If
now, while the discs are strongly charged, the wires
are removed and the discs are drawn backwards
from one another, the two charges will not hold
one another bound so strongly, and there will be more
free electrification
than before over cf
their surfaces. This
would be rendered
evident to the ex-
perimenter by the
little pith-ball elec-
troscopes fixed to
them (see the Fig.),
which would fly out
as the brass discs
were moved apart. ' We have put no further charge on
the disc B, and yet, from the indications of the electroscope,
we should conclude that by moving it away from disc A
it has become electrified to a higher degree. The fact is,
that while the conductor B was near the charge of A
the capacity of B was greatly increased, but on moving
it away from A its capacity has diminished, and hence
the same quantity of electricity now electrifies it to a
higher degree than before. The presence, therefore, of
an earth -connected plate near an insulated conductor
increases its capacity, and permits it to accumulate a
greater charge by attracting and condensing the elec-
I
Fig. 30.
56 ELEMENTARY LESSONS ON [CHAP. I.
tricity upon the face nearest the earth-plate, the surface-
density on this face being therefore very great. Such
an arrangement is sometimes called a condenser, some-
times an accumulator. We shall call such an arrange-
ment a condenser when the object of the earth-connected
plate is to increase the surface-density of the charge
upon one face of the insulated conductor. The term
accumulator is now more often applied to batteries for
storing the energy of electric currents (Art. 415).
The stratum of .air between the two discs will suffice
to insulate the two charges one from the other. The
brass discs thus separated by a stratum of air constitute
an air-condenser. Such condensers were first devised
by Wilke and Aepinus.
49. Dielectrics. In these experiments the sheet of
glass or layer of air plays an important part by permitting
the inductive electric influences to act across or through
them. On account of this property these substances
were termed by Faraday dielectrics. All dielectrics
are insulators, but equally good insulators are not neces-
sarily equally good dielectrics. Air and glass are far better
insulators than ebonite or paraffin in the sense of being
much worse conductors. But induction takes place better
across a slab of glass than across a slab of ebonite or
paraffin of equal thickness, and better still across these
than across a layer of air. In other words, glass is a
better dielectric than ebonite, or paraffin, or air.
Those substances which are good dielectrics are said to
possess a high inductive capacity.
50. Capacity of a Condenser. It appears,
therefore, that the capacity of a condenser will depend
upon
(1) The size and form of the metal plates or coatings.
(2) The thinness of the stratum of dielectric between
them ; and
(3) The inductive capacity of the dielectric.
51. The Leyden Jar. The Leyden Jar, called after
CHAP, i.] ELECTRICITY AND MAGNETISM.
57
Fig. 31.
: earth " by a wire or chain.
the city where it was invented, is a convenient form of
condenser. It usually consists (Fig. 31) of a glass jar
coated up to a certain height on the inside and outside
with tinfoil. A brass knob
fixed on the end of a stout
brass wire passes downward
through a lid or top of dry
well -varnished wood, and
communicates by a loose bit
of brass chain with the inner
coating of foil. To charge
the jar the knob is held to
the prime conductor of an
electrical machine, the outer
coating being either held in
the hand or connected to
When a + charge of electricity is imparted thus to the
inner coating, it acts inductively on the outer coating,
attracting a - charge into the face of the outer coating
nearest the glass, and repelling a + charge to the outside
of the outer coating, and thence through the hand or wire
to earth. After a few moments the
jar will have acquired its full charge,
the outer coating being - and the
inner +. If the jar is of good glass,
and dry, and free from dust, it will
retain its charge for many hours or
days. But if a path be provided by
which the two mutually attracting
electricities can flow to one another,
they will do so, and the jar will be
instantaneously discharged. If the
outer coating be grasped with one
hand, and the knuckle of the other
hand be presented to the knob of the jar, a bright
spark will pass between the knob and the knuckle
with a sharp report, and at the same moment a convulsive
58 ELEMENTARY LESSONS ON [CHAP. i.
" shock " will be communicated to the muscles of the
wrists, elbows, and shoulders. A safer means of dis-
charging the jar is afforded by the discharging 1 tongs
or 'discharger (Fig. 32), which consists of a jointed
brass rod provided with brass knobs and a glass handle.
One knob is laid against the outer coating, the other is
then brought near the knob of the jar, and a bright
snapping spark leaping from knob to knob announces
that the two accumulated charges have flowed together,
completing the discharge.
52. Discovery of the Leyden Jar. The dis-
covery of the Leyden jar arose from the attempt of
Musschenbroek and his pupil Cuneus 1 to collect the
supposed electric "fluid" in a bottle half filled with
water, which was held in the hand and was provided
with a nail to lead the " fluid " down through the cork
to the water from the electric machine. Here the
water served as an inner coating and the hand as an
outer coating to the jar. Cuneus on touching the nail
received a shock. This accidental discovery created
the greatest excitement in Europe and America.
53. Residual Charges. If a Leyden jar be
charged and discharged and then left for a little time to
itself, it will be found on again discharging that a small
second spark can be obtained. There is in fact a
residual charge which seems to have soaked into the
glass or been absorbed. The return of the residual
charge is hastened by tapping the jar. The amount of
the residual charge varies with the time that the jar has
been left charged ; it also depends on the kind of the glass
of which the jar is made. There is no residual charge
discoverable in an air-condenser after it has once been
discharged.
54. Batteries of Leyden Jars. A large Leyden
jar will give a more powerful shock than a small one,
1 The honour of the invention ot the jar is also claimed for Kleist,
Bishop of Pomerania.
CHAP, i.] ELECTRICITY AND MAGNETISM.
59
for a larger charge can be put into it ; its capacity is
greater. A Leyden jar made of thin glass has a
greater capacity as an accumulator than a thick one of
the same size ; but if it is too thin it will be destroyed
when powerfully charged by a spark actually piercing
the glass. " Toughened " glass is less easily pierced
than ordinary glass, and hence Leyden jars made
Fig. 33-
of it may be made thinner, and so will hold a greater
charge.
If, however, it is desired to accumulate a very great
charge of electricity, a number of jars must be em-
ployed, all their inner coatings being connected together,
and all their outer coatings being united. This arrange-
ment is called a Battery of Leyden jars, or Leyden
6o
ELEMENTARY LESSONS ON [CHAP. i.
battery, Fig. 33. As it has a large capacity it will
require a large quantity of electricity to charge it fully.
When charged it produces very powerful effects ; its
spark will pierce glass readily, and every care must be
taken to avoid a shock from it passing through the
person, as it might be fatal. The " Universal Dis-
charger " as employed with the Leyden battery is shown
in the figure.
55. Seat of the charge. Benjamin Franklin
discovered that the charges of the
Leyden jar really resided on the
surface of the glass, not on the
metallic coatings. This he proved
by means of a jar whose coatings
could be removed, Fig. 34. The
jar was charged and placed upon
an insulating stand. The inner
coating was then lifted out, and the
glass jar was then taken out of the
outer coating. Neither coating
was found to be electrified to any
extent, but on again putting the jar
together it was found to be highly
charged. The charges had all the
time remained upon the inner and
outer surfaces of the glass dielectric.
56. Dielectric Strain. Fara-
day proved that the medium across
which induction takes place really
plays an important part in the
phenomena. It is now known
that all dieletrics across which inductive actions are at
work are thereby strained}- Inasmuch as a good
vacuum is a good dielectric, it is clear that it is not
1 In the exact sciences a strain means an alteration of form or volume
due to the application of a stress. A stress is the force, pressure, or other
agency which produces a strain.
Fig. 34-
CHAP, i.] ELECTRICITY AND MAGNETISM. 61
necessarily the material particles of the dielectric sub-
stance that are thus affected ; hence it is believed that
electrical phenomena are due to stresses and strains in
the so-called "aether," the thin medium pervading all
matter and all space, whose highly elastic constitution
enables it to convey to us the vibrations of light though
it is millions of times less dense than the air. As the
particles of bodies are intimately surrounded by " aether,"
the strains of the "aether" are also communicated to
the particles of bodies, and they too suffer a strain.
The glass between the two coatings of tinfoil in the
Leyden jar is actually strained or squeezed between the
attracting charges of electricity. When an insulated
charged ball is hung up in a room an equal amount of
the opposite kind of electricity is attracted to the inside
of the walls, and the air between the ball and the walls
is strained (electrically) like the glass of the Leyden
jar. If a Leyden jar is made of thin glass it may give
way under the stress ; and when a Leyden jar is dis-
charged the layer of air between the knob of the jar and
the knob of the discharging tongs is more and more
strained as they are approached towards one another,
till at last the stress becomes too gi*eat, and the layer of
air gives way, and is " perforated " by the spark that
discharges itself across. The existence of such stresses
enables us to understand the residual charge of Leyden
jars in which the glass does not recover itself ail at once,
by reason of its viscosity, from the strain to which it
has been subjected. This hypothesis, that electric
force acts across space in consequence of the
transmission of stresses and strains in the
medium -with -which space is filled, is now entirely
superseding the old theory of action-at-a-distance, which
was logically unthinkable, and which, moreover, failed to
account for the facts of observation.
62 ELEMENTARY LESSONS ON [CHAP. i.
LESSON VII. Other Sources of Electricity.
57. It was remarked at the close of Lesson I.
(p. 10), that friction was by no means the only source
of electricity. Some of the other sources will now be
named.
58. Percussion. A violent blow struck by one
substance upon another produces opposite electrical
states on the two surfaces. It is possible indeed to
draw up a list resembling that of Art. 5, in such an
order that each substance will take a -f- charge on being
struck with one lower on the list. Erman, who drew up
such a list for a number of metals, remarked that the
order was the same as that of the thermo-electric series
given in Article 381.
59. Vibration. Volpicelli showed that vibrations
set up within a rod of metal coated with sulphur or
other insulating substance, produced a separation of
electricities at the surface separating the metal from the
non-conductor.
60. Disruption and Cleavage. If a card be torn
asunder in the dark, sparks are seen, and the separated
portions, when tested with an electroscope, will be found
to be electrical. The linen faced with paper used in
making strong envelopes and for paper collars, shows
this very well. Lumps of sugar, crunched in the dark
between the teeth, exhibit pale flashes of light. The
sudden cleavage of a sheet of mica also produces sparks,
and both laminae are found to be electrified.
61. Crystallisation and Solidification. Many
substances, after passing from the liquid to the solid state,
exhibit electrical conditions. Sulphur fused in a glass
dish and allowed to cool is violently electrified, as may
be seen by lifting out the crystalline mass with a glass rod.
Chocolate also becomes electrical during solidification.
When arsenic acid crystallises out from its solution in
CHAP, i.] ELECTRICITY AND MAGNETISM. 63
hydrochloric acid, the formation of each crystal is accom-
panied by a flash of light, doubtless due to an electrical
discharge. A curious case occurs when the sulphate of
copper and potassium is fused in a crucible. It solidi-
fies without becoming electrical, but on cooling a little
further the crystalline mass begins to fly to powder with
an instant evolution of electricity.
62. Combustion. Volta showed that combustion
generated electricity. A piece of burning charcoal, or a
burning pastille, such as is used for fumigation, placed in
connection with the knob of a gold-leaf electroscope, will
cause the leaves to diverge.
63. Evaporation. The evaporation of liquids
is often accompanied by electrification, the liquid and
the vapour assuming opposite states. A few drops of a
solution of sulphate of copper thrown into a hot plati-
num crucible produce violent electrification as they
evaporate.
64. Atmospheric Electricity. Closely connected
with the electricity of evaporation is the atmospheric
electricity always present in the air, and due, in part
at least, to evaporation going on over the oceans. The
subject ot atmospheric electricity is treated of sepa-
rately in Lesson XXIV. -
65. Pressure. A large number qf substances when
compressed exhibit electrification on their surface. Thus
cork becomes + when pressed against amber, gutta-
percha, and metals ; while it takes a - charge when
pressed against spars and animal substances. Abbe*
Haiiy found that a crystal of calcspar pressed between
the dry fingers, so as to compress it along the blunt
edges of the crystal, became electrical, and that it re-
tained its electricity for some days. He even proposed
to employ a squeezed suspended crystal as an electro-
scope. A similar property is alleged of mica, topaz,
and fluorspar. Pressure also produces opposite kinds of
electrification at opposite ends of a crystal of tourmaline,
64 ELEMENTARY LESSONS ON [CHAP. I.
and of other crystals mentioned in the next para-
graph.
66. Pyro-electricity. There are certain crystals
which, while being heated or cooled, exhibit electrical
charges at certain regions or poles. Crystals thus
electrified by heating or cooling are said to be pyro-
electric. Chief of these is the Tourmaline, whose
power of attracting light bodies to its ends after being
heated has been known for some centuries. It is alluded
to by Theophrastus and Pliny under the name of Lapis
Lyncurius. The tourmaline is a hard mineral, semi-
transparent when cut into thin slices, and of a dark
green or brown colour, but looking perfectly black and
opaque in its natural condition, and possessing the power
of polarising light. It is usually found in slightly irregu-
lar three-sided prisms which, when perfect, are pointed
at both ends. It belongs to the " hexagonal " system
of crystals, but is only hemihedral, that is to say, has
the alternate faces only developed. Its form is given
in Fig. 35, where a general view is first shown, the two
ends A and B being depicted in separate plans. It will
be noticed that these two ends are slightly different
from each other. Each is made up of three sloping
faces terminating in a point. But at A the edges
between these faces run down to the corners of the
prism, while in B the edges between the terminal faces
run down to the middle points of the long faces of the
prism. The end A is known as the analogous pole,
and B as the antilogous pole. While the crystal is
rising in temperature A exhibits + electrification, B ;
but if, after having been heated, it is allowed to cool,
the polarity is reversed ; for during the time that the
temperature is falling B is + and A is - . If the
temperature is steady no such electrical effects are
observed either at high or low temperatures ; and the
phenomena cease if the crystal be warmed above 150
C. This is not, however, due, as -Gaugain declared, to
CHAP. I.] ELECTRICITY AND MAGNETISM.
the crystal becoming a conductor at that temperature ;
for its resistance at even higher temperatures is still so
great as to make it practically a non-conductor. A
heated crystal of tourmaline suspended by a silk fibre
may be attracted and repelled by electrified bodies, or
by a second heated tourmaline ; the two similar poles
repelling one another, while the two poles of opposite
form attract one another. If a crystal be broken up,
each fragment is found to possess also an analogous and
an antilogous pole.
67. Many other crystals beside the tourmaline are
more or less pyro-electric. Amongst these are silicate of
112
Fig- 35-
zinc (" electric calamine "), boracite, cane-sugar, quartz,
tartrate of potash, sulphate of quinine, and several others.
Boracite crystallises in the form shown in Fig. 36, which
represents a cube having four alternate corners trun-
cated. The corners not truncated behave as analogous
poles, the truncated ones as antilogous. This peculiar
skew- symmetry or hemihedry is exhibited by all the
crystals enumerated above, and is doubtless due to the
same molecular peculiarity which determines their sin-
gular electric property, and which also, in many cases,
determines the optical behaviour of the crystal in
polarised light.
F
66
ELEMENTARY LESSONS ON [CHAP. i.
68. Animal Electricity. Several species of crea-
tures inhabiting the water have the power of producing
electric discharges by certain portions of their organism.
The best known of these are the Torpedo, the Gym-
notus, and the Silurus^ found in the Nile and the
Niger. The Raia Torpedo, 1 or electric ray, of which
there are three species in-
habiting the Mediterranean
and Atlantic, is provided with
an electric organ on the back
of its head, as shown in Fig.
37. This organ consists of
laminae composed of polygonal
cells to the number of 800 or
1000, or more, supplied with
four large bundles of nerve
fibres ; the under surface of
the fish is , the upper + .
I n the Gymnotus electricus,
or Surinam eel (Fig. 38), the
electric organ goes the whole
length of the body along both
sides. It is able to give a
most terrible shock, and is a
formidable antagonist when it
has attained its full length of
5 or 6 feet. Humboldt gives
a lively account of the combats
between the electric eels and
the wild horses, driven by the
natives into the swamps in-
habited by the Gymnotus.
Nobili, Matteucci, and others, have shown that nerve-
1 It is a curious point that the Arabian name for the torpedo, ra-ad,
: signifies lightning. This is perhaps not so curious as that the Electro, of
'the Homeric legends should possess certain qualities that would tend to
suggest that she is a personification of the lightning. The resemblance
.between the names electra and electron (amber) cannot be accidental.
CHAP. i.J ELECTRICITY AND MAGNETISM. 67
excitations and muscular contractions of human beings
also give rise to feeble discharges of electricity.
Fig. 38.
69. Electricity of Vegetables. Buff thought he
detected electrification produced by plant life ; the roots
and juicy parts being negatively, and the leaves posi-
tively, electrified. The subject has, however, been little
investigated.
70. Thermo-electricity. Heat applied at the
junction of two dissimilar metals produces a flow oi
electricity across the junction. This subject is discussed
in Lesson XXXIV. on Ther?no-electric Currents.
71. Contact of dissimilar Metals. Volta showed
that the contact of two dissimilar metals produced
opposite kinds of electricity on the two surfaces, one
becoming positively, and the other negatively, electrified.
This he proved in several ways, one of the most con-
clusive proofs being that afforded by his condensing
electroscope. This consisted of a gold-leaf elec-
troscope combined with a small condenser. A metallic
plate formed the top of the electroscope, and on this
was placed a second metallic plate furnished with a
handle, and insulated from the lower one by being well
varnished at the surface (Fig. 68). As the capacity of
such a condenser is considerable, a very feeble source
may supply a quantity of electricity to the condenser with-
out materially raising its potential, or causing the gold
leaves to diverge. But if the upper plate be lifted, the
capacity of the lower plate diminishes enormously, and
68 ELEMENTARY LESSONS ON [CHAP. I.
the potential of its charge rises as shown by the diverg-
ence of the gold leaves. To prove by the condensing
electroscope that contact of dissimilar metals does
produce electrification, a small compound bar made of
two dissimilar metals say zinc and copper soldered
together, is held in the hand, and one end of it is touched
against the lower plate, the upper plate being placed in
contact with the ground or touched with the finger.
When the two opposing charges have thus collected in
the condenser the upper plate is removed, and the
diverging of the gold leaves shows the presence of a
free charge, which can afterwards be examined to see
whether it be + or . For a long time the existence
of this electricity of contact was denied, or rather it was
declared to be due (when occurring in voltaic combina-
tions such as are described in Lesson XIII.) to chemical
actions going on ; whereas the real truth is that the
electricity of contact and the chemical action are both
due to molecular conditions of the substances which
come into contact with one another, though we do not
yet know the precise nature of the molecular conditions
which give rise to these two effects. Later experiments,
especially those made with the delicate electrometers of
Sir W. Thomson (Fig. 101), put beyond doubt the reality
of Volta's discovery. One simple experiment explains the
method adopted. A thin strip or
needle of metal is suspended so as
to turn about a point C. It is elec-
trified from a known source. Under
it are placed (Fig. 39) two semicir-
cular discs, or half-rings of dissimilar
metals. Neither attracts or repels
the electrified needle until the two are
brought into contact, or connected by
a third piece of metal, when the needle immediately turns,
being attracted by the one that is oppositely electrified, and
repelled by the one that is similarly electrified with itself.
CHAP. I.j ELECTRICITY AND MAGNETISM. 69
72. Volta found, moreover, that the differences of
electric potential between the different pairs of metals
were not all equal. Thus, while zinc and lead were
respectively + and to a slight degree, he found zinc
and silver to be respectively + and to a much greater
degree. He was able to arrange the metals in a series
such that each one enumerated became positively elec-
trified when placed in contact with one below it in the
series. Those in italics are added from observations
made since Volta's time
CONTACT SERIES OF METALS (IN AIR).
+ Sodium.
Magnesium.
Zinc.
Lead.
Tin.
Iron.
Copper.
Silver.
Gold.
Platinum.
- Graphite (Carbon).
Though Volta gave rough approximations, the actual
numerical values of the differences of potential for
different pairs of metals have only lately been measured
by Ayrton and Perry, a few of whose results are tabu-
lated here
Difference of Potential
(in volts).
Zinc
Lead
} . . . -069
Tin
Iron
313
70 ELEMENTARY LESSONS ON [CHAP. I.
Difference of Potential
(in volts).
Iron > -146
Platinum
Carbon [ * ' ' II3
The difference of potential between zinc and carbon is
the same as that obtained by adding the successive
differences, or 1-09 volts. 1 Volta's observations may
therefore be stated in the following generalised form,
known as Volta's Law. The difference of potential
between any two metals is equal to the sum of the differ-
ences of potentials between the intervening metals in the
contact-series.
73. A difference of potential is also produced by the
contact of two dissimilar liquids with one another.
A liquid and a metal in contact with one another
also exhibit a difference of potential.
A hot metal placed in contact with a cold piece of
the same metal also produces a difference of potential,
electrical separation taking place across the surface of
contact.
Lastly, it has been shown by Joseph Thomson that the
surface of contact between two non-conducting substances,
such as sealing-wax and glass, is the seat of a difference
of potentials.
74. Magneto-electricity. Electricity, in the form
of currents flowing along in wires, can be obtained from
magnets by moving closed conducting circuits in their
neighbourhood. As this source of electricity yields
currents rather than statical charges of electricity, the
account of it is deferred to Lesson XXXVI.
75. Summary. We have seen in the preceding
paragraphs how almost all conceivable agencies may
1 For the definition of the volt, or unit of difference of potential, see Art
323-
CHAP, i.] ELECTRICITY AND MAGNETISM. 71
produce electrification in bodies. The most important
of these are friction, heat, chemical action, magnetism,
and the contact of dissimilar substances. We noted
that the production of electricity by friction depended
largely upon the molecular condition of the surfaces.
We may here add that the difference of potentials pro-
duced by contact of dissimilar substances also varies
with the temperature and with the nature of the medium
(air, vacuum, etc.) in which the experiments are made.
Doubtless this source also depends upon the molecular
conditions of dissimilar substances being different ; the
particles at the surfaces being of different sizes and
shapes, and vibrating with different velocities and with
different forces. There are (see Art. 10) good reasons
for thinking that the electricity of friction is really due
to electricity of contact, excited at successive portions of
the surfaces as they are moved over one another. But
of the molecular conditions of bodies which determine
the production of electricity where they come into con-
tact, little or nothing is yet known.
It is most important to notice that the order of the metals
in the contact series in air is almost identical with that of the
metals arranged according to their electro-chemical power, as
calculated from their chemical equivalents and their heat of
combination with oxygen (see Table, Art. 422 (bis]. From
this it would appear that the difference of potentials between
a metal and the air that surrounds it measures the tendency of
that metal to become oxidised by the air. If this is so, and if
(as is the case) the air is a bad conductor while the metals are
good conductors, it ought to follow that when two different
metals touch they equalise their own potentials by conduction
but leave the films of air that surround them at different
potentials. All the exact experiments yet made have measured
the difference of potentials not between the metals themselves,
but between the air near one metal and that near another
metal.
72 ELEMENTARY LESSONS ON [CHAP. n.
CHAPTER II.
MAGNETISM.
LESSON VIII. Magnetic Attraction and Repulsion.
76. Natural Magnets or Lodestones. The
name Magnet (Magnes Lapis) was given by the
ancients to certain hard black stones found in various
parts of the world, notably at Magnesia in Asia Minor,
which possessed the property of attracting to them small
pieces of iron or steel. This magic property, as they
deemed it, made the magnet-stone famous ; but it was
not until the tenth or twelfth century that such stones
were discovered to have the still more remarkable pro-
perty of pointing north and south when hung up by
a thread. This property was turned to advantage in
navigation, and from that time the magnet received the
name of Lodestone 1 (or "leading- stone"). The
natural magnet or lodestone is an ore of iron, known to
mineralogists as magnetite and having the chemical
composition Fe 3 O 4 . This ore is found in quantities in
Sweden, Spain, Arkansas, the Isle of Elba, and other
parts of the world, though not always in the magnetic
condition. It frequently occurs in crystals ; the usual
form being the regular octahedron.
77. Artificial Magnets. If a piece of iron, or,
better still, a piece of hard steel, be rubbed with a lode-
stone, it will be found to have also acquired the properties
characteristic of the magnet ; it will attract light bits of
1 The common spelling /mrfstone is due to misapprehension.
CHAP. XL] ELECTRICITY AND MAGNETISM.
73
iron, and, if hung up by a thread it will point north
and south. Figures
40 and 41 represent
a natural lodestone
and an artificial
magnet of steel, each
of which has been
dipped into iron-
filings ; the filings
are attracted and
11 r Fiers. 40 and 41.
adhere in tufts.
78. Discoveries of Dr. Gilbert. This was all, or
nearly all, that was known of the magnet until 1600,
when Dr. Gilbert published a large number of magnetic
discoveries in his famous work " De Magnete" He
observed that the attractive power of a magnet appears
to reside at two regions, and in a long-shaped magnet
these regions, or poles, are usually at the ends (see Figs.
40 and 41). The portion of the magnet which lies be-
tween the two poles is apparently less magnetic, and
does not attract iron-filings so strongly ; and all round
the magnet, halfway between the poles, there is no
attraction at all. This region Gilbert called the equator
of the magnet, and the imaginary line joining the poles
he termed the axis.
79. Magnetic Needle. To investigate more fully
the magnetic forces a magnetic needle is employed.
This consists (Fig. 42) of a light needle cut out of steel,
and fitted with a little cap of brass, glass, or agate, by
means of which it can be hung upon a sharp point, so
as to turn with very little friction. It is made into a
magnet by being rubbed upon a magnet ; and when
thus magnetised will turn into the north -and -south
position, or, as we should say, will set itself in the
" magnetic meridian" (Art. 136). The compass sold
by opticians consists of such a needle balanced above a
card marked with the " points of the compass. "
74
ELEMENTARY LESSONS ON [CHAP. n.
SO. Magnetic Attractions and Repulsions.
If we take a magnet
(either natural or
artificial) in our hand
and present the two
" poles " of it succes-
sively to the north-
pointing end of a
magnetic needle, we
shall observe that
one pole of the mag-
net attracts it, while
the other repels it.
(Fig. 43.) If we
repeat the experi-
ment on the south-
pointing end of the
magnetic needle, we
shall find that it is
repelled by one pole
and attracted by
the other ; and that the same pole which attracts the
north-pointing end
of the needle re-
pels the south-
pointing end.
If we try a simi-
lar experiment on
the magnetic
needle, using for
a magnet a second
magnetised needle
which has previ-
ously been sus-
pended, and which has its north-pointing end marked
to distinguish it fiom the south-pointing end, we shall
discover that the N. -pointing pole repels the N. -pointing
Fig. 43-
CHAP, ii.] ELECTRICITY AND MAGNETISM. 75
pole, and that the S. -pointing pole repels the S. -pointing
pole ; but that a N.-pointing pole attracts and is attracted
by a S.-pointing pole.
81. Two kinds of Magnetic Poles. There would
therefore appear to be two opposite kinds of magnetism,
or at any rate two opposite kinds of magnetic poles,
which attract or repel one another in very much the
same fashion as the two opposite kinds of electricity do ;
and one of these kinds of magnetism appears to have a
tendency to move toward the north and the other to
move toward the south. It has been proposed to call
these two kinds of magnetism "north-seeking magnet-
ism " and " south-seeking magnetism," but for our pur-
pose it is sufficient to distinguish between the two kinds
of poles. In common parlance the poles of a magnet
are called the " North Pole " and " South Pole " respect-
ively, and it is usual for the makers of magnets to mark
the N.-pointing pole with a letter N. It is therefore
sometimes called the " marked " pole, to distinguish it
from the S.-pointing or " unmarked " pole. We shall, to
avoid any doubt, 1 call that pole of a magnet which
would, if the magnet were suspended, tend to turn to the
1 It is necessary to be precise on this point, as there is some confusion in
the existing text-books. The cause of the confusion is this : If the north-
pointing pole of a needle is attracted^ magnetism residing near the North
Pole of the earth, the law of attraction (that unlike poles attract), shows us
that these two poles are really magnetically of opposite kinds. Which are
we then to call north magnetism? That which is at the N. pole of the earth?
If so, we must say that the N.-pointing pole of the needle contains south
magnetism. And if we call that north magnetism which points to the north,
then we must suppose the magnetic pole at the north pole of the earth to have
south magnetism in it. In either case there is then a difficulty. The Chinese
and the French call the N.-pointing pole of the needle a south pole, and the
S.-pointing pole a north pole. Sir Wm. Thomson also calls the N.-pointing
pole a "True South" pole. But common practice goes the other way, and
calls the N.-pointing pole of a magnet its " North" pole. For experimental
purposes it is usual to paint the two poles of a magnet of different colours,
the N. -seeking pole being coloured red and the S. -seeking pole blue; but
here again, strangely enough, authorities differ, for in the collections of
apparatus at the Royal Institution and Royal School of Mines, the colours
are used in exactly the opposite way to this, which is due to Sir G. Airy.
76 ELEMENTARY LESSONS ON [CHAP. n.
north, the " North -seeking " pole, and the other the
" South-seeking " pole.
We may therefore sum up our observations in the
concise statement : Like magnetic poles repel one another;
unlike poles attract one another. This we may call the
first law of magnetism.
82. The two Poles inseparable. It is impossible
to obtain a magnet with only one pole. If we magnetise
a piece of steel wire, or watch spring, by rubbing it with
one pole of a magnet, we shall find that still it has two
poles one N.-seeking, the other S. -seeking. And if we
break it into two parts, each part will still have two
poles of opposite kinds.
83. Magnetic Force. The force with which a
magnet attracts or repels another magnet, or any piece
of iron or steel, we shall call magnetic forced The
force exerted by a magnet upon a bit of iron or on another
magnet is not the same at all distances, the force being
greater when the magnet is nearer, and less when the
magnet is farther off. In fact the attraction due to a
magnet-pole falls off inversely as the square of the
distance from the pole. (See Art. 117.)
Whenever a force acts thus between two bodies, it acts
on both of them, tending to move both. A magnet will
attract a piece of iron, and a piece of iron will attract a
magnet. This was shown by
Sir Isaac Newton, who fixed a
magnet upon a piece of cork and
floated it in a basin of water
(Fig. 44), and found that it moved
across the basin when a piece of
Flg> 44< iron was held near. A compass
needle thus floated turns round and points north and
south ; but it does not rush towards the north as a
whole, nor towards the south. The reason of this will
be explained later, in Art. 117.
1 See footnote on " Force," Art. 155.
CHAP, ii.] ELECTRICITY AND MAGNETISM. 77
Gilbert suggested that the force of a magnet might be
measured by making it attract a piece of iron hung to
one arm of a balance, weights being placed in the scale-
pan hanging to the other arm ; and he found, by hang-
ing the magnet to the balance and placing the iron
beneath it, that the effect produced was the same. The
action and reaction are then equal for magnetic forces.
84. Attraction across bodies. If a sheet of
glass, or wood, or paper, be interposed between a magnet
and the piece of iron or steel it is attracting, it will still
attract it as if nothing were interposed. A magnet
sealed up in a glass tube still acts as a magnet. Lucre-
tius found a magnet put into a brass vase attracted iron
filings through the brass. Gilbert surrounded a magnet
by a ring of flames, and found it still to be subject to
magnetic attraction from without. Across water, vacuum,
and all known substances, the magnetic forces will act ;
with the single exception, however, that magnetic force
will not act across a screen of iron or other magnetic
material. If a small magnet is suspended inside a
hollow ball made of iron, no outside magnet will affect it.
A hollow shell of iron will therefore act as a magnetic
cage, and screen the space inside it from magnetic
influences.
85. Magnetic Substances. A distinction was
drawn by Gilbert between magnets and magnetic
substances. A magnet attracts only at its poles, and
they possess opposite properties. But a lump of iron
will attract either pole of the magnet, no matter what
part of the lump be presented to the magnet. It has no
distinguishable fixed "poles," and no magnetic "equator."
A true magnet has poles, one of which is repelled by the
pole of another magnet.
86. Other Magnetic Metals. Later experimenters
have extended the list of substances which are attracted
by a magnet. In addition to iron (and steel) the follow-
ing metals are recognised as magnetic :
78 ELEMENTARY LESSONS ON [CHAP, n
Nickel. Chromium.
Cobalt. Cerium.
Manganese,
and a few others. But only nickel and cobalt are at all
comparable with iron and steel in magnetic power, and
even they are very far inferior. Other bodies, sundry salts
of iron and other metals, paper, porcelain, and oxygen
gas, are also very feebly attracted by a powerful magnet.
87. Diamagnetism. A number of bodies, notably
bismuth, antimony, phosphorus, and copper, are repelled
from the poles of a magnet. Such bodies are called
diamagnetic bodies; a fuller account of them will be
found in Lesson XXVIII.
88. The Earth a Magnet. The greatest of
Gilbert's discoveries was that of the inherent magnetism
of the earth. The earth is itself a great magnet,
whose " poles " coincide nearly, but not quite, with the
geographical north and south poles, and therefore it causes
a freely-suspended magnet to turn into a north and south
position. The subject of Terrestrial Magnetism is
treated of in Lesson XII. It is evident from the first
law of magnetism that the magnetic condition of the
northern regions of the earth must be the opposite to
that of the north-seeking pole of a magnetised needle.
Hence arises the difficulty alluded to on page 75.
89. Magnetic Induction. Magnetism may be
communicated to a piece of iron, without actual contact
with a magnet. If a short, thin unmagnetised bar of
iron, be placed near some iron filings, arid a magnet be
brought near to the bar, the presence of the magnet
will induce magnetism in the iron bar, and it will now
attract the iron filings (Fig. 45). This inductive action
is very similar to that observed in Lesson III. to take
place when an electrified body was brought near a non-
electrified one. The analogy, indeed, goes farther than
this, for it is found that the iron bar thus magnetised by
induction will haye two poles ; the pole nearest to the
CHAP, ii.] ELECTRICITY AND MAGNETISM. 79
pole of the inducing magnet being of the opposite kind,
while the pole at the farther end of the bar is of the
same kind as the inducing pole. Magnetism can, how-
ever, only be induced in those bodies which we have
enumerated -as magnetic bodies ; and those bodies in
which a magnetising force produces a high degree of
magnetisation are said to possess a high co- efficient
of magnetisation. It will be shown presently that
magnetic induction takes place along certain direc-
tions called lines of magnetic induction, or lines of
magnetic force, which may pass either through iron
and other magnetic media, or through air, vacuum,
glass, or other non-magnetic media : and, since induction
goes on most freely in bodies of high magnetic suscepti-
bility, those lines of force are sometimes (though not
too accurately) said to " pass by preference through
magnetic matter," or, that "magnetic matter conducts
the lines of force."
Although magnetic induction takes place at a distance
across an intervening layer of air, glass, or vacuum,
there is no doubt that the intervening medium is directly
concerned in the transmission of the magnetic force,
though probably the true medium is the "aether" of
space surrounding the molecules of matter, not the
molecules themselves.
8o ELEMENTARY LESSONS ON [CHAP. n.
We now can see why a magnet should attract a not-
previously-magnetised piece of iron ; it first magnetises
it by induction and then attracts it : for the nearest end
will have the opposite kind of magnetism induced in it,
and will be attracted with a force exceeding that with
which the more distant end is repelled. But induction
precedes attraction.
9O. Retention of Magnetisation. Not all mag-
netic substances can become magnets permanently.
Lodestone, steel, and nickel, retain permanently the
greater part of the magnetism imparted to them. Cast
iron and many impure qualities of wrought iron also
retain magnetism imperfectly.
Pure soft iron is, however, only
temporarily magnetic. The
following experiment illustrates
the matter : Let a few pieces
of iron rod, or a few soft iron
nails be taken. If one of these
(see Fig. 46) be placed in con-
tact with the pole of a perma-
nent steel magnet, it is attracted
to it, and becomes itself a tem-
porary magnet. Another bit of
iron may then be hung to it, and another, until a chain
of four or five pieces is built up. But if the steel
magnet be removed from the top of the chain, all the
rest drop off, and are found to be no longer magnetic.
A similar chain of steel needles may be formed, but
they will retain their magnetism permanently.
It will be found, however, that a steel needle is more
difficult to magnetise than an iron needle of the same
dimensions. It is harder to get the magnetism into
steel than into iron, and it is harder to get the magnetism
out of steel than out of iron ; for the steel retains the
magnetism once put into it. This power of resisting
magnetisation or demagnetisation, is sometimes called
CHAP, ii.] ELECTRICITY AND MAGNETISM. 81
coercive force; a much better term, due to Lament,
is retentivity. The retentivity of hard-tempered steel
is great ; that of soft wrought iron is very small. The
harder the steel, the greater its retentivity.
91. Theories of Magnetism. The student will
not have failed to observe the striking analogies between
the phenomena of attraction, repulsion, induction, etc.,
of magnetism and those of electricity. Yet the two sets
of phenomena are quite distinct. A positively electrified
body does not attract either the North -pointing or the
South -pointing pole of .the magnet as such; in fact, it
attracts either pole quite irrespective of its magnetism,
just as it will attract any other body. There does
exist, indeed, a direct relation between magnets and
currents of electricity, as will be later explained. There
is none known, however, between magnets and stationary
charges of electricity.
No theory as to the nature of magnetism has yet
been placed before the reader, who has thus been told
the fundamental facts without bias. In many treatises
it is the fashion to speak of a magnetic fluid or fluids ;
it is, however, absolutely certain that magnetism is not
a fluid, whatever else it may be. The term, which is a
relic of bygone times, is only tolerated because, under
certain circumstances, magnetism distributes itself in
magnetic bodies in the same manner as an elastic
fluid would do. Yet the reasons against its being a
fluid are even more conclusive than in the case of
electricity. An electrified body when touched against
another conductor, electrifies the conductor by giving
up a part of its electricity to it. But a magnet when
rubbed upon a piece of steel magnetises it 'without
giving up or losing any of its own magnetism. A fluid
cannot possibly propagate itself indefinitely without loss.
The arguments to be derived from the behaviour of
a magnet on breaking, and from other experiments
narrated in Lesson X., are even stronger. No theory
G
82 ELEMENTARY LESSONS ON [CHAP. n.
of magnetism will therefore be propounded until these
facts have been placed before the student.
LESSON IX. Methods of Making Magnets.
92. Magnetisation by Single Touch. It has
been so far assumed that bars or needles of steel were
to be magnetised by simply touching them, or stroking
them from end to end with the pole of a permanent magnet
of lodestone or steel. In this case the last touched point
of the bar will be a pole of opposite kind to that used
to touch it ; and a more certain effect is produced if one
pole of the magnet be rubbed on one end of the steel
needle, and the other pole upon the other end. There
are, however, better ways of magnetising a bar or needle.
93. Magnetisation by Divided Touch. In this
method the bar to be magnetised is laid down hori-
zontally ; two bar magnets are then placed down upon it,
their opposite poles being together. They are then
drawn asunder from the middle of the bar towards its
B"\
Fig- 47-
ends, and back, several times. The bar is then turned
over, and the operation repeated, taking care to leave off
at the middle (see Fig. 47). The process is more
effectual if the ends of the bar are meantime supported
on the poles of other bar magnets, the poles being of
the same names as those of the two magnets above
them used for stroking the steel bar.
94. Magnetisation by Double Touch. Another
CHAP, ii.] ELECTRICITY AND MAGNETISM. 83
method, known as double touch, differs slightly from
that last described. A piece of wood or cork is inter-
posed between the ends of the two bar magnets employed,
and they are then both moved backwards and forwards
along the bar that is to be magnetised. By none of
these methods, however, can a steel bar be magnetised
beyond a certain degree of intensity.
95. Laminated Magnets. It is found that long
thin steel magnets are more powerful in proportion to
their weight than thicker ones. Hence it was proposed
by Scoresby L to construct compound magnets, consisting
of thin laminae of steel separately magnetised, and after-
wards bound together in bundles. These laminated
magnets are more powerful than simple bars of steel.
96. Magnetisation derived from the Earth.
The magnetism of the earth may be utilised, where no
other permanent magnet is available, to magnetise a bar /
of steel. Gilbert states that iron bars set upright for
a long time, acquire magnetism from the earth. If a
steel poker be held in the magnetic meridian, with the
north end dipping down, and in this position be struck
with a wooden mallet, it will be found to have acquired
magnetic properties. Wires of steel subjected to torsion,
while in the magnetic meridian, are also found to be
thereby magnetised.
97. Magnetisation after Heating. Gilbert dis-
covered also that if a bar of steel be heated to redness,
and cooled, either slowly or suddenly, while lying in the
magnetic meridian, it acquires magnetic polarity. No
such property is acquired if it is cooled while lying east-
and-west. It has been proposed to make powerful
magnets by placing hot bars of steel to cool between the
poles of very powerful electro-magnets ; and Carre' has
recently produced strong magnets of iron cast in moulds
lying in an intense magnetic field.
1 A similar suggestion was made by Geuns of Venlo in 1768. Similar
magnets have been constructed recently by Jamin.
84 ELEMENTARY LESSONS ON [CHAP, n,
98. Magnetisation by Currents of Electricity.
A strong current of electricity carried in a spiral wire
around a bar of iron or steel, magnetises it more power-
fully than in any of the preceding operations. In the
case of a soft iron bar, it is only a magnet while the
current continues to flow. Such a combination is
termed an. Electro-magnet ; it is fully described in
Lesson XXVI. Elias of Haarlem proposed to mag-
netise steel bars by passing them through a wire coiled
up into a ring of many turns, through which a strong
current was sent by a voltaic battery. Tommasi claims
to have magnetised steel bars by passing a current of
hot steam round them in a spiral tube : but the matter
needs further evidence.
99. Destruction of Magnetism. A steel magnet
loses its magnetism partially or wholly if subjected to
rough usage, or if purposely hit or knocked about. It
also loses its magnetism, as Gilbert showed, on being
raised to a red-heat.
100. Effects of Heat on Magnetisation. If a
permanent steel magnet be warmed by placing it in hot
or boiling water, its strength will be thereby lessened,
though it recovers partially on cooling Chilling a
magnet increases its strength. Cast iron ceases to
be attracted by a magnet at a bright red-heat, or at a
temperature of about 700 C. Cobalt retains its mag-
netism at the highest temperatures. Chromium ceases
to be magnetic at about 500 C, and Nickel at 350
C. Manganese exhibits magnetic attraction only when
cooled to 20 C. It has therefore been surmised that
other metals would also become magnetic if cooled to a
low enough temperature ; but a very severe cooling to
1 00 below zero destroys the magnetism of steel magnets,
The magnetic metals at high temperatures do not be-
come diamagnetic, but are still feebly magnetic.
101. Forms of Magnets. Natural Magnets are
usually of irregular form, though they are sometimes
CHAP, ii.] ELECTRICITY AND MAGNETISM. 85
reduced to regular shapes by cutting or grinding.
Formerly it was the fashion to mount them with soft iron
cheeks or " armatures " to serve as pole-pieces.
For scientific experiments bar -magnets of hardened
steel are commonly used ; but for many purposes the
horse-shoe shape is preferred. In the horse-shoe magnet
the poles are bent round so as to approach one another,
the advantage here being that so both poles can attract
one piece of iron. The " armature," or " keeper," as
the piece of soft iron placed across the poles is named, is
itself rendered a magnet by induction when placed across
the poles ; hence, when both poles magnetise it, the force
with which it is attracted to the magnet is the greater.
1O2. Magnetic Saturation. A magnet to which
as powerful a degree of magnetisation as it can attain to
has been given is said to be "saturated." Many of
the methods of magnetisation described will excite in a
magnet a higher degree of magnetism than it is able to
retain permanently. A recently magnetised magnet will
occasionally appear to be supersaturated, even after
the application of the magnetising force has ceased.
Thus a horse-shoe-shaped steel magnet will support a
greater weight immediately after being magnetised than
it will do after its armature has been once removed from
its poles. Even soft iron after being magnetised retains
a small amount of magnetism when its temporary mag-
netism has disappeared. This small remaining magnetic
charge is spoken of as residual magnetism.
Strength of a Magnet. The "strength" of a
magnet is not the same thing as its " lifting-power." The
" strength " of a magnet is the " strength " of its poles.
The " strength " of a magnet pole must be measured by
the magnetic force which it exerts. Thus, suppose there
are two magnets, A and B, whose strengths we compare
by making them each act upon the N. pole of a third
magnet C. If the N. pole of A repels C with twice as
much force as that with which the N. pole of B placed
86 ELEMENTARY LESSONS ON [CHAP, n,
at the same distance would repel C, then we should say
that the " strength " of A was twice that of B. Another
way of putting the matter is to say that the " strength "
of a pole is the amount of free magnetism at that pole.
By adopting the unit of strength of magnet poles as
defined in Art. 125, we can express the strength of any
pole in numbers as so many " units " of strength.
1O3. Lifting Power. The lifting power of a magnet
(also called its "portative force ") depends both upon
the form of the magnet and on its magnetic strength. A
horse-shoe magnet will lift a load three or four times as
great as a bar magnet of the same weight will lift. The
lifting power is greater if the area of contact between the
poles and the armature is increased. Also the lifting
power of a magnet grows in a very curious and unex-
plained way by gradually increasing the load on its
armature day by day until it bears a load which at the
outset it could not have done. Nevertheless, if the load
is so increased that the armature is torn off, the power
of the magnet falls at once to its original value. The
attraction between a powerful electro-magnet and its
armature may amount to 200 Ibs. per square inch, or
14,000 grammes per square centimetre. Small magnets-
lift a greater load in proportion to their own weight than
large ones. 1 A good steel horse-shoe magnet weighing
itself one pound ought to lift twenty pounds' weight.
Sir Isaac Newton is said to have possessed a little lode-
stone mounted in a signet ring which would lift a piece
of iron 200 times its own weight.
1 Bernoulli! gave the following rule for finding the lifting-power p of a
magnet whose weight was -w :
where a is a constant depending on the goodness of the steel and the method
of magnetising it. In the best steel magnets made at Haarlem by V.
Wetteren this coefficient was from 19-5 to 23. In Breguet's magnets, made
from Allevard steel, the value is equally high.
CHAP, ii.] ELECTRICITY AND MAGNETISM. 87
LESSON X. Distribution of Magnetism.
104. Normal Distribution. In an ordinary bar
magnet the poles are not quite at the ends of the bar,
but a little way from it ; and it can be shown that this is
a result of the way in which the magnetism is distributed
in the bar. A very long, thin, uniformly magnetised bar
has its poles at the ends ; but in ordinary thick magnets
the " pole " occupies a considerable region, the " free
magnetism " falling off gradually from the ends of the
bar. In each region, however, a point can be determined
at which the resultant magnetic forces act, and which
may for most purposes be considered as the pole. In
certain cases of irregular magnetisation it is possible to
have one or more poles between those at the ends.
Such poles are called consequent poles (see Fig. 51).
105. Magnetic Field. The space all round a
magnet pervaded by the magnetic forces is termed the
"field" of that magnet. It is most intense near the pole
of the magnet, and is weaker and weaker at greater dis-
tances away from it. At every point in a magnetic field
the force has a particular strength, and the magnetic
induction acts in a particular direction or line. In the
horse-shoe magnet the field is most intense between the
two poles, and the lines of magnetic induction are curves
which pass from one pole to the other across the field.
A practical way of investigating the distribution of the
lines of induction in a field is given in Art. 108, under the
title " Magnetic Figures." When the armature is placed
upon the poles of a horse-shoe magnet, the force of the
magnet on all the external regions is weakened, for the
induction now goes on through the iron of the keeper,
not through the surrounding space. In fact a closed
system of magnets such as that made by placing four
bar magnets along the sides of a square, the N. pole of
one touching the S. pole of the next has no external
field of force. A ring of steel may thus be magnetised
88
ELEMENTARY LESSONS ON [CHAP. n.
so as to have neither external field nor poles ; or rather
any point in it may be regarded as a N. pole and a S.
pole, so close together that they neutralise one another's
forces.
That poles of opposite name do neutralise one another
may be shown by the well-known experiment of hanging
a small object a steel ring or a key to the N. pole of
a bar magnet. If now the S. pole of another bar magnet
be made to touch the first the two poles will neutralise
each other's actions, and the ring or key will drop down.
1O6. Breaking 1 a Magnet. We have already stated
that when a magnet is broken into two or more parts, each
is a complete magnet, possessing poles, and each is
nearly as strongly magnetised as the original magnet.
Fig. 48 shows this. If the broken parts be closely joined
Fig. 48.
these adjacent poles neutralise one another and disappear,
leaving only the poles at the ends as before. If a magnet
be ground to powder each fragment will still act as a
little magnet and exhibit polarity. A magnet may there-
fore be regarded as composed of many little magnets
N
S'N'
n s
n ,s
n s
n .s
n s
n .s
n .s
n s
n s
n s
n s
n s
n ,s
n .s
n s
n s
n s
n s
n s
n $
n s
n s
n s
n s
n .v
n .s
n s
n .s
#- ,s
n s
?l S
n ,
N SN' S
Fig. 49-
put together, so that their like poles all face one way.
Such an arrangement is indicated in Fig. 49, from which
it will be seen that if the magnet be broken asunder across
any part, one face of the fracture will present only N.
CHAP, ii.] ELECTRICITY AND MAGNETISM. 89
poles, the other only S. poles. This would be true no
matter how small the individual particles.
If the ^intrinsic magnetisation^ of the steel at every
part of a magnet were equal, the free poles would be
found only at the ends ; but the fact that the free mag-
netism is not at the ends merely, but diminishes from
the ends towards the middle, shows that the intensity of
the intrinsic magnetisation must be less towards and at
the ends than it is at the middle of the bar.
107. Lamellar Distribution of Magnetism.
Magnetic Shells. Up to this point the ordinary
distribution of magnetism along a bar has been the only
distribution considered. But it is possible to have
magnetism distributed over a thin sheet so that the
whole of one face of the sheet shall have one kind of
magnetism, and the other face the other kind of magnet-
ism. If an immense number of little magnets were
placed together side by side, like the cells in a honey
comb, all with their N. -seeking ends upwards, and S.-
seeking ends downwards, the whole of one face of the
slab would be one large flat N. -seeking pole, and the
other face S.-seeking. Such a distribution as this over a
surface or sheet is termed a lamellar distribution, to
distinguish it from the ordinary distribution along a line
or bar, which is termed, for distinction, the solenoidal
distribution. A lamellarly magnetised magnet is some-
times spoken of as a magnetic shell. The properties
of magnetic shells are extremely important on account of
their analogy with those of closed voltaic circuits.
108. Magnetic Figures. Gilbert showed 1 that if
a sheet of paper or card be placed over a magnet, and
iron-filings are dusted over the paper, they settle down
in curving lines, forming a magnetic figure ', the general
form of which is shown in Fig. 50. The filings should
be fine, and sifted through a bit of muslin ; to facilitate
their settling in the lines, the sheet of paper should be
1 The magnetic figures were known to Lucretius.
90
ELEMENTARY LESSONS ON [CHAP. n.
lightly tapped. The figures thus obtained can be fixed
permanently by several processes. The best of these
consists in employing a sheet of glass which has been
previously gummed and dried, instead of the sheet of
paper ; after this has been placed above the magnet the
filings are sifted evenly over the surface, and then the
glass is tapped ; then a jet of steam is caused to play
gently above the sheet, softening the surface of the gum,
which, as it hardens, fixes the filings in their places. In-
spection of the figure will show that the lines diverge
nearly radially from each pole, and curve round to meet
these from the opposite pole. Faraday, who made a
great use of this method of investigating the distribution
of magnetism in various " fields," gave to the lines the
name of lines of force. They represent, as shown
by the action on little magnetic particles which set them-
selves thus in obedience to the attractions and repulsions
CHAP. IT.] ELECTRICITY AND MAGNETISM. 91
in the field, the resultant direction of the forces at every
point ; for each particle tends to assume the direction of
the magnetic induction due to the simultaneous action of
both poles ; hence they may be taken to represent the
lines of magnetic induction.^- Faraday pointed out
that these " lines of force " map out the magnetic field,
showing by their position the direction of the magnetic
force, and by their number its intensity. If a small N.-
seeking pole could be obtained alone, and put down on
any one of these lines of force, it would tend to move
along that line from N. to S. ; a single S. -seeking pole
would tend to move along the line in an opposite direc-
tion. Faraday also assigned to these lines of force
certain physical properties (which are, however, only
true of them in a secondary sense), viz., that they tend
to shorten themselves from end to end, and that they
repel one another as they lie side by side. The modern
view, which holds that magnetism results from certain
properties of the "aether" of space, is content to say
that in every magnetic field there are certain stresses,
which produce a tension along the lines of force, and a
pressure across them.
109. This method may be applied to ascertain the
presence of " consequent poles " in a bar of steel, the
figure obtained resembling that depicted in Fig. 51.
Such a state of things is produced when a strip of very
hard steel is purposely irregularly magnetised by touching
it with strong magnets at certain points. A strip thus
magnetised virtually consists of several magnets put end
to end, but in reverse directions, N.-S., S.-N., etc.
110. The forces producing attraction between unlike
poles, and repulsion between like poles, are beautifully
illustrated by the magnetic figures obtained in the fields
between the poles in the two cases, as given in Figs.
1 Or rather the component part of the magnetic induction resolved into
the plane of the figure ; which is not quite the same thing, for above the
poles the filings stand up nearly vertically to this plane.
92 ELEMENTARY LESSONS ON [CHAP. n.
52 and 53. In Fig. 52 the poles are of opposite kinds,
and the lines of force curve across out of one pole into
the other; while in Fig. 53, which represents the action
ST.
of two similar poles, the lines of force curve away as if
repelling one another, and turn aside at right angles.
Musschenbroek first pointed out the essential difference
between these two figures.
Fig. 52. Fig. 53.
111. Magnetic Writing. Another kind of magnetic
figures was discovered by De Haldat, who wrote with the
pole of a magnet upon a thin steel plate (such as a saw-
blade), and then sprinkled filings over it. The writing,
which is quite invisible in itself, comes out in the lines
of filings that stick to the magnetised parts ; this magic
writing will continue in a steel plate many months. The
author of these Lessons has produced similar figures in
CHAP, ii.] ELECTRICITY AND MAGNETISM. 93
iron filings by writing upon a steel plate with the wires
coming from a powerful voltaic battery.
112. Surface Magnetisation. In many cases the
magnetism imparted to magnets is confined chiefly to
the outer layers of steel. If a steel magnet be put into
acid so that the outer layers are dissolved away, it is
found that it has lost its magnetism when only a thin
film has been thus removed. Magnets which have been
magnetised very thoroughly, however, exhibit some
magnetism in the interior. A hollow steel tube when
magnetised is nearly as strong a magnet as a solid rod
of the same size. If a bundle of steel plates are mag-
netised while bound together, it will be found that only
the outer ones are strongly magnetised. The inner ones
may even exhibit a reversed magnetisation.
113. Mechanical effects of Magnetisation.
When a steel or iron bar is powerfully magnetised it
grows a little longer than before ; and, since its volume
is the same as before, it at the same time contracts in
thickness. Joule found an iron bar to increase by yWoinT
of its length when magnetised to its maximum. This
phenomenon is believed to be due to the magnetisation
of the individual particles, which, when magnetised, tend
to set themselves parallel to the length of the bar. This
supposition is confirmed by the observation of Page, that
at the moment when a bar is magnetised or demagnetised,
a faint metallic clink is heard in the bar. Sir W. Grove
showed that when a tube containing water rendered
muddy by stirring up in it finely divided magnetic oxide
of iron was magnetised, the liquid became clearer in the
direction of magnetisation, the particles apparently setting
themselves end-on, and allowing more light to pass be-
tween them. A twisted iron wire tends to untwist itself
when magnetised. A piece of iron, when powerfully mag-
netised and demagnetised in rapid succession, grows hot,
as if magnetisation were accompanied by internal friction.
114. Action of Magnetism on Light. Faraday
94 ELEMENTARY LESSONS ON [CHAP. 11,
~\
discovered that a ray of polarised light passing through
certain substances in a powerful magnetic field has the
direction of its vibrations changed. This phenomenon,
which is sometimes called "The Magnetisation of Light,"
is better described as " The Rotation of the Plane of
Polarisation of Light by Magnetism." The amount of
rotation differs in different media, and varies with the
magnetising force. More recently Kerr has shown that
a ray of polarised light is also rotated by reflection at
the end or side of a powerful magnet. Further mention
is made of these discoveries in the Chapter on Electro-
optics, Lesson XXXV.
115. Physical Theory of Magnetism. All these
various phenomena point to a theory of magnetism very
different from the old notion of fluids. It appears that
every particle of a magnet is itself a magnet, and that
the magnet only becomes a magnet as a whole by the
particles being so turned as to point one way. This
conclusion is supported by the observation that if a glass
tube full of iron filings is magnetised, the filings can be
seen to set themselves endways, and that, when thus once
set, they act as a magnet until shaken up. It appears
to be harder to turn the individual molecules of solid
steel, but when so once set, they remain end-on unless
violently struck or heated. l The optical phenomena
led Clerk Maxwell to the further conclusion that these
longitudinally-set molecules are rotating round their long
axes, and that in the " aether " of space there is also a
vortical motion along the lines of magnetic induction ;
this motion, if occurring in a perfect medium (as the
" aether " may be considered), producing tensions along
the lines and pressures at right angles to them, would
afford a satisfactory explanation of the magnetic attrac-
1 It follows from this theory that when all the particles were turned end-
on, the limits of possible magnetisation would have been attained. Some
careful experiments of Beetz entirely confirm this conclusion, and add weight
to the theory.
CHAP, ii.] ELECTRICITY AND MAGNETISM. 95
tions and repulsions which apparently act across empty
space.
LESSON XI. Laws of Magnetic Force.
116. Laws of Magnetic Force.
FIRST LAW. Like magnetic poles repel one
another j unlike magnetic poles attract one
another.
SECOND LAW. The force exerted between two
magnetic poles is proportional to the product
of their strengths, and is inversely propor-
tional to the square of the distance between
them.
117. The Law of Inverse Squares. The second
of the above laws is commonly known as the law of
inverse squares. The similar law of electrical attrac-
tion has already been explained and illustrated (Art.
1 6). This law furnishes the explanation of a fact men-
tioned in an earlier Lesson, Art. 77, that small pieces
of iron are drawn bodily up to a magnet pole. If a
small piece of iron wire, a b (Fig. 54), be suspended by
a thread, and the
N.- pointing pole
A of a magnet be
brought near it,
the iron is thereby
inductively mag-
netised ; it turns
round and points Fi
towards the mag-
net pole, setting itself as nearly as possible along a line
of force, its near end b becoming a S. -seeking pole, and
its further end a becoming a N.-seeking pole. Now the
pole b will be attracted and the pole a will be repelled.
But these two forces do not exactly equal one another,
since the distances are unequal. The repulsion will
96 ELEMENTARY LESSONS ON [CHAP. n.
(by the law of inverse squares) be proportional to
/ Ag \ a ; an d the attraction will be proportional to '
Hence the bit of iron a b will experience a pair of forces,
turning it into a certain direction, and also a total force
drawing it bodily toward A. Only those bodies are
attracted by magnets in which magnetism can thus be
induced ; and they are attracted only because of the
magnetism induced in them.
We mentioned, Art. 83, that a magnet needle floating
freely on a bit of cork on the surface of a liquid, is acted
upon by forces that give it a certain direction, but that,
unlike the last case, it does not tend to rush as a whole
either to the north or to the south. It experiences a
rotation, because the attraction and repulsion of the
magnetic poles of the earth act in a certain direction ;
but since the magnetic poles of the earth are at a dis-
tance enormously great as compared with the length
from one pole of the floating magnet to the other, we
may say that, for all practical purposes, the poles of the
magnet are at the same distance from the N. pole of the
earth. The attracting force on the N. -pointing pole of
the needle is therefore practically no greater than the
repelling force acting on the S. -pointing pole, hence
there is no motion of translation given to the floating
needle as a whole.
118. Measurement of Magnetic Forces. The
truth of the law of inverse squares can be demonstrated
by measuring the attraction between two magnet poles
at known distances. But this implies that we have
some means of measuring accurately the amount of the
magnetic forces of attraction or repulsion. Magnetic
force may be measured in any one of the four following
ways : ( I ) by balancing it against the torsion of an
elastic thread ; (2) by observing the time of swing of
a magnetic needle oscillating under the influence of the
force ; (3) by observing the deflection it produces upon a
CHAP, ii.] ELECTRICITY AND MAGNETISM. 97
magnetic needle which is already attracted into a different
direction by a force of known intensity ; (4) by balanc-
ing it against the force of gravity as brought into play
in attempting to deflect a magnet hung by two parallel
strings (called the bifilar suspension), for these strings
cannot be twisted out of their parallel position without
raising the centre of gravity of the magnet. The first
three of these methods must be further explained.
119. The Torsion Balance. Coulomb also applied
the Torsion Balance to the measurement of magnetic
Fig- 55-
forces. The main principles of this instrument (as used
to measure electrostatic forces of repulsion) were de-
scribed on p. 15. Fig. 55 shows how it is arranged for
H
ELEMENTARY LESSONS ON [CHAP. n.
measuring magnetic repulsions. By means of the
torsion balance we may prove the law of inverse squares.
We may also, assuming this law proved, employ the
balance to measure the strengths of magnet poles by
measuring the forces they exert at known distances.
To prove the law of inverse squares, Coulomb made
the following experiment : The instrument was first
adjusted so that a magnetic needle, hung in a copper
stirrup to the fine silver thread, lay in the magnetic
meridian without the wire being twisted. This was done
by first putting in the magnet and adjusting roughly,
then replacing it by a copper bar of equal weight, and
once more adjusting, thus diminishing the error by
repeated trials. The next step was to ascertain through
what number of degrees the torsion -head at the top
of the thread must be twisted in order to drag the
needle i out of the magnetic meridian. In the par-
ticular experiment cited it was found that 35 of torsion
corresponded to the i of deviation of the magnet; then
a magnet was introduced, that pole being downwards
which repelled the pole of the suspended needle. It was
found (in this particular experiment) to repel the pole of
the needle through 24. From the preliminary trial we
know that this directive force corresponds to 24 x 35
of the torsion -head, and to this we must add the
actual torsion on the wire, viz., the 24, making a total
of 864, which we will call the " torsion equivalent " of
the repelling force when the poles are thus 24 apart.
Finally, the torsion -head was turned round so as to
twist the suspended magnet round, and force it nearer
to the fixed pole, until the distance between the repelling
poles was reduced to half what it was at first. It was
found that the torsion -head had to be turned round 8
complete rotations to bring the poles to 12 apart.
These 8 rotations were an actual twist of 8 x 360, or
2880. But the bottom of the torsion thread was still
twisted 12 as compared with the top, the force pro-
CHAP, ii.] ELECTRICITY AND MAGNETISM. 99
ducing this twist corresponding to 12 x 35 (or 420) of
torsion ; and to these the actual torsion of 1 2 must be
added, making a total of 2880 + 420 + 12 = 3312.
The result then of halving the distance between the
magnet poles was to increase the force foitrfold, for
3312 is very nearly four times 864. Had the distance
between the poles been reduced to one-third the force
would have been nine times as great.
120. Method of Oscillations. 1 If a magnet sus-
pended by a fine thread, or poised upon a point, be
pushed aside from its position of rest, it will vibrate
backwards and forwards, performing oscillations which,
although they gradually decrease in amplitude, are
executed in very nearly equal times. In fact, they follow
a law similar to that of the oscillations executed by a pen-
dulum swinging under the influence of gravity. The law
of pendular vibrations is, that the square of the number
of oscillations executed* in a given time is proportional to
the force. Hence we can measure magnetic forces by
counting the oscillations made in a minute by a magnet.
It must be remembered, however, that the actual number
of oscillations made by any given magnet will depend
on the weight, length, and form of the magnet, as well
as upon the strength of its poles, and of the " field "
in which it may be placed.
121. We can use this method to compare the intensity
of the force of the earth's magnetism 2 at any place with
that at any other place on the earth's surface, by oscil-
lating a magnet at one place and then taking it to the
other place and oscillating it there. If, at the first, it
makes a oscillations in one minute, and at the second, b
oscillations a minute, then the magnetic forces at the
1 It is possible, also, to measure electrical forces by a "method of oscil-
lations ;" a small charged ball at the end of a horizontally-suspended arm
being caused to oscillate under the attracting force of a charged conductor
near it, whose " force" at that distance is proportional to the square of the
number of oscillations in a given time.
2 Or, more strictly, of its horizontal component.
ELEMENTARY LESSONS ON [CHAP. ii.
two places will be to one another in the ratio of a 2
to 6*.
Again, we may use the method to compare the force
exerted at any point by a magnet near it with the force
of the earth's magnetism at that point. For, if we swing
a small magnetic needle there, and find that it makes m
oscillations a minute under the joint action l of the earth's
magnetism, and that of the neighbouring magnet, and
that, when the magnet is removed, it makes n oscillations
a minute under the influence of the earth's magnetism
alone, then m 2 will be proportional to the joint forces,
n 2 to the force due to the earth's magnetism, and the
difference of these, or ;/z 2 ;z 2 will be proportional to the
force due to the neighbouring magnet.
122. We will now apply the method of oscillations to
measure the relative quantities of free magnetism at
different points along a bar magnet. The magnet to
be examined is set up vertically (Fig. 56). A small
magnet, capable of swinging horizontally, is brought near
it and set at a short distance away
from its extremity, and then oscillated,
while the rate of its oscillations is
counted. Suppose the needle were
such that, when exposed to the earth's
magnetism alone, it would perform 3
complete oscillations a minute, and
that, when vibrating at its place near
the end of the vertical magnet it
oscillated 14 times a minute, then
the force due to the magnet will be
proportional to J4 2 3 2 = 196 9 =
187. Nextly, let the oscillating mag-
net be brought to an equal distance
opposite a point a little away from
the end of the vertical magnet. If, here, it oscillated
1 We are here assuming that the magnet is so placed that its force is in a
line with that of the earth's magnetism at the point, and that the other pole
of the magnet is so far away as not to affect the oscillating needle.
CHAP, ii.] ELECTRICITY AND MAGNETISM. 101
12 times a minute, we know that the force will be pro-
portional to I2 2 3 2 = 144 9= 135. So we shall find
that as the force falls off the oscillations will be fewer,
until, when we put the oscillating magnet opposite the
middle of the vertical magnet, we shall find that the
number of oscillations is 3 per minute, or that the
earth's force is the only force affecting the oscillations.
In Fig. 57 we have indicated the number of oscillations
at successive points, as 14, 12, 10, 8, 6, 5, 4, and 3.
If we square these numbers and subtract 9 from each,
we shall get for the forces at the various points the
following: 187, 135, 91, 55, 27, 16, 7, and o. These
forces may be taken to represent the strength of the
free magnetism at the various points, and it is convenient
to plot them out graphically in the manner shown in
N
Fig, 57-
Fig. 57, where the heights of the dotted lines are chosen
to a scale to represent proportionally the forces. The
curve which joins the tops of these " ordinates " shows
graphically how the force, which is greatest at the end,
falls off toward the middle. On a distant magnet pole
these forces, thus represented by this curvilinear triangle,
would act as if concentrated at a point in the magnet
ELEMENTARY LESSONS ON [CHAP. n.
opposite the " centre of gravity " of this triangle ; or, in
other words, the " pole," which is the centre of the result-
ant forces, is not at the end of the magnet. In thin
bars of magnetised steel it is at about T V of the magnet's
length from the end.
123. Method of Deflections. There are a number
of ways in which the deflection of a magnet by another
magnet may be made use of to measure magnetic forces. 1
We cannot here give more than a glance at first principles.
When two equal and opposite forces act on the ends of
a rigid bar they simply tend to turn it round. Such a
pair of forces form what
is called a " couple," and
the effective power or
" moment " of the couple
is obtained by multiplying
one of the two forces by
the perpendicular distance
between the directions of
JE the forces. Such a couple
/ tends to produce a motion
of rotation, but not a
motion of translation.
Now, a magnetic needle
placed in a magnetic field
across the lines of force,
experiences a " couple,"
tending to rotate it round
into the magnetic meridian,
for the N. - seeking pole is urged northwards, and
the S. -seeking pole is urged southwards, with an equal
and opposite force. The force acting on each pole
is the product of the strength of the pole and the
intensity of the " field," that is to say, of the horizontal
component of the force of the earth's magnetism at the
1 The student desirous of mastering these methods of measuring magnetic
forces should consult Sir G. Airy's Treatise on Magnetism.
CHAP, ii.] ELECTRICITY AND MAGNETISM. 103
place. We will call the strength of the N.- seeking pole
m; and we will use the symbol H to represent the
force exerted in a horizontal direction by the earth's
magnetism. (The value of H is different at different
regions of the globe.) The force on the pole A (see
Fig. 58) will be then mxli or m H, and that on pole
B will be equal and opposite. We take N S as the
direction of the magnetic meridian, and the forces will
be parallel to this direction. Now, the needle A B lies
obliquely in the field, and the magnetic force acting on
A is in the direction of the line P A, and that on B in
the direction Q B, as shown by the arrows. P Q is the
perpendicular distance between these forces ; hence the
" moment " of the couple will be got by multiplying the
length P Q by the force exerted on one of the poles.
Using the symbol G for the moment of the couple we
may write
G = P Q x m-H.
But P Q is equal to the length of the magnet multiplied
by the sine 1 of the angle A O R, which is the angle of
deflection, and which we will call 8. Hence, using / for
the length between the poles of the magnet, we may
write the expression for the moment of the couple.
G = mlH-sm 8.
In words this is : the " moment of the couple " acting
on the needle is proportional to its " magnetic moment,"
(m x /) to the horizontal force of the earth's magnetism,
and to the sine of the angle of deflection.
The reader will not have failed to notice that if the
needle were turned more obliquely, the distance P Q
would be longer, and would be greatest if the needle
were turned round east-and-west, or in the direction E W.
Also the " moment " of the couple tending to rotate the
magnet will be less and less as the needle is turned
more nearly into the direction N S.
1 If any reader is unacquainted with trigonometrical terms he should con-
sult the note at the end of this Lesson, on " Ways of reckoning Angles."
104 ELEMENTARY LESSONS ON [CHAP. n.
124. Now, let us suppose that the deflection 8 were
produced by a magnetic force applied at right angles to
the magnetic meridian, and tending to draw the pole A
in the direction R A. The length of the line R T multi-
plied by the new force will be the " moment " of the
new couple tending to twist the magnet into the direction
E W. Now, if the needle has come to rest in equilibrium
between these two forces, it is clear that the two oppos-
ing twists are just equal and opposite in power, or that
the moment of one couple is equal to the moment of the
other couple. Hence, the force in the direction W E
will be to the force in the direction S N in the same
ratio as P Q is to R T, or as P O is to R O.
Or, calling this force/
/: H = PO : RO
^ / P =Hg
But P O = A R and ^ = tan 8 hence
KO
f= H tan S;
or, in other words, the magnetic force which, acting at
right angles to the meridian, produces on a magnetic
needle the deflection 8, is equal to the horizontal force of
the earths magnetism at that point, multiplied by the
tangent of the angle of deflection. Hence, also, two
different magnetic forces acting at right angles to the
meridian would severally deflect the needle through
angles whose tangents are proportional to the forces.
This very important theorem is applied in the con-
struction of certain galvanometers (see Art. 199).
The name Magnetometer is given to- ajgy magnet
specially arranged as an instrument forlS| purpose
of measuring magnetic forces by the iflefl^Rions they
produce. The methods of observing the absolute
values of magnetic forces |JK dynes or other abstract
units of force will be explain^ in the Note at the end of
CHAP. IT.] ELECTRICITY AND MAGNETISM. 105
Lesson XXV. See also Sir George Airy's Treatise on
Magnetism.
125. Unit Strength of Pole. We found in Cou-
lomb's torsion-balance a convenient means of comparing
the strengths of poles of different magnets ; for the force
which a pole exerts is proportional to the strength of the
pole. The Second Law of Magnetic Force (see Art.
1 1 6) stated that the force exerted between two poles
was proportional to the product of their strengths, and
was inversely proportional to the square of the distance
between them. It is possible to choose such a strength
of pole that this proportionality shall become numerically
an equality. In order that this may be so, we must
adopt the following as our unit of strength of a pole, or
unit magnetic pole : A Unit Magnetic Pole is one of sttch
a strength that, when placed at a distance of one centi-
metre from a similar pole of equal strength it repels it
with a force of one dyne (see Art. 255). If we adopt
this definition we may express the second law of magnetic
force in the following equation :
where f is the force (in dynes), m and m* the strengths
of the two poles, and d the distance between them (in
centimetres). This subject is resumed in Lesson XXV.,
Art. 310, on the Theory of Magnetic Potential.
126. Theory of Magnetic Curves. We saw (Art.
1 08) that magnetic figures are produced by iron-filings
setting themselves in certain directions in the field of
force around a magnet. We can now apply the law of
inverse squares to aid us in determining the direction
in which a filing will set itself at any point in the field.
Let N S (Fig. 59) be a long thin magnet, and P any
point in the field due to its magnetism. If the N.-
seeking pole of a small magnet be put at P, it will be
attracted by S and repelled by N ; the directions of these
two forces will be along the lines P S and P N. The
io6 ELEMENTARY LESSONS ON [CHAP. n.
amounts of the forces may be represented by certain
lengths marked out along these lines. Suppose the
distance P N is twice as great as P S, the repelling force
along P N will be ^ as strong as the attracting force
along P S. So measure a distance out, P A towards S
four times as long as the length P B measured along P N
away from N. Find the resultant force 1 in the usual
way of compounding mechanical forces, by completing
the parallelogram PARE, and the diagonal P R represents
by its length and direction the magnitude and the
\
1
Fig. 59-
direction of the resultant magnetic force at the point P.
In fact the line P R represents the line along which a
small magnet or an iron filing would set itself. In a
similar way we might ascertain the direction of the lines
of force at any point of the field. The little arrows in
Fig. 59 show how the lines of force start out from the N.
pole and curve round to meet in the S. pole. The
student should compare this figure with the lines of
filings of Fig. 50.
1 See Balfour Stewart's Lessons in Elementary Physics, page 26 ; or
Todhunter's Natural Philosophy for Beginners, page 55.
CHAP, ii.] ELECTRICITY AND MAGNETISM. 107
127. Force due to a Magnetic Shell. A mag-
netic shell (Art. 107) exerts a magnetic force upon a mag-
net pole placed at a point in its neighbourhood. If the
shell be flat and very great, as compared with the distance
of the point considered, this force will be independent of
that distance, will be normal to the shell in direction, and
will depend only upon the amount of magnetism on the
shell, and will be numerically equal to 2?r times the
quantity of magnetism per square centimetre l (i.e. to
2Tcr when er is the "surface density" of magnetism on
the face of the shell).
If the shell is bounded, however, by a limiting area,
the force exerted by a shell upon a point outside it will
be greater near to the shell than at a distance away.
In this case it is most convenient to measure not the
force but the potential due to the shell. The defini-
tion of " magnetic potential " is given in Art. 310 ; mean-
time we may content ourselves with stating that the
potential due to a magnetic shell at a point near it, is
eq^lal to the strength of the shell tmtltiplied by the solid
angle? subtended by the shell at that point.
128. A Magnetic Paradox. If the N.-seeking
pole of a strong magnet be held at some distance from
the N.-seeking pole of a weak magnet, it will repel it ;
but if it is pushed up quite close it will be found now to
attract it. This paradoxical experiment is explained
b'y the fact that the magnetism induced in the weak
magnet by the powerful one will be of the opposite kind,
and will be attracted ; and, when the powerful magnet is
near, this induced magnetism may overpower and mask
the original magnetism of the weak magnet. The
student must be cautioned that in most of the experi-
ments on magnet poles similar perturbing causes are at
work. The magnetism in a magnet is not quite fixed,
1 The proof of this proposition is similar to that given at end of Lesson
XX., for the analogous proposition concerning the force due to a flat plate
charged with electricity.
2 See Note on " Ways of Reckoning Angles," at the end of this Lesson.
io8 ELEMENTARY LESSONS ON [CHAP. n.
but is liable to be disturbed in its distribution by the
near presence of other magnet poles, for no steel is so
hard as not to be temporarily affected by magnetic
induction. The law of inverse squares is only true when
the distance between the poles is so great that the dis-
placement of their magnetism due to mutual induction
is so small that it may be neglected.
NOTE ON WAYS OF RECKONING ANGLES AND
SOLID-ANGLES.
129. Reckoning in Degrees. When two straight lines cross
one another they form an angle between them ; and this angle
may be defined as the amount of rotation which one of the lines
has performed round a fixed point in the other line. Thus we
may suppose the line C P in Fig. 60 to
have originally lain along C O, and then
turned round to its present position. The
amount by which it has been rotated is
clearly a certain fraction of the whole way
" round ; and the amount of rotation round
C we call "the angle which PC makes
with O C," or more simply " the angle
PCO." But there are a number of
270* different ways of reckoning this angle.
Fig. 60. The common way is to reckon the angle
by "degrees" of arc. Thus, suppose a circle to be drawn
round C, if the circumference of the circle were divided into
360 parts each part would be called "one degree" (i), and
the angle would be reckoned by naming the number of such
degrees along the curved arc OP. In the figure the arc is
about 57 J, or ^| of the whole way round, no matter what size
the circle is drawn.
130. Reckoning in Radians. A more sensible but less
usual way to express an angle is to reckon it by the ratio between
the length of the curved arc that "subtends" the angle and the
length of the radius of the circle. Suppose we have drawn
round the centre C a circle whose raditis is one centimetre,
the diameter will be two centimetres. The length of the
circumference all round is known to be about 3y times the
length of the diameter, or more exactly 3*14159
This number is so awkward that, for convenience, we always
CHAP, ii.] ELECTRICITY AND MAGNETISM. 109
use for it the Greek letter TT. Hence the length of the circum-
ference of our circle, whose radius is one centimetre, will be
6*28318 . . . centimetres, or 2ir centimetres. We can then
reckon any angle by naming the length of arc that subtends it
on a circle one centimetre in radius. If we choose the angle
P C O, such that the curved arc O P shall be just one centimetre
long, this will be the angle one, or unit of angular measure, or,
as it is sometimes called, the angle PCO will be one "* radian"
360
In degree-measure one radian = = 57 if nearly. All the
27T
way round the circle will be 2ir radians. A right -angle will be
~ radians.
131. Reckoning by Sines or Cosines. In trigonometry
other ways of reckoning angles are used, in which, however, the
angles themselves are not reckoned, but
certain "functions" of them called "sines,"
"cosines," "tangents," etc. For readers
not accustomed to these we will briefly ex-
plain the geometrical nature of these
"functions." Suppose we draw (Fig. 61)
our circle as before round centre C, and
then drop down a plumb-line P M, on
to the line C O ; we will, instead of reckon-
ing the angle by the curved arc, reckon it Fi 6l
by the length of the line P M. It is clear
that if the angle is small P M will be short ; but as the angle
opens out towards a right angle, P M will get longer and
longer (Fig. 62). The ratio between the length of this line and
the radius of the circle is called the "sine"
of the angle, and if the radius is I the
length of P M will be the value of the sine.
It can never be greater than I, though it
may have all values between I and - I.
The length of the line C M will also
p. 62 depend upon the amount of the angle. If
the angle is small C M will be nearly as
long as CO; if the angle open out to nearly a right angle
C M will be very short. The length of C M (when the radius
is i) is called the "cosine" of the angle. If the angle be
called 6, then we may for shortness write these functions :
132. Reckoning by Tangents. Suppose we draw our circle
ELEMENTARY LESSONS ON [CHAP. n.
as before (Fig. 63), but at the point O draw a straight line
touching the circle, the tangent line at O ;
let us also prolong C P until it meets the
tangent line at T. We may measure the
angle between O C and O P in terms of
the length of the tangent O T as compared
with the length of the radius. Since our
radius is I, this ratio is numerically the
length of O T, and we may therefore call
the length of O T the "tangent" of the
angle O C P. It is clear that smaller angles
will have smaller tangents, but that larger
angles may have very large tangents ; in
fact, the length of the tangent when P C was
moved round to a right angle would be
infinitely great. It can be shown that the
ratio between the lengths of the sine and
\
C M
Fig. 63.
of the cosine of the angle is the same as the ratio between the
length of the tangent and that of the radius ; or the tangent of
an angle is equal to its sine divided by its cosine. The formula
for the tangent may be written :
133. Solid Angles. When three or more surfaces intersect
at a point they form a solid angle: there is a solid angle, for
example, at the top of a pyramid, or of a cone, and one at every
corner of a diamond that has
been cut. If a surface of any
given shape be near a point, it
is said to subtend a certain solid
angle at that point, the solid
angle being mapped out by
drawing lines from all points
of the edge of this surface to the
point P (Fig. 64. ) An irregular
cone will thus be generated
whose solid angle is the solid
angle subtended at P by the
surface E F. To reckon this
Fig. 64.
solid angle we adopt an expedient similar to that adopted when
we wished to reckon a plane angle in radians. About the point
P, with radius of I centimetre, describe a sphere , which will
intercept the cone over an area M N : the area thus intercepted
measures the solid angle. If the sphere have the radius I, its
total surface is 471-. The solid angle subtended at the centre by
a hemisphere would be 27r.
CHAP, ii.] ELECTRICITY AND MAGNETISM.
TABLE OF NATURAL SINES AND TANGENTS.
Arc.
Sine.
Tangent.
O'OOO
O.OOO
90
I
017
017
89
2
035
035
88
3
052
052
87
4
070
070
86
5
087
087
85
6
-105
105
84
7
122
123
83
8
139
141
82
9
I 5 6
158
81
10
174
I 7 6
80
15
259
268
75
20
342
3 6 4
70
25
423
466
65
30
500
577
60
35
'574
700
55
40
. lii.
greatest electromotive -force, or be the most " intense,"
in which those materials are used which give the
greatest difference of potentials on contact, or which are
widest apart on the " contact-series " given in Art. 72.
Zinc and copper are very convenient in this respect ;
and zinc and silver would be better but for the expense.
For more powerful batteries a zinc-platinum or a zinc-
carbon combination is preferable.
158. Resistance. The same electromotive -force
does not, however, always produce a current of the same
strength. The strength of the current depends not only on
the force tending to drive the electricity round the circuit,
but also on the resistance which it has to encounter
and overcome in its flow. If the cells be partly choked
with sand or sawdust (as is sometimes done in so-
called " Sawdust Batteries " to prevent spilling), or, if the
wire provided to complete the circuit be very long or
very thin, the action will be partly stopped, and the
current will be weaker, although the E.M.F. may be
unchanged. The analogy of the water-pipes will again
help us. The pressure which forces the water through
pipes depends upon the 'difference of level between the
cistern from which the water flows and the tap to which
it flows ; but the amount of water that runs through will
depend not on the pressure alone, but on the resistance
it meets with ; for, if the pipe be a very thin one, or
choked with sand or sawdust, the water will only run
slowly through.
Now the metals in general conduct well : their resist-
ance is small ; but metal wires must not be too thin or
too long, or they will resist too much, and permit only
a feeble current to pass through them. The liquids in
the battery do not conduct nearly so well as the metals,
and different liquids have different resistances. Pure
water will hardly conduct at all, and is for the feeble
electricity of the voltaic battery almost a perfect in-
sulator, though for the high -potential electricity of the
CHAP, in.] ELECTRICITY AND MAGNETISM. 13!
frictional machines it is, as we have seen, a fair conductor.
Salt and saltpetre dissolved in water are good con-
ductors, and so are dilute acids, though strong sul-
phuric acid is a bad conductor. The resistance of the
liquid in the cells may be reduced, if desired, by using
larger plates of metal and putting them nearer together.
Gases are bad conductors ; hence the bubbles of hydro-
gen gas which are given off at the copper plate during
the action of the cell, and which stick to the surface
of the copper plate, increase the internal resistance of
the cell by diminishing the effective surface of the plates.
LESSON XIV. Chemical Actions in the Cell.
159. The production of a current of electricity by a
voltaic cell is always accompanied by chemical actions
in the cell. One of the metals at least must be readily
oxidisable, and the liquid must be one capable of acting^)
on the metal. As a matter of fact, it is found that zinc
and the other metals which stand at the electropositive
end of the contact -series (see Art. 72) are oxidisable;
whilst the electronegative substances copper, silver,
gold, platinum, and graphite are less oxidisable, and
the last three resist the action of every single acid.
There is no proof that their electrical behaviour is due to
their chemical behaviour ; nor is their chemical behaviour
due to their electrical. Probably both result from a
common cause. (See Article 422 (bis), and also p. 71.)
160. A piece of quite pure zinc when dipped alone
into dilute sulphuric acid is not attacked by the liquid.
But the ordinary commercial zinc is not pure, and when
plunged into dilute sulphuric acid dissolves away, a large
quantity of bubbles of hydrogen gas being given off from
the surface of the metal. Sulphuric acid is a complex
substance, in which every molecule is made up of a
group of atoms, 2 of Hydrogen, i of Sulphur, and 4 of
132 ELEMENTARY LESSONS ON [CHAP. in.
Oxygen ; or, in symbols, H 2 SO 4 . The chemical reaction
by which the zinc enters into combination with the
radical of the acid, turning out the hydrogen, is expressed
in the following equation :
Zn + H 2 SO 4 ZnSO 4 + H 2
Zinc and Sulphuric Acid produce Sulphate of Zinc and Hydrogen.
The sulphate of zinc produced in this reaction remains
in solution in the liquid.
Now, when a plate of pure zinc and a plate of some
less-easily oxidisable metal copper or platinum, or, best
of all, carbon (the hard carbon from the gas retorts)
are put side by side into the cell containing acid, no
appreciable chemical action takes place until the circuit
is completed by joining the two plates with a wire, or by
making them touch one another. Directly the circuit is
completed a current flows and the chemical actions
begin, the zinc dissolving in the acid, and the acid giving
up its hydrogen in streams of bubbles. But it will be
noticed that these bubbles of hydrogen are evolved not
at the zinc plate, nor yet throughout the liquid, but at the
surface of the copper plate (or the carbon plate if carbon
is employed). This apparent transfer of the hydrogen
gas through the liquid from the surface of the zinc plate
\to the surface of the copper plate where it appears is
'very remarkable. The ingenious theory framed by
Grotthuss to account for it, is explained in Lesson
XXXVIII. on Electro-Chemistry.
These chemical actions go on as long as the current
passes. The quantity of zinc used up in each cell is
proportional to the amount of electricity which flows
round the circuit while the battery is at work ; or, in
other words, is proportional to the strength of the
current. The quantity of hydrogen gas evolved is also
proportional to the amount of zinc consumed, and also
to the strength of the current. After the acid has thus
dissolved zinc in it, it will no longer act as a corrosive
CHAP, in.] ELECTRICITY AND MAGNETISM. 133
solvent ; it has been " killed," as workmen say, for it
has been turned into sulphate of zinc. The battery will
cease to act, therefore, either when the zinc has all dis-
solved away, or when the acid has become exhausted,
that is to say, when it is all turned into sulphate of zinc.
Stout zinc plates will last a long time, but the acids
require to be renewed frequently, the spent liquor being
emptied out.
161. Local Action. When the circuit is not closed
the current cannot flow, and there should be no chemical
action so long as the battery is producing no current.
The impure zinc of commerce, however, does not re-
main quiescent in the acid, but is continually dissolving
and giving off hydrogen bubbles. This local action,
as it is termed, is explained in the following manner :
The impurities in the zinc consist of particles of iron,
arsenic, and other metals. Suppose a particle of iron to
be on the surface anywhere and in contact with the acid.
It will behave like the copper plate of a battery towards
the zinc particles in its neighbourhood, for a local differ-
ence of potential will be set up at the point where there
is metallic contact, causing a local current to run from
the particles of zinc through the acid to the particle of
iron, and so there will be a constant wasting of the zinc,
both when the battery circuit is closed and when it is open.
162. Amalgamation of Zinc. We see now why a
piece of ordinary commercial zinc is attacked on being
placed in acid. There is local action set up all over its
surface in consequence of the metallic impurities in it.
To do away with this local action, and abolish the
wasting of the zinc while the battery is at rest, it is usual
to amalgamate the surface of the zinc plates with
mercury. The surface to be amalgamated should be
cleaned by dipping into acid, and then a few drops of
mercury should be poured over the surface and rubbed
into it with a bit of linen rag tied to a stick. The
mercury unites with the zinc at the surface, forming a
134 ELEMENTARY LESSONS ON [CHAP. in.
pasty amalgam. The iron particles do not dissolve in
the mercury, but float up to the surface, whence the hydro-
gen bubbles which may form speedily carry them off. As
the zinc in this pasty amalgam dissolves into the acid the
film of mercury unites with fresh portions of zinc, and so
presents always a clean bright surface to the liquid.
If the zinc plates of a battery are well amalgamated
there should be no evolution of hydrogen bubbles when
the circuit is open. Nevertheless there is still always a
little wasteful local action accompanying the action of
the battery. Jacobi found that while one part of
hydrogen was evolved at the positive pole, 33*6 parts of
zinc were actually dissolved at the negative pole, instead
of the 32-5 parts which are the chemical equivalent of
the hydrogen.
163. Polarisation. The bubbles of hydrogen gas
liberated at the surface of the copper plate stick to
it in great numbers, and form a film over its surface ;
hence the effective amount of surface of the copper plate
is very seriously reduced in a short time. When a
simple cell, or battery of such cells, is set to produce a
current, it is found that the strength of the current after
a few minutes, or even seconds, falls off very greatly,
and may even be almost stopped. This immediate
falling off in the strength of the current, which can be
observed with any galvanometer and a pair of zinc and
copper plates dipping into acid, is almost entirely due to
the film of hydrogen bubbles sticking to the copper pole.
A battery which is in this condition is said to be
" polarised."
164. Effects of polarisation. The film of hydro-
gen bubbles affects the strength of the current of the cell
in two ways.
Firstly, It weakens the current by the increased resist-
ance which it offers to the flow, for bubbles of gas are
bad conductors ; and,
Secondly, It weakens the current by setting up an
CHAP. HI.] ELECTRICITY AND MAGNETISM. 13$
opposing electromotive-force; for hydrogen is almost as
oxidisable a substance as zinc, especially when freshly
deposited (or in a "nascent " state), and is electropositive,
standing high in the series on p. 69. Hence the
hydrogen itself produces a difference of potential, which
would tend to start a current in the opposite direction to
the true zinc-to-copper current.
It is therefore a very important matter to abolish this
polarisation, otherwise the currents furnished by batteries
would not be constant.
165. Remedies against Internal Polarisation.
Various remedies have been practised to reduce or
prevent the polarisation of cells. These may be classed
as mechanical, chemical, and electro-chemical.
1. Mechanical Means. If the hydrogen bubbles be
simply brushed away from the surface of the positive
pole, the resistance they caused will be diminished. If
air be blown into the acid solution through a tube, or if
the liquid be agitated or kept in constant circulation by
siphons, the resistance is also diminished. If the surface
be rough or covered with points, the bubbles collect more
freely at the points and are quickly carried up to the
surface, and so got rid of. This remedy was applied in
Smee's Cell, which consisted of a zinc and a platinised
silver plate dipping into dilute sulphuric acid ; the silver
plate, having its surface thus covered with a rough coat-
ing of finely divided platinum, gave up the hydrogen
bubbles freely ; nevertheless, in a battery of Smee Cells
the current. falls off greatly after a few minutes.
2. Chemical Means. If a highly-oxidising substance
be added to the acid it will destroy the hydrogen bubbles
whilst they are still in the nascent state, and thus will
prevent both the increased internal resistance and the
opposing electromotive - force. Such substances are
bichromate of potash, nitric acid, and bleaching powder
(so-called chloride of lime). These substances, however,
would attack the copper in a zinc-copper cell. Hence
136
ELEMENTARY LESSONS ON [CHAP. in.
^
r^ CO
-^V
they can only be made use of in zinc-carbon or zinc-
platinum cells. Nitric acid also attacks zinc when the
circuit is open. Hence it cannot be employed in the
same single cell with the zinc plate. In the Bichro-
mate Battery, invented by Poggendorf, bichromate
of potash is added
to the sulphuric acid.
This cell is most con-
veniently made up as
a " bottle battery "
(Fig. 72), in which a
plate of zinc is the
carbon plates, one on
each side of the zinc,
=IMB!S== ^. are joined together at
^ the to P as a + pole.
As this solution acts
on the metal zinc
when the circuit is
open, the zinc plate
is fixed to a rod by
which it can be drawn
up out of the solution
..
<
**
when the cell is not being worked. Other cases of
chemical prevention of polarisation are mentioned in
describing other forms of battery.
3- Electro-chemical Means. It is possible by employ-
ing double cells, as explained in the next Lesson, to so
arrange matters that some solid metal, such as copper,
shall be liberated instead of hydrogen bubbles, at the
point where the current leaves the liquid. This electro-
chemical exchange entirely obviates polarisation.
166. Simple Laws of Chemical Action in the
Cell. We will conclude this section by enumerating the
two simple laws of chemical action in the cell.
I. The amount of chemical action in the cell is propor-
CHAP, in.] ELECTRICITY AND MAGNETISM. 137
tional) to the quantity of electricity that passes through it j
that is to say, is proportional to the strength of the
ciirrent while it passes.
One coulomb 1 of electricity in passing through the cell
liberates ^ 6 ^ (or -0000105) of a gramme of hydrogen,
and causes -M'-fa (or '00034125) of a gramme of zinc to
dissolve in the acid.
II. The amount of chemical action is equal in each cell
of a battery consisting of cells joined in series.
The first of these laws was thought by Faraday, who
discovered it, to disprove Volta's contact theory. He
foresaw that the principle of the conservation of energy
would preclude a mere contact force from furnishing a
continuous supply of current, and hence ascribed the
current to the chemical actions which were proportional
in quantity to it. How the views of Volta and Faraday
are to be harmonised has been indicated in the last
paragraph of page 71.
LESSON XV. Voltaic Batteries.
167. A good Voltaic Battery should fulfil all or most
of the following conditions :
1. Its electromotive-force should be high and con-
stant.
2. Its internal resistance should be small.
3. It should give a constant current, and therefore
must be free from polarisation, and not liable
to rapid exhaustion, requiring frequent renewal
of the acid.
4. It should be perfectly quiescent when the circuit
is open.
5. It should be cheap and of durable materials.
6. It should be manageable, and if possible, should
not emit corrosive fumes.
1 For the definition of the coulomb, or practical unit of quantity of
electricity, see Art. 323.
138 ELEMENTARY LESSONS ON [CHAP. in.
168. No single battery fulfils all these conditions,
however, and some batteries are better for one purpose
and some for another. Thus, for telegraphing through
a long line of wire a considerable internal resistance in
the battery is no great disadvantage ; while, for producing
an electric light, much internal resistance is absolutely
fatal. The electromotive-force of a battery depends on
the materials of the cell, and on the number of cells
linked together, and a high E.M.F. can therefore be
gained by choosing the right substances and by taking
a large number of cells. The resistance within the cell
can be diminished by increasing the size of the plates,
by bringing them near together, so that the thickness
of the liquid between them may be as small as possible,
and by choosing liquids that are good conductors. Of
the innumerable forms of battery that have been invented,
only those of first importance can be described. Batteries
may be classified into two groups, according as they
contain one or two fluids.
SINGLE-FLUID CELLS.
169. The simple cell of Volta, with its zinc and copper
plates, has been already described. Cruickshank suggested
to place the plates vertically in a trough, producing a
more powerful combination. Dr. Wollaston proposed
to use a plate of copper of double size, bent round so as
to approach the zinc on both sides, thus diminishing the
resistance. Smee, as we have seen, replaced the copper
plate by platinised silver, and Walker suggested the use
of plates of hard carbon instead of copper or silver,
thereby saving cost, and at the same time increasing the
electromotive-force. The simple bichromate cell (Fig.
72) is the only single-fluid cell free from polarisation,
and even in this form the strength of the current falls
off after a few minutes' working, owing to the chemical
CHAP, in.] ELECTRICITY AND MAGNETISM.
139
reduction of the liquid. Complete depolarisation is only
obtained by two-fluid cells.
TWO-FLUID BATTERIES.
17O. Daniell's Battery. Each cell or " element "
of Daniell's Battery consists of an inner and an outer
cell, divided by a porous partition
to keep the separate liquids in
the two cells from mixing. The
outer cell (Fig. 73) is usually of
copper, and serves also as a
copper plate. Within it is placed
a cylindrical cell of unglazed
porous porcelain (a cell of parch-
ment, or even of brown paper,
will answer), and in this is a
rod of amalgamated zinc for the
negative pole. The liquid in
the inner cell is dilute sulphuric
Fig. 73.
acid ; that in the outer cell is a saturated solution of
sulphate of copper (" blue vitriol "), some spare crystals
of the same substance being contained in a perforated
shelf at the top of the cell, in order that they may
dissolve and replace that which is used up while the
battery is in action.
When the circuit is closed the zinc dissolves in the
dilute acid, forming sulphate of zinc, and liberating hydro-
gen gas ; but this gas does not appear in bubbles on the
surface of the copper cell, for, since the inner cell is
porous, the molecular actions (by which the freed atoms
of hydrogen are, as explained by Fig. 155, handed on
through the acid) traverse the pores of the inner cell,
and there, in the solution of sulphate of copper, the
hydrogen atoms are exchanged for copper atoms, the
result being that pure copper, and not hydrogen gas, is
deposited on the outer coppe-r plate. Chemically these
i 4 o ELEMENTARY LESSONS ON [CHAP, in,
actions may be represented as taking place in two stages.
Zn + H 2 SO 4 = Zn SO 4 + H 2
Zinc and Sulphuric Acid produce Sulphate of Zinc and Hydrogen.
And then
H 2 Cu SO 4 := H 2 SO 4 + Cu.
Hydrogen and Sulphate of Copper produce Sulphuric Acid and Copper.
The hydrogen is, as it were, translated electro-chemi-
cally into copper during the round of changes, and so
while the zinc dissolves away the copper grows, the dilute
sulphuric acid gradually changing into sulphate of zinc,
and the sulphate of copper into sulphuric acid. There
I is no polarisation, and the battery, though not powerful
K (owing to its internal resistance), is quite constant, 1
r.nd hence affords a valuable standard of comparison
by which to measure the electromotive -force of other
batteries. When the dilute acid used consists of one part
(by weight) of acid to twelve parts of water, the E.M.F.
of one element is 1-079 volts. Owing to its constancy
this battery, made in a flat form, many cells of which
can be readily set up side by side in a wooden trough
divided into partitions (see Fig. 77), is much used in
telegraphy.
171. Grove's Battery. Sir Wm. Grove devised a
form of battery having both greater E.M.F. and smaller
internal resistance than Daniell's Cell. In Grove's
\element there is an outer cell of glazed ware or of
[ebonite, containing the t amalgamated zinc plate and
Milute sulphuric acid. In the inner porous cell a piece
of platinum foil serves as the negative pole, and it dips
into the strongest nitric acid. There is no polarisation
in this cell, for the hydrogen liberated by the solution of
the zinc in dilute sulphuric acid, in passing through the
1 That is to say, sufficiently so for ordinary purposes. Mr. Latimer Clark
says that its E.M. F. may vary between 1*079 an( ^ 0*978 volts, according to its
condition. For very exact testing he suggests a standard cell described in
Art. 177. M. Bailie gives i'i^B volts as E.M.F. of Daniell's cell.
CHAP, in.] ELECTRICITY AND MAGNETISM. 141
nitric acid in order to appear at the platinum pole, de-
composes the nitric acid and is itself oxidized, producing
water* and the red fumes of nitric peroxide gas. This
gas does not, however, produce polarisation, for as it is
very soluble in nitric acid it does not form a film upon
the face of the platinum plate, nor does it, like hydrogen,
set up an opposing electromotive -force with the zinc.
The Grove cells may be made of a flat shape, the zinc
being bent up so as to embrace the flat porous cell on
both sides. This reduces the internal resistance, which
is already small on account of the good conducting
powers of nitric acid. Hence the Grove's cell will
furnish for three or four hours continuously a powerful
current. The E.M.F. of one cell is about 1-9 volts. A
single cell will readily raise to a bright red heat two or
three inches of thin platinum wire, or drive a small
electro -magnetic engine. For producing larger effects
a number of cells must be joined up " in series," the
platinum of one cell being clamped to the zinc of the
next to it. Fifty such cells, each holding about a quart
of liquid, amply suffice to produce an electric light, as
will be explained in Lesson XXXII.
172. Bunsen's Battery. The battery which bears
Bunsen's name is a modification of that of Grove, and
was indeed originally suggested by him. In the Bunsen
cell the expensive 1 platinum foil is replaced by a rod or
slab of hard gas carbon. The difficulty of cutting this
into thin slabs causes a cylindrical form of battery, with
a rod of carbon, as shown in Fig. 74, to be preferred to
the flat form. The difference of potentials for a zinc-
carbon combination is a little higher than for a zinc-
platinum one, which is an advantage ; but the Bunsen
cell is troublesome to keep in order, and there is some
difficulty in making a good contact between the rough
1 Platinum, costs about 30 shillings an ounce nearly half as much as gold ;
while a hundredweight of the gas carbon may be had for a mere trifle, often
for nothing more than the cost of carrving it from the gasworks,
^ * ^.X^v-' * a^~*s\^
142
ELEMENTARY LESSONS ON [CHAP. in.
surface of the carbon and the copper strap which
connects the carbon of one cell to the zinc of the next.
Fig. 75 shows the usual way of
coupling up a series of five such
cells. The Bunsen's battery will
continue to furnish a current for
a longer time than the flat
Grove's cells, on account of the
larger quantity of acid contained
by the cylindrical pots. 1
173. Leclanche's Battery :
Niaudet's Battery. For work-
ing electric bells and telephones,
and also to a limited extent in
telegraphy, a zinc-carbon cell is
employed, invented by Mons.
Fig- 74-
Leclanche*, in which the exciting liquid is not dilute
acid, but a solution of salammoniac. In this the zinc
dissolves, forming a double chloride of zinc and am-
monia, while ammonia gas and hydrogen are liberated
Fig. 75-
at the carbon pole. To prevent polarisation the carbon
plate is packed inside a porous pot along with frag-
1 Callan constructed a large battery in which cast-iron formed the positive
pole, being immersed in strong nitric acid, the zincs dipping into dilute acid.
The iron under these circumstances is not acted upon by the acid, but
assumes a so-called "passive state." In this condition its surface appears
to be impregnated with a film of magnetic peroxide, or of oxygen.
CHAP, in.] ELECTRICITY AND MAGNETISM.
merits of carbon and powdered binoxide of manga-
nese, a substance which slowly yields up oxygen and
destroys the hydrogen bubbles. If used to give a
continuous current for many minutes together, the
power of the cell falls off owing to the accumulation of
the hydrogen bubbles ; but if left to itself for a time the
cell recovers itself, the binoxide gradually destroying the
polarisation. As the cell is in other respects perfectly
constant, and does not require renewing for months or
years, it is well adapted for domestic purposes. Three
Leclanche' cells are shown joined in series, in Fig. 76.
Fig. 76.
In more recent forms the binoxide of manganese is
applied in a conglomerate attached to the face of the
carbon, thus avoiding the necessity of using a porous
inner cell.
Mons. Niaudet has also constructed a zinc-carbon cell
in which the zinc is placed in a solution of common salt
(chloride of sodium), and the carbon is surrounded by
the so-called chloride-of-lime (or bleaching-powder), which
readily gives up ' chlorine and oxygen, both of which
substances will , destroy the hydrogen bubbles and
prevent polarisation. This cell has a higher E.M.F.
and a less resistance than the Leclanche'.
174. De la Rue's Battery. Mr. De la Rue has
constructed a perfectly constant cell in which zinc and
144 ELEMENTARY LESSONS ON [CHAP. in.
silver are the two metals, the zinc being immersed in
chloride of zinc, and the silver embedded in a stick of
fused chloride of silver. As the zinc dissolves away,
metallic silver is deposited upon the + pole, just as the
copper is in the Daniell's cell. Mr. De la Rue has con-
structed an enormous battery of over 11,000 little cells.
The difference of potential between the first zinc and
last silver of this gigantic battery was over 11,000 volts,
yet even so no spark would jump from the + to the
pole until they were brought to within less than a quarter
of an inch of one another. With 8040 cells the length
of spark was only 0-08 of an inch.
175. Marie* Davy's Battery. In this cell the zinc
dips into sulphate of zinc, while a carbon plate dips into
a pasty solution of mercurous sulphate. When the cell
is in action mercury is deposited on the surface of the
carbon, so that the cell is virtually a zinc-mercury cell.
It was largely used for telegraphy in France before the
introduction of the Leclanche' cell.
176. Gravitation Batteries. Instead of employing
a porous cell to keep the two liquids separate, it is pos-
sible, where one of the liquids is heavier than the other,
to arrange that the heavier liquid shall form a stratum
at the bottom of the cell, the lighter floating upon it.
Such arrangements are called gravitation batteries; but
the separation is never perfect, the heavy liquid slowly
diffusing upwards. Daniell's cells arranged as gravi-
tation batteries have been contrived by Meidinger,
Minotto, Callaud, and Sir. W. Thomson. In Siemens'
modification of Daniell's cell paper -pulp is used to
separate the two liquids. The " Sawdust Battery " of
Sir W. Thomson is a Daniell's battery, having the cells
filled with sawdust, to prevent spilling and make them
portable.
177. Latimer Clark's Standard Cell. A standard
cell whose E.M.F. is even more constant than that of
the Daniell was suggested by Latimer Clark. This
CHAP, in.] ELECTRICITY AND MAGNETISM. 145
battery is composed of pure mercury, on whic h floats a
paste of mercurous sulphate, a plate of zinc resting on
the paste. Contact with the mercury, which acts as the
positive pole, is made with a platinum wire. The
E.M.F. is 1-457 volts.
178. The following table gives the electromotive-forces
of the various batteries enumerated :
Name of Battery, etc.
E.M.F. in Volts.
Single Fluid Cells.
Volta (Wollaston, etc.)
Smee.
Poggendorf.
Two Fluid Cells.
Daniell (Meidinger, Minotto, etc.)
Grove.
Bunsen.
Leclanche.
Niaudet.
De la Rue.
Marie Davy.
Latimer Clark.
Secondary Batteries.
Ritter.
Plante (Faure, etc.)
0-82 1-048
0-65 ?
1796 2-3
0-978 1-079 1-138
1-78 1*956
1-751-964
1-417 1-48 1-61
1.65
1.059
1-52
1-457
1-98 2-25
1-98 2-25
179. Strength of Current. The student must not
mistake the figures given in the above table for the
strength of current which the various batteries will
yield; that depends, as was said in Lesson XIII., on
the internal resistance of the cells as well as on their
E.M.F. The E.M.F. of a cell is independent of its
size, and is determined solely by the materials chosen
and their condition. The resistance depends on the
L
146 ELEMENTARY LESSONS ON [CHAP. HI.
size of ths cell, the conducting qualities of the liquid,
the thickness of the liquid which the current must
traverse, etc.
The exact definition of the strength of a current is
as follows : The strength of a current is the qtiantity oj
electricity which flows past any point of the circuit in one
second^ Suppose that during 10 seconds 25 coulombs
of electricity flow through a circuit, then the average
strength of that strong current during that time has been
i\ coulombs per second, or 2^ amperes. The usual
strength of currents used in telegraphing over main
lines is only from five to ten thousandths of an ampere.
If in t seconds a quantity of electricity Q has flowed
through the circuit, then the strength C of the current
during that time is represented by the equation :
Moreover, if C represents the strength of the current,
the total quantity of electricity that has passed through
the circuit in a given time, / is found by multiplying the
strength of the current by the time ; or
Q = c/.
For the quantity of electricity that is thus transferred
will be proportional to the strength of the flow, and to
the time that it continues.
The laws which determine the strength of a current
in a circuit were first enunciated by Dr. G. S. Ohm, who
stated them in the following law :
ISO. Ohm's Law. The strength of the current
varies directly as the electromotive-force, and inversely
1 The terms "strong," "great," and "intense," as applied to currents,
mean precisely the same thing. Formerly, before Ohm's Law was properly
understood, electricians used to talk about "quantity currents," and
" intensity currents," meaning by the former term a current flowing through
a circuit in which there is very small resistance inside the battery or out ;
and by the latter expression they designated a current due to a high electro-
motive-force. The terms were convenient, but should be avoided as mis-
leading.
CHAP, in.] ELECTRICITY AND MAGNETISM.
147
as the resistance of the circuit; or, in other words, any-
thing that makes the E.M.F. of the cell greater will
increase the strength of the current, while anything that
increases the resistance (either the internal resistance in
the cells themselves or the resistance of the external
wires of the circuit) will diminish the strength of the
current. (See further concerning Ohm's Law in Lesson
XXIX.)
Now the internal resistances of the cells we have
named differ very greatly, and differ with their size.
Roughly speaking we may say that the resistance in a
Darnell's cell is about five times that in a Grove's cell of
equal size. The Grove's cell has therefore both a
higher E.M.F. and less internal resistance. It would
in fact send a current about eight times as strong as
the Daniell's cell of equal size through a short stout
wire.
181. We may then increase the strength of a battery
in two ways :
(1) by increasing its E.M.F.
(2) by diminishing its internal resistance.
The electromotive -force of a cell being determined
by the materials of which it is made, the only way to
Fig. 77.
increase the total E.M.F. of a battery of given materials
is to increase the number of cells joined in series. It is
148 ELEMENTARY LESSONS ON [CHAP. in.
frequent in the telegraph service to link thus together
two or three hundred of the flat Daniell's cells ; and
they are usually made up in trough-like boxes, containing
a series of 10 cells, as shown in Fig. 77.
To diminish the internal resistance of a cell the follow-
ing expedients may be resorted to :
(i.) The plates may be brought nearer together, so
that the current shall not have to traverse so thick a
stratum of liquid.
(2.) The size of the plates may be increased, as this
affords the current, as it were, a greater number of
possible paths through the stratum of liquid.
(3.) The zincs of several cells may be joined together,
to form, as it were, one large zinc plate, the coppers
being also joined to form one large copper plate. Cells
thus joined are said to be united " in compound circuit,"
or " for quantity," to distinguish this method of joining
from the joining in simple series. Suppose four similar
cells thus joined, the current has four times the available
number of paths by which it can traverse the liquid
from zinc to copper ; hence the internal resistance of the
whole will be only J of that of a single cell. But the
E.M.F. of them will be no greater thus than that of
one cell.
It is most important for the student to remember that
the strength of the current is also affected by the resist-
ances of the wires of the external circuit ; and if the
external resistance be already great, as in telegraphing
through a long line, it is little use to diminish the internal
resistance if this is already much smaller than the resist-
ance of the line wire.
The E.M.F. of the single-fluid cells of Volta and Smee
is marked as doubtful, for the opposing E.M.F. of polar-
isation sets in almost before the true E.M.F. of the cell
can be measured. The different values assigned to other
cells are accounted for by the different degrees of con-
centration of the liquids. Thus in the Daniell's cells
CHAP, in.] ELECTRICITY AND MAGNETISM. 149
used in telegraphy, water only is supplied at first in the
cells containing the zincs ; and the E.M.F. of these is less
than if acid or sulphate of zinc were added to the water.
182. Other Batteries. Numerous other forms of battery
have been suggested by different electricians. There are three,
of theoretical interest only, in which the electromotive-force is
due, not to differences of potential at the contact of dissimilar
metals^ but to differences of potential at the contact of a metal
or metals with liquids. The first of these was invented by the
Emperor Napoleon III. Both plates were of copper, dipping
respectively into solutions of dilute sulphuric acid and of cyanide
of potassium, separated by a porous cell. The second of these
combinations, due to Wohler, employs plates of aluminium only,
dipping respectively into strong nitric acid and a solution of
caustic soda. In the third, invented by Dr. Fleming, the two
liquids do not even touch one another, being joined together by
a second metal. In this case the liquids chosen are sodium
persulphide and nitric acid, and the two metals copper and lead.
A similar battery might be made with copper and zinc, using
solutions of ordinary sodium sulphide, and dilute sulphuric acid
in alternate cells, a bent zinc plate dipping into the first and
second cells, a bent copper plate dipping into second and third,
and so on ; for the electromotive - force of a copper - sodium
sulphide-zinc combination is in the reverse directipn to that of a
copper-sulphuric acid-zinc combination.
Bennett has lately described a cheap and most efficient battery,
in which the metals are iron and zinc, and the exciting liquid a
strong solution of caustic soda. Old meat-canisters packed with
iron filings answer well for the positive element, and serve to
contain the solution. Scrap zinc thrown into mercury in a
shallow inner cup of porcelain forms the negative pole.
Skrivanoff has modified the zinc-carbon cell of Latimer Clark,
by employing a stiff paste made of ammonio-mercuric chloride
and common salt, thereby rendering the cells dry and portable.
Jablochkoff has described a battery in which plates of carbon
and iron are placed in fused nitre ; the carbon is here the
electro-positive element, being rapidly consumed in the liquid.
Plante's and Faure's Secondary Batteries, and Grove's
Gas Battery, are described in Arts. 415, 416.
The so-called Dry Pile of Zamboni deserves notice.
It consists of a number of paper discs, coated with zinc-
150 ELEMENTARY LESSONS ON ICHAP. in.
foil on one side and with binoxide of manganese on the
other, piled upon one another, to the number of some
thousands, in a glass tube. Its internal resistance is
enormous, as the internal conductor is the moisture of
the paper, and this is slight ; but its electromotive-force
is very great, and a good dry pile will yield sparks.
Many years may elapse before the zinc is completely
oxidised or the manganese exhausted. In the Clarendon
Laboratory at Oxford there is a dry pile, the poles of
which are two metal bells : between them is hung a
small brass ball, which, by oscillating to and fro, slowly
discharges the electricity. It has now been continuously
ringing the bells for over forty years.
183. Effect of Heat on Batteries. If a cell be
warmed it yields a stronger current than when cold.
This is chiefly due to the fact that the liquids conduct
better when warm, the internal resistance being thereby
reduced. A slight change is also observed in the E.M.F.
on heating; thus the E.M.F. of a DanielPs cell is about
i J per cent higher when warmed to the temperature of
boiling water, while that of a bichromate battery falls off
nearly 2 per cent under similar circumstances.
LESSON XVI. Magnetic Actions of the Current.
184. About the year 1802, Romagnosi, of Trente,
discovered that a current of electricity affects a magnet-
ised needle, and causes it to turn aside from its usual
position. The discovery, however, dropped into oblivion,
having never been published. A connection of some
kind between magnetism and electricity had long been
suspected. Lightning had been known to magnetise
knives and other objects of steel ; but almost all
attempts to imitate these effects by powerful charges of
electricity, or by sending currents of electricity through
CHAP, in.] ELECTRICITY AND MAGNETISM.
steel bars, had failed. 1 The true connection between
magnetism and electricity remained to be discovered.
In 1819, Oerstedt, of Copenhagen, showed that a
magnet tends to set itself at right-angles to a wire carry-
ing an electric current. He also found that the way in
which the needle turns, whether to the right or the left
of its usual position, depends upon the position of the
wire that carries the current whether it is above or
below the needle, and on the direction in which the
current flows through the wire.
185. Oerstedt's Experiment. Very simple appar-
atus suffices to repeat the fundamental experiment. Let
a magnetic needle be suspended on a pointed pivot, as
in Fig. 78. Above it, and parallel to it, is held a stout
Fig. 78.
copper wire, one end of which is joined to one pole of a
battery of one or two cells. The other end of the wire
is then brought into contact with the other pole of the
battery. As soon as the circuit is completed the current
flows through the wire and the needle turns briskly aside.
If the current be flowing along the wire above the needle
1 Down to this point in these lessons there has been no connection between
magnetism and electricity, though something has been said about each. The
student who cannot remember whether a charge of electricity does or does
not affect a magnet, should turn back to what was said in Art. 91.
152
ELEMENTARY LESSONS ON [CHAP. in.
in the direction from north to south, it will cause the
N.- seeking end of the needle to turn eastwards : if the
current flows from south to north in the wire the N. -seek-
ing end of the needle will be deflected westwards. If
the wire is, however, below the needle, the motions will
be reversed, and a current flowing from north to south
will cause the N. -seeking pole to turn westwards.
186. Ampere's Rule. To keep these movements
in memory, Ampere suggested the following fanciful but
useful rule. Suppose a man swimming' in the wire with
the current, and that he turns so as to face the needle ', then
the N. -seeking pole of the needle will be deflected towards
his left hand. In other words, the deflection of the
N. -seeking pole of a magnetic needle, as viewed from
the conductor, is towards the left of the current.
For certain particular cases in which a fixed magnet pole acts
on a movable circuit, the following converse to AmpZrJs Rule
will be found convenient. Suppose a man swimming in the
wire with the current, and that he turns so as to look along the
direction of the lines of force of the pole (i.e. as the lines of
force run, from the pole if it be N. -seeking, towards the pole if it
be S. -seeking), then he and the conducting wire with him will be
urged toward his left.
187. A little consideration will show that if a current
be carried below a needle in one direc-
tion, and then back in the opposite
direction above the needle, by bending
the wire round, as in Fig. 79, the
forces exerted on the needle by both
portions of the current will be in the
same direction. For let a be the
N. -seeking, and b the S. -seeking, pole
of the suspended needle, then the
Fig 79- tendency of the current in the lower
part of the wire will be to turn the
needle so that a comes towards the observer, while b
CHAP, in.] ELECTRICITY AND MAGNETISM. 153
retreats ; while the current flowing above, which also
deflects the N. -seeking pole to its left, will equally urge
a towards the observer, and b from him. The needle
will not stand out completely at right -angles to the
direction of the wire conductor, but will take an oblique
position. The directive forces of the earth's magnetism
are tending to make the needle point north-and-south.
The electric current is acting on the needle, tending
to make it set itself west -and -east. The resultant
force will be in an oblique direction between these,
and will depend upon the relative strength of the two
conflicting forces. If the current is very strong the
needle will turn widely round ; but could only turn com-
pletely to a right-angle if the current were infinitely strong.
If, however, the current is feeble in comparison with the
directive magnetic force, the needle will turn very little.
188. This arrangement will, therefore, serve roughly
as a G-alvanoscope or indicator of currents ; for the
movement of the needle shows the direction of the
current, and indicates whether it is a strong or a weak
one. This apparatus is too rough to detect very delicate
currents. To obtain a more sensitive instrument there
are two possible courses : (z.) Increase the effective
action of the current by carrying the wire more than
once round the needle : (.) Decrease the opposing
directive force of the earth's magnetism by some com-
pensating contrivance.
189. Schweigger's Multiplier. The first of the
above suggestions was carried out by Schweigger, who
constructed a multiplier of many turns of wire. A suit-
able frame of wood, brass, or ebonite, is prepared to
receive the wire, which must be " insulated," or covered
with silk, or cotton, or guttapercha, to prevent the
separate turns of the coil from coming into contact with
each other. Within this frame, which may be circular,
elliptical, or more usually rectangular, as in Fig. 80, the
needle is suspended, the frame being placed so that the
154 ELEMENTARY LESSONS ON [CHAP. in.
wires lie in the magnetic meridian. The greater the
number of turns the more
powerful will be the mag-
netic deflection produced
by the passage of equal
quantities of current. But
if the wire is thin, or the
number of turns of wire
numerous, the resistance
thereby offered to the flow
of electricity may very
V* greatly reduce the strength
of the current. The student
lg ' c will grasp the importance
of this observation when he has read the chapter on
Ohm's Law.
19O. Astatic Combinations. The directive force
exercised by the earth's magnetism on a magnetic needle
may be reduced or obviated by one of two methods :
(a.) By employing a compensating magnet. An ordinary
long bar magnet laid in the magnetic meridian, but with
its N.- seeking pole directed towards the north, will, if
placed horizontally above or below a suspended magnetic
needle, tend to make the needle set itself with its S. -seek-
ing pole northwards. If near the needle it may over-
power the directive force of the earth, and cause the
needle to reverse its usual position. If it is far away, all
it can do is to lessen the directive force of the earth.
At a certain distance the magnet will just compensate
this force, and the needle will be neutral. This arrange-
ment for reducing the earth's directive force is applied
in the reflecting galvanometer shown in Fig. 91, in
which .the magnet at the top, curved in form and capable
of adjustment to any height, affords a means of adjust-
ing the instrument to the desired degree of sensitiveness
by raising or lowering it.
(b.) By using an astatic pair of magnetic needles.
CHAP, in.] ELECTRICITY AND MAGNETISM. 155
If two magnetised needles of equal strength and size are
bound together by a light wire of brass, or aluminium,
in reversed positions, as
shown in Fig. 8 1 , the force
urging one to set itself in
the magnetic meridian is
exactly counterbalanced by
the force that acts on the
other. Consequently this
pair of needles will remain
in any position in which it is
set, and is independent of the
earth's magnetism. Such a
combination is known as an
astatic pair. It is, however, difficult in practice to
obtain a perfectly astatic pair, since it is not easy to
magnetise two needles exactly to equal strength, nor is
it easy to fix them perfectly parallel to one another.
Such an astatic pair is, however,
readily deflected by a current flowing
in a wire coiled around one of the
needles ; for, as shown in Fig. 82,
the current which flows above one
needle and below the other will urge
both in the same direction, because
they are already in reversed positions.
It is even possible to go farther, and
to carry the wire round both needles,
winding the coil around the upper in
the opposite sense to that in which the coil is wound
round the lower needle.
Nobili applied the astatic arrangement of needles to
the multiplying coils of Schweigger, and thus constructed
a very sensitive instrument, the Astatic Galvanometer,
Shown in Fig. 88. The special forms of galvanometer
adapted for the measurement of currents are described
in the next Lesson.
i$6 ELEMENTARY LESSONS ON [CHAP. in.
191. Magnetic field due to Current. Arago
found that if a current be passed through a piece of copper
wire it becomes capable of attracting iron filings to it
so long as the current flows. These filings set them-
selves at right angles to the wire, and cling around it,
but drop off when the circuit is broken. There is, then,
a magnetic " field," around the wire which carries the
current ; and it is important to know how the lines of
force are distributed in this field.
Let the central spot in Fig. 83 represent an imaginary
cross-section of the wire, and let us suppose the current
to be flowing in through the paper at that point. Then
by Ampere's rule a magnet needle placed below will tend
to set itself in the position shown, with its N. pole
pointing to the left. 1 The current will urge a needle
above the wire into the reverse position. A needle on
the right of the current will set itself at right angles to
the current (i.e. in the plane of the paper), and with its
N. pole pointing down,
while the N. pole of a
needle on the left would
* / ^ St.* X be urged uj>. In fact the
\
x
tendency would be to urge
the N. pole round the
Fig. 83. Fig. 84. ,
conductor m the same
way as the hands of a watch move ; while the S. pole
would be urged in the opposite cyclic direction to that of
the hands of a watch. If the current is reversed, and is
regarded as flowing towards the reader, i.e. coming up
out of the plane of the paper, as in the diagram of Fig.
1 If the student has any difficulty in applying Ampere's rule to this case and
the others which succeed, he should carefully follow out the following mental
operation. Consider the spot marked " in " as a hole in the ground into
which the current is flowing, and into which he dives head-foremost. While
in the hole he must turn round so as to face each of the magnets in succession,
and remember that in each case the N. -seeking pole will be urged to his left.
In diagram 84 he must conceive himself as coming up out of the hole in the
ground where the current is flowing out.
CHAP, in.] ELECTRICITY AND MAGNETISM. 157
84, then the motions would be just in the reverse sense.
It would seem from this as if a N.- seeking pole of a
magnet ought to revolve continuously round and round a
current ; but as we cannot obtain a magnet with one
pole only, and as the S. -seeking pole is urged in an
opposite direction, all that occurs is that the needle sets
itself as a tangent to a circular curve surrounding the
conductor. This is what Oerstedt meant when he
described the electric current as acting " in a revolving
manner," upon the magnetic needle. The field of force
with its circular lines surrounding
a current flowing in a straight
conductor, can be examined ex-
perimentally with iron filings in
the following way : A card is
placed horizontally and a stout
copper wire is passed vertically
through a hole in it (Fig. 85).
Iron filings are sifted over the
card (as described in Art. 108),
i r i Fig. 85.
and a strong current from three
or four large cells is passed through the wire. On
tapping the card gently the filings near the wire set
themselves in concentric circles round it.
192. Equivalent Magnetic Shell: Ampere's
Theorem. For many purposes the following way of
regarding the magnetic action of electric currents is
more convenient than the preceding. Suppose we take
a battery and connect its terminals by a circuit of wire,
and that a portion of the circuit be twisted, as in Fig. 86,
into a looped curve, it will be found that the entire
space enclosed by the loop possesses magnetic properties.
In our figure the current is supposed to be flowing round
the loop, as viewed from above, in the same direction as
the hands of a clock move round ; an imaginary man
swimming round the circuit and always facing towards
the centre would have his left side down. By Ampere's
158
ELEMENTARY LESSONS ON [CHAP. in.
rule, then, a N. pole would be urged downwards through
the loop, while a S. pole would be urged upwards. In
fact the space enclosed by the loop of the circuit behaves
Fig. 86.
like a magnetic shell (see Art. 107), having its upper face
of S. -seeking magnetism, and its lower face of N. -seeking
magnetism. It can be shown in every case that a closed
(voltaic circidt is equivalent to a magnetic shell whose
edges coincide in position with the circitit, the shell being
of such a strength that the number of its lines of force is
the same as that of the lines of force due to the current
in the circuit. The circuit acts on a magnet attracting
or repelling it, and being attracted or repelled by it, just
exactly as its equivalent magnetic shell would do. Also,
the circuit itself, when placed in a magnetic field, experi-
ences the same force as its equivalent magnetic shell
would do.
193. Maxwell's Rule. Professor Clerk Maxwell,
who developed this method of treating the subject, has
given the following elegant rule for determining the
mutual action of a circuit and a magnet placed near it.
Every portion of the circuit is acted upon by a force
urging it in such a direction as to make it enclose
within its embrace the greatest possible number of lines of
CHAP, in.] ELECTRICITY AND MAGNETISM.
159
force. If the circuit is fixed and the magnet movable,
then the force acting on the magnet will also be such as to
tend to make the number of lines of force that pass
through the circuit a maximum (see also Art. 317).
194. De la Rive's Floating Battery. The pre-
ceding remarks may be illustrated experimentally by
the aid of a little floating battery. A plate of zinc and one
of copper (see -Fig. 87) are fixed side by side in a large
Fig. 87.
cork, and connected above by a coil of covered copper wire
bent into a ring. This is floated upon a dish containing
dilute sulphuric acid. If one pole of a bar magnet be
held towards the ring it will be attracted or repelled
according to the pole employed. The floating circuit
will behave like the floating magnet in Fig. 44, except
that here we have what is equivalent to a floating
magnetic shell. If the S. pole of the magnet be pre-
sented to that face of the ring which acts as a S. -seeking
pole (viz. that face round which the current is flowing
160 ELEMENTARY LESSONS ON [CHAP. in.
in a clockwise direction), it will repel it. If the pole be
thrust right into the ring, and then held still, the battery
will be strongly repelled, will draw itself off, float away,
turn round so as to present toward the S. pole of the
magnet its N. -seeking face, will then be attracted up,
and will thread itself on to the magnet up to the middle,
in which position as many magnetic lines of force as
possible cross the area of the ring.
It can be shown also that two circuits traversed by
currents attract and repel one another just as two
magnetic shells would do.
It will be explained in Lesson XXVI. on Electro-
magnets how a piece of iron or steel can be magnetised
by causing a current to flow in a spiral wire round it.
195. Strength of the Current in Magnetic
Measure. When a current thus acts on a magnet pole
near it, the force f which it exerts will be proportional
to the strength i of the current, and proportional also
to the strength m of the magnet pole, and to the length
/ of the wire employed : it will also vary inversely as
the square of the distance r from the circuit to the
magnet pole. Or, f= *^-^ dynes. Suppose the wire
looped up into a circle round the magnet pole, then
/=2?rr, and f^1 m dynes. Suppose also that the
circle is of one centimetre radius, and that the magnet
pole is of strength of one unit (see Art. 125), then the
force exerted by the current of strength i will be x i ,
or 2m dynes. In order, therefore, that a current of
strength i should exert a force of i dynes on the unit pole,
one must consider the current as travelling round only
27T
part of the circle, or round a portion of the circum-
ference equal in length to the radius.
196. Unit of Current Strength. A current is
said to have a strength of one " absolute " unit when it
CHAP, in.] ELECTRICITY AND MAGNETISM. 161
is such that if one centimetre length of the circuit is bent
into an arc of one centimetre radius, the current in it
exerts a force of one dyne on a magnet-pole of unit
strength placed at the centre of the arc. The practical
unit of " one ampere r ' is only -n> of this theoretical unit.
(See also Art. 323.)
LESSON XVII. Galvanometers.
197. The term Galvanometer is applied to an
instrument for measuring the strength of electric
currents by means of the deflection of a magnetic needle,
round which the current is caused to flow through a coil
of wire. The simple arrangement described in Art. 188
was termed a " Galvanoscope," or current indicator, but
it could not rightly be termed a "galvanometer ?;1 or
current measurer, because its indications were only
qualitative, not quantitative. The indications of the
needle did not afford accurate knowledge as to the exact
strength of current flowing through the instrument. A
good galvanometer must fulfil the essential condition that
its readings shall really measiire the strength of the
current in some certain way. It should also be suffici-
ently sensitive for the currents that are to be measured
to affect it. The galvanometer adapted for measuring
very small currents (say a current of only one or two
millionth parts of an ampere) will not be suitable for
measuring very strong currents, such as are used in pro-
ducing an electric light. Moreover, if the current to be
measured has already passed through a circuit of great
resistance (as, for example, some miles of telegraph
wire), a galvanometer whose coil is a short one, consist-
1 The terms " Rheoscope" and " Rheometer" are still occasionally applied
to these instruments. A current interrupter is sometimes called a " Rheo-
tome" and the Commutator or Current Reverser, shown in Fig. 149, is
in some books called a " Rheo trope ; but these terms are dropping out of use.
M
1 62
ELEMENTARY LESSONS ON [CHAP. iii.
ing only of a few turns of wire, will be of no use, and a
long-coil galvanometer must be employed with many
turns of wire round the needle. The reason of this is
explained hereafter (Art. 352). Hence it will be seen
that different styles of instrument are needed for different
kinds of work ; but of all the requisites are that they
should afford quantitative measurements, and that they
should be sufficiently sensitive for the current that is to
be measured.
198. Nobili's Astatic Galvanometer. The
instrument constructed by Nobili, consisting of an astatic
pair of needles delicately hung, so that the lower one lay
within a coil of wire
wound upon an ivory
frame (Fig. 88), was
for long the favourite
form of sensitive
galvanometer. The
needles of this instru-
ment, being indepen-
dent of the earth's
magnetism, take their
position in obedience
to the torsion of the
fibre by which they
are hung. The frame
on which the coil is
wound must be set
carefully parallel to
the needles ; and three screw feet serve to adjust the
base of the instrument level. Protection against cur-
rents of air is afforded by a glass shade. When a
current is sent through the wire coils the needles move
to right or left over a graduated circle. When the
deflections are small (i.e. less than 10 or i 5), they are
very nearly proportional to the strength of the currents
that produce them. Thus, if a current produces a
CHAP, in.] ELECTRICITY AND MAGNETISM. 163
deflection of 6 it is known to be approximately three
times as strong as a current which only turns the needle
through 2. But this approximate proportion ceases to
be true if the deflection is more than 15 or 20; for
then the needle is not acted upon so advantageously by
the current, since the poles are no longer within the coils,
but are protruding at the side, and, moreover, the needle
being oblique to the force acting on it, part only of the
force is turning it against the directive force of the fibre ;
the other part of the force is uselessly pulling or pushing
the needle along its length. It is, however, possible to
" calibrate " the galvanometer, that is, to ascertain by
special measurements, or by comparison with a standard
instrument, to what strengths of current particular
amounts of deflection correspond. Thus, suppose it once
known that a deflection of 32 on a particular galvano-
meter is produced by a current of TW of an ampere, then
a current of that strength will always produce on that
instrument the same deflection, unless from any accident
the torsion force or the intensity of the magnetic field is
altered.
199. The Tangent Galvanometer. It is not
for the reasons mentioned above possible to construct
a galvanometer in which the angle (as measured in
degrees of arc) through which the needle is deflected is
proportional throughout its whole range to the strength
of the current. But it is possible to construct a very
simple galvanometer in which the tangent * of 'the angle
of deflection shall be accurately proportional to the
strength of the current. Fig. 89 shows a frequent form
of Tangent Galvanometer. The coil of this instru-
ment consists of a simple circle of stout copper wire
from ten to fifteen inches in diameter. At the centre is
delicately suspended a magnetised steel needle not
exceeding one inch in length, and usually furnished with
a light index of aluminium. The instrument is adjusted
1 See note on Ways of Reckoning Angles, p. 109.
\
164
ELEMENTARY LESSONS ON [CHAP. in.
by setting the coil in the magnetic meridian, the small
needle lying then in the plane of the coil. One essential
feature of this arrangement is, that while the coil is very
large, the needle is relatively very small. The " field "
due to a current passing round the circle is very uniform
at and near the centre, and the lines of force are there
truly normal to the plane of the coil. 1 This is not true
of other parts of the space inside the ring, the force
being neither uniform nor normal in direction, except in
the plane of the coil and at its centre. The needle being
l In order to ensure uniformity of field, Gaugain proposed to hang the
needle at a point on the axis of the coil distant from its centre by a distance
equal to half tha radius of the coils. Helmholtz's arrangement of two
parallel coils, symmetrically set on either side of the needle,Js better ; and a
three-coil galvanometer having the central coil larger than weathers, so that
all three may lie in the surface of a sphere having the smaft^bedle at its
centre, is the best arrangement of all for ensuring that the field at the centre
\a uniform.
CHAP, in.] ELECTRICITY AND MAGNETISM. 165
small its poles are never far from the centre, and hence
never protrude into the regions where the magnetic force
is irregular. Whatever magnetic force the current in
the coil can exert on the needle is exerted normally to
the plane of the ring, and therefore at right angles to
the magnetic meridian. Now, it was proved in Art. 124
that the magnetic force which, acting at right angles to
the meridian, produces on a magnetic needle the de-
flection 8 is equal to the horizontal force of the earth's
magnetism at that place multiplied by the tangent of the
angle of deflection. Hence a current flowing in the coil
will turn the needle aside through an angle such that the
tangent of the angle of deflection is proportional to the
strength of the ciirrent.
EXAMPLE. Suppose a certain battery gave a deflection of
15 on a tangent galvanometer, and another battery
yielding a stronger current gave a deflection of 30. The
strengths currents are not in the proportion of 1 5 : 30,
but in the proportion of tan 15 to tan 30. These
values must be obtained from a Table of natural tangents
like that given on p. 1 1 1, from which it will be seen
that the ratio between the strengths of the currents is
268 : *577, or about 10 : 22.
Or, more generally, if current C produces deflection 5, and
current C' deflection 5', then
C :C' = tan 8 : tan tf
To obviate reference to a table of figures, the circular
scale of the instrument is sometimes graduated into
tangent values instead of being divided into equal
degrees of arc. Let a tangent O T be drawn to the
circle, as in Fig. 90, and along this line let any number
of equal divisions be set off, beginning at O. From
these points draw blUk to the centre. The circle will
thus be divided into a number of pieces, of which those
near O are nearly equal, but which get smaller and
smaller away from O. These unequal pieces correspond
i66
ELEMENTARY LESSONS ON [CHAP. in.
to equal increments of the tangent. If the scale were
divided thus, the readings would be proportional to
the tangents. It is, however, harder to divide an arc
Fig. 90.
into tangent-lines with accuracy than to divide it into
equal degrees ; hence this graduation, though convenient,
is not used where great accuracy is needed.
200. Absolute Measure of Current by Tangent Gal-
vanometer. The strength of a current may be determined in
"absolute" units by the aid of the tangent galvanometer if the
" constants " of the instrument are known. The tangent of the
angle of deflection represents (see Art. 124) the ratio between
the magnetic force due to the current and the horizontal com-
ponent of the earth's magnetic force. Both these forces act on
the needle, and depend equally upon the magnetic moment of the
needle, which, therefore, we need not know for this purpose.
We know that the force exerted by the current at centre of the
coil is proportional to the horizontal force of the earth's mag-
netism multiplied by the tangent of the angle of deflection.
These two quantities can be found from the tables, and from
them we calculate the absolute value of the current, as follows :
Let r represent the radius of the galvanometer coil (measured in
centimetres) ; its total length (if of one turn only) is zirr. The
distance from the centre to all parts of the coil is of course r.
From our definition of the unit of strength of current (Art. 196),
x g- = force (in dynes) at centre,
27T
it follows that
hence i =
= H ' tan 5 ;
- H ' tan
27T
CHAP, in.] ELECTRICITY AND MAGNETISM. 167
The quantity is called the "constant" of the galvanometer.
Hence we obtain the value of the current in absolute (electro-
magnetic) units l by multiplying together the galvanometer con-
stant, the horizontal magnetic force at the place, and the tangent
of the angle of deflection. Tangent galvanometers are often
made with more than one turn of wire. In this case the " con-
stant " is where n is the number of turns in the coil.
2O1. Sine Galvanometer. The disadvantage of
the tangent galvanometer just described is that it is not
very sensitive, because the coil is necessarily very large
as compared with the needle, and therefore far away
from it. A galvanometer with a smaller coil or a larger
needle could not be used as a tangent galvanometer,
though it would be more sensitive. Any sensitive
galvanometer in which the needle is directed by the
earth's magnetism can, however, be used as a Sine
Galvanometer, provided the frame on which the coils
are wound is capable of being turned round a central
axis. When the instrument is so constructed, the
following method of measuring currents is adopted.
The coils are first set parallel to the needle (i.e. in the
magnetic meridian) ; the current is then sent through
it, producing a deflection ; the coil itself is rotated round
in the same sense, and, if turned round through a wide
1 The student will learn (Art. 196 and 323) that the practical unit of
current which we call " one ampere" is only -^ of one "absolute" unit of the
centimetre-gramme-second system.
168 ELEMENTARY LESSONS ON [CHAP, in,
enough angle, will overtake the needle, which will once
more lie parallel to the coil. In this position two forces
are acting on the needle : the directive force of the
earth's magnetism acting along the magnetic meridian,
and the force due to the current passing in the coil,
which tends to thrust the poles of the needle out at
right angles ; in fact there is a " couple " which exactly
balances the " couple " due to terrestrial magnetism.
Now it was shown in the Lesson on the Laws of Mag-
netic Force (Art. 123), that when a needle is deflected
the " moment " of the couple is proportional to the sine
of the angle of deflection. Hence in the sine galvano-
meter, when the coil has been turned round so that the
needle once more lies along it, the strength of the current
in the coil is proportional to the sine of the angle through
which the coil has been turned. *
2O2. The Mirror Galvanometer. When a gal-
vanometer of great delicacy is needed, the moving parts
must be made very light and small. To watch the
movements of a very small needle an index of some
kind must be used ; indeed, in the tangent galvanometer
it is usual to fasten to the short stout needle a delicate
stiff pointer of aluminium. A far better method is to
fasten to the needle a very light mirror of silvered glass,
by means of which a beam of light can be reflected on
to a scale, so that every slightest motion of the needle
is magnified and made apparent. The mirror galvano-
1 Again the student who desires to compare the strength of two currents
will require the help of a Table of natural sines, like that given on page in.
Suppose that with current C the coils had to be turned through an angle of
Q degrees ; and that with a different current C' the coils had to be turned
through Q' degrees, then
C : C' = sin : sin ff.
It is of course assumed that the instrument is provided with a scale of
degrees on which to read off the angle through which the coils have been
turned. It is possible here also, for rough purposes, to graduate the circle
not in degrees of arc but in portions corresponding to equal additional
values of the sine. The student should try this way of dividing a circle
after reading the note On Ways of Reckoning Angles, p. 109.
CHA?. in.] ELECTRICITY AND MAGNETISM.
169
meters devised by Sir. W. Thomson for signalling through
submarine cables, are admirable examples of this class
of instrument. In Fig. 91 the general arrangements of
this instrument are shown. The body of the galvano-
meter is supported on three screw feet by which it can
be adjusted. The magnet consists of one or more
small pieces of steel watch-spring attached to the back
Fig. 91.
of a light concave silvered glass mirror about as large
as a threepenny piece. This mirror is hung by a single
fibre of cocoon silk within the coil, and a curved magnet,
which serves to counteract the magnetism of the earth,
or to direct the needle, is carried upon a vertical support
above. Opposite the galvanometer is placed the scale.
A beam of light from a paraffin lamp passes through
a narrow aperture under the scale and falls on the
mirror, which reflects it back on to the scale. The
mirror is slightly concave, and gives a well defined spot
of light if the scale is adjusted to suit the focus of the
1 70 ELEMENTARY LESSONS ON [CHAP. in.
mirror. 1 The adjusting magnet enables the operator to
bring the reflected spot of light to the zero point at the
middle of the scale. The feeblest current passing through
the galvanometer will cause the spot of light to shift to
right or left. The tiny current generated by dipping
into a drop of salt water the tip of a brass pin and a
steel needle (connected by wires to the terminals of the
galvanometer) will send the spot of light swinging right
across the scale. If a powerful lime -light is used, the
movement of the needle can be shown to a thousand
persons at once. For still more delicate work an astatic
pair of needles can be used, each being surrounded by
its coil, and having the mirror rigidly attached to one of
the needles.
Strong currents must not be passed through very
sensitive galvanometers, for, even if they are not spoiled,
the deflections of the needle will be too large to give
accurate measurements. In such cases the galvan-
ometer is used with a shunt^ or coil of wire arranged so
that the greater part of the current shall flow through it,
and pass the galvanometer by, only a small portion of the
current actually traversing the coils of the instrument.
The resistance of the shunt must bear a known ratio to
the resistance of the instrument, according to the prin-
ciple laid down in Art. 353 about branched circuits.
2O3. Differential Galvanometer. For the pur-
pose of comparing two currents a galvatlpfheter is
sometimes employed, in which the coil consists of two
separate wires wound side by side. If two equal currents
are sent in opposite directions through these wires, the
needle will not move. If the currents are, however,
unequal, then the needle will be moved by the stronger
1 As concave mirrors are expensive, a plain mirror behind a lens of
suitable focus may be substituted. The thin discs of glass used in
mounting objects for the microscope form, when silvered, excellent light
mirrors. Where great accuracy is desired a fine wire is placed in the
aperture traversed by the beam of light, and the image of this appears
when focused on the screen as a dark line crossing the spot of light.
CHAP, in.] ELECTRICITY AND MAGNETISM. 171
of them, with an intensity corresponding to the difference
of the strengths of the two currents
204. Ballistic Galvanometer. In order to measure
the strength of currents which last only a very short time,
galvanometers are employed in which the needle takes
a relatively long time to swing. This is the case with
long or heavy needles ; or the needles may be weighted
by enclosing them in leaden cases. As the needle swings
slowly round, it adds up, as it were, the varying impulses
received during the passage of a transient current.
The sine oj half the angle of the first swing is proportional
to the quantity of electricity that has flowed through the
coil. The charge of a condenser may thus be measured
by discharging it through a ballistic galvanometer.
LESSON XVIII. Chemical Actions of the Current :
Voltameters.
205. In addition to the chemical actions inside the
cells of the battery, which always accompany the produc-
tion of a current, there are also chemical actions produced
outside the battery when the current is caused to pass
through certain liquids. Liquids may be divided into
three classes (i) those which do not conduct at all, such
as turpentine and many oils, particularly petroleum ; (2)
those which conduct without decomposition , viz. mercury
and other molten metals, which conduct just as solid
metals do ; (3) those which are decomposed when they
conduct a current, viz. the dilute acids, solutions of
metallic salts, and certain fused solid compounds.
206. Decomposition of "Water. In the year 1 800
Carlisle and Nicholson discovered that the voltaic current
could be passed through water, and that in passing through
it decomposed a portion of the liquid into its constituent
gases. These gases appeared in bubbles on the ends of
the wires which led the current into and out of the
liquid ; bubbles of oxygen gas appearing at the point
172 ELEMENTARY LESSONS ON [CHAP. in.
where the current entered the liquid, and hydrogen
bubbles where it left the liquid. It was soon found that
a great many other liquids, particularly dilute acids and
solutions of metallic salts, could be similarly decomposed
by passing a current through them.
207. Electrolysis. To this process of decomposing
a liquid by means of an electric current Faraday gave
the name, of electrolysis (i.e. electric analysis) ; and
those substances which are capable of being thus decom-
posed or " electrolysed " he termed electrolytes.
The ends of the wires leading from and to the battery
are called electrodes ; and to distinguish them, that by
which the current enters is called the anode, that by
which it leaves the kathode. The vessel in which a
liquid is placed for electrolysis is termed an electrolytic cell.
208. Electrolysis of "Water. Returning to the
de'composition of water, we may remark that perfectly
pure water appears not to conduct, but its resistance is
greatly reduced by the addition of a few drops of sul-
phuric or of hydrochloric acid. The apparatus shown in
Fig. 92 is suitable for this purpose. Here a battery of
two cells (those shown are circular Bunsen's batteries)
is seen with its poles connected to two strips of metallic
platinum as electrodes, which project up into a vessel con-
taining the acidulated water. Two tubes closed at one
end, which have been previously filled with water and
inverted, receive the gases evolved at the electrodes.
Platinum is preferred to other metals such as copper or
iron for electrodes, since it is less oxidisable and resists
every acid. It is found that there is almost exactly
twice as much hydrogen gas (by volume) evolved at the
kathode as there is of oxygen at the anode. This fact
corresponds with the known chemical composition of
water, which is produced by combining together these
two gases in the proportion of two volumes of the
former to one of the latter. The proportions of gases
evolved, however, are not exactly two to one, for at first a
CHAP, in.] ELECTRICITY AND MAGNETISM.
173
very small quantity of the hydrogen is absorbed or
" occluded " by the platinum surface, while a more con-
siderable proportion of the oxygen about I per cent
Fig 02.
is given off in the denser allotropic form of ozone, which
occupies less space and is also slightly soluble in the
water. When a sufficient amount of the gases has been
evolved and collected they may be tested ; the hydrogen
by showing that it will burn, the oxygen by its causing
a glowing spark on the end of a splinter of wood to burst
into flame. If the two gases are collected together in a
common receiver, the mixed gas will be found to possess
the well known explosive property of mixed hydrogen
and oxygen gases. The chemical decomposition is ex-
pressed in the following equation :
H 2 H 2 + O
Water yields 2 vols. of Hydrogen and i vol. of Oxygen.
2O9. Electrolysis of Sulphate of Copper. We
will take as another case the electrolysis of a solution of
the well-known " blue vitriol " or sulphate of copper. If
174 ELEMENTARY LESSONS ON [CHAP. in.
a few crystals of this substance are dissolved in water
a blue liquid is obtained, which is easily electrolysed
between two electrodes of platinum foil, by the current
from a single cell of any ordinary battery. The chemical
formula for sulphate of copper is CuSO 4 . The result of
the electrolysis is to split it up into metallic copper,
which is deposited in a film upon the kathode, and
" Sulphion " an easily decomposed compound of sulphur
and oxygen, which is immediately acted upon by the
wafer forming sulphuric acid and oxygen. This oxygen
is liberated in bubbles at the anode. The chemical
changes are thus expressed :
CuSO 4 Cu + SO 4
Sulphate of Copper becomes Copper and Sulphion ;
SO 4 + H 2 O H 2 SO 4 + O"^
Sulphion and water produce Sulphuric acid and Oxygen,
In this way, as the current continues to flow, copper is
continually withdrawn from the liquid and deposited on
the kathode, and the liquicl gets more and more acid. If
copper electrodes are used, instead of platinum, no oxygen
is given off at the anode, but the copper anode itself dis-
solves away into the liquid at exactly the same rate as
the copper of the liquid is deposited on the kathode.
21O. Anions and Kathions. The atoms which
thus are severed from one another and carried invisibly
by the current to the electrodes, and there deposited,
are obviously of two classes : one set go to the anode,
the other to the kathode. Faraday gave the name of
ions to these wandering atoms ; those going to the
anode being anions, and those going to the kathode
being kathions. Anions are sometimes regarded as
" electro-negative " because they move as if attracted
toward the + pole of the battery, while the kathions
are regarded as " electro-positive." Hydrogen and the
metals are kathions, moving apparently with the direction
assumed as that of the current, and are deposited where
CHAP. Hi.] ELECTRICITY AND MAGNETISM. 175
the current leaves the electrolytic cell. The anions are
oxygen, chlorine, etc. When, for example, chloride of
tin is electrolysed, metallic tin is deposited on the kath-
ode, and chlorine gas is evolved at the anode.
211. Quantitative Laws of Electrolysis.
(i.) The amount of chemical action is equal at all points
of a circuit. If two or more electrolytic cells are placed
at different points of a circuit the amount of chemical
action will be the same in all, for the same quantity of
electricity flows past every point of the circuit in the
same time. If all these cells contain acidulated water,
the quantity, for example, of hydrogen set free in *each
will be the same ; or, if they contain a solution of
sulphate of copper, identical quantities of copper will be
deposited in each. If some of the cells contain acidu-
lated water, and others contain sulphate of copper, the
weights of hydrogen and of copper will not be equal,
but will be in chemically equivalent quantities.
(ii.) The amount of an ion liberated at an electrode
in a given time is proportional to the strength of the
current. A current of 2 amperes will cause just twice
the quantity of chemical decomposition to take place as
a current of I ampere would do in the same time.
(iii.) The amount of an ion liberated at an electrode
in one second is equal to the strength of the current
multiplied by the " electro -chemical equivalent" of the
ion. It has been found by experiment that the passage
of one coulomb of electricity through water liberates
0000105 gramme i of hydrogen. Hence, a current
the strength of which is C (amperes') will liberate
C x -0000105 grammes of hydrogen per second. The
quantity -0000105 is called the electro-chemical equiva-
lent of hydrogen. The " electro -chemical equivalents"
of other elements can be easily calculated if their
chemical " equivalent " is known. Thus the chemical
1 Kohlrausch says '000010521 ; Mascart says '000010415.
176 ELEMENTARY LESSONS ON [CHAP. in.
" equivalent >jl of copper is 31*5; multiplying this by
0000105 we get as the electro -chemical equivalent of
copper the value -00033075 (grammes).
212. TABLE OF ELECTRO-CHEMICAL EQUIVALENTS, ETC.
Atomic
Weight.
Val-
ency.
Chemical
Equivalent.
Electro-chemical
Equivalent
(grammes
per coulomb).
Electropositive
-/ Hydrogen ....
Potassium ....
Sodium ....
Gold
Silver
I*
39'i
23-
196-6
108-
I
I
I
3
I
39'i
23-
65-5
108-
0000105
OOO4 1 05
0002415
0006875
*OO I I 34.O
-Copper (Cupric) .
,, (Cuprose)
Mercury (Mercuric) .
,, (Mercurose)
Tin (Stannic) .
,, (Stannose)
Iron (Ferric) .
(FeiTose) . .
Nickel
63-
63--
200'
200-
118-
118-
56-
56-
CQ
2
I
2
4
2
2
31*5
63-
IOO*
200'
29'5
59'
14'
28-
2Q'C
' -0003307
0006615
OOIO5OO
0021000
0003097
0006195
OOOI47O
0002940
'OOO^OQ?
"Zinc
6;-
2
12'<
'OOO34.I2
Lead .....
Electronegative
^Oxygen ....
Chlorine ....
Iodine . .
Bromine ....
Nitrogen ....
207-
16-
35'5
127-
80-
M>
2
I
I
I
3
I03-5
8-
35'5
127-
80-
4'3
ODI0867
iH?
000084O
0003727
0013335
0008400
OO00490
1
1 The chemical "equivalent" must not be confounded with the "atomic
weight." The atomic weight of copper is 63, that is to say, its atoms are 63
times as heavy as atoms of hydrogen. But in chemical combinations one
atom of copper replaces, or is "worth," two atoms of hydrogen ; hence the
weight of copper equivalent to i of hydrogen is 6 -/ = 31^. In all cases the
atomic weight,
chemical equivalent is the quotient j g The above Table
gives full statistical infoitnation.
CHAP, in.] ELECTRICITY AND MAGNETISM. 177
213. The following equation embodies the rule for
finding the weight of any given ion disengaged from an
electrolytic solution during a known time by a current
whose strength is known. Let C be the strength of the
current (reckoned in amperes), t the time (in seconds),
z the electro-chemical equivalent, and w the weight (in
grammes) of the element liberated ; then
or, in words, the weight (in grammes) of an element
deposited by electrolysis is found by multiplying its
electro-chemical equivalent by the strength of the current
(reckoned in amperes), and by the time (in seconds),
during which the current continues to flow.
EXAMPLE. A current from five Darnell's cells was passed
through two electrolytic cells, one containing a solution
of silver, the other acidulated water, for ten minutes.
A tangent galvanometer in the circuit showed the
strength of the current to be *5 amperes. The weight
of silver deposited will be "0011340 x -5 x 10 x 60
= '3402 gramme. The weight of hydrogen evolved
in the second cell will be -0000105 x -5 x 10 x 60
= '00315 gramme.
214. Voltameters. The second of the above laws,
that the amount of an ion liberated in a given time is
proportional to the strength of the current, is sometimes
known as Faradafs Law, from its discoverer. Faraday
pointed out that it affords a chemical means of measur-
ing the strength of currents. He gave the name of
voltameter to an electrolytic cell arranged for the
purpose of measuring the strength of the current by
the amount of chemical action it effects.
215. Water -Voltameter. The apparatus shown
in Fig. 92 might be appropriately termed a Water-
Voltameter, provided the tubes to collect the gases
be graduated, so as to measure the quantities evolved.
N
i78 ELEMENTARY LESSONS ON [CHAP. itt.
The weight of each measured cubic centimetre of hydro-
gen (at the standard temperature of o C, and pressure
of 760 millims.) is known to be -0000896 grammes.
Hence, if the number of cubic centimetres liberated
during a given time by a current of unknown strength
be ascertained, the strength of the current can be calcu-
lated by first reducing the volume to weight, and then
dividing by the electro-chemical equivalent, and by the
time. Each coulomb of electricity liberates in its flow
1176 cubic centimetres of hydrogen, and -0588 c. c.
of oxygen. If these gases are collected together in a
mixed-gas voltameter there will be '1764 c. c. of the
mixed gases evolved for every coulomb of electricity
which passes. To decompose 9 grammes of water,
liberating I gramme of H and 8 grammes of O, requires
95,050 coulombs.
216. Copper Voltameter. As mentioned above,
if sulphate of copper is electrolysed between two elec-
trodes of copper, the anode is slowly dissolved, and the
kathode receives an equal quantity of copper as a
deposit on its surface. One coulomb of electricity will
cause '0003307 grammes to be deposited ; and to deposit
one gramme weight requires a total quantity of 3024
coulombs to flow through the electrodes.
By weighing one of the electrodes before and after the passage of a current,
the gain (or loss) will be proportional to the quantity of electricity that has
passed. In 1879 Edison, the inventor, proposed to apply this method for
measuring the quantity of electricity supplied to houses for electric lights in
them ; a small copper Voltameter being placed in a branch of the circuit
which supplied the house, to serve as a meter. Various other kinds of
Coulombmeters have been proposed, having clockwork counters, rolling
integrating discs, and other mechanical devices to add up the total quantity
of electricity conveyed by the current.
217. Comparison of Voltameters -with Gal-
vanometers. It will be seen that both Galvanometers
and Voltameters are intended to measure the strength of
currents, one by magnetic, the other by chemical means.
Faraday demonstrated that the magnetic and the chemical
actions of a current are proportional to one another.
CHAP, in.] ELECTRICITY AND MAGNETISM. 179
The galvanometer shows, however, the strength of the
current at any moment; and its variations in strength
from one moment to another, by the position of the
needle. In the Voltameter, a varying current may
liberate the bubbles of gas or the atoms of copper rapidly
at one moment, and slowly the next, but all the varying
quantities will be simply added together in the total
yield. In fact, the voltameter gives us the "time
integral " of the current. It tells us what quantity of
electricity has flowed through it during the experiment,
rather than how strong the current was at any one
moment.
218. Chemical Test for Weak Currents. A
very feeble current suffices to produce a perceptible
amount of change in certain chemical substances. If
a few crystals of the white salt iodide of potassiitm are
dissolved in water, and then a little starch paste is added,
a very sensitive electrolyte is obtained, which turns to
an indigo blue colour at the anode when a very weak
current passes through it. The decomposition of the
salt liberates iodine at the anode, which, acting on the
starch, forms a coloured compound. White blotting-
paper, dipped into the prepared liquid, and then laid on
the kathode and touched by the anode, affords a con-
venient way of examining the discoloration due to a
current. A solution of Ferrocyanide of Potassium affords
similarly on electrolysis the well-known tint of Prussian
Blue. Bain proposed to utilise this in a Chemical
Writing Telegraph, the short and long currents trans-
mitted along the line from a battery being thus recorded
in blue marks on a strip of prepared paper, drawn along
by clockwork under the terminal of the positive wire.
Faraday showed that chemical discoloration of paper
moistened with starch and iodide of potassium was pro-
duced by the passage of all different kinds of electricity
frictional, voltaic, thermo-electric, and magneto -electric,
even by that evolved by the Torpedo and the
i8o ELEMENTARY LESSONS ON [CHAP, m,
Gymnotus. In fact, he relied on this chemical test as
one proof of the identity of the different kinds.
219. Internal and External Actions. In an
earlier Lesson it was shown that the quantity of chemical
action inside the cells of the battery was proportional to
the strength of the current. Hence, Law (i.) of Art. 211,
applies both to the portion of the circuit within the
battery and to that without it.
Suppose 3 Daniell's cells are being employed to decompose
water in a voltameter. Then while I gramme weight (11,200
cub. centims.) of hydrogen and 8 grammes (5,600 c. c.) of
oxygen are set free in the voltameter, 31*5 grammes of copper
will be deposited in each cell of the battery, and (neglecting loss
by local action), 32*5 grammes of zinc will be dissolved in each
cell.
220. It will therefore be evident that the electrolytic
cell is the converse of the voltaic cell. The chemical work
done in the voltaic cell furnishes the energy of the current
which that cell sets up in the circuit. In the electrolytic
cell chemical work is performed, the necessary energy
being furnished by the current of electricity which is
sent into the cell from an independent battery or other
source.
A theory of electrolysis, and some examples of its
application, are given in Chapter XXXVIII. on Electro-
chemistry.
LESSON XIX. Physical and Physiological Effects of
the Current.
221. Molecular Actions. Metal Conductors, when
subjected to the prolonged action of currents, undergo
slow molecular changes. Wires of copper and brass
gradually become brittle under its influence. During
the passage of the current through metallic wires their
CHAP, in.] ELECTRICITY AND MAGNETISM. 181
cohesion is temporarily lessened, and there also appears
to be a decrease in their coefficient of elasticity. It was
thought by Edlund that a definite elongation could be
observed in strained wires when a current was passed
through them ; but it has not yet been satisfactorily
shown that this elongation is independent of the elonga-
tion due to the heating of the wire owing to the resistance
it opposes to the current.
222. Electric Osmose. Porret observed that if a
strong current is led into certain liquids, as if to electro-
lyse them, a porous partition being placed between the
electrodes, the current mechanically carries part of the
liquid through the porous diaphragm, so that the liquid
is forced up to a higher level on one side than on the
other. This phenomenon, known as electric osmose, is
most manifest when badly conducting liquids, such as
alcohol and bisulphide of carbon, are used. The transfer
through the diaphragm takes place in the direction of
the current ; that is to say, the liquid is higher about
the kathode than round the anode.
223. Electric Distillation. Closely connected
with the preceding phenomenon is that of the electric
distillation of liquids. It was noticed by Beccaria that
an electrified liquid evaporated more rapidly than one
not electrified. Gernez has recently shown that in a
bent closed tube, containing two portions of liquid, one
of which is made highly + and the other highly , the
liquid passes over from + to - . This apparent distilla-
tion is not due to difference of temperature, nor does it
depend on the extent of surface exposed, but is effected
by a slow creeping of the liquid along the interior surface
of the glass tubes. Bad conductors, such as turpentine,
do not thus pass over.
224. Diaphragm Currents. Professor Quincke
discovered that a current is set up in a liquid when it is
forced by pressure through a porous diaphragm. This
phenomenon may be regarded as the converse of electric
182 ELEMENTARY LESSONS ON [CHAP. in.
osmose. The E.M.F. of the current varies with the
pressure and with the nature of the diaphragm. When
water was forced at a pressure of one atmosphere
through sulphur, the difference of potential was over 9
volts. With diaphragms of porcelain and bladder the
differences were only -35 and -01 volts respectively.
225. Electro-Capillary Phenomena. If a hori-
zontal glass tube, turned up at the ends, be filled with
dilute acid, and a single drop of mercury be placed at
about the middle of the tube, the passage of a current
through the tube will cause the drop to move along
towards the negative pole. It is believed that the
liberation of very small quantities of gas by electrolysis at
the surface where the mercury and acid meet alters the
surface-tension very considerably, and thus a movement
results from the capillary forces. Lippmann, Dewar,
and others, have constructed upon this principle capillary
electrometers ', in which the pressure of a column of liquid
is made to balance the electro-capillary force exerted at
the surface of contact of mercury and dilute acid, the
electro-capillary force being nearly proportional to the
electromotive-force when this does not exceed one volt.
Fig. 93 shows the capillary electrometer of Dewar.
A glass tube rests horizontally between two glass dishes
in which holes have been bored to receive the ends of
Fig- 93-
the tube. It is filled with mercury, and a single drop
of dilute acid is placed in the tube. Platinum wires to
serve as electrodes dip into the mercury in the dishes.
An E.M.F. of only ^ volt suffices to produce a measure-
CHAP, in.] ELECTRICITY AND MAGNETISM. 183
able displacement of the drop. The direction of the
displacement varies with that of the current.
226. Physiological Actions. Currents of elec-
tricity passed through the limbs affect the nerves with
certain painful sensations, and cause the muscles to
undergo involuntary contractions. The sudden rush of
even a small charge of electricity from a Leyden jar
charged to a high potential, or from an induction coil
(see Fig. 148), gives a sharp and painful shock to the
system. The current from a few strong Grove's cells,
conveyed through the body by grasping the terminals
with moistened hands, gives a very different kind of
sensation, not at all agreeable, of a prickling in the joints
of the arms and shoulders, but not producing any
spasmodic contractions, except it be in nervous or
weakly persons, at the sudden making or breaking of
the circuit. The difference between the two cases lies
in the fact that the tissues of the body offer a very con-
siderable resistance, and that the difference of potential
in the former case may be many thousands of volts ;
hence, though the actual quantity stored up in the
Leyden jar is very small, its very high E.M.F. enables
it at once to overcome the resistance. The battery,
although it might, when working through a good con-
ductor, afford in one second a thousand times as much
electricity, cannot, when working through the high re-
sistance of the body, transmit more than a small fraction,
owing to its limited E.M.F.
After the discovery of the shock of the Leyden jar by
Cunaeus in 1745 many experiments were tried. Louis
XV. of France caused an electric shock from a battery of
Leyden jars to be administered to 700 Carthusian monks
joined hand in hand, with prodigious effect. Franklin
killed a turkey by a shock from a Leyden jar.
227. In 1752 Sulzer remarked that " if you join two
pieces of lead and silver, and then lay them upon the
tongue, you will notice a certain taste resembling that of
184 ELEMENTARY LESSONS ON [CHAP. in.
green vitriol, while each piece apart produces no such
sensation." This galvanic taste, not then suspected
to have any connection with electricity, may be ex-
perienced by placing a silver coin on the tongue and a
steel pen under it, the edges of them being then brought
into metallic contact. The same taste is noticed if the
two wires from the poles of a voltaic cell are placed in
contact with the tongue.
228. Ritter discovered that a feeble current trans-
mitted through the eyeball produces the sensation as of
a bright flash of light by its sudden stimulation of the
optic nerve. A stronger current transmitted by means
of moistened conductors attached to the battery terminals
gave a sensation of blue and green colours in flowing
between the forehead and the hand. Helmholtz, re-
peating this experiment, observed only a wild rush of
colour. Dr. Hunter saw flashes of light when a piece
of metal placed under the tongue was touched against
another which touched the moist tissues of the eye.
Volta and Ritter heard musical sounds when a current
was passed through the ears ; and Humboldt found a
sensation to be produced in the organs of smell when a
current was passed from the nostril to the soft palate.
Each of the specialised senses can be stimulated into
activity by the current. Man possesses no specialised
sense for the perception of electrical forces, as he does
for light and for sound ; but there is no reason for denying
the possibility that some of the lower creatures may be
endowed with a special electrical sense.
The following experiment shows the effect of feeble
currents on cold-blooded creatures. If a copper (or silver)
coin be laid on a piece of sheet zinc, and a common
garden snail be set to crawl over the zinc, directly
it comes into contact with the copper it will suddenly
pull in its horns, and shrink in its body. If it is set to
crawl over two copper wires, which are then placed in
contact with a feeble voltaic cell, it immediately an-
CHAP, in.] ELECTRICITY AND MAGNETISM.
185
nounces the establishment of a current by a similar
contraction. 1
229. Muscular Contractions. In 1678 Swam-
merdam showed to the Grand Duke of Tuscany that when
a portion of muscle of a frog's leg hanging by a thread of
nerve bound with silver wire was held over a copper
support, so that both nerve and wire touched the copper,
the muscle immediately contracted. More than a cen-
Fig. 94.
tury later Galvani's attention was drawn to the subject
by his observation of spasmodic contractions in the legs
of freshly-killed frogs under the influence of the " return-
shock " experienced every time a neighbouring electric
machine was discharged. Unaware of Swammerdam's
experiment, he discovered in 1786 the fact (alluded to in
1 It will scarcely be credited that a certain Jules Alix once seriously pro-
posed a system of telegraphy based on this physiological phenomenon.
186 ELEMENTARY LESSONS ON [CHAP. in.
Art. 148 as leading ultimately to the discovery of the
Voltaic Pile) that when nerve and muscle touch two
dissimilar metals in contact with one another a con-
traction of the muscle takes place. The limbs of the
frog, prepared as directed by Galvani, are shown in Fig.
94. After the animal has been killed the hind limbs
are detached and skinned ; the crural nerves and their
attachments to the lumbar vertebrae remaining. For
some hours after death the limbs retain their contractile
power. The frog's limbs thus prepared form an ex-
cessively delicate galvanoscope : with them, for example,
the excessively delicate induction-currents of the tele-
phone (Lesson XL.) can be shown, though the most '
sensitive galvanometers barely detect them. Galvani
and Aldini proved that other creatures undergo like
effects. With a pile of 100 pairs Aldini experimented
on newly killed sheep, oxen, and rabbits, and found them
to suffer spasmodic muscular contractions. Humboldt
proved the same on fishes ; and Zanotti, by sending a
current through a newly killed grasshopper, caused it to
emit its familiar chirp. Aldini, and later Dr. Ure of
Glasgow, experimented on the bodies of executed crimi-
nals, with a success terrible to behold. The facial
muscles underwent horrible contortions, and the chest
heaved with the contraction of the diaphragm. This
has suggested the employment of electric currents as an
adjunct in reviving persons who have been drowned, the
contraction of the muscles of the chest serving to start
respiration into activity. The small muscles attached
to the roots of the hairs of the head appear to be
be markedly sensitive to electrical conditions from the
readiness with which electrification causes the hair to
stand on end.
23O. Conditions of Muscular Contraction. To
produce muscular contraction the current must traverse
apportion of the nerve longitudinally. In a freshly pre-
pared frog the current causes a contraction only momen-
CHAP, in.] ELECTRICITY AND MAGNETISM. 187
tarily when the circuit is made or broken. A rapidly
interrupted current will induce a second contraction
before the first has had time to pass off, and the muscle
may exhibit thus a continuous contraction resembling
tetanus. The prepared frog after a short time becomes
less sensitive, and a " direct " current (that is to say, one
passing along the nerve in the direction from the brain
to the muscle) only produces an effect when circuit is
made, while an " inverse " current only produces an
effect when the circuit is broken. Matteucci, who
observed this, also discovered by experiments on living
animals that there is a distinction between the con-
ductivity of sensory and motor nerves, a "direct"
current affecting the motor nerves on making the
circuit, and the sensory nerves on breaking it ; while
an " inverse " current produced inverse results. Little
is, however, yet known of the conditions of con-
ductivity of the matter of the nerves ; they conduct
better than muscular tissue, cartilage, or bone ; but of
all substances in the body the blood conducts best.
Powerful currents doubtless electrolyse the blood to
some extent, coagulating it and the albumin it contains.
The power of contracting under the influence of the
current appears to be a distinguishing property of
protoplasm wherever it occurs. The amoeba, the
most structureless of organisms, suffers contractions.
Ritter discovered that the sensitive plant shuts up when
electrified, and Burdon Sanderson has shown that this
property extends to other vegetables, being exhibited by
the carnivorous plant, the Dionaea or Venus' Fly Trap.
231. Animal Electricity. Although, in his later
writings at least, Galvani admitted that the electricity
thus operating arose from the metals employed, he
insisted on the existence of an animal electricity resident
in the muscular and nervous structures. He showed
that contractions could be produced without using any
metals at all by merely touching a nerve at two different
i88 ELEMENTARY LESSONS ON [CHAP. in.
points along its length with a morsel of muscle cut from
a living frog ; and that a conductor of one metal when
joining a nerve to a muscle also sufficed to cause con-
traction in the latter. Galvani and Aldini regarded
these facts as a disproof of Volta's contact -theory.
Volta regarded them as proving that the contact
between nerve and muscle itself produced (as in the
case of two dissimilar metals) opposite electrical con-
ditions. Nobili, later, showed that when the nerve and
the muscle of the frog were respectively connected by a
water -contact with the terminals of a delicate galvan-
ometer, a current is produced which lasts several hours :
he even arranged a number of frogs' legs in series,
like the cells of a battery, and thus increased the current.
Matteucci showed that through the muscle alone there is
an electromotive-force. Du Bois Reymond has shown
that if the end of a muscle be cut across, the ends of the
muscular fibres of the transverse section are negative,
and the sides of the muscular fibres are positive, and
that this difference of potential will produce a current
even while the muscle is at rest. To demonstrate this
he employed a fine astatic galvanometer with 20,000
turns of wire in its coils ; and to obviate errors arising
from the contact of the ends of the wires with the tissues
unpolarisable electrodes were used, made by plunging
terminal zinc points into a saturated solution of sulphate
of zinc, contained in a fine glass tube, the end of which
was stopped with a porous plug of moistened china clay.
The contraction of muscles also produces currents.
These Du Bois Reymond obtained from his own muscles
by dipping the tips of his fore -fingers into two cups
of salt water communicating with the galvanometer
terminals. A sudden contraction of the muscles of
either arm produced a current from the contracted
toward the uncontracted muscles. Dewar has shown
that when light falls upon the retina of the eye an
electric current is set up in the optic nerve.
CHAP, in.] ELECTRICITY AND MAGNETISM. 189
232. Medical Applications. Electric currents
have been successfully employed as an adjunct in
restoring persons rescued from drowning ; the contrac-
tion of the diaphragm and chest muscles serving to start
respiration. Since the discovery of the Leyden jar
many attempts have been made to establish an electrical
medical treatment. Discontinuous currents, particularly
those furnished by small induction-coils and magneto-
electric machines, are employed by practitioners to
stimulate the nerves in paralysis and other affections.
Electric currents should not be used at all except with
great care, and under the direction of regularly trained
surgeons. 1
1 It is not out of place to enter an earnest caution on this head against the
numerous quack doctors who deceive the unwary with magnetic and
galvanic "appliances." In many cases these much-advertised shams have
done incalculable harm : in the very few cases where some fancied good has
accrued the curative agent is probably not magnetism, but flannel 1
ELEMENTARY LESSONS ON [CHAP. iv.
Second
CHAPTER IV.
/
ELECTROSTATICS.
LESSON XX. Theory of Potential.
233. By the Lessons in Chapter I. the student will
have obtained some elementary notions upon the exist-
ence and measurement of definite quantities of electricity.
In the present Lesson, which is both one of the hardest
and one of the most important to the beginner, and
which he must therefore study the more carefully, the
laws which concern the magnitude of electrical quantities
and their measurement are more fully explained. In no
branch of knowledge is it more true than in electricity,
that " science is measurement." That part of the science
of electricity which deals with the measurement of
charges of electricity is called Electrostatics. We
shall begin by discussing first the simple laws of electric
force, which were brought to light in Chapter I. by
simple experimental means.
234. First Law of Electrostatics. Electric
charges of similar sign repel one another, but electric
charges of opposite signs attract one another. The funda-
mental facts expressed in this Law were fully explained
in Lesson I. Though familiar to the student, and
apparently simple, these facts require for their complete
explanation the aid of advanced mathematical analysis.
They will here be treated as simple facts of observation.
CHA*>. tvj ELECTRICITY AND MAGNETISM. 191
235. Second Law of Electrostatics. The force
exerted between two charges of electricity (supposing them
to be collected at points or on two small spheres), is
directly proportional to their prodiict^ and inversely
proportional to the square of the distance between them.
This law, discovered by Coulomb, and called Coulomb's
Law, was briefly alluded to (on page 16) in the account
of experiments made with the torsion -balance ; and
examples were there given in illustration of both parts of
the law. We saw, too, that a similar law held good for
the forces exerted between two magnet poles. Coulomb
applied also the method of oscillations to verify the
indications of the torsion-balance and found the results
entirely confirmed. We may express the two clauses of
Coulomb's law, in the following symbolic manner. Let
/stand for the force, q for the quantity of electricity in
one of the two charges, and q' for that of the other
charge, and let d stand for the distance between them.
Then,
(i.) /is proportional to q x /,
and (2.) /is proportional to~ 2 -
These two expressions may be combined into one ;
and it is most convenient so to choose our units or
standards of measurement that we may write our symbols
as an equation :
236. Unit of Electric Quantity. If we are, how-
ever, to write this as an equality, it is clear that we
must choose our unit of electricity in accordance with
the units already fixed for measuring force and distance.
All electricians are now virtually agreed in adopting a
system which is based upon three fundamental units :
viz., the Centimetre for a unit of length; the Gramme
for a unit of mass; the Second for a unit of time. All
192 ELEMENTARY LESSONS ON [CHAP. iv.
other units can be derived from these, as is explained
in the Note at the end of this Lesson. Now, amongst
the derived units of this system is the unit of force,
named the Dyne, which is that force which, acting for
one second on a mass of one gramme, imparts to it
a velocity of one centimetre per second. Taking the
dyne then as the unit of force, and the centimetre as
the unit of length (or distance), we must find a unit of
electric quantity to agree with these in our equation.
It is quite clear that if q, q' , and d were each made equal
to i (that is, if we took two charges of value i each,
and placed them one centimetre apart), the value of
j- would be j-~j , which is equal to i. Hence we
adopt, as our Definition of a Unit of Electricity, the
following, which we briefly gave at the end of Lesson II.
One Unit of Electricity is that quantity which, when placed
at a distance of one centimetre (in air) from a similar and
equal quantity, repels it with a force of one dyne.
An example will aid the student to understand the
application of Coulomb's law.
EXAMPLE. Two small spheres, charged respectively with
6 units and 8 units of + electricity, are placed 4
centimetres apart ; find what force they exert on one
another. By the formula, / = ^jjjjpi we find / =
^- = *g 3 dynes. Examples for the student
are given in the Questions at the end of the Book.
The force in the above example would clearly be a force
of repulsion. Had one of these charges been negative,
the product q x q' would have had a value, and the
answer would have come out as minus 3 dynes. The
presence of the negative sign, therefore, prefixed to a
force, will indicate that it is a force of attraction, whilst
the + sign would signify a force of repulsion.
237. Potential. We must next define the term
potential, as applied to electric forces ; but to make
CHAP, iv.] ELECTRICITY AND MAGNETISM. 193
the meaning plain a little preliminary explanation is
necessary. Suppose we had a charge of + electricity
on a small insulated sphere A (See Fig. 95), placed by
itself and far removed from all other electrical charges
and electrical conductors. If we were to bring another
body B near it, charged also with + electricity, A would
repel B. But the repelling force would depend on the
quantity of the new charge, and on the distance at which
it was placed. Suppose the new charge thus brought
A P Q B" B'
Q- e- e- -e $-"
Fig. 95-
near to be one unit of + electricity ; when B was a long
way off it would be repelled with a very slight force, and
very little work need be expended in bringing it up
nearer against the repelling forces exerted by A ; but as
B was brought nearer and nearer to A, the repelling
force would grow greater and greater, and more and
more work would have to be done against these oppos-
ing forces in bringing up B. Suppose that we had
begun at an infinite distance away, and that we pushed
up our little test charge B from B' to B" and then to Q,
and so finally moved it up to the point P, against the
opposing forces exerted by A, we should have had to
spend a certain amount of work; that work represents
the potential 1 at the point P due to A. For the follow-
ing is the definition of electrostatic potential : The
potential at any point is the work that must be spent
1 In its widest meaning the term "potential" must be understood as
"power to do work." For if we have to do a certain quantity of work
against the repelling force of a charge in bringing up a unit of electricity
from an infinite distance, just so much work has the charge power to do, for
it will spend an exactly equal amount of work in pushing the unit of electri-
city back to an infinite distance. If we lift a pound five feet high against
the force of gravity, the weight of the pound can in turn do five foot-pounds
'of work in falling back to the ground. See the Lesson on Energy in Pro-
fessor Balfour Stewart's Lessons in Elementary Physics.
O
194 ELEMENTARY LESSONS ON [CHAP. iv.
upon a unit of positive electricity in bringing it up to
that point from an infinite distance. Had the charge on
A been a charge, the force would have been one of
attraction, in which case we should have theoretically to
measure the potential at P, either by the opposite
process of placing there a + unit, and then removing it
to an infinite distance against the attractive forces, or
else by measuring the amount of work which would be
done by a + unit in being attracted up to P from an
infinite distance.
It can be shown that where there are more electrified
bodies than one to be considered, the potential due to
them at any point is the sum of the potentials (at that
point) of each one taken separately.
238. It can also be shown that the potential at a
point P, near an electrified particle A, is equal to the
quantity of electricity at A divided by the distance
between A and P. Or, if the quantity be called g>, and
the distance r, the potential is -.* If there are a
number of electrified particles at different distances
from P, the separate values of the potential due to
each electrified particle separately can be found, and
therefore the potential at P can be found by dividing the
quantity of each charge by its distance from the point P,
and then adding lip together the separate amounts so
obtained. The symbol V is generally used to represent
potential. The potential at point P we will call V P , then
V P = + < + C + ---- etc.
r r r
This expression 2 L represents the work done on or
* The complete proof would require an elementary application of the
integral calculus, but an easy geometrical demonstration, sufficient for
present purposes, is given below
CHAP, iv.] ELECTRICITY AND MAGNETISM. 195
by a unit of + electricity when moved up to the given
point P from an infinite distance, according as the
potential at P is positive or negative.
Proof. First determine the difference of potential between
point P and point Q due to a charge of electricity q on a small
sphere at A.
Fig. 96.
Call distance AP = r, and AQ = r 1 . Then PQ =
r 1 r. The difference of potential between Q and P is the
work done in moving a + unit from Q to P against the force ;
and since
work = (average) force x distance through which it
is overcome
V P - V Q = f(r> - r).
The force at P exerted by q on a + unit = - 2 ,
and the force at Q exerted by q on a 4- unit. -^j.
Suppose now that the distance PQ be divided into any
number (n) of equal parts rr l9 r-^r^ r a r s , r n _ l r.
The force at r -%
r
,, r t = -^2 . . . . etc.
r i
Now since r t may be made as close to r as we choose, if we
only take n a large enough number, we shall commit no serious
error in supposing that r x r t is a fair mean between r 2 and
r-f ; hence we may assume the average force over the short
length from r to r\ to be -*-
196 ELEMENTARY LESSONS ON [CHAP, iv,
Hence the work done in passing from r to r will be
On a similar assumption, the work done in passing from r
to r lf will be
^ C T "" ~ ) anc ^ tnat done from r.j to r 2 will be
= $ { --- )> etc., giving us w equations, of which
\ r^ r 3 /
the last will be the work done in passing from r to r n _ l
Adding up all these portions of the work, the intermediate
values of r cancel out, and we get for the work done in pass-
ing from Q to P
Next suppose Q to be an infinite distance from A. Here
r = infinity, and j- = o. In that case the equation
becomes
V =
p r
If instead of one quantity of electricity ^, there were a
number of electrified particles having charges q', q", q'" ....
etc., at distances of r, r", r'" ..... etc., respectively from
P, then
Vp = 2 - 9 which was to be proved.
239. Zero Potential. At a place infinitely distant
from all electrified bodies there would be no electric
forces and the potential would be zero. For purposes
of convenience it is, however, usual to "consider the
potential of the earth for the time being as an arbitrary
CHAP, iv.] ELECTRICITY AND MAGNETISM. 197
zero, just as it is convenient to consider " sea-level " as
a zero from which to measure heights or depths.
240. Difference of Potentials. Since potential
represents the work that must be done on a + unit in
bringing it up from an infinite distance, the difference
of potential between two points is the work to be done on
or by a + unit of electricity in carrying it from one point
to the other. Thus if V P represents the potential at P,
and V Q the potential at another point Q, the difference
of potentials V P V Q denotes the work done in moving
up the + unit from Q to P. It is to be noted that since
this value depends only on the values of the potential
at P and at Q, and not on the values of the potential at
intermediate points, the work done will be the same,
whatever the path along which the particle moves from
Q to P. In the same way it is true that the expenditure
of energy in lifting a pound against the earth's attraction
from one point, to another on a higher level, will be the
same whatever the path along which the pound is lifted.
241. Electric Force. The definition of " work " is
the product of the force overcome into the distance
through which the force is overcome, or 'work = force
x distance through which it is overcome.
Hence, if the difference of potential between two
points is the work done in moving up our + unit from
one point to the other, it follows that the average electric
force between those points will be found by dividing
the work so done by the distance between the points :
or p ~ Q =f (the average electric force along the line
PQ). The (average) electric force is therefore the rate
of change of potential per unit of length. If P and Q
are near together the force will be practically uniform
between P and Q.
242. Equipotential Surfaces. A charge of elec-
tricity collected on a small sphere acts on external
bodies as if the charge were all collected into one point
198 ELEMENTARY LESSONS ON [CHAP, iv,
at its centre. 1 We have seen that the force exerted by
such a charge falls off at a distance from the ball, the
force becoming less and less as the square of the
distance increases. But the force is the same in
amount at all points equally distant from the small charged
sphere. And the potential is the same at all points
that are equally distant from the charged sphere. If, in
Fig. 96, the point A represents the sphere charged with
q units of electricity, then the potential at P, which we
will call V P , will be equal to -, where r is the distance
from A to P. But if we take any other point at the
same distance from A its potential will also be ?- Now
all the points that are the same distance from A as
P is, will be found to lie upon the surface of a sphere
whose centre is at A, and which is represented by the
circle drawn through P, in Fig. 97. All round this circle
the potential will have equal values ; hence this circle
represents an equipotential surface. The work to
be done in bringing up a + unit from an infinite distance
will be the same, no matter what point of this equi-
potential surface it is brought to, and to move it about
from one point to another in the equipotential surface
requires no further overcoming of the electrical forces,
and involves therefore no further expenditure of work.
At another distance, say at the point Q, the potential
will have another value, and through this point Q
another equipotential surface may be drawn. Suppose
we chose Q so far from P that to push up a unit of -f-
electricity against the repelling force of A required the
expenditure of just one erg of work (for the definition
1 The student must be warned that this ceases to be true if other charges
are brought very near to the sphere, for then the electricity will no longer
be distributed uniformly over its surface. It is for this reason that we have
said, in describing the measurement of electrical forces with the torsion
balance, that " the balls must be very small in proportion to the distances
between them."
CHAP, iv.] ELECTRICITY AND MAGNETISM. 199
of one erg see the Note on Units at the end of this
lesson); there will be then unit difference of potential
? ^
\ k / / .
\,^ ;y/ / /
Fig. 97.
between the surface drawn through Q and that drawn
through P, and it will require one erg of work to carry
a + unit from any point on the one surface to any point
on the other. In like manner we might construct a
whole system of equipotential surfaces about the point A,
choosing them at such distances that there should be
unit difference of potential between each one and the
next. The widths between them would get wider and
wider, for, since the force falls Off as you go further from
A, you must, in doing one erg of work, bring up the
+ unit through a longer distance against the weaker
opposing force.
The form of the equipotential surfaces about two small
electrified bodies placed near to one another would not
be spherical ; and around a number of electrified bodies
placed near to one another the equipotential surfaces
would be highly irregular in form.
243. Lines of Force. The electric force, whether
of attraction or repulsion, always acts across the equi-
potential surfaces in a direction normal to the surface.
The lines which mark the direction of the resultant
electric forces are sometimes called Lines of Electric
200 ELEMENTARY LESSONS ON [CHAP, iv
Induction. In the case of the single electrified sphere
the lines of force would be straight lines, radii of the sys-
tem of equipotential spheres. In general, however, lines
of force are curved ; in this case the resultant force at
any point would be in the direction of the tangent to the
curve at that point. Two lines of force cannot cut one
another, for it is impossible ; the resultant force at a point
cannot act in two directions at once. The positive
direction along a line of force is that direction in which
a small body charged with + electricity would be im-
pelled by the electric force, if free to move. A space
bounded by a number of lines of force is sometimes
spoken of as a tube of force. All the space, for example,
round a small insulated electrified sphere may be re-
garded as mapped out into a number of conical tubes,
each having their apex at the centre of the sphere. The
total electric force exerted across any section of a tube
of force is constant wherever the section be taken.
244. Potential "within a Closed Conductor.
The experiments related in Arts. 29 to 32 prove most
convincingly that there is no electric force inside a closed
conductor. Now we have shown above that electric
force is the rate of change of potential per unit of length.
If there is no electric force there is no change of
potential. The potential within a closed conductor (for
example a hollow sphere) is therefore the same all over
the interior ; the same as the potential of the surface.
The surface of a closed conductor is therefore necessarily
an equipotential surface. If it were not at one potential
there would be a flow of electricity from the higher
potential to the lower, which would instantaneously
establish equilibrium and reduce the whole to one
potential. The power of an electric system to do
work does not depend upon the accidental surface-
density at any one point. We know, for instance,
that when an electrified body is placed near an insulated
conductor the nearer and farther portions of that con-
CHAP, iv.] ELECTRICITY AND MAGNETISM. 201
ductor exhibit induced charges of opposite kinds. The
explanation of the paradox is that in the space round the
charged body the potential is not uniform. Suppose the
body to have a + charge, the potential near it is higher
than in the space farther away. The end of the insulated
conductor nearest to the charge is in a region of high
potential, while its farther end is in a region of lower
potential. It will, as a whole, take a mean potential, \
which will, relatively to the potential of the surrounding
medium, appear negative at the near end, positive at the
far end.
245. Law of Inverse Squares. An important
consequence follows from the absence of electric force
inside a closed conductor ; this fact enables us to de-
monstrate the necessary truth of the " law of inverse
squares " which was first experimentally, though roughly,
proved by Coulomb with the torsion balance. Suppose
a point P anywhere inside a hollow sphere charged with
electricity (Fig. 98). The charge is uniform all over,
and the quantity of electricity
on any small portion of its
surface will be proportional
to the area of that portion.
Consider a small portion of (
the surface AB. The charge
on AB would repel a + unit
placed at P with a certain
force. Now draw the lines
AD and BC through P, and
regard these as mapping out
a small conical surface of Flg * 98<
two sheets, having its apex at P ; the small area CD
will represent the end of the opposed cone, and the
electricity on CD will also act on the -f- unit placed at P,
and repel it. Now these surfaces AB and CD, and the
charges on them, will be directly proportional to the
squares of their respective distances from P. If, then
202 ELEMENTARY LESSONS ON [CHAP, iv
the forces which they exercise on P exactly neutralise
one another (as experiment shows they do), it is clear
that the electric force must fall off inversely as the
squares of the distances; for the whole surface of the
sphere can be mapped out similarly by imaginary cones
drawn through P. The reasoning can be extended also
to hollow conductors of any form.
246. Capacity. In Lesson IV. the student was
given some elementary notions on the subject of the
Capacity of conductors. We are now ready to give
the precise definition. The Electrostatic Capacity of
a conductor is measured by the quantify of electricity
which must be imparted to it in order to raise its potential
from zero to unity. A small conductor, such as an
insulated sphere of the size of a pea, will not want so
much as one unit of electricity to raise its potential
from o to I ; it is therefore of small capacity while
a large sphere will require a large quantity to raise its
potential to the sa'me degree, and would therefore be
said to be of large capacity. If C stand for capacity,
and Q for a quantity of electricity,
C = Q and C V = Q.
This is equivalent to saying in words that the quantity
of electricity necessary to charge a given conductor to
a given potential, is numerically equal to the product of
the capacity into the potential through which it is raised.
247. Unit of Capacity. A conductor that required
only one unit of electricity to raise its potential from o
to I, would be said to possess unit capacity. A sphere
one centimetre in radius possesses unit capacity ; for
if it be charged with a quantity of one unit, this charge
will act as if it were collected at its centre. At the
surface, which is one centimetre away from the centre,
the potential, which is measured as - , will be I. Hence,
as i unit of quantity raises it to unit i of potential, the
CHAP, iv.] ELECTRICITY AND MAGNETISM. 203
sphere possesses unit capacity. The capacities of spheres
are proportional to their radii. Thus, a sphere of one
metre radius has a capacity of 100. The earth has a
capacity of about 630 millions (in electrostatic units).
It is almost impossible to calculate the capacities of
conductors of other shapes. It must be noted that the
capacity of a sphere, as given above, means its capacity
when far removed from other conductors or charges of
electricity. The capacity of a conductor is increased by
bringing near it a charge of an opposite kind ; for the
potential at the surface of the conductor is the sum of
the potential due to its own charge, and of the potential
of opposite sign due to the neighbouring charge. Hence,
to bring up the resultant potential to unity, a larger
quantity of electricity must be given to it ; or, in other
words, its capacity is greater. This is the true way of
regarding the action of Leyden jars and other accumu-
lators, and must be remembered by the student when he
advances to the consideration of the theory of accumu-
lators, in Lesson XXII.
248. Surface-density. 1 Coulomb applied this term
to denote the amount of electricity per unit of area at any
point of a surface. It was mentioned in Lesson IV. that
a charge of electricity was never distributed uniformly
over a conductor, except in the case of an insulated
sphere. Where the distribution is unequal, the density
at any point of the surface may be expressed by con-
sidering the quantity of electricity which exists upon a
small unit of area at that point. If Q be the quantity
of electricity on the small surface, and S be the area of
1 The word Tension is sometimes used for that which is here precisely
defined as Coulomb defined it. The term tension is, however, unfortunate ;
and it is so often misapplied in text-books to mean not only surface-density
but also potential, and even electric force (i.e., the mechanical force exerted
upon a material body by electricity), that we avoid its use altogether. The
term would be invaluable if we might adopt it to denote only the mechanical
stress across a dielectric, due to accumulated charges ; but so long as the
above confusion lasts, it is better to drop the term entirely, and the student
will have one thing fewer to learn and to unlearn.
204 ELEMENTARY LESSONS ON [CHAP, iv,
that small surface, then the surface density (denoted by
the Greek letter p) will be given by the equation,
In dry air, the limit to the possible electrification is
reached when the density reaches the value of about 20
units of electricity per square centimetre. If charged to
a higher degree than this, the electricity escapes in
" sparks " and " brushes " into the air. In the case of
uniform distribution over a surface (as with the sphere,
and as approximately obtained on a flat disc by a parti-
cular device known as a guard-ring), the density is found
by dividing the whole quantity of the charge by the
whole surface.
249 Surface-Density on a Sphere. The surface
of a sphere whose radius is r, is 4 ?rr 2 . Hence, if a
charge Q be imparted to a sphere of radius r, the surface-
density all over will be p = ; or, if we know the
47rr 2 '
surface - density, the quantity of the charge will be
Q =- 4^V
The surface-density on two spheres joined by a thin
wire is an important case. If the spheres are unequal,
they, will share the charge in proportion to their capacities
(see Art. 37), that is, in proportion to their radii. If the
spheres are of radii 2 and I, the ratio of their charges
will also be as 2 to I. But their respective densities will
be found by dividing the quantities of electricity on each
by their respective surfaces. But the surfaces are pro-
portional to the squares of the radii, z>., as 4 : I ; hence,
the densities will be as I : 2, or inversely as the radii.
Now, if one of these spheres be very small no bigger
than a point the density on it will be relatively
immensely great, so great that the air particles in con-
tact with it will rapidly carry off the charge by convection.
This explains the action of points in discharging con
ductors, noticed in Chapter I. Arts. 35 c, 42 and 43.
CHAP, iv.] ELECTRICITY AND MAGNETISM. 205
250. Electric Images. It can be shown mathe-
matically that if + q units of electricity are placed at a
point near a non-electrified conducting sphere of radius
r, at a distance d from its centre, the negative induced
charge will be equal to -,q, and will be distributed over
the nearest part of the surface of the sphere with a
surface-density inversely proportional to the cube of the
distance from that point. Sir W. Thomson pointed out
that, so far as all external points are concerned, the
potential due to this peculiar distribution on the surface
would be exactly the same as if this negative charge were
all collected at an internal point at a distance of r ~
behind the surface. Such a point may be regarded as a
virtual image of the external point, in the same way as in
optics we regard certain points behind mirrors "as the
virtual images of the external points from which the rays
proceed. Clerk Maxwell has given the following defini-
tion of an Electric Image : An electric image is an
electrified 'point ', or system of points, on one side of a surf ace ,
which would produce on the other side of that surface the
same electrical action which the actual electrification of
that surface really does produce. A charge of + elec-
tricity placed one inch from a flat metallic plate induces
on it a negative charge distributed over the neighbouring
region of the plate (with a density varying inversely as
the cube of the distance from the point) ; but the
electrical action of this distribution would be precisely
represented by its " image," namely, by an equal quantity
of negative electricity placed at a point one inch behind
the plate. Many beautiful mathematical applications of
this method have been made, enabling the distribution
to be calculated in difficult cases, as, for example, the
distribution of the charge on the inner surface of a hollow
bowl.
251. Electric Force exerted by a Charged
206 ELEMENTARY LESSONS ON [CHAP. iv.
Sphere at a point near to it. It was shown
above that the quantity of electricity Q upon a sphere
charged until its surface-density was /o, was
Q = 4 77r 2 /o.
The problem is to find the force exercised by this
charge upon a + unit of electricity, placed at a point
infinitely near the surface of the sphere. The charge on
the sphere acts as if at its centre. The distance between
the two quantities is therefore r. By Coulomb's law the
r _,. Q x I 4 7rr 2 p
force / = ^r = *~jsr- = 4*v>.
This important result may be stated in words as
follows : The force (in dynes) exerted by a charged
sphere upon a unit of electricity placed infinitely near to
its surface, is numerically equal to 477 times the surface-
density of the charge.
252.' Electric Force exerted by a charged
plate of indefinite extent on a point near it.
Suppose a plate of indefinite extent to be charged so that
it has a surface-density p. This surface-density will be
uniform, for the edges of the plate are supposed to be
so far off as to exercise no influence. It can be shown
that the force exerted by siich a plate upon a + unit any-
where near it, will be expressed (in dynes) numerically .
as 277p. This will be of opposite signs on opposite sides
of the plate, being + 277/0 on one side, and 277/0 on the
other side, since in one case the force tends to move the
unit from right to left, in the other from left to right.
It is to be observed, therefore, that the force changes its
value by the amount of 477/3 as the point passes through
the surface. The same was true of the charged sphere,
where the force outside was 477/0, and inside was zero.
The same is true of all charged surfaces. These two
propositions are of the utmost importance in the theory
of Electrostatics.
253. The elementary geometrical proof of the latter theorem
is as follows :
CHAP, iv.] ELECTRICITY AND MAGNETISM.
207
Required the Electric Force at point at any distance from a
plane of infinite extent charged to surface-density p.
Let P be the point,
and PX or a the normal
to the plane. Take any
small cone having its
apex at P. Let the
solid-angle of this cone
be w ; let its length be
r\ and the angle its
axis makes with a. The
cone meets the surface
of the plane obliquely,
and if an orthogonal
section be made where
it meets the plane, the
angle between these sections will be = 0.
Now solid-angle is by definition = orthogonal area of section .
Hence, area of oblique section = r 2 w x
Fig. 99.
charge on oblique section =
cos
Hence if a + unit of electricity were placed at P, the force
exerted on this by this small charge = -^-^ x i -^- r 2
cos
up
or = -
cos
Resolve this force into two parts, one acting along the plane,
the other along a, normal to the plane. The normal component
wp
along a is cos x *- = wp
But the whole surface of the plane may be similarly mapped
out into small surfaces, all forming small cones, with their summits
at P. If we take an infinite number of such small cones meeting
every part, and resolve their forces in a similar way, we shall
find that the components along the plane will neutralise one
another all round, while the normal components, or the resolved
forces along #, will be equal to the sum of all their solid-angles
multiplied by the surface-density ; or
Total resultant force along a = 2wp,
208 ELEMENTARY LESSONS ON [CHAP, iv
But the total solid -angle subtended by an infinite plane at a
point is 27r, for it subtends a whole hemisphere.
. . Total resultant force = 2irp.
NOTE ON FUNDAMENTAL AND DERIVED UNITS.
254. Fundamental Units. All physical quantities, such as
force, velocity, etc., can be expressed in terms of the three
fundamental quantities : length, mass, and time. Each of these
quantities must be measured in terms of its own units.
The system of units, adopted by almost universal consent,
and used throughout these Lessons, is the so-called "Centi-
metre-Gramme-Second" system, in which the fundamental
units are :
The Centimetre as a unit of length ;
The Gramme as a unit of mass ;
The Second as a unit of time.
The Centimetre is equal to 0*3937 inch in length, and no-
minally represents one thousand-millionth part, or ^oTo^oo.o'oo
of a quadrant of the earth.
The Metre is 100 centimetres, or 39 '3 7 inches.
The Kilometre is 1000 metres, or about 1093-6 yards.
The Millimetre is the tenth part of a centimetre, or 0*03937
inch.
The Gramme is equal to 15*432 grains, and represents the
mass of a cubic centimetre of water at 4 C : the Kilogramme is
1000 grammes or 2*2 pounds.
255. Derived Units.
Area. The unit of area is the sqtiare centimetre.
Volume. The unit of volume is the cubic centimetre.
Velocity. The unit of velocity is the velocity of a body
which moves through unit distance in unit time, or the
velocity of one centimetre per second.
Acceleration. The unit of acceleration is that acceleration
which imparts unit velocity to a body in unit time, or
an acceleration of one centimetre-per-second per second.
The acceleration due to gravity imparts in one second
a velocity considerably greater than this, lor the velocity
it imparts to falling bodies is about 981 centimetres per
CHAP, iv.j ELECTRICITY AND MAGNETISM. 209
second (or about 32*2 feet per second). The value differs
slightly in different latitudes. At Bristol the value of
the acceleration of gravity is g = 98 1 I ; at the Equator
g = 978-1; at the North Pole^= 983-1.
Force. The unit of force is that force which, acting for one
second on a mass of one gramme, gives to k a velocity
of one centimetre per second. It is called one Dyne.
The force with which the earth attracts any mass is
usually called the "weight" of that mass, and its value
obviously differs at different points of the earth's surface.
The force with which a body gravitates, i.e. its weight
(in dynes), is found by multiplying its mass (in grammes)
by the value of g at the particular place where the force
is exerted.
Work. The unit of work is the work done in overcoming
unit force through unit distance, i.e. in pushing a body
through a distance of one centimetre against a force of
one dyne. It is called one Erg. Since the "weight"
of one gramme is I x 981 or 981 dynes, the work of
raising one gramme through the height of one centimetre
against the force of gravity is 981 ergs.
Energy. The unit of energy is also the erg; for the energy
of a body is measured by the work it can do.
Heat. The unit of heat (sometimes called a calorie] is the
amount of heat required to warm one gfamme mass of
water from o to i (C) ; and the dynamical equivalent
of this amount of heat is 42 million ergs> which is the
value of Joule's equivalent, as expressed in absolute
(C.G.S.) measure. (See also Art. 367.)
These units are sometimes called "absolute" units; the term absolute,
introduced by Gauss, meaning that they are independent of the size of any
particular instrument, or of the value of gravity at any particular place, or of
any other arbitrary quantities than the three standards of length, mass, and
time. It is, however, preferable to refer to them by the more appropriate
name of " C.G.S. units," as being derived from the centimetre, the gramme,
and the second.
256. Electrical Units. There are two systems of electrical
units derived from the fundamental "C.G.S." units, one set
being based upon the force exerted between two quantities of
electricity, and the other upon the force exerted between two
magnet poles. The former set are termed electrostatic units, the
latter electromagnetic units. The important relation between the
two sets is explained in the note at the end of Lesson XXX.
P
210 ELEMENTARY LESSORS ON [CHAP. iv.
257. Electrostatic Units. No special names have been
assigned to the electrostatic units of Quantity, Potential,
Capacity, etc. The reasons for adopting the following values
as units are given either in Chapter I. or in the present Chapter.
Unit of Quantity. The unit of quantity is that quantity of
electricity which, when placed at a distance of one
centimetre from a similar and equal quantity, repels it
with a force of one dyne (Art. 236).
Potential. Potential being measured by work done in moving
a unit of + electricity against the electric forces, the unit
of potential will be measured by the unit of work, the erg.
Unit Difference of Potential. Unit difference of potential
exists between two points, when it requires the expendi-
ture of one erg of work to bring a unit of + electricity
from one point to the other against the electric force
(Art. 242).
Unit of Capacity. That conductor possesses unit capacity
which requires a charge of one unit of electricity to bring
it up to unit potential. A sphere of one centimetre
radius possesses unit capacity (Art. 247).
Specific Inductive Capacity is defined in Art. 268 as the ratio
between two quantities of electricity. The specific
inductive capacity of the air is taken as unity.
258. Dimensions of Units. It has been assumed above
that a velocity can be expressed in centimetres per second ; for
velocity is rate of change of place, and it is clear that if change
of place may be measured as a length in centimetres, the rate
of change of place will be measured by the number of centi-
metres through which the body moves in unit of time. It is
impossible, indeed, to express a velocity without regarding it as
the quotient of a certain number of units of length divided by
a certain number of units of time. In other words, a velocity
= ^ ; or, adopting L as a symbol for length, and T as a
symbol for time, V = ^, which is still more conveniently written
V = L x T ~ . in a similar way acceleration being rate of
change of velocity, we have A = ^ = ^~ = ^- a = L x T ~ 2>
Now these physical quantities, "velocity," and "acceleration,"
are respectively always quantities of the same nature, no matter
whether the centimetre, or the inch, or the mile, be taken as the
unit of length, or the second or any other interval be taken as
CHAP, iv.] ELECTRICITY AND MAGNETISM.
the unit of time. Hence we say that these abstract equations
express the "dimensions" of those quantities with respect to the
fundamental quantities length and time. A little consideration
will show the student that the following will therefore be the
dimensions of the various units mentioned above :
UNITS.
DIMENSIONS.
(Fundamental. }
m
t
Length
Mass
Time
L
M
T
(Derived.}
Area =
L x L
L 2
Volume =
L x L x L
L 3
V
Velocity =
L ^ T
LT- 1
a
Acceleration =
velocity -f- time =
LT~ 2
f
Force . =
mass x acceleration =
MLT~ 2
Work
force x length =
ML 2 T~ 2
(Electrostatic.}
Quantity
M^ L^ T ~ X
= Vforce X (distance) 2
i
Current
= quantity -=- time =
M^ L^ T ~ 2
V
Potential
work -T- quantity =
M 4 L T - 1
R
k
Resistance = potential -4- current =
Capacity = quantity -f- potential =
Sp. Ind. Capacity = quantity -=- another quantity
L
a numeral
Electromotive Intensity = force -r- quantity =
M* L* T J
The dimensions of magnetic units are given in the note on
Magnetic Units, Art. 324.
LESSON XXI. Electrometers.
259. In Lesson II. we described a number of electro-
scopes or instruments for indicating the presence and
212 ELEMENTARY LESSONS ON [CHAP, iv
sign of a charge of electricity ; some of these also served
to indicate roughly the amount of these charges, but none
of them save the torsion balance could be regarded as
affording an accurate means of measuring either the
quantity or the potential of a given charge. An instru-
ment for measuring differences of electrostatic potential is
termed an Electrometer. Such instruments can also
be used to measure electric quantity indirectly, for the
quantity of a charge can be ascertained by measuring
the potential to which it can raise a conductor of known
capacity. The earliest electrometers attempted to measure
the quantities directly. Lane and Snow Harris constructed
" Unit Jars " or small Leyden jars, which, when it was
desired to measure out a certain quantity of electricity,
were charged and discharged a certain number of times.
The discharging gold-leaf electroscope of Gaugain was
invented with a similar idea.
26O. Repulsion Electrometers. The torsion
balance, described in Art. 1 5, measures quantities by
measuring the forces exerted by the charges given to the
fixed and movable balls. It can only be applied to the
measurement of repelling forces, for the equilibrium is
unstable in the case of a force of attraction.
There are, besides the gold-leaf electroscope and the
Lane's electroscope, described in Lesson II., a number
of finer electrometers based upon the principle of repul-
sion, some of which resemble the torsion balance in
having a movable arm turning about a central axis.
Amongst these are the electrometers of Dellmann and of
Peltier ; the latter of these is shown in Fig. 1 1 1, in the
Lesson on Atmospheric Electricity. In this apparatus a
light arm of aluminium, balanced upon a point, carries
also a small magnet to direct it in the magnetic meridian.
A fixed arm, in metallic contact with the movable one,
also lies in the magnetic meridian. A charge imparted
to this instrument produces a repulsion between the fixed
and movable arms, causing an angular deviation. Here,
CHAP, iv.] ELECTRICITY AND MAGNETISM. 213
however, the force is measured not by being pitted against
the torsion of an elastic fibre, or against gravitation, but
against the directive magnetic force of the earth acting
on the small needle. Now this depends on the intensity
of the horizontal component of the earth's magnetism at
the place, on the magnetic moment of the needle, and
on the sine of the angle of its deviation. Moreover, the
repulsion here is not between two charges collected on
small spheres, but between the fixed arm and the mov-
able one. Hence, to obtain quantitative values for the
readings of this electrometer, it is necessary to make
preliminary experiments and to " calibrate " the degree-
readings of the angular deviation to an exact scale.
261. Attracted - Disc Electrometers. Snow
Harris was the first to construct an electrometer for
measuring the attraction between an electrified and a
non-electrified disc ; and the instrument he devised may
be roughly described as a balance for weighing a charge
of electricity. More accurately speaking, it was an
instrument resembling a balance in form, carrying at one
end a light scale pan ; at the other a disc was hung
above a fixed insulated disc, to which the charge to be
measured was imparted. The disadvantages of this
instrument were manifold, the chief objection being due
to the irregular distribution of the charge on the disc.
The force exerted by an electrified point falls off inversely
as the square of the distance, since the lines of force
emanate in radial lines. But in the case of a uniformly
electrified plane surface, the lines of force are normal to
the surface, and parallel to one another ; and the force
is independent of the distance. The distribution over
a small sphere nearly fulfils the first of these conditions.
The distribution over a flat disc would nearly fulfil the
latter condition, were it not for the perturbing effect of
the edges of the disc where the surface-density is much
greater (see Art. 35); for this reason Snow Harris's
electrometer was very imperfect.
214 ELEMENTARY LESSONS ON [CHAP. iv.
Sir W. Thomson has introduced several very import-
ant modifications into the construction of attracted-disc
electrometers, the chief of these being the employment
of the " guard-plate " and the providing of, means for
working with a definite standard of potential. It would
be beyond the scope of these lessons to give a complete
description of all the various forms of attracted-disc
electrometer ; but the main principles of them all can be
readily explained.
The disc, C, whose attraction is to be measured, is sus-
pended (Fig. 100) within a fixed guard-plate, B, which
Fig. 100.
surrounds it without touching it, and which is placed
in metallic contact with it by a fine wire. A lever, L,
supports the disc, and is furnished with a counterpoise ;
whilst the aluminium wire which serves as a fulcrum may
be also employed to produce a torsion force. In order
to know whether the disc is precisely level with the
lower surface of the guard-plate a little gauge or index
is fixed above, and provided with a lens, /, to observe
its indications. Beneath the disc and guard -plate is
CHAP, iv.] ELECTRICITY AND MAGNETISM. 215
a second disc, A, supported on an insulating stand. This
lower disc can be raised or lowered at will by a micro-
meter screw, great care being taken in the mechanical
arrangements that it shall always be parallel to the
plane of the guard -plate. Now, since the disc and
guard-plate are in metallic connection with one another,
they form virtually part of one surface, and as the
irregularities of distribution occur at the edges of the
surface, the distribution over the surface of the disc is
practically uniform. Any attraction of the lower plate
upon the disc might be balanced either by increasing
the weight of the counterpoise, or by putting a torsion
on the wire ; but in practice it is found most convenient
to obtain a balance by altering the distance of the lower
plate until the electric force of attraction exactly
balances the forces (whether of torsion or of gravity
acting on the counterpoise) which tend to lift the disc
above the level of the guard-plate.
The theory of the instrument is simple also. The
force F just outside a charged conducter is 4717) (Art.
252); and since electric force is the same thing as
the rate of change of potential per unit of length
(Art. 241), it will be equal to ^, where V is the
difference of potentials between the upper and lower
plates, and D the distance between them : hence p = =y
If the surface of the movable disc be S, the quantity of
the charge on it will be S/o. Now, let us suppose that
the electricity on the lower plate has an equal density
but of opposite sign, as will be the case if either plate is
connected to "earth." Since its density is p it will
exercise a force of 2irp on a + unit placed near the disc ;
(but as this force is a force exerted from the upper side
of the plate we must change its sign again and call it
+ 27T/3, where the + sign signifies a force tending to
move a + unit downwards.) Now on the disc there are
216 ELEMENTARY LESSONS ON [CHAP, iv,
Sp units of electricity ; hence the total force of attraction
on the disc will be F ~ 2irp x Sp.
= 27TS/0 2 .
TT S V 2
F= 8^D5
whence V = D A|?.
From this we gather that, if the force F remain the
same throughout the experiments, the difference of po-
tentials between the discs will be simply proportional to
the distance between them when the disc is in level
/ Q Tf
ity /
equilibrium. And the quantity / may be deter-
mined once for all as a " constant " of the instrument.
In the more elaborate forms of the instrument, such
as the "absolute electrometer," and the "portable
electrometer," the disc and guard -plate are covered
with a metallic cage, and are together placed in com-
munication with a condenser to keep them at a known
potential. This obviates having to make measurements
with zero readings, for the differences of potential will
now 'be proportional to differences of micrometer readings^
The condenser is provided in these instruments with
a gauge, itself an attracted-disc, to indicate when it is
charged to the right potential, and with a replenisher to
increase or decrease the charge, the replenisher being
a little convection-induction machine (see Art. 45).
262. The Quadrant Electrometer. The Quad-
rant Electrometer of Sir W. Thomson is an example of
a different class of electrometers, in which use is made
of an auxiliary charge of electricity previously imparted
to the needle of the instrument. The needle, which con-
CHAP, iv.] ELECTRICITY AND MAGNETISM.
217
sists of a thin flat piece of metal hung horizontally by a
fibre or thin wire, thus charged with, say, + electricity,
will be attracted by a charge, but repelled by a +
charge ; and such attraction or repulsion will be stronger
in proportion to these charges, and in proportion to the
charge on the needle. Four quadrant -pieces of brass
are fixed horizontally below the needle without touching
it or one another. Opposite quadrants are joined with
fine wires.
Fig. 1 01 shows a very simple form of the Quadrant
Electrometer, as arranged for qualitative experiments.
Fig. 101.
The four quadrants are enclosed within a glass case, and
the needle, which carries a light mirror, M, below it, is
suspended from a torsion head, C, by a very thin metallic
wire, F. It is electrified to a certain potential by being
connected, through a wire attached to C, with a charged
218 ELEMENTARY LESSONS ON [CHAP, iv,
Leyden jar or other condenser. In order to observe
the minutest motions of the needle, a reading-telescope
and scale are so placed that the observer looking through
the telescope sees an image of the zero of the scale
reflected in the little mirror. The wires connecting
quadrants i and 3, 2 and 4, are seen above the top of
the case. The needle and quadrants are shown in plan
separately above. If there is the slightest difference of
potential between the pairs of quadrants, the needle,
which is held in its zero position by the elasticity of the
wire, will turn, and so indicate the difference of potential.
When these deflections are small, the scale readings will
be very nearly proportional to the difference of potential.
The instrument is sufficiently delicate to show a difference
of potential between the quadrants as small as the T V f
that of the DanielPs cell.
For very exact measurements many additional refine-
ments are introduced into the instrument. Two sets of
quadrants are employed, an upper and a lower, having
the needle between them. The torsion wire is replaced
by a delicate bifilar suspension (Art. 118). To keep
up the charge of the Leyden jar a " Replenisher " is
added ; and an " attracted-disc," like that of the Absolute
Electrometer, is employed in order to act as a gauge to
indicate when the jar is charged to the right potential.
In these forms the jar consists of a glass vessel placed
below the quadrants, coated externally with strips of tin-
foil, and containing strong sulphuric acid which serves
the double function of keeping the apparatus dry by
absorbing the moisture and of acting as an internal
coating for the jar. It is also more usual to throw a
spot of light from a lamp upon a scale by means of the
little mirror (as described in the case of the Mirror
Galvanometer, in Art. 202), than to adopt the subjective
method with the telescope, which only one person at a
time can use. When the instrument is provided with
replenisher and gauge, the measurements can be made in
CHAP, iv.] ELECTRICITY AND MAGNETISM. 219
terms of absolute units, provided the " constant " of the
particular instrument (depending on the suspension of
the needle, size and position of needle and quadrants,
potential of the gauge, etc.) is once ascertained.
263. An example will illustrate the mode of using the instru-
ment. It is known that when the two ends of a thin wire are
kept at two different potentials a current flows through the wire,
and that if the potential is measured at different points along
the wire, it is found to fall off in a perfectly uniform manner
from the end that is at a high potential down to that at the low
potential. At a point one quarter along the potential will have
fallen off one quarter of the whole difference. This could be
proved by joining the two ends of the wire through which the
current was flowing to the terminals of the Quadrant Electro-
meter, when one pair of quadrants would be at the high
potential and the other at the low potential. The needle would
turn and indicate a certain deflection. Now, disconnect one of
the pairs of quadrants from the low potential end of the wire,
and place them in communication with a point one quarter
along the wire from the high potential end. The needle will
at once indicate that the difference of potential is but one quarter
of what it was before.
Often the Quadrant Electrometer is employed simply as a
very delicate electro.rayte in systems of measurement in which a
difference of electric potential is measured by being balanced
against an equal and opposite difference of potential, exact
balance being indicated by there being no deflection of the
Electrometer needle. Such methods of experimenting are known
as " Null Methods," or "Zero Methods."
264. Dry-Pile Electrometer. The principle of
symmetry observed in the Quadrant Electrometer was
previously employed in the Electroscope of Bohnenberger
a much less accurate instrument in which the charge
to be examined was imparted to a single gold leaf, placed
symmetrically between the poles of a dry-pile (Art. 182),
toward one or other pole of which the leaf was attracted.
Fechner modified the instrument by connecting the +
pole of the dry-pile with a gold leaf hanging between
two metal discs, from the more + of which it was re-
220 ELEMENTARY LESSONS ON [CHAP. iv.
pelled. The inconstancy of dry -piles as sources of
electrification led Hankel to substitute a battery of a
very large number of small Daniell's cells.
265. CapiHary Electrometers. The Capillary
Electrometer of Lippmann, as modified by Dewar, was
described in Art. 225.
LESSON XXII. Specific Inductive Capacity, etc.
266. In Lesson VI. it was shown that the capacity
of a Leyden jar or other condenser depended upon the
size of the conducting coatings or surfaces, the thinness
of the glass or other dielectric between them, and upon
the particular "inductive capacity" of the dielectric
used. We will now examine the subject in a more
rigorous way. In Art. 246 it was laid down that the
capacity of a conductor was measured by the quantity
of electricity required to raise its potential to unity ; or
if a quantity of electricity Q raise the potential from
V to V then its capacity is
C - -_
^ - v'-v
Now, a Leyden jar or other condenser may be
regarded as a conductor, in which (owing to the parti-
cular device of bringing near together the two oppositely-
charged surfaces) the conducting surface can be made
to hold a very large quantity of electricity without its
potential (whether + or ) rising very high. The
capacity of a condenser, like that of a simple con-
ductor, will be measured by the quantity of electricity
required to produce unit rise of potential.
267. Theory of Spherical Air -Condenser.
Suppose a Leyden jar made of two concentric metal
spheres, one insfde the other, the space between them
being filled by air. The inner one, A, will represent the
interior coating of tinfoil, and the outer sphere, B (Fig.
CHAP, iv.] ELECTRICITY AND MAGNETISM. 221
102), will represent the exterior coating. Let the radii
of these spheres be r and /
respectively. Suppose a charge
of Q units to be imparted
to A ; it will induce on the
inner side of B an equal
negative charge Q, and to
the outer side of B a charge
+ Q will be repelled. This
latter is removed by contact
with " earth," and need be
no further considered. The
potential 1 at the centre M,
calculated by the rule given
in Art. 238, will be
V - Q
V M - ~
Fig. 102.
Q
At a point N, outside the outer sphere and quite near to
it, the potential will be the same as if these two charges,
+ Q and - Q, were both concentrated at M. Hence
V N = t^Q = .
So then the difference of potentials will be
whence A7 -^V = -^ .
VM Vw r r
But, by the preceding Article, the capacity C = y _ y >
therefore C ~-^.
We see from this formula that the capacity of the
condenser is proportional to the size of the metal globes,
and that if the insulating' layer is very thin, that is, if
r be very nearly as great as r', r' r will become very
1 The student must remember that' as there is no electric force within a
closed conductor the potential at the middle is just the same as at any other
point inside ; so that it is somewhat a stretch of language to talk of the
middle point M as having a potential*
222 ELEMENTARY LESSONS ON [CHAP. iv.
small, and the value of the expression -^- will become
very great ; which proves the statement that the capacity
of a condenser depends upon the thinness of the layer
of dielectric.
268. Specific Inductive Capacity. Cavendish
was the first to discover that the capacity of a condenser
depended not on its actual dimensions only, but upon
the inductt 've power of the material used as the dielectric
between the two surfaces. If two condensers (of any of
the forms to be described) are made of exactly the same
size, and in one of them the dielectric be a layer of air,
and in the other a layer of some other insulating sub-
stance, it is found that equal quantities of electricity
imparted to them do not produce equal differences- of -
potentials ; or, in other words, it is found that they have
not the same capacity. If the dielectric be sulphur,
for example, it is found that the capacity is about three
times as great ; for sulphur possesses a high inductive
power and allows the transmission across it of electro-
static influence three times as well as air does. The
name specific inductive capacity 1 was assigned by
Faraday to the ratio between the capacities of two con-
densers equal in size, one of them being an air-condenser,
the other filled with the specified dielectric. The
specific inductive capacity of dry air at the temperature
o C, and pressure 76 centims., is taken as the standard
and reckoned as unity.
Cavendish, about the year 1775, measured the specific
inductive capacity of glass, bees -wax, and other sub-
stances, by forming them into condensers between two
circular metal plates, the capacity of these condensers
being compared with that of an air condenser (resem-
bling Fig. 30) and with other condensers which he
1 The name is not a very happy one, specific inductivity would have been
better, and is the analogous term, for dielectrics, to the term "specific con-
ductivity" used for conductors. The term dielectric capacity is also used by
some modern writers.
CHAP, iv.j ELECTRICITY AND MAGNETISM.
223
called " trial-plates." He even went so far as to com-
pare the capacities of these " trial-plates " with that of a
sphere of 12^ inches diameter hung up in the middle of
a room.
269. Faraday's Experiments. In 1837 Faraday,
who did not know of the then un-
published researches of Caven-
dish, independently discovered
specific inductive capacity, and
measured its value for several
substances, using for this pur-
pose two condensers of the form
shown in Fig. 103. Each
consisted of a brass ball A,
enclosed inside a hollow sphere
of brass B, and insulated
by a long plug of shellac, up
which passed a wire terminating
in a ball a. The outer sphere
consisted of two parts which
could be separated from each
other in order to fill the hollow
space with any desired material :
the experimental process then
was to compare their capacities
when one was filled with the
substance to be examined, the
other containing only dry air.
The method of experimenting
was simple. One of the condensers was charged with
electricity. It was then made to share its charge with the
other condenser, by putting the two inner coatings into
metallic communication with one another, the outer
coatings also being in communication with one another.
If their capacities were equal they would share the charge
equally, and the potential after contact would be just
half what it was in the charged condenser before con-
Fig. 103.
224 ELEMENTARY LESSONS ON [CHAP. iv.
tact. If the capacity of one was greater than the other
the final potential would not be exactly half the original
potential, because they would not share the charge
equally, but in proportion to their capacities. The
potentials of the charges were measured before and
after contact by means of a torsion balance. * Faraday's
results showed the following values: Sulphur, 2*26;
shellac, 2-0; glass, 1-76 or more.
27O. Recent Researches. Since 1870 large addi-
tions to our knowledge of this subject have been made.
Gibson and Barclay measured the inductive capacity of
paraffin by comparing the capacity of an air condenser
with one of paraffin by means of a sliding condenser, and
a divided condenser called a " platymeter," using a
quadrant electrometer as a sensitive electroscope to
adjust the capacity of the condensers exactly to equality.
Wiillner, Boltzmann, and others, have also examined
the inductive capacity of solid bodies by several methods.
Hopkinson has examined that of glass of various kinds,
using a constant battery to produce the required differ-
ence of potentials, and a condenser provided with a
guard -ring for a purpose similar to that of the guard^
ring in absolute electrometers. Gordon has still more
recently made a large number of observations, using a
delicate apparatus known as a statical " induction
balance," which is a complicated condenser, so arranged
in connection with a quadrant electrometer that when
the capacities of the separate parts are adjusted to
equality there shall be no deflection in the electrometer,
whatever be the amount or sign of the actual electrifi-
1 The value of the specific inductive capacity k could then be calculated
as follows :
Q = VC = V'C + V'Ck
(where C is the capacity of the first apparatus and V its potential, and V
the potential after communication with the second apparatus, whose
capacity is G) :
hence V = V (i + k)
CHAP, iv.] ELECTRICITY AND MAGNETISM. 225
cation employed for the moment. This arrangement,
when employed in conjunction with an induction coil
(Fig. 148) and a rapid commutator, admits of the in-
ductive capacity being measured when the duration of
the actual charge is only very small, the electrification
being reversed 12,000 times per second. Such an instru-
ment, therefore, overcomes one great difficulty besetting
these measurements, namely, that owing to the apparent
absorption of part of the charge by the dielectric (as
mentioned in Art. 53), the capacity of the substance,
when measured slowly, is different from its " instantane-
ous capacity." This electric absorption is discussed
further in Art. 272. The amount of the absorbed charge
is found to depend upon the time that the charge has
been accumulated. For this reason the values assigned
by different observers for the inductive capacity of various
substances differ to a most perplexing degree, especially
in the case of the less perfect insulators. The following
Table summarises Gordon's observations :
Air . . . i -oo
Glass .... 3*013 to 3-258
Ebonite . . . .2-284
Guttapercha . . . 2-462
Indiarubber . . . 2-220 to 2*497
Paraffin (solid) I '9936
Shellac . . . .2-74
Sulphur . . . . 2-58
Gordon's values would probably have been more
reliable had the plates of the induction balance been
provided with guard-rings (Art. 248). Hopkinson,
whose method was a " slow " one, found for glass
much higher inductive capacities, ranging from 6-5 to
lo-i, the denser kinds having higher capacities. Row-
land has lately examined the inductive capacity of
plates of quartz cut from a homogeneous crystal, and
finds it perfectly devoid of electric absorption. Caven-
dish observed that the apparent capacity of glass
Q
226
ELEMENTARY LESSONS ON [CHAP, iv,
became much greater at those temperatures at which it
begins to conduct electricity. Boltzmann has announced
that in the case of two crystalline substances, Iceland
spar and sulphur, the inductive capacity is different in
different directions, according to their position with
respect to the axes of crystallisation.
271. Specific Inductive Capacity of Liquids
and Gases. The inductive capacity of liquids also
has specific values. The following table is taken from
the data of Silow and of Gordon :
Turpentine .
Petroleum .
Bisulphide of Carbon
2-16
2-03 to 2-07
I -81
Faraday examined the inductive capacity of several
gases by means of his apparatus (Fig. 103), one of the
condensers being filled with air, the other with the gas
which was let in through the tap below the sphere after
exhaustion by an air pump. The method was too rough,
however, to enable him to detect any difference between
them, although many experiments were made with dif-
ferent pairs of gases at different temperatures and under
varying pressures. More recently Boltzmann, and inde-
pendently Ayrton and Perry, have measured the specific
inductive capacities of different gases by very exact
methods ; and their results agree very fairly.
Boltzmann.
Ayrton and Perry.
Air
(I)
(I)
Vacuum ....
(0-999410)
(0-9985)
Hydrogen
0-999674
0*9998
Carbonic Acid .
1-000356
I -0008
Olefiant Gas . .
I -000722
Sulphur Dioxide
1-0037
272. Mechanical Effects of Dielectric Stress.
- That different insulating substances have specific
CHAP. iv.J ELECTRICITY AND MAGNETISM. 227
inductive power sufficiently disproves the idea that
.induction is merely an "action at a distance," for it is
evident that the dielectric medium is itself concerned in
the propagation of induction, and that some media allow
induction to take place across them better than others.
The existence of a residual charge (Art. 53) can be
explained either on the supposition that the dielectric is
composed of heterogenous particles which have unequal
conducting powers, as Maxwell has suggested, or on the
hypothesis that the molecules are actually subjected to
a strain from which, especially if the stress be long-con-
tinued, they do not recover all at once. Kohlrausch and
others have pointed out the analogy between this pheno-
menon and that of the "elastic recovery" of solid bodies
after being subjected to a bending or a twisting strain.
A fibre of glass, for example, twisted by a certain force,
flies back when released to almost its original position,
a slight sub -permanent set remains, from which, how-
ever, it slowly recovers itself, the rate of its recovery
depending upon the amount and duration of the original
twisting strain. Hopkinson has shown that it is possible
to superpose several residual charges, even charges of
opposite signs, which apparently " soak out " as the
strained material gradually recovers itself. Perry and
Ayrton have also investigated the question, and have
shown that the polarisation charges in voltameters exhibit
a similar recovery. 1 Air condensers exhibit no residual
charges.
When a condenser is discharged a sound is often heard.
This was noticed by Sir W. Thomson in the case of air
condensers ; and Varley even constructed a telephone in
which the rapid charge and discharge of a condenser
gave rise to distinct tones.
1 It would appear, therefore, probable that Maxwell's suggestion of hetero-
geneity of structure, as leading to residual electrification at the bounding
surface of the particles whose electric conductivities differ, is the true
explanation of the "residual" charge. The phenomenon of elastic recovery
may itself be due to heterogeneity of structure.
228
ELEMENTARY LESSONS ON [CHAP. IV.
As to the precise nature of the molecular or mechanical
operations in the dielectric when thus subjected to the
stress of electrostatic induction, nothing is known. One
pregnant experiment of Faraday is of great importance,
by showing that induction is, as he expressed it, "an
action of contiguous particles." In a glass trough (Fig.
104), is placed
some oil of tur-
pentine, in which
are put some fibres
of dry silk cut into
Fig. 104.
small bits. Two
wires pass into
the liquid, one of which is joined to earth, the other
being put into connection with the collector of an
electrical machine. The bits of silk come from all
parts of the liquid and form a chain of particles from
wire to wire. On touching them with a glass rod they
resist being pushed aside, though they at once disperse
if the supply of electricity is stopped. Faraday regarded
this as typical of the internal actions in every case of
induction across a dielectric, the particles of which he
supposed to be " polarised," that is, to be turned into
definite positions, each particle having a positive and a
negative end. The student will perceive an obvious
analogy, therefore, between the condition of the particles
of a dielectric across which electrostatic induction is
taking place, and the molecules of a piece of iron or
steel when subjected to magnetic induction.
Siemens has shown that the glass of a Leyden jar is
/ sensibly warmed after being several times rapidly charged
and discharged. This obviously implies that molecular
movement accompanies the changes of dielectric stress.
273. Electric Expansion. Fontana noticed that
the internal volume of a Leyden jar increased when it
was charged. Volta sought to explain this by suggesting
that the attraction between the two charged surfaces
CHAP, iv.] ELECTRICITY AND MAGNETISM. 229
compressed the glass and caused it to expand laterally.
This idea had previously occurred to Priestley. Duter
showed that the amount of apparent expansion- was\
inversely proportional to the thickness of the glass, and ]
varied as the square of the potential difference. Quincke
has recently shown that though glass and some other
insulators exhibit electrical expansion, an apparent con-
traction is shown by resins and oily bodies under
electrostatic stress. He connects with these properties
the production of optical strain and of double refraction
discovered by Kerr. (See Lesson on Electro-optics,
Art. 386.)
274. Submarine Cables as Condensers. A
submarine telegraph cable may act as a condenser, the I
ocean forming the outer coating, the internal wire the
inner coating, while the insulating layers of guttapercha
correspond to the glass of the Leyden jar. When one
end of a submerged cable is connected to, say, the + pole
of a powerful battery, + electricity flows into it. Before
any signal can be received at the other end, enough
electricity must flow in to charge the cable to a consider-
able potential, an operation which may in the case of
long cables require some seconds. Faraday predicted
that this retardation would occur. It is, in actual fact, a
serious obstacle to signalling with speed through the
Atlantic cables and others. Professor Fleeming Jenkin
has given the following experimental demonstration of
the matter. Let a mile of insulated cable wire be coiled
up in a tub of water (Fig. 105), one end, N, being
insulated. The other end is joined up through a long-
coil galvanometer, G, to the + pole of a large battery,
whose pole is joined by a wire to the water in the tub.
Directly this is done, the needle of the galvanometer will
show a violent deflection, + electricity rushing through it
into the interior of the cable, and a - charge being
accumulated on the outside of it where the water touches
the guttapercha. For perhaps an hour the flow will go
230
ELEMENTARY LESSONS ON [CHAP. iv.
on, though diminishing, until the cable is fully charged.
Now remove the battery, and instead join up a and b by
a wire ; the charge in the cable will rush out through the
Fig. 105.
galvanometer, which will show an opposite deflection, and
the residual charge will continue ' ; soaking out " for a
long time.
Since the speed of signalling, and therefore the
, economical working through a cable, depends upon its
Incapacity" as a condenser, 1 and since its capacity
depends upon the specific inductive power of the in-
sulating substance used, Hooper's compound, which has
an inductive capacity of only 17, and is cheap, is pre-
ferred to gutta-percha, which is expensive, and has a
specific inductive capacity as high as 2-46.
275. Use of Condensers. To avoid this retarda-,
tion and increase the speed of signalling in cables several
devices are adopted. Very delicate receiving instruments
are used, requiring only a feeble current ; for with the
feebler batteries the actual charge given to the cable is
less. In some cases a key is employed which, after
every signal, immediately sends into the cable a charge
of opposite sign, to sweep out, as it were, the charge left
behind. In duplex signalling (Lesson XXXIX.) the
1 The capacity of the " Direct" Atlantic cable from Ballinskelligs (Ireland)
to Nova Scotia is 992 microfarads.
CHAP, iv.] ELECTRICITY AND MAGNETISM. 231
resistance and electrostatic capacity of the cable have to
be met by balancing against them an " artificial cable "
consisting of a wire of equal resistance, and a condenser
of equal capacity. Messrs. Muirhead constructed for
duplexing the Atlantic Cable a condenser containing
100,000 square feet (over two acres of surface) of tinfoil.
Such condensers are also occasionally used on telegraph
lines in single working to avoid earth currents. They
are constructed by placing sheets of tinfoil between
sheets of mica or of paraffined paper, alternate sheets of
foil being connected together. Small condensers of
similar construction are used in connection with induc-
tion coils (Fig. 148).
276. Practical Unit of Capacity. Electricians adopt a unit \
of capacity, termed one farad, based on the system of electro-
magnetic units. A condenser of one farad capacity would be
raised to a potential of one volt by a charge of one we~ber of
electricity. 1 In practice such a con-
denser would be too enormous to be
constructed. As a practical unit
of capacity is therefore chosen the
microfarad, or one millionth of a
farad ; a capacity about equal to
that of three miles of an Atlantic
cable. Microfarad condensers are
made containing about 3600 square
inches of tinfoil. Their general form
is shown in Fig. 106, which re- pj gi IO Q t
presents a microfarad condenser.
The two brass pieces upon the ebonite top are connected re-
spectively with the two series of alternate sheets of tinfoil. The
plug between them serves to keep the condenser discharged
when not in use.
Methods of measuring the capacity of a condenser
are given in Art. 362.
277. Formulae for Capacities of Conductors
and Condensers. The following formulae give the
1 See Note on Electromagnetic Units, Art. 321.
232 ELEMENTARY LESSONS ON [CHAP. iv.
capacity of condensers of all ordinary forms, in electro-
static units :
Sphere: (radius = r. See Art. 247).
C = r.
Two Concentric Spheres: (radii r and /, specific
inductive capacity of the dielectric = k).
C = k ~7^~r
Cylinder : (length = /, radius = r).
Two Concentric Cylinders : (length = /, specific in-
ductive capacity of dielectric = ^, internal radius
= r, external radius = r f .
r
Circular Disc : (radius = r, thickness negligible).
Two Circular Discs: (like air condenser, Art. 48,
radii = r, surface = S, thickness of dielectric = ,
its specific inductive capacity = k).
or C = k,
$irb
(The latter formula applies to any two parallel discs
of surface S, whether circular or otherwise, provided they
are large as compared with the distance b between
them.)
278. Energy of Discharge of Leyden Jar or
Condenser. It follows from the definition of potential,
given in Art. 237, that in bringing up one + unit of
CHAP, iv.] ELECTRICITY AND MAGNETISM. 233
electricity to the potential V, the work done is V ergs.
This assumes, however, that the total potential V is not
thereby raised, and on this assumption the work done
in bringing up Q units would be QV. If, however, the
potential is nothing to begin with and is raised to V by
the charge Q, the average potential during the operation
is only ^V ; hence the total work done in bringing up
the charge Q, from zero potential to potential V is ^QV
ergs. Now, according to the principle of the con-
servation of energy, the work done in charging a jar
or condenser with electricity is equal to the work which
could be done by that quantity of electricity when the
jar is discharged. Hence a ^QV represents also the
energy of the discharge, where V stands for the dif-
ference of potential between the two coatings.
Since Q = VC, it follows that we may write |QV in
the form J^. That is to say, if a condenser of capacity .
C is charged by having a quantity Q of electricity
imparted to it, the energy of the charge is proportional |
directly to the square of the quantity, and inversely to
the capacity of the condenser.
If two equal Leyden jars are charged to the same
potential, and then their inside and outside coatings are
respectively joined, their united charge will be the same
as that of a jar of equal thickness, but having twice the
amount of surface.
If a charged Leyden jar is placed similarly in com-
munication with an uncharged jar of equal capacity, the
charge will be shared equally between the two jars, and
the passage of electricity from one to the other will be
evidenced by the production of a spark when the
respective coatings are put into communication. Here,
however, half the energy of the charge is lost in the
operation of sharing the charge, for each jar will have
only ^Q for its charge and V for its potential ; hence
the energy of the charge of each being half the product
of charge and potential will only be one quarter of the
234 ELEMENTARY LESSONS ON [CHAP. iv.
original energy. The spark which passes in the
operation of dividing the charge is, indeed, evidence of
the loss of energy ; it is about half as powerful as the
spark would have been if the first jar had been simply
discharged, and it is just twice as powerful as the small
sparks yielded finally by the discharge of each jar after
the charge has been shared between them.
The energy of a charge of the jar manifests itself,
as stated above, by the production of a spark at dis-
charge ; the sound, light, and heat produced being the
equivalent of the energy stored up. If discharge is
effected slowly through a long thin wire of high resistance
the air spark may be feeble, but the wire may be
perceptibly heated. A wet string being a feeble con-
ductor affords a slow and almost silent discharge ; here
probably the electrolytic conduction of the moisture is
accompanied by an action resembling that of secondary
batteries (Lesson XXXVIII.) tending to prolong the
duration of the discharge.
279. Charge of Jars arranged in Cascade.
Franklin suggested that a series of jars might be
arranged, the outer coating of one being connected with
the inner one of the next, the outer coating of the last
being connected to earth. The object of this arrange-
ment was that the second jar might be charged with the
electricity repelled from the outer coating of the first,
the third from that of the second, and so on. This
" cascade " arrangement, however, is of no advantage,
r the whole charge accumulated in the series being only
equal to that of one single jar. For if the inner coating
of the first jar be raised to V, that of the outer coating
of the last jar remaining at zero in contact with earth,
the difference of potential between the outer and inner
coating of any one jar will be only - V, where n is
number of jars. And as the charge in each jar is equal
to its capacity C, multiplied by its potential, the charge
in each will only be - CV, and in the whole n jars the
CHAP, iv.] ELECTRICITY AND MAGNETISM. 235
total charge will be n ^ CV, or CV, or equals the charge /
of one jar of capacity C raised to the same potential V.
LESSON XXIII. Phenomena of Discharge.
280. An electrified conductor may be discharged in
at least three different ways, depending on the medium
through which the discharge is effected, and varying
with the circumstances of the discharge.
281. Disruptive Discharge. In the preceding
Lesson it has been shown that induction across a non-
conducting medium is always accompanied by a mechani-
cal stress upon the medium. If this stress is very great
the non-conducting medium will suddenly give way and
a spark will burst across it. Such a discharge is called
a " disruptive " discharge.
A very simple experiment, carefully considered, will
set the matter in a clear light. Suppose a brass ball
charged with + electricity to be hung by a silk string
above a metal plate lying on the ground. If we lower
down the suspended ball a spark will pass between it
and the plate when they come very near together, and
the ball will then be found to have lost all its previous
charge. It was charged with a certain quantity of
electricity, and as it had, when suspended out of the
range of other conductors, a certain capacity (numeri-
cally equal to its radius in centimetres), the electricity
on it would be at a certain potential (namely = ^), and
the charge would be distributed with a certain surface
density all over it. The plate lying on the earth would
be all the while at zero potential. But when the sus-
pended ball was lowered down towards the plate the
previous state of things was altered. In the presence
of the + charge of the ball the potential 1 of the plate
l The student must remember that, by the definition of potential in
Art. 237, the potential at a point is the sum of all the separate quantities of
electricity near it, divided each by its distance from the point.
236 ELEMENTARY LESSONS ON [CHAP. iv.
would rise, were it not that, by the action termed
induction, just enough negative electrification appears on
it to keep its potential still the same as that of the earth.
The presence of the induced negative electricity on the
plate will attract the + electricity of the ball downwards,
and alter the distribution of the electricity on the ball,
the surface - density becoming greater at the under
surface, and less on the upper. The capacity of the
ball will be increased, and therefore its potential will
fall correspondingly. The layer of air between the ball
and the plate is acting like the glass of a Leyden jar.
The more the ball is lowered down the greater is the
accumulation of the opposite kinds of electricity on each
side of the layer of air, and the stress across the layer
becomes greater and greater, until the limit of the
dielectric strength is reached ; the air suddenly gives
way and the spark tears a path across. The greater
the difference of potential between the two bodies, the
thicker will be the layer which can thus be pierced, and
the longer will be the spark.
282. Conductive Discharge. If the discharge
takes place by the passage of a continuous current,
as when electricity flows through a thin wire from the
collector of a machine back to the rubbers, or from the
positive pole of a battery to the negative pole, the opera-
tion is termed a " conductive " discharge. The laws
of the conductive discharge are explained in Lessons
XXIX. and XXX.
283. Convective Discharge. A third kind of
discharge, differing from either of those above mentioned,
may take place, and occurs chiefly when electricity of a
high potential discharges itself at a pointed conductor
by accumulating there with so great a density as to
electrify the neighbouring particles of air ; these particles
then flying off by repulsion, conveying away part of the
charge with them. Such connective discharges may
occur either in gases or in liquids, but are best mani-
CHAP, iv.] ELECTRICITY AND MAGNETISM. 237
Tested in air and other gases at a low pressure, in tubes
exhausted by an air pump.
The discharge of a quantity of electricity in any of
the above ways is always accompanied by a transform-
ation of its energy into energy of some other kind,
sound, light, heat, chemical actions, and other pheno-
mena being produced. These effects must be treated in
detail.
284. Mechanical Effects. Chief amongst the
mechanical effects of the disruptive spark discharge is
the shattering and piercing of glass and other insulators.
The dielectric strength of glass, though much greater
than that of air, is not infinitely great. A slab of glass
3 inches thick has been pierced by the discharge of a
powerful induction-coil. The so-called "toughened"
glass has a greater dielectric strength than ordinary
glass, and is more difficult to pierce. A sheet of glass
may be readily pierced by a spark from a large Leyden
jar or battery of jars, by taking the following precau-
tions : The glass to be pierced is laid upon a block of
glass or resin, through which a wire is led by a suitable
hole, one end of the wire being connected with the outer
coating of the jar, the other being cut off flush with the
surface. Upon the upper surface of the sheet of glass
that is to be pierced another wire is fixed upright, its
end being exactly opposite the lower wire, the other
extremity of this wire being armed with a metal knob to
receive the spark from the knob of the jar or discharger.
To ensure good insulation a few drops of paraffin oil, or
of olive oil, are placed upon the glass round the points
where the wires touch it. A piece of dry wood similarly
treated is split by a powerful spark.
If a spark is led through a tightly corked glass tube
containing water, the tube will be shattered into small
pointed fragments by the sudden expansion of the
liquid.
The mechanical action of the brush discharge at
238 ELEMENTARY LESSONS ON [CHAP. iv.
points is mentioned in Art. 43, and the mechanical
effects of a current of electricity were described in
Lesson XIX.
285. Lullin's Experiment. If a piece of card-
board be perforated by a spark between two metal points,
two curious facts are observed. Firstly, there is a slight
burr raised on each side, as if the hole had been pierced
from the middle outwards. Secondly, if the two points
are not exactly opposite one another the hole is found
to be nearer the negative point. But if the experiment
is tried under the air pump in a vacuum, there is no
such displacement of the hole ; it is then midway
exactly.
286. Chemical Effects. The chemical actions
produced by currents of electricity have been described
in Lessons XIV. and XVIII. Similar actions can be
produced by the electric spark, and by the silent glow
discharge (see Art. 290). Faraday showed, indeed, that
all kinds of electricity from different sources produced the
same kinds of chemical actions, and he relied upon this
as one proof of the essential identity of the electricity
produced in different ways. If sparks from an electric
machine are received upon a piece of white blotting-
-paper moistened with a solution of iodide of potassium,
brown patches are noticed where the spark has effected
a chemical decomposition and liberated the iodine.
When a stream of sparks is passed through moist air
in a vessel, the air is found to have acquired the property
of changing to a red colour a piece of paper stained
blue with litmus. This, Cavendish showed, was due to
the presence of nitric acid, produced by the chemical
union of the nitrogen and oxygen of the air. The effect
is best shown with the stream of sparks yielded by a
small induction coil (Fig. 148), in a vessel in which the
air has been compressed beyond the usual atmospheric
pressure.
The spark will decompose ammonia gas, and olefiant
CHAP, iv.] ELECTRICITY AND MAGNETISM. 239
gas, and it will also cause chemical combination to take
place with explosion, when passed through detonating
mixtures of gases. Thus equal volumes of chlorine and
hydrogen are exploded by the spark. So are oxygen and
hydrogen gases, when mixed in the proportion of two
volumes of the latter to one of the former. Even the
explosive mixture of common coal gas mixed with from
four to ten times its own volume of common air, can be
thus detonated. A common experiment with the so-
called electric pistol consists in filling a small brass vessel
with detonating gases and then exploding them by a
spark. The spark discharge is sometimes applied to
the firing of blasts and mines in military operations, a
small quantity of fulminating powder being placed in
the path of the spark to kindle the larger charge of
gunpowder or other explosive. (See also Art. 37-)
287. Physiological Effects. The physiological
effects of the current have been described in Lesson
XIX. Those produced by the spark discharge are more
sudden in character, but of the same general nature.
The bodies of persons killed by the lightning spark I
frequently exhibit markings of a reddish tint where the
discharge in passing through the tissues has lacerated or
destroyed them. Sometimes these markings present a
singular ramified appearance, as though the discharge
had spread in streams over the surface at its entry.
288. Calorific Effects. The flow of electricity
through a resisting medium is in every case accompanied
by an evolution of heat. The laws of heating due to
currents are given in Art. 367. The disruptive discharge
is a transfer of electricity through a medium of great
resistance and accompanied by an evolution of heat.
A few drops of ether in a metallic spoon are easily
kindled by an electric spark. The spark from an electric
machine, or even from a rubbed glass rod, is hot enough
to kindle an ordinary gas-jet. In certain districts of
America, during the driest season of the year, the mere
240 ELEMENTARY LESSONS ON [CHAP. iv.
rubbing of a person's shoes against the carpet, as he
shuffles across the floor, generates sufficient electricity to
enable sparks to be drawn from his body, and he may
light the gas by a single spark from his outstretched
finger. Gunpowder can be fired by the discharge of a
Leyden jar, but the spark should be retarded by being
passed through a wet thread, otherwise the powder will
simply be scattered by the spark.
The Electric Air- Thermometer, invented by Kin-
nersley, 1 serves to investigate the heating powers of the
discharge. It consists of a glass vessel enclosing air,
and communicating with a tube partly filled with water
or other liquid, in order to observe changes of volume or
of pressure. Into this vessel are led two metal rods,
between which is suspended a thin wire, or a filament
of gilt paper ; or a spark can be allowed simply to cross
between them. When the discharge passes the enclosed
'air is heated, expands, and causes a movement of the
indicating column of liquid. Mascart has further de-
veloped the instrument by making it self- registering.
The results of observation with these instruments are
as follows: The heating effect produced by a given
I charge in a wire of given length is inversely proportional
! to the square of the area of the cross section of the wire.
The heating effect is greater, the slower the discharge.
The total heat evolved is jointly proportional to the
charge, and to the potential through which it falls. In
fact, if the entire energy of the discharge is expended
in producing heat, and in doing no other kind of work,
then the heat developed will be the thermal equivalent
of \ QV, or will be -2_ units of heat, where J repre-
sents the mechanical equivalent of heat, (J = 42 million ;
1 This instrument differs in no essential respect from that devised ninety
years later by Riess, to whom the instrument is often accredited. Riess,
however, deduced quantitative laws, while Kinnersley contented him-
self with qualitative observations. Snow Harris also anticipated Riess in
several points of his researches.
CHAP, iv.] ELECTRICITY AND MAGNETISM. 241
since 42 x io 6 ergs = i gramme- water-degree of heat),
and Q and V are expressed in C. G. S. units.
When a powerful discharge takes place through very
thin wires, they may be heated to redness, and even
fused by the heat evolved. Van Marum thus once
heated 70 feet of wire by a powerful discharge. A
narrow strip of tinfoil is readily fused by the charge of
a large Leyden jar, or battery of jars. A piece of gold
leaf is in like manner volatilised under the sudden heat-
ing of a powerful discharge ; and Franklin utilised this
property for a rude process of multiplying portraits or
other patterns, which, being first cut out in card, were
reproduced in a silhouette of metallic particles on a
second card, by the device of laying above them a film
of gold or silver leaf covered again with a piece of card
or paper, and then transmitting the charge of a Leyden
battery through the leaf between the knobs of a universal
discharger.
289. Luminous Effects. The luminous effects
of the discharge exhibit many beautiful and interesting
variations under different conditions. The spark of the
disruptive discharge is usually a thin brilliant streak of
light. When it takes place between two metallic balls,
separated only by a short interval, it usually appears
as a single thin and brilliant line. If, however, the
distance be as much as a few centimetres, the spark
takes an irregular zig-zag form. In any case its path is
along the line of least resistance, the presence of minute
motes of dust floating in the air being quite sufficient to
determine the zig-zag character. In many cases the
spark exhibits curious ramifications and forkings, of
which an illustration is given in Fig. 107, which is drawn
of one eighth of the actual size of the spark obtained
from a Cuthbertson's electrical machine. The discharge
from a Leyden jar affords a much brighter, shorter,
noisier spark than the spark drawn direct from the
collector of a machine. The length (see Art. 291)
R
242 ELEMENTARY LESSONS ON [CHAP. iv.
depends upon the potential, and upon the pressure and
temperature of the air in which the discharge takes
place. The brilliance depends chiefly upon the quantity
Fig. 107.
of electricity discharged. The colour of the spark varies
with the nature of the metal surfaces between which
the discharge takes place. Between copper or silver
terminals the spark takes a green tint, while between
iron knobs, it is of a reddish hue. Examination with
the spectroscope reveals the presence in the spark of the
rays characteristic of the incandescent vapours of the
several metals ; for the spark tears away in its passage
small portions of the metal surfaces, and volatilises
them.
29O. Brush Discharge: Glow Discharge. If
an electric machine is vigorously worked, but no sparks
be drawn from its collector, a fine diverging brush of
pale blue light can be seen (in a dark room) streaming
from the brass ball at the end of it farthest from the
collecting comb ; a hissing or crackling sound always
accompanies this kind of discharge. The brush dis-
charge consists of innumerable fine twig-like ramifications,
presenting a form of which Fig. 108 gives a fine example.
The brightness and size of the brush is increased by
holding a flat plate of metal a little way from it. With
a smaller ball, or with a bluntly pointed wire, the brush
CHAP, iv.] ELECTRICITY AND MAGNETISM. 243
appears smaller*, but is more distinct and continuous.
The brush discharge is larger and more ramified when a
positive charge is escaping, than when the electrification
Fig. 108.
is negative. Wheatstone found by using his rotating
mirror that the brush discharge is really a series of
successive partial sparks at rapid intervals.
If the blunt or rounded conductor be replaced by a
pointed one, the brush disappears and gives place to a
quiet and continuous glow where the electrified particles
of air are streaming away at the point. If these con-
vection-streams are impeded the glow may once more
give place to the brush. Where a negative charge is
being discharged at a point, the glow often appears to
be separated from the surface of the conductor by a dark
space, where the air, without becoming luminous, still
conveys the electricity. This phenomenon, to which
Faraday gave the name of the " dark " discharge, is very
well seen when electricity is discharged through rarefied
air and other gases in vacuum tubes.
291. Length of Sparks. Roughly speaking, the
244 ELEMENTARY LESSONS ON [CHAP. iv.
length of spark between two conductors increases with
the difference between their potentials. It is also found
to increase when the pressure of the air is diminished.
r
vary, not only with the exhaustion but with the difference
of potentials of the electrodes. When striae are pro-
duced by the intermittent discharges of the induction
coil, examination of them in a rotating mirror reveals
that they move forward from the positive electrode
towards the negative.
1 Holtz has more recently produced "electric shadows," by means of
discharges in air at ordinary pressure, between the poles of his well-known
machine (Fig. 29), the discharge taking place between a point and a disc
covered with silk, on which the shadows are thrown.
248 ELEMENTARY LESSONS ON [CHAP. iv.
The discharges in vacuum tubes are affected by the
magnet at all degrees of exhaustion, behaving like flexible
conductors. Under certain conditions also, the dis-
charge is sensitive to the presence of a conductor on the
exterior of the tube, retreating from the side where it is
touched. This sensitive state appears to be due to a
periodic intermittence in the discharge ; an intermittence
or partial intermittence in the flow would also probably
account for the production of striae.
295. Electric Oscillations. Feddersen examined
the spark of a Leyden jar by means of a rotating mirror,
and found that instead of being a single instantaneous
discharge, it exhibited l certain definite fluctuations.
With very small resistances in the circuit, there was a true
i oscillation of the electricity backward and forward for
a brief time, these alternate partial discharges being
probably due to the self-induction of the circuit. With
a certain higher resistance the discharge became con-
tinuous but not instantaneous. With a still higher
resistance, the discharge consisted of a series of partial
intermittent discharges, following one another in the
same direction. Such sparks when viewed in the rotating
mirror showed a series of separate images at nearly
equal distances apart. The period of the oscillations
was found to be proportional to the square root of the
capacity of the condenser.
296. Velocity of Propagation of Discharge.
The earliest use of the rotating mirror to analyse phe-
nomena of short duration was made by Wheatstone,
who attempted by this means to measure " the velocity
of electricity " in conducting wires. What he succeeded
in measuring was not, however, the velocity of electricity,
but the time taken by a certain quantity of electricity
to flow through a conductor of considerable resistance
and capacity. Viewed in a rotating mirror, a spark of
1 This phenomenon of oscillation was predicted from purely theoretical con-
siderations, arising out of the equations of self-induction, by Sir W. Thomson.
CHAP, iv.] ELECTRICITY AND MAGNETISM. 249
definite duration would appear to be drawn out into an
elongated streak. Such an elongation was found to be
visible when a Leyden jar was discharged through a
copper wire half a mile long ; and when the circuit was
interrupted at three points, one in the middle and one at
each end of this wire, three sparks were obtained, which,
viewed in the mirror, showed a lateral displacement,
indicating (with the particular rate of rotation employed)
that the middle spark took place r-rr^r-- of a second
1,152,000
later than those at the ends. Wheatstone argued from this
a velocity of 288,000 miles per second. But Faraday
showed that the apparent rate of propagation of a
quantity of electricity must be affected by the capacity
of the conductor ; and he even predicted that since a
submerged insulated cable acts like a Leyden jar (see
Art. 274), and has to be charged before the potential
at the distant end can rise, it retards the apparent flow
of electricity through it. Professor Fleeming Jenkin
says of one of the Atlantic cables, that, after contact
with the battery is made at one end, no effect can be
detected at the other for two -tenths of a second, and
that then the received current gradually increases, until
about three seconds afterwards it reaches its maximum,
and then dies away. This retardation is proportional
to the square of the length of the cable as well as to
its capacity and to its resistance ; hence it becomes
very serious on long cables, as it reduces the speed
of signalling. There is in fact no definite assignable
" velocity of electricity."
A very simple experiment will enable the student to
realise the excessively short duration of the spark of a
Leyden jar. Let a round disc of cardboard painted
with black and white sectors be rotated very rapidly so
as to look by ordinary light like a mere gray surface.
When this is illuminated by the spark of a Leyden jar it
appears to be standing absolutely still, however rapidly
it may be turning. A flash of lightning is equally in-
250
ELEMENTARY LESSONS ON [CHAP. iv.
stantaneous ; it is utterly impossible to determine at
which end the flash begins. 1
297. Electric Dust-figures. Electricity may creep
slowly over the surface of bad conductors. Lichtenberg
devised an ingenious way of investigating the distribution
of electricity by means of certain dust -figures. The
experiment is very easy. Take a charged Leyden jar
and write with the knob of it upon a cake of shellac
or a dry sheet of glass. Then sift, through a bit of
Fig. 109.
muslin, over the cake of shellac a mixture of powdered
red lead and sulphur (vermilion and lycopodium powder
answer equally well). The powders in this process rub
against one another, the red lead becoming + , the
sulphur . Hence the sulphur will be attracted to
those parts where there is + electrification on the disc,
and settles down in curious branching yellow streaks like
1 Sometimes the flash seems to strike downwards from the clouds some-
times upwards from the earth. This is an optical illusion, resulting from the
unequal sensitiveness to light of different portions of the retina of the eye.
CHAP, iv.] ELECTRICITY AND MAGNETISM.
251
those shown in Fig. 109. The red lead settles down in
little red heaps and patches where the electrification is
negative. Fig. 1 1 o shows the general appearance of
the Lichtenberg's figure produced by holding the knob of
Fig. no.
the Leyden jar at the centre of a shellac plate that has
previously been rubbed with flannel, the negative elec-
trification being attracted upon all sides toward the
central positive charge.
Powdered tourmaline, warmed and then sifted over a
sheet of glass previously electrified irregularly, will show
similar figures, though not so well defined.
Breath-figures can be made by electrifying a coin or
other piece of metal laid upon a sheet of dry glass,
and then breathing upon the glass where the coin lay,
revealing a faint image of it on the surface of the glass.
298. Production of Ozone. Whenever an elec-
tric machine is worked a peculiar odour is perceived.
This was formerly thought to be evidence of the existence
252 ELEMENTARY LESSONS ON [CHAP. iv.
of an electric "effluvium" or fluid; it is now known to be
due to the presence of ozone, a modified form of oxygen
gas, which differs from oxygen in being denser, more
active chemically, and in having a characteristic smell.
The discharge of the Holtz-machine and that of the
induction coil are particularly favourable to the pro-
duction of this substance.
299. Dissipation of Charge. However well in-
sulated a charged conductor may be, and however dry
the surrounding air, it nevertheless slowly loses its
charge, and in a few days will be found to be completely
discharged. The rate of loss of charge is, however, not
uniform. It is approximately proportional to the dif-
ference of potential between the body and the earth.
Hence the rate of loss is greater at first than afterwards,
and is greater for highly charged bodies than for those
feebly charged. The law of dissipation of charge
therefore resembles Newton's law of cooling, according
to which the rate of cooling of a hot body is propor-
tional to the difference of temperature between it and
the surrounding objects. If the potential of the body
be measured at equal intervals of time it will be found
to have diminished in a decreasing geometric series ; or
the logarithms of the potentials at equal intervals of time
will differ by equal amounts.
This may be represented by the following equation :
v t =v -*,
where V represents the original potential and V t the potential
after an interval /. Here e stands for the number 2 "] 1828 . . .
(the base of the natural logarithms), and p stands for the "co-
efficient of leakage," which depends upon the temperature,
pressure, and humidity of the air.
The rate of loss is, however, greater at negatively
electrified surfaces than at positive.
300. Positive and Negative Electrification.
The student will not have failed to notice throughout
CHAP, iv.] ELECTRICITY AND MAGNETISM. 253
this Lesson frequent differences between the behaviour
of positive and negative electrification. The striking dis-
similarity in the Lichtenberg's figures, the displacement
of the perforation - point in Lullin's experiment, the
unequal tendency to dissipation at surfaces, the remark-
able differences in the various forms of brush and glow
discharge, are all points that claim attention. Gassiot
described the appearance in vacuum tubes as of a force
emanating from the negative pole. Crookes's experi-
ments in high vacua show molecules to be violently
discharged from the negative electrode, the vanes of a
little fly enclosed in such tubes being moved from the
side struck by the negative discharge. Holtz found that
when funnel-like partitions were fixed in a vacuum tube
the resistance is much less when the open mouths of the
funnels face the negative electrode. These matters are
yet quite unaccounted for by any existing theory of
electricity.
The author of these Lessons is disposed to take the following view on this
point : If electricity be really one and not two, either the so-called positive
or the negative electrification must be a state in which there is more electricity
than in the surrounding space, and the other must be a state in which there
is less. The student was told, in Art. 6, that in the present state of the science
we do not know for certain whether "positive" electrification is really an
excess of electricity or a defect. Now some of the phenomena alluded to in
this Article seem to indicate that the so-called "negative" electrification
really is the state of excess. In particular, the fact that the rate of dissipa-
tion of charge is greater for negative electrification than for positive, points
this way ; because the law of loss of charge is the exact counterpart of the
law of the loss of heat, in which it is quite certain that, for equal differences
of temperature between a body and its surroundings, the rate of loss of heat
is greater at higher temperatures than at lower ; or the body that is really
hotter loses its heat fastest.
LESSON XXIV. Atmospheric Electricity.
3O1. The phenomena of atmospheric electricity are
of two kinds. There are the well-known 'electrical pheno-
mena of thunderstorms ; and there are the phenomena
254 ELEMENTARY LESSONS ON [CHAP. iv.
of continual slight electrification in the air, best observed
when the weather is fine. The phenomena of the Aurora
constitute a third branch of the subject.
3O2. The Thunderstorm an Electrical Pheno-
menon. The detonating sparks drawn from electrical
machines and from Leyden jars did not fail to suggest
to the early experimenters, Hawkesbee, Newton, Wall,
Nollet, and Gray, that the lightning flash and the thunder-
clap were due to electric discharges. In 1749, Ben-
jamin Franklin, observing lightning to possess almost
all the properties observable in electric sparks, 1 suggested
that the electric action of points (Art. 43), which was
discovered by him, might be tried on thunderclouds,
and so draw from them a charge of electricity. He
proposed, therefore, to fix a pointed iron rod to a high
tower. Before he could carry his proposal into effect,
Dalibard, at Marly-la-ville, near Paris, taking up Franklin's
hint, erected an iron rod 40 feet high, by which, in 1752,
he succeeded in drawing sparks from a passing cloud.
Franklin shortly after succeeded in another way. He
sent up a kite during the passing of a storm,%nd found
the wetted string to conduct electricity to the earth, and
to yield abundance of sparks. These he drew from a
key tied to the string, a silk ribbon being interposed
between his hand and the key for safety. Leyden. jars
could be charged, and all other electrical effects pro-
duced, by the sparks furnished from the clouds. The
proof of the identity was complete. The kite experi-
ment was repeated by Romas, who drew from a metallic
1 Franklin enumerates specifically an agreement between electricity and
lightning in the following respects : Giving light ; colour of the light ;
crooked direction ; swift motion ; being conducted by metals ; noise in
exploding ; conductivity in water and ice ; rending imperfect conductors ;
destroying animals ; melting metals ; firing inflammable substances ; sul-
phureous smell (due to ozone, as we now know) ; and he had previously found
that needles could be magnetised both by lightning and by the electric spark.
He also drew attention to the similarity between the pale-blue flame seen
during thundery weather playing at the tips of the masts of ships (called by
sailors St. Elmo's Fire), and the "glow" discharge at points.
CHAP, iv.] ELECTRICITY AND MAGNETISM. 255
string sparks 9 feet long, and by Cavallo, who made
many important observations on atmospheric electricity,
In 1753 Richmann, of St. Petersburg, who was experi-
menting with an apparatus resembling that of Dalibard,
was struck by a sudden discharge and killed.
3O3. Theory of Thunderstorms. Solids and
liquids cannot be charged throughout their substance ;
if charged at all the electricity is upon their surface (see
Art. 29). But gases and vapours, being composed of
myriads of separate particles, can receive a bodily charge.
The air in a room in which an electric machine is
worked is found afterwards to be charged. The clouds
are usually charged more or less with electricity, derived,
probably, from evaporation l going on at the earth's
surface. The minute particles of water floating in the
air being better conductors than the air itself become
more highly charged. As they fall by gravitation and
unite together, the strength of their charges increases.
Suppose eight small drops to join into one. That one
will have eight times the quantity of electricity dis-
tributed over the surface of a single sphere of twice the
radius (and, therefore, of twice the capacity, by Art. 247)
of the original drops ; and its electrical potential will
therefore be four times as great. Now a mass of cloud
may consist of such charged spheroids, and its potential
may gradually rise, therefore, by the coalescence of the
drops, and the electrification at the lower surface of the
cloud will become greater and greater, the surface of the
earth beneath acting as a condensing plate and becom-
ing inductively charged with the opposite kind of elec-
trification. Presently the difference of potential becomes
so great that the intervening strata of air give way under
the strain, and a disruptive discharge takes place at the
point where the air offers least resistance. This light-
ning spark, which may be more than a mile in length,
discharges only the electricity that has been accumulat-
1 See Art. 63.
256 ELEMENTARY LESSONS ON [CHAP. iv.
ing at the surface of the cloud, and the other parts of
the cloud will now react upon the discharged portion,
producing internal attractions and internal discharges.
The internal actions thus set up will account for the
usual appearance of a thundercloud, that it is a well-
defined flat-bottomed mass of cloud which appears at the
top to be boiling or heaving up with continual move-
ments.
3O4. Lightning and Thunder. Three kinds of
lightning have been distinguished by Arago : (i.) The
Zig-zag flash or " Forked lightning" of ordinary occur-
rence. The zig-zag form is probably due either to the
presence of solid particles in the air or to local electrifi-
cation at certain points, making the crooked path the
one of least resistance, (ii.) Sheet lightning, in which
whole surfaces are lit up at once, is probably only the
reflection on the clouds of a flash taking place at some
other part of the sky. It is often seen on the horizon at
night, reflected from a storm too far away to produce
audible thunder, and is then known as " summer light-
ning." (iii.) Globular lightning, in the form of balls of
fire, which move slowly along and then burst with a
sudden explosion. This form is very rare, but must be
admitted as a real phenomenon, though some of the
accounts of it are greatly exaggerated. Similar phe-
nomena on a small scale have been produced (though
usually accidentally) with electrical apparatus. Cavallo
gives an account of a fireball slowly creeping up the
brass wire of a large highly charged Leyden jar, and
then exploding as it descended ; and Plante' has recently
observed similar but smaller globular discharges from
his "rheostatic machine" charged by powerful second-
ary batteries.
The sound of the thunder may vary with the con-
ditions of the lightning spark. The spark heats the air
in its path, causing sudden expansion and compression
all round, followed by as sudden a rush of air into the
CHAP, iv.] ELECTRICITY AND MAGNETISM. 257
partial vacuum thus produced. If the spark be straight
and short, the observer will hear but one short sharp clap.
If its path be a long one and not straight, he will hear
the successive sounds one after the other, with a charac-
teristic rattle, and the echoes from other clouds will
come rolling in long afterwards. The lightning -flash
itself never lasts more than nnnnnr of a second.
The damage done by a lightning-flash when it strikes
an imperfect conductor appears sometimes as a disrup-
tive mechanical disintegration, as when the masonry
of a chimney-stack or church-spire is overthrown, and
sometimes as an effect of heat, as when bell-wires and
objects of metal in the path of the lightning-current are
fused. The physiological effects of sudden discharges
are discussed in Art. 226. The remedy against disaster
by lightning is to provide an efficient conductor com-
municating with a conducting stratum in the earth.
The " return-stroke " experienced by persons in the
neighbourhood of a flash is explained in Art. 26.
3O5. Lightning Conductors. The first suggest-
ion to protect property from destruction by lightning
was made by Franklin in 1749, in the following words :
" May not the knowledge of this power of points be of use
to mankind, in preserving houses, churches, ships, etc., from
the stroke of lightning, by directing us to fix on the highest
parts of those edifices upright rods of iron made sharp as a
needle, and gilt to prevent rusting, and from the foot of those
rods a wire down the outside of the building into the ground,
or round one of the shrouds of a ship, and down her side till
it reaches the water ? Would not these pointed rods probably
draw the electrical fire silently out of a cloud before it came
nigh enough to strike, and thereby secure us from that most
sudden and terrible mischief."
The four essential points of a good lightning-conductor
are (i) that its apex be a fine point elevated above the
highest point of the building ; (2) that its lower end passes
either into a stream or into wet stratum of ground ; (3)
S
258 ELEMENTARY LESSONS ON [CHAP, iv,
that the conductor between the apex and the ground be
perfectly continuous and of sufficient conducting power ;
(4) that the leads and any iron work or metal work about
the roofs or chimneys be connected by stout wires with
the main conductor. Too great importance cannot be
attached to the second and third of these essentials.
A copper rod of one square centimetre of sectional area
would probably form a trustworthy conductor. Maxwell
has proposed to cover houses with a network of con-
ducting wires, without any main conductor, the idea
being that then the interior of the building will, like
Faraday's hollow cube (Art. 31), be completely pro-
tected from electric force. Preece has lately calculated
that a lightning-conductor of a given height above the
surface of the ground will protect from the external
action of electricity a conical space the radius of whose
base is equal to the height of the rod, but whose side is
hollowed in the form of a quadrantal arc.
3O6. Atmospheric Electricity. In 1752 Le-
monnier observed that the atmosphere usually was in
an electrical condition. Cavallo, Beccaria, Ceca, and
others, added to our knowledge of the subject, and
more recently Quetelet and Sir W. Thomson have
generalised from more careful observations. The main
result is that the air above the surface of the earth is
usually, during fine weather, positively electrified, or at
least that it is positive with respect to the earth's
surface, the earth's surface being relatively negative.
The so-called measurements of " atmospheric electricity "
are really measurements of difference of potential between
a point of the earth's surface, and a point somewhere in
the air above it. In the upper regions of the atmosphere
the air is highly rarefied, and conducts electricity as do
the rarefied gases in Geissler's tubes (Art. 292). The
lower air is, when dry, a non-conductor. The upper
stratum is believed to be charged with + electricity,
while the earth's surface is itself negatively charged j
CHAP, iv.] ELECTRICITY AND MAGNETISM. 259
the stratum of denser air between acting like the
glass of a Leyden jar in keeping the opposite charges
separate. If we could measure the electric potential at
different points within the thickness of the glass of a
Leyden jar, we should find that the values of the
potential changed in regular order from a + value at
one side to a value at the other, there being a point
of zero potential about half way between the two. Now, ,
the air in fine weather always gives 4- indications, and
the potential of it is higher the higher we go to j
measure it. Cavallo found more electricity in the air
just outside the cupola of St. Paul's Cathedral than
at a lower point of the building. Sir W. Thomson
found the potential in the island of Arran to increase
from 23 to 46 volts for a rise of one foot in level ; but
the difference of potential was sometimes eight or ten
times as much for the same difference of level, and
changed rapidly, as the east wind blew masses of cloud
charged with + or electricity across the sky. Joule
and .Thomson, at Aberdeen, found the rise of potential
to be equal to 40 volts per foot, or 1-3 volts per centi-
metre rise of level.
During fine weather a negative electrification of the
air is extremely rare. Beccaria only observed it six
times in fifteen years, and then with accompanying
winds. But in broken weather and during rain it is
more often than +, and exhibits great fluctuations,
changing from to + , and back, several times in hall
an hour. A definite change in the electrical conditions
usually accompanies a change of weather. " If, when
the rain has ceased (said Ceca), a strong excessive ( + )
electricity obtains, it is a sign that the weather will
continue fair for several days."
307. Methods of Observation. The older
observers were content to affix to an electroscope (with
gold leaves or pith -balls) an insulated pointed rod
stretching out into the air above the ground, or to fly a
260 ELEMENTARY LESSONS ON [CHAP. iv.
kite, or (as Becquerel did) to shoot into the air an arrow
communicating with an electroscope by a fine wire, which
was removed before it fell. Gay Lussac and Biot lowered
a wire from a balloon, and found a difference of potential
between the upper and lower strata of the air. None
of these methods is quite satisfactory, for they do not
indicate the potential at any one point. To bring the
tip of a rod to the same potential as the surrounding air,
it is necessary that material particles should be discharged
from that point for a short time, each particle as it
breaks away carrying with it a + or a charge until
the potentials are equalised between the rod and the
air at that point. Volta did this by means of a small
flame at the end of an exploring rod. Sir W. Thomson
has employed a " water -dropper," an insulated cistern
provided with a nozzle protruding into the air, from
which drops issue to equalise the potentials : in winter
he uses a small roll of smouldering touch-paper. Dell-
mann adopted another method, exposing a sphere to
induction by the air, and then insulating it, and bringing
it within doors to examine its charge. Peltier adopted
the kindred expedient of placing, on or near the ground,
an electrometer of the form shown in Fig. 1 1 1 , which
during exposure was connected to the ground, then
insulated, then removed in-doors for examination. This
process really amounted to charging the electrometer
by induction with electricity of opposite sign to that of
the air. The principle of this particular electrometer
was explained in Art. 260. Of recent years the more
exact electrometers of Sir W. Thomson, particularly the
" quadrant " electrometer, described in Art. 262, the
" divided-ring " electrometer, and a " portable " electro-
meter on the same general principle, have been used
for observations on atmospheric electricity. These
electrometers have the double advantage of giving
quantitative readings, and of being readily adapted to
automatic registration, by recording photographically the
CHAP, iv.] ELECTRICITY AND MAGNETISM.
261
movements of a spot of light reflected from a small
mirror attached to their needle. Using a water-dropping
collector and a Thomson electrometer, Everett made
Fig. in.
a series of observations in Nova Scotia, and found the
highest + electrification in frosty weather, with a dry
wind charged with particles of ice.
3O8. Diurnal Variations. Quetelet found that at
Brussels the daily indications (during fine weather)
showed two maxima occurring in summer at 8 a.m. and
9 p.m., and in winter at 10 a.m. and 6 p.m. respectively,
262 ELEMENTARY LESSONS ON [CHAP. iv.
and two minima which in summer were at the hours of
3 p.m. and about midnight. He also found that in January
the electricity was about thirteen times as strong as in
June. Observations made by Prof. B. Stewart at Kew
show a maximum at 8 a.m. in summer at 10 a.m. in
winter, and a second minimum at I o p.m. in summer
and 7 p.m. in winter. The maxima correspond fairly
with hours of changing temperature, the minima with
those of constant temperature. In Paris, M. Mascart
finds but one maximum just before midnight : at sun-
rise the electricity diminishes until about 3 p.m., when it
has reached a minimum, whence it rises till nightfall.
Our knowledge of this important subject is still very
imperfect. We do not even know whether all the
changes of the earth's electrification relatively to the air
are due to causes operating above or below the earth's
surface. Simultaneous observations at different places
and at different levels are greatly wanted.
3O9. The Aurora. In all the northern regions of
the earth the Aurora borealis, or " Northern Lights," is
an occasional phenomenon ; and within and near the
Arctic circle is of almost nightly occurrence. Similar
lights are seen in the south polar regions of the earth,
and are denominated Aurora aitstralis. As seen in
European latitudes, the usual form assumed by the
aurora is that of a number of ill -defined streaks or
streamers of a pale tint (sometimes tinged with red and
other colours), either radiating in a fan -like form from
the horizon in the direction of the (magnetic) north, or
forming a sort of arch across that region of the sky, of
the general form shown in Fig. 112. A certain flicker-
ing or streaming motion is often discernible in the
streaks. Under very favourable circumstances the
aurora extends over the entire sky. The appearance of
an aurora is usually accompanied by a magnetic storm
(Art. 145), affecting the compass -needles over whole
regions of the globe. This fact, and the position of the
CHAP, iv.] ELECTRICITY AND MAGNETISM.
263
auroral arches and streamers with respect to the
magnetic meridian, directly suggest an electric origin
for the light, a conjecture which is confirmed by the
many analogies found between auroral phenomena and
Fig. 112.
those of discharge in rarefied air (Arts. 292 and 294).
Yet the presence of an aurora does not, at least in our
latitudes, affect the electrical conditions of the lower
regions of the atmosphere. On September i, 1859, a
severe magnetic storm occurred, and auroras were
observed almost all over the globe ; at the same time
a remarkable outburst of energy took place in the
photosphere of the sun ; but no simultaneous develop-
ment of atmospheric electricity was recorded. Auroras
appear in greater frequency in periods of about 1 1 J
264 ELEMENTARY LESSONS ON [CHAP. iv.
years, which agrees pretty well with the cycles of
maximum of magnetic storms (see Art. 144) and of
sun-spots.
The spectroscope shows the auroral light to be due
to gaseous matter, its spectrum consisting of a few
bright lines not referable with certainty to any known
terrestrial substance, but having a general resemblance
to those seen in the. spectrum of the electric discharge
through rarefied dry air.
The most probable theory of the aurora is that origin-
ally due to Franklin, namely, that it is due to electric
discharges in the upper air, in consequence of the differ-
ing electrical conditions between the cold air of the polar
regions and the warmer streams of air and vapour raised
from the level of the ocean in tropical regions by the
heat of the sun. For evaporation of water containing
saline matter is a source of electrification (see Art. 63),
the escaping vapour becoming positively electrified.
According to Nordenskiold the terrestrial globe is
perpetually surrounded at the poles with a ring or crown
of light, single or double, to which he gives the name of
the " aurora-glory." The outer edge of this ring he esti-
mates to be at 120 miles above the earth's surface, and
its diameter about 1250 miles. The centre of the aurora-
glory is not quite at the magnetic pole, being in lat.
81 N., long. 80 E. This aurora-glory usually appears
as a pale arc of light across the sky, and is destitute of
the radiating streaks shewn in Fig. 112, except during
magnetic and auroral storms.
An artificial aurora has been produced by Lemstrom,
who erected on a mountain in Lapland a network of
wires presenting many points to the sky. By insulating
this apparatus and connecting it by a telegraph wire
with a galvanometer at the bottom of the mountain, he
was able to observe actual currents of electricity when
the auroral beam rose above the mountain
CHAP, v.] ELECTRICITY AND MAGNETISM. 265
CHAPTER V.
ELECTROMAGNETICS.
LESSON XXV. Theory of Magnetic Potential.
31O. That branch of the science of electricity which
treats of the relation between electric currents and mag-
netism is termed Electromagnetics. In Art. 1 1 7 the
law of inverse squares as applied to magnets was explained,
and the definition of " unit magnetic pole " was given in
Art. 125. The student also learned to express the strength
of poles of magnets in terms, of the unit pole, and to apply
the law to the measurement of magnetic forces. It is,
however, much more convenient, for the purpose of study,
to express the interaction of magnetic and electromagnetic
systems in terms not of "force" but of " potential" \
i.e. in terms of their power to do work. In Art. 237
the student was shown how the electric potential due
to a quantity of electricity may be evaluated in terms of
the work done in bringing up as a test charge a unit of
+ electricity from an infinite distance. Magnetic
potential can be measured similarly by the ideal pro-
cess of bringing up a unit magnetic pole (N. -seeking)
from an infinite distance, and ascertaining the amount
of work done in the operation. Hence a large number
of the points proved in Lesson XX. concerning electric
potential will also hold true for magnetic potential. The
student may compare the following propositions with the
corresponding ones in Articles 237 to 243 :
266 ELEMENTARY LESSONS ON [CHAP. v.
(a) The magnetic potential at any point is the work
that must be spent upon a unit magnetic (N. -seek-
ing) pole in bringing it up to that point from an
infinite distance.
(b) The magnetic potential at any point due to a
system of magnetic poles is the sum of the separate
magnetic potentials due to the separate poles.
The student must here remember that the potentials due
to S.-seeking poles will be of opposite sign to those due
to N.-seeking poles, and must be reckoned as negative.
(c) The (magnetic) potential at any point due to a
system of magnetic poles may be calculated (com-
pare with Art. 238) by summing up the strengths
of the separate poles divided each by its own
distance from that point. Thus, if poles of
strengths m', m" , m" ', etc., be respectively at
distances of r , r" , r"' , (centimetres)
from a point P, then the following equation gives
the potential at P :
T , m' m n m'"
V P = -" ' + -^ + 7*r +
V 171
P = 2 -
(d) The difference of (magnetic) potential between
two points is the work to be done on or by a
unit (N.-seeking) pole in moving it from one
point to the other.
(e) Magnetic force is the rate of change of (magnetic)
potential per unit of length.
(f) Eqtiipotential surfaces are those (imaginary) sur-
faces siirrounding a magnetic pole or system of
poles, over which the (magnetic) potential has
equal values. Thus, around a single magnetic
pole, supposing all the magnetism to be collected
at a point far removed from all other poles, the
potential would be equal all round at equal
CHAP, v.] ELECTRICITY AND MAGNETISM. 267
distances ; and the equipotential surfaces would
be a system of concentric spheres at such dis-
tances apart that it would require the expendi-
ture of one erg of work to move a unit pole up
from a point on the surface of one sphere to any
point on the next (see Fig. 97). Around any real
magnet possessing two polar regions the equi-
potential surfaces would be much more com-
plicated. Magnetic force, whether of attraction
or repulsion, always acts across the equipotential
surfaces in a direction normal to the surface; the
magnetic lines of force are everywhere perpen-
dicular to the equipotential surfaces.
311. Tubes of Force. The following proposi-
tion is also important : From a single magnetic pole
(supposed to be a point far removed from all other
poles) the lines of force diverge radially in all directions.
The space around may be conceived as thus divided up
into a number of conical regions, each having their apex
at that pole ; and through each cone, as through a tube, a
certain number of lines of force will pass. Such a conical
space may be called a "tube of force." No matter
where you cut across a tube of force the cross-section
will cut through all the enclosed lines of force, though
they diverge more widely as the tube widens. Hence,
(g) The total magnetic force exerted across any section
of a tube of force is constant wherever the section
be taken.
In case the magnetism is not concentrated at one
point, but distributed over a surface, we shall have to
speak of the " amount of magnetism " rather than of the
" strength of pole," and in such a case the
(h) Magnetic density is the amount of free magnetism
per unit of surface. In the case of a simple
magnetic shell over the face of which the
magnetism is distributed with uniform density,
268 ELEMENTARY LESSONS ON [CHAP, v,
the " strength " of the shell will be equal to the
thickness of the shell multiplied by the surface-
density.
312. Intensity of Field. We have seen (Art. 105)
that every magnet is surrounded by a certain " field,"
within which magnetic force is observable. We may
completely specify the properties of the field at any
point by measuring the strength and the direction of that
force, that is, by measuring the "intensity of the
field" and the direction of the lines offeree. We might
take as a measure of the intensity of the field at any point
the number of lines of force that pass through the region
about -that point ; but for the present we will define it as
follows: The "intensity of the field" at any point is
measured by the force with which it acts on a unit
magnetic pole placed at that point. Hence, unit intensity
of field is that intensity of field which acts on a unit pole
with a force of one dyne. There is therefore a field of
unit intensity at a point one centimetre distant from
the pole of a magnet of unit strength. Suppose a
magnet pole, whose strength is m, placed in a field at a
point where the intensity is H, then the force will be m
times as great as if the pole were of unit strength, and
/= m x H.
313. Intensity of Magnetisation. When a piece
of a magnetic metal is placed in a magnetic field, some
of the lines of force run through it and magnetise it.
The intensity of its magnetisation will depend upon the
intensity of the field into which it is put, and upon the
metal itself. A metal in which, like soft iron, a high
degree of magnetisation is thus produced is said to
possess a high coefficient of magnetisation. Every
magnetic substance has a positive coefficient of mag-
netisation ; but there are many substances, such as
bismuth, copper, water, etc., which possess negative
coefficients of magnetisation. The latter are termed
CHAP, v.] ELECTRICITY AND MAGNETISM. 269
" diamagnetic " bodies (see Art. 339). Bodies which
have a high coefficient of magnetisation may be re-
garded as good conductors of magnetism. When a
piece of soft iron is placed in a magnetic field the lines
of force gather themselves up and run in greater quan-
tities through the space now occupied by iron ; whereas,
if a piece of bismuth or copper is placed in the field,
fewer lines of force than before pass through the space
occupied by the diamagnetic metal. The intensity of
magnetisation through the substance of a magnet is
measured by dividing its "magnetic moment" 1 by its
volume. A permanent steel magnet has a certain per-
manent intensity of magnetisation ; a piece of soft iron
laid along the lines of force in a magnetic field has
induced in it a certain temporary intensity of magnetisa-
tion equal to the product of the "intensity" of the field H
into the coefficient of magnetisation of the iron k.
Intensity of magnetisation = -^- = k H.
volume
It is, however, found that there is a certain maximum
of intensity of magnetisation for each magnetic metal,
which cannot be exceeded, no matter how powerful the
field in which the metal is placed. According to Row-
land, the following are the maximum intensities for
different metals :
Iron and Steel . . . 1390
Cobalt .... 800
Nickel .... 494
Steel will not retain all the magnetism that can be
temporarily induced in it, its permanent maximum of
intensity being only 785.2 Everett has calculated (from
Gauss's observations) that the intensity of magnetisation
of the earth is only 0-0790, or only IT^THF of what it
would be if the globe were wholly iron. The fact that
1 The " magnetic moment " is the product of the strength of either pole
of a magnet by its length, or = m X I.
2 According to Weber, it is 400 ; according to Van Waltenhofen, 470 ,
according to Schneebeli (in thin wires) from 710 to 1060.
270 ELEMENTARY LESSONS ON [CHAP, v,
a maximum is reached shows that the coefficient of
magnetisation k is not constant, but that it is less
at higher degrees of magnetisation than at lower. A
piece of nickel placed in a field of small intensity is
magnetised about five times as strongly as a piece of
iron of the same size would be, but in a strong field the
iron would be the more strongly magnetised. Measure-
ments of the values of k in fields of different intensity
have been made by Rowland and Stoletow.
314. Potential due to a (Solenoidal) Magnet.
A long thin uniformly magnetised magnet exhibits
free magnetism only at the two ends, and acts on
external objects just as if there were two equal quantities
of opposite kinds of magnetism collected at these two
points. Such a magnet is sometimes called a solenoid
to distinguish it. from a magnetic shell (Art. 107).
Ordinary straight and horse-shoe shaped magnets are
imperfect solenoids. The magnetic potential due to a
solenoid, and all its magnetic effects, depend only on
the position of its two poles, and on their strength, and
not on the form of the bar between them, whether straight
or curved. In Art. 310 (c) was given the rule for finding
the potential due to a system of poles. Suppose the
two poles of a solenoid have strengths + m and m
(taking S. -seeking pole as of negative value), and that
the respective distances of these poles from an external
point P, are r^ and r z : then .the potential at P will be,
Suppose a magnet curled round until its N. and S.
poles touch one another : it will not act as a magnet
on an external object, and will have no "field" (Art.
105) ; for if the two poles are in contact, their distances
r v and r a to an external point P will be equal, and
315. Potential due to a Magnetic Shell.
Gauss demonstrated that the potential due to a magnetic
CHAP, v.] ELECTRICITY AND MAGNETISM. 271
shell at a point near it is equal to the strength of the
shell multiplied by the solid-angle subtended by the shell
at that point; the " strength " of a magnetic shell
being the product of its thickness into its surface-density
of magnetisation.
If co represents the solid-angle subtended at the point
P, and i the strength of the shell, then
V P = co i.
Proof. To establish this proposition would require an easy
application of the integral calculus. But the following geo-
metrical demonstration, though incomplete, must here suffice.
Let us consider the shell as composed, like that drawn, of
a series of small elements of
thickness /, and having each an
area of surface s. The whole
solid -angle subtended at P by
the shell may likewise be con-
ceived as made up of a number
of elementary small cones, each
of solid-angle c6 : Let r and r 2
be the distances from P to the F}
two faces of the element : Let
a section be made across the small cone orthogonally, or at
right angles to r v and call the area of this section a : Let the
angle between the surfaces s and a be called angle (3 : then
s - -^-77. Let i be the "strength" of the shell (i.e. = its
COS p
surface-density of magnetisation x its thickness) ; then =
surface-density of magnetisation, and s = strength of either
pole of the little magnet = m.
area of its orthogonal section
Now solid angle 6 = -j-*-
therefore a = dr 2 ,
and * = c^7-
^2
Hence <6? - a =. w.
/cos /3
272 ELEMENTARY LESSONS ON [CHAP. v.
But the potential at P of the magnet whose pole is m t will be
=r jfo' -.f 8 ( l L \
/cos "J3 V ^i ' *,/
but =' which we may write ^ -
because r and r^ may be made as nearly equal as we please.
And since r - r% = t cos j3
/ cos j3
or the potential due to the element of the shel = the strength
of the shell x the solid-angle subtended by the element of the
shell. Hence, if V be the sum of all the values of v for all the
different elements, and if w be the whole solid-angle (the sum
of all the small solid-angles such as c6),
V P = ui
or, the potential due to a magnetic shell at a point is equal to
the strength of the shell multiplied by the solid -angle subtended
by the whole of the shell at that point.
Hence wz represents the work that would have to be
done on or by a unit -pole, to bring it up from an
infinite distance to the point P, where the shell subtends
the solid-angle to. At a point Q where the solid-angle
subtended by the shell is different, the potential will be
different, the difference of potential between P and Q
bdn S V Q -V P = ,'(, -o, P ).
If a magnet-pole whose strength is m were brought
up to P, m times the work would have to be done, or
the mutual potential would be = mui.
316. Potential of a Magnet-pole on a ShelL
It is evident that if the shell of strength i is to be
placed where it subtends a solid-angle u at the pole ;/?,
it would require the expenditure of the same amount of
work to bring up the shell from an infinite distance
on the one hand, as to bring up the magnet-pole from
CHAP, v.] ELECTRICITY AND MAGNETISM. 273
an infinite distance on the other; hence mut represents'
both the potential of the pole on the shell and the
potential of the shell on the pole. Now the lines of
force from a pole may be regarded as proportional in
number to the strength of the pole, and from a single
pole they would radiate out in all directions equally.
Therefore, if a magnet-pole was placed at P, at the apex
of the solid-angle of a cone, the number of lines of force
which would pass through the solid-angle would be pro-
portional to that solid-angle. It is therefore convenient
to regard ma* as representing the number of lines of force
of the pole which pass through the shell, and we may call
the number so intercepted N. Hence the potential of a
magnet-pole on a magnetic shell is equal to the strength
of the shell multiplied by the number of lines of force
(due to the magnet-pole) which pass through the shell;
or V = Nz. If either the shell or the pole were moved
to a point where a different number of lines of force
were cut, then the difference of potential would be,
This formula is of great importance : but the student
must be specially cautioned as to the signs to be
attributed in applying it to the various quantities. A
magnet has two poles (N.-seeking and S.-seeking), whose
strengths are + m and m, and the two faces of a
magnetic shell are of opposite sign. To bring up a N.-
seeking (or +) pole against the repelling force of the
N.-seeking face of a magnetic shell requires a positive
amount of work to be done ; and their mutual reaction
would enable work to be done afterwards by virtue of
their position : in this case then the potential is +. But
in moving a N.-seeking pole up to the S.-seeking face of
a shell work will be done by the pole, for it is attracted
up ; 'and as work done by the pole may be regarded as
our doing negative work, the potential here will have a
negative value.
T
274 ELEMENTARY LESSONS ON [CHAP. V,
Again, suppose we could bring up a unit N. -seeking
pole against the repulsion of the N. -seeking face of a
shell of strength z, and should push it right up to the
shell ; when it actually reached the plane of the shell the
shell would occupy a whole horizon, or half the whole
space around the pole, the solid-angle it subtended being
therefore 2-r, 1 and the potential will be + 2*1. If we
had begun at the S. -seeking face, the potential at that
face would be 2 en. It appears then that the potential
alters its value by 4
the force of at- _
traction or repul- ..,.
. , Fig. 119.
sion acts at right-
angles to the currents themselves.
An example of laws ii. and iii. is afforded by the
case shown in Fig. 120. Here two currents ab
2Q2
ELEMENTARY LESSONS ON [CHAP.
and cd are movable round O as a centre. There
will be repulsion between a and d and between c
and b, while in the
other quadrants there
will be attraction, a
attracting c, and b at-
tracting d.
The foregoing laws
Fig. 120.
may be summed up in
one, by saying that two portions of circuits, how-
ever situated, experience a mutual force tending
to set them so that their currents flow as nearly
in the same path as possible.
(iv.) The force exerted between two parallel portions
of circuits is proportional to the product of the strengths
of the two currents, to the length of the portions, and
inversely proportional to the distance between them.
333. Ampere's Table. In order to observe these
attractions and repulsions, Ampere devised the piece of
apparatus known as Ampere's Table, shown in Fig. 121,
CHAP, v.] ELECTRICITY AND MAGNETISM. 293
consisting of a double supporting stand, upon which
conductors formed of wire, shaped in different ways, can
be hung in such a way as to be capable of rotation.
In the figure a simple loop is shown as hung upon the
supports. The ends of the wires of the movable
portion dip into two mercury cups so as to ensure good
contact. The solenoid, Fig. 1 1 6, is intended to be hung
upon the same stand.
By the aid of this piece of apparatus Ampere further
demonstrated the following points :
(a) A circuit doubled back upon itself, so that the
current flows back along a path close to itself,
exerts no force upon external points.
(b) A circuit bent into zig-zags or sinuosities, pro-
duces the same magnetic effects on a neigh-
bouring piece of circuit as if it were straight.
(c) There is in no case any force tending to move a
conductor in the direction of its own length.
(d) The force between two conductors of any form is
the same, whatever the linear size of the system,
provided the distances be increased in the same
proportion, and that the currents remain the
same in strength.
The particular case, given in Fig. 122, will show the
value of these experiments. Let AB and CD represent
two wires carrying currents, lying neither parallel nor in
the same plane. It follows from (), that if we replace
the portion PQ by the crooked wire PRSQ, the force
will remain the same. The portion PR is drawn verti-
cally downwards, and, as it can, by (<:), experience no
force in the direction of its length, this portion will
neither be attracted nor repelled by CD. In the portion
RS the current runs at right angles to CD, and this
portion is neither attracted nor repelled by CD. In the
portion SQ the current runs parallel to CD, and in the
same direction, and will therefore be attracted down-
294
ELEMENTARY LESSONS ON [CHAP. v.
wards. On the whole, therefore, PQ will be urged to-
wards CD. The portions PR and RS will experience
forces of rotation however, P being urged round R as a
Fig. 122.
centre towards C, and R being urged horizontally round
S towards C. These actions would tend to make AB
parallel with CD.
334. Ampere's Theory. From the four preceding
experimental data, Ampere built up an elaborate mathe-
matical theory, assuming that, in the case of these forces
acting apparently at a distance across empty space, the
action took place in straight lines between two points,
the total attraction being calculated as the sum of the
separate attractions on all the different parts. The
researches of Faraday have, however, led to other views,
and we now regard the mutual attractions and repulsions
of currents as being due to actions taking place in the
medium which fills the space around and between the
conductors. That space we regard rather as being full
of curving " lines of force. ' Every wire carrying a
current has a magnetic field, like that of Fig. 85, sur-
rounding it ; and every closed circuit acts as a magnetic
shell. Hence all these electrodynamic actions are
capable of being regarded as magnetic actions, and they
can be predicted beforehand for any particular case on
that supposition. Thus, the author of these Lessons
CHAP, v.] ELECTRICITY AND MAGNETISM. 295
has shown 1 that in the case of two parallel concurrent
circuits the " lines of force " due to the two systems
run into one another, embracing both circuits, while in
the case of two parallel and non-concurrent circuits the
" lines of force " due to the two currents indicate mutual
repulsion. The theory of Maxwell, that a voltaic circuit
acts like a magnetic shell (a direct deduction from Fara-
day's work), is in practice a more fruitful conception than
that of Ampere. On Maxwell's theory two circuits will
tend, like two magnetic shells, to move so as to include
as many of one another's " lines of force " as possible
(Art. 193 and 320). This will be the case when they
coincide as nearly as possible ; t.e. 9 when the two wires
are parallel in every part, and when the currents run
round in the same direction. In fact, all the electro-
dynamic laws of parallel and oblique circuits can be
deduced from Maxwell's theory in the simplest manner.
An interesting experiment, showing an apparent
mutual self-repulsion between contiguous portions of the
circuit, was devised by Ampere. A trough divided by
a partition into two parts, and made of non-conducting
materials, is filled with mercury. Upon it floats a
Fig. 123.
metallic bridge formed of a bent wire, of the form shown
in Fig. 123, or consisting of a glass tube filled siphon-
wise with mercury. When a current is sent through
the floating conductor from X over MN, and out at
1 Philosophical Magazine ', November 1878, p. 348.
296 ELEMENTARY LESSONS ON [CHAP. v.
Y, the floating bridge is observed to move so as to
increase the length of the circuit. But Maxwell has
shown that the true explanation depends upon the self-
induction (Art. 404) of the two parallel portions of the
floating conductor, and that the force would be diminished
indefinitely if the two parallel parts could be made to
lie quite close to one another.
335. Electromagnetic Rotations. Continuous
rotation can be produced between a magnet and a
circuit, or between two parts of one -circuit, provided
that one part of the circuit can move while another part
remains fixed, or that the current in one, part can be
reversed. The latter device is adopted in the construc-
tion of the electromagnetic engines described in Art. 375 ;
the former alternative is applied in a good many interest-
ing pieces of apparatus for showing rotations, a sliding-
contact being made between one part of the circuit and
another. Several different forms of rotation-apparatus
were devised by Faraday and by Ampere. One of the
simplest of these is shown in Fig. 124, in which a
Fig. 124.
current rising through a and passing through the lightly
pivoted wire b b' in either direction, passes down into
a circular trough containing mercury. The trough is
made of copper, and is connected with a wire which is
also wound in a coil round the outside of the trough,
CHAP, v.] ELECTRICITY ANI> MAGNETISM. 297
and which forms part of the circuit. The arrows show
the direction of the currents. The currents in the
circular coils constitute a magnetic shell, whose N. -seek-
ing face is uppermost. The lines of force due to this
shell therefore run vertically in an upward direction.
According to the converse to Ampere's Rule (Art. 186),
a man swimming in one of the horizontal branches
from the centre a outwards, and looking along the lines
of force, i.e. turned on to his back, so as to look upwards,
will be carried, along with the conductor, toward his left
hand. And the pivoted conductor as seen from above
will rotate continuously in the same sense as the hands
of a clock around the centre a. A pole of a magnet
can also be made to rotate round a current ; and if a
vertical magnet be pivoted so as to turn around its
own axis it will rotate when a current is led into its
middle region and out at either end. If the current is
led in at one end and out at the other there will be no
rotation, since the two poles will thus be urged to rotate
in opposite ways, which is impossible. Liquid con-
ductors too can exhibit electromagnetic rotations. Let a
cylindrical metallic vessel connected to one pole of a
battery be filled with mercury or dilute acid, and let
a wire from the other pole dip into its middle, so that
a current may flow radially from the centre to the
circumference, or vice versa; then, if this be placed
upon the pole of a powerful magnet, or if a magnet
be held vertically over it, the liquid may be seen to
rotate.
336. Electrodynamometer. Weber devised an
instrument known as an electrodynamometer for measur-
ing the strength of currents by means of the electro-
dynamic action of one part of the circuit upon another part.
It is in fact a sort of galvanometer, in which, instead of
a needle, there is a small coil suspended. One form of
this instrument, in which both the large outer and small
inner coils consist of two parallel coils of many turns, is
298 ELEMENTARY LESSONS ON [CHAP. v.
shown in Fig. 125. The inner coil CD is suspended with
its axis at right angles to that of the outer coils AA, BB,
and is supported bifilarly (see Art. 1 1 8) by two fine
metal wires. If
one current flows
round both coils in
either direction the
inner bobbin tends
to turn and set its
coils parallel to
the outer coils ;
the sine of the
angle through
which the sus-
pending wires are
twisted being pro-
portional to the
square of the
strength of the cur-
rent. The chief
advantage of this
instrument over a
Fig. 125. .
galvanometer is,
that it may be used for induction-currents in which there
are very rapid alternations, a current in one direction
being followed by a reverse current, perhaps thousands of
times in a minute. Such currents hardly affect a galvano-
meter needle at all, because of the slowness of its swing.
Siemens employs an electrodynamometer with coils made of
very thick wire for the absolute measurement of strong currents,
such as are used in producing electric light. It is possible also
to use an electrodynamometer as a " Power-meter " to measure
the electric horse power evolved by a battery or consumed in
an electric lamp or machine. In this case the whole current is
sent through a fixed coil of thick wire, while the movable coil,
made of many turns of thin wire, is connected as a shunt across
the terminals of the lamp or machine being thus traversed by a
current proportional to the difference of potential between those
points (see Art. 360 d). The sine of the angle of deflection
CHAP, v.] ELECTRICITY AND MAGNETISM. 299
will be proportional to the product of the two currents, and
therefore, to the product of the whole current into the difference
of potential (see Art. 378 bis.)
337. Electromagnetic Actions of Convection Currents.
According to Faraday a stream of particles charged with elec-
tricity acts magnetically like a true conduction-current. This
was first proved in 1876 by Rowland, who found a charged disc *.
rotated rapidly to act upon a magnet as a feeble circular current
would do. Convection currents, consisting of streams of elec-
trified particles, are also acted upon by magnets. The convec-
tive discharges in vacuum-tubes (Art. 292) can be drawn aside
by a magnet, or caused to rotate around a magnet-pole. The
' ' brush " discharge when taking place in a strong magnetic field
is twisted. The voltaic arc (Art. 371) also behaves like a flexible
conductor, and can be attracted or repelled by a magnet. Two
stationary positively electrified particles repel one another, but
two parallel currents attract one another (Art. 332), and if
electrified particles flowing along act like currents, there should
be an (electromagnetic) attraction between two electrified particles
moving along side by side through space. According to Max-
well's theory (Art. 390) the electrostatic repulsion will be just
equal to the electromagnetic attraction when the particles move
with a velocity equal to the velocity of light.
Quite recently Hall has discovered that when a powerful
magnet is made to act upon a current flowing along in a strip
of very thin metal, the equipotential lines are no longer at right -
angles to the lines of flow of the current in the strip. This
action appears to be connected with the magnetic rotation of
polarized light (Art. 387), the co-efficient of this transverse
thrust of the magnetic field on the current being -j- in gold,
and in iron.
338. Ampere's Theory of Magnetism. Ampere, finding
that solenoids (such as Fig. 116) act precisely as magnets, con-
ceived that all magnets are simply collections of currents, or
that, around every individual molecule of a magnet an electric
current is ceaselessly circulating. We know that such currents
could not flow perpetually if there were any resistance to them,
and we know that there is resistance when electricity flows from
one molecule to another. As we know nothing about the interior
of molecules themselves, we cannot assert that Ampere's sup-
position is impossible. Since a whirlpool of electricity acts like
a magnet, there seems indeed reason to think that magnets may
be merely made up of rotating portions of electrified matter.
300
ELEMENTARY LESSONS ON [CHAP. v.
LESSON XXVI 1 1 . Diamagnetism.
339. Diamagnetic Experiments. In 1778
Brugmans of Leyden observed that when a lump of
bismuth was held near either pole of a magnet needle it
repelled it. In 1827 Le Baillif and Becquerel observed
that the metal antimony also could repel and be repelled
by the pole of a magnet. In 1 845 Faraday, using power-
ful electromagnets, examined the magnetic properties
of a large number of substances, and found that whilst a
great many are, like iron, attracted to- a magnet, others
are feebly repelled. To distinguish between these two
classes of bodies, he termed those which are attracted
paramagnetic, 1 and those which are repelled diamag-
netic. The property of being thus repelled from a magnet
he termed diamagnetism.
Faraday's method of experiment consisted in suspend-
ing a small bar of the substance in a powerful magnetic
field between the two poles of
an electromagnet, and observing
whether the small bar was at-
tracted into an axial position, as
in Fig. 126, with its length along
the line joining the two poles, or
whether it was repelled into an
equatorial position, at right
angles to the line joining the poles,
across the lines of force of the
field, as is shown by the position
of the small bar in Fig 127, sus-
pended between the poles of an electromagnet con-
structed on RuhmkorfFs pattern.
1 Or simply " magnetic." Some authorities use the term " ferro-
magnetic." Sidero-magnetic would be less objectionable than this hybrid
word.
Fig. 126.
CHAP. V.] ELECTRICITY AND MAGNETISM. 301
Fig. 127.
The following are the principal substances examiner!
by the method :
Paramagnetic.
Iron.
Nickel.
Cobalt.
Manganese.
Chromium.
Cerium.
Titanium,
Platinum. 1
Many ores and salts
containing the
above metals.
Oxygen gas.
Diamagnetic.
Bismuth.
Phosphorus
Antimony.
Zinc.
Mercury*
Lead.
Silver.
Copper.
Gold.
Water.
Alcohol.
Tellurium.
Selenium.
Sulphur.
Thallium.
Hydrogen gas.
Air.
1 Chemically pure Platinum is diamagnetic, according to Wiedemann.
302 ELEMENTARY LESSONS ON [CHAP. v.
Liquids were placed in glass vessels and suspended between
the poles of the electromagnet. Almost all liquids are dia-
magnetic, except solutions of salts of the magnetic metals, some
* of which are feebly magnetic ; but blood is diamagnetic though
it contains iron. To examine gases bubbles are blown with
them, and watched as to whether they were drawn into or pushed
out of the field. Oxygen gas was found to be magnetic : ozone
has recently been found to be still more strongly so.
340. Quantitative Results. The magnetic or diamagnetic
power of a substance may be expressed in terms of a certain
coefficient of magnetisation k (Art. 313), which is the ratio of
the intensity of magnetisation to the magnetising-force of the
field in which the substance is placed. Sir W. Thomson calls
this coefficient the magnetic susceptibility of the substance. If
the intensity of magnetisation be represented by the symbol /',
and the strength of the magnetising field by H, then
i = k H.
For paramagnetic substances k has + values ; for diamagnetic
substances k has - values. According to Thalen the value of
k for iron is + 45 ; but Barlow's highest value for iron was only
32*8. Ewing has lately observed soft iron in thin wires, mag-
netised within a solenoid, to exhibit a value of k equal to 1300
or 1400. For bismuth the value of k is '0000025 according
to Maxwell. The repulsion of bismuth is immensely feebler
than the attraction of iron. Pliicker compared the magnetic
powers of equal weights of substances, and reckoning that of
iron as one million, he found the following values for the
" specific magnetism " of bodies :
Iron + 1,000,000
Lodestone Ore + 402,270
Ferric Sulphate + i,no
Ferrose Sulphate + 780
Water 7-8
Bismuth 23 '6
341. Apparent Diamagnetism due to sur-
rounding Medium. It is found that feebly magnetic
bodies behave as if they were diamagnetic when
CHAP, v.] ELECTRICITY AND MAGNETISM. 303
suspended in a more highly magnetic fluid. A small
glass tube filled with a weak solution of ferric chloride,
when suspended in air between the poles of an electro-
magnet points axially, or is paramagnetic ; but if it be
surrounded by a stronger (and therefore more magnetic)
solution of the same substance, it points equatorially, and
is apparently repelled like diamagnetic bodies. All that
the equatorial pointing of a body proves then is, that it is
less magnetic than the medium that fills the surrounding
space. A balloon, though it possesses mass and weight,
rises through the air in obedience to the law of gravity,
because the medium surrounding it is more attracted
than it is. But it is found that diamagnetic repulsion
takes place even in a vacuum : hence it would appear
that space itself 1 is more magnetic than the substances
classed as diamagnetic.
342. Diamagnetic Polarity. At one time Faraday
thought that diamagnetic repulsion could be explained
on the supposition that there existed a " diamagnetic
polarity " the reverse of the ordinary magnetic polarity.
According to this view, which, however, Faraday him-
self quite abandoned, a magnet, when its N. pole is pre-
sented to the end of a bar of bismuth, induces in that
end a N. pole (the reverse of what it would induce in a
bar of iron or other magnetic metal), and therefore repels
it. Weber adopted this view, and Tyndall warmly
advocated it, especially after discovering that the repell-
ing diamagnetic force varies as the square of the
magnetic power employed, a law which is the counter-
part of the law (Art. 330) of attraction due to induction.
Many experiments have been made to establish this
view ; and some have even imagined that when a
diamagnetic bar lies equatorially across a field of force,
its east and west poles possess different properties. The
experiments named in the preceding paragraph suggest,
however, an explanation less difficult to reconcile with
1 Or, possibly, the " aether " filling all space.
304 ELEMENTARY LESSONS ON CCHAP. v.
the facts. There can be no doubt that the phenomenon
is due to magnetic induction : and it has been pointed
out (Art. 89) that the amount of induction which goes
on in a medium depends upon the magnetic inductive
capacity (or " permeability ") of that medium. This
magnetic permeability may be specified in terms of a
" coefficient of magnetic induction," 1 which represents
, the ratio between the actual induction and the magnetis-
ing-force producing it. This coefficient will always be
positive ; it has values greater than I for magnetic
media, less than I for diamagnetic media : for empty
space it is I. The student may think of it in the
following way : Suppose a certain magnetising-force to
act in a certain direction, there would naturally result
from its action induction along a certain number of
lines of induction (or so-called "lines of force"), and
in a vacuum the number of " lines of induction " would
numerically represent the force. But if the space con-
sidered were occupied by iron, the same magnetising-
force would induce many more " lines of induction "
through it, since iron has a large coefficient of magnetic
induction. If, however, the space considered were
occupied by bismuth, the same magnetising-force would
induce in the bismuth fewer " lines of induction " than
in vacuum. But those lines which were induced would
still run in the same general direction as in the vacuum ;
not in the opposite direction, as Weber and Tyndall
, maintain. The result of there being a less induction
through diamagnetic substances can be shown to be
that such substances will be urged from places where
the magnetic force is strong, to places where it is
weaker. This is why a ball of bismuth moves away
from a magnet, and why a little bar of bismuth between
1 The student must not confound this " coefficient of magnetic induction,"
for which we may use the symbol #, with the " coefficient of magnetisation ''
k, in Arts. 313 and 340. The two coefficients are, however, related in a
manner expressed by the equation u = i -f ^k.
CHAP, v.] ELECTRICITY AND MAGNETISM. 305
the conical poles of the electro-magnet (Fig. 127) turns
equatorially so as to put its ends into the regions that
are magnetically weaker. There is no reason to doubt
that in a magnetic field of uniform strength a bar of
bismuth would point along the lines of induction.
343. Magne - Crystallic Action. In 1822
Poisson predicted that a body possessing crystalline
structure would, if magnetic at all, have different
magnetic powers in different directions. In 1847,
Pliicker discovered that a piece of tourmaline, which
is itself feebly paramagnetic, behaved as a diamagnetic
body, when so hung that the axis of the crystal was
horizontal. Faraday repeating the experiment with a
crystal of bismuth, found that it tended to point with
its axis of crystallisation along the lines of the field
axially. The magnetic force acting thus upon crystals
by virtue of their possessing a certain structure, he
named magne - cry stallic force. Pliicker endeavoured to
connect the magne -crystallic behaviour of crystals with
their optical behaviour, giving the following law : there
will be either repulsion or attraction of the optic axis
(or, in the case of bi-axial crystals, of both optic axes)
by the poles of a magnet ; and if the crystal is a
" negative " one (i.e., optically negative, having an extra-
ordinary index of refraction less than its ordinary index),
there will be repulsion, if a " positive " one, there will
be attraction. Tyndall has endeavoured to show that
this law is insufficient in not taking into account the
paramagnetic or diamagnetic powers of the substance as
a whole. He finds that the magne-crystallic axis of
bodies is in general an axis of greatest density p , and that
if the mass itself be paramagnetic this axis will point
axially ; if 'diamagnetic ; equatorially. In bodies which,
like slate and many crystals, possess cleavage, the planes
of cleavage are usually at right angles to the magne-
crystallic axis.
344. Diamagnetism of Flames. In 1847 Ban-
X
306 ELEMENTARY LESSONS ON [CHAP. v.
calari discovered that Flames are repelled from the axial
line joining the poles of an electromagnet. Faraday
showed that all kinds of flames, as well as ascending
streams of hot air and of smoke, are acted on by the
magnet and tend to move from places where the mag-
netic forces are strong to those where they are weaker.
Gases (except oxygen and ozone), and hot gases especi-
ally, are feebly diamagnetic. But the active repulsion
and turning aside of flames may possibly be in part
due to an electromagnetic action like that which the
magnet exercises on the convection-current of the voltaic
arc and on other convection-currents. The electric pro-
perties of flame are mentioned in Arts. 7 and 291.
CHAP, vi.] ELECTRICITY AND MAGNETISM. 307
CHAPTER VI.
MEASUREMENT OF CURRENTS, ETC.
LESSON XXIX. Ohm's Law and its Consequences.
345. In Art. 180 the important law of Ohm was
stated in the following terms: The strength of the
current varies directly as the electromotive -force, and in-
versely as the (total) resistance of the circtiit.
Using the units adopted by practical electricians, and
explained in Art. 323, we may now restate Ohm's law in
the following definite manner : The number of amperes
of current flowing through a circuit is equal to the number
of volts of electrom-otive-force divided by the number of
ohms of resistance in the entire circuit. Or,
Current = Electromotive-force
Resistance
In practice, however, the matter is not quite so simple,
for if a number of cells are used and the circuit be made
up of a number of different parts through all of which
the current must flow, we have to take into account not
only the electromotive-forces of the cells, but their resist-
tances, and the resistance of all the parts of the circuit.
For example, the current may flow from the zinc plate of
the first cell through the liquid to -the copper (or carbon)
3o8 ELEMENTARY LESSONS ON [CHAP. vi.
plate, then through a connecting wire or screw to the next
cell, through its liquid, through the connecting screws and
liquids of the rest of the cells, then through a wire to a
galvanometer, then through the coils of the galvanometer,
then perhaps through an electrolytic cell, and finally
through a return wire to the zinc pole of the battery. In
this case there are a number of separate electromotive-forces
all tending to produce a flow, and a number of different
resistances, each impeding the flow and adding to the
total resistance. If in such a case we knew the separate
values of all the different electromotive-forces and all the
different resistances we could calculate what the current
would be, for it would have the value,
Total electromotive-force
~~ Total resistance
If any one of the cells were set wrong way round its
electromotive-force would oppose that of the other cells ;
an opposing electromotive-force must therefore be sub-
tracted, or reckoned as negative in the algebraic sum.
The "polarisation" (Arts. 163 and 413) which occurs
in battery cells and in electrolytic cells after working for
some time is an opposing electromotive - force, and
diminishes the total of the electromotive -forces in the
circuit. So, also, the induced back-current which is set
up when a current from a battery drives a magneto-
electric engine (Art. 377) reduces the strength of the
working current.
346. Conductivity and Resistance. The term
conductivity is sometimes used as the inverse of
resistance ; and the reciprocal represents the con-
iductivity of a conductor whose resistance is r ohms. In
practice, however, it is more usual to speak of the
resistances of conductors than of their conductivities.
CHAP, vi.] ELECTRICITY AND MAGNETISM. 309
347. Laws of Resistance. Resistances in a cir-
cuit may be of two kinds -first, the resistances of the
conductors themselves ; second, the resistances due to
imperfect contact at points. The latter kind of resistance
is affected by pressure, for when the surfaces of two
conductors are brought into more intimate contact with
one another, the current passes more freely from one
conductor to the other. The contact-resistance of two
copper conductors may vary from infinity down to a
small fraction of an ohm, according to the pressure.
The variation of resistance at a point of imperfect con-
tact is utilised in Telephone Transmitters (Arts. 434,
436). The following are the laws of the resistance of
conductors :
i. The resistance of a conducting wire is proportional
to its length. If the resistance of a mile of
telegraph wire be 13 ohms, that of fifty miles
will be 50 x 13 = 650 ohms.
ii. The resistance of a conducting wire is inversely
proportional to the area of its cross section, and
therefore in the usual round wires is inversely
proportional to the square of its diameter. Ordi-
nary telegraph wire is about |th of an inch thick ;
a wire twice as thick would conduct four times as
well, having four times the area of cross section :
hence an equal length of it would have only ^th
the resistance.
iii. The resistance of a conducting wire of gdven length
and thickness depends upon the material of which
it is made, that is to say, upon the specific }
resistance of the material.
348. Specific Resistance. The specific resistance
of a substance is best stated as the resistance in
"absolute" C.G.S. units (i.e. in thousand millionths of
an ohm) of a centimetre cube of the substance. The
following Table also gives the relative conductivity when
that of silver is taken as 100.
3 io
ELEMENTARY LESSONS ON [CHAP. vi.
TABLE OF SPECIFIC RESISTANCE.
Substance.
Specific Resistance.
Relative Conductivity.
Metals.
Silver
1,609
100
Copper
1,642
9 6
Gold
2,154
74
Iron (soft)
9,827
16
Lead
19,847
8
German Silver
21,170
7 '5
Mercury (liquid)
96,146
1-6
Selenium (annealed)
6 x io 13
i
40,000.000.000
Liquids.
Pure Water )
at 22c $
Dilute H 2 SO 4 )
(T\ acid) \
7-18 x io 10
332 x io 10
less than one
millionth part.
Dilute H 2 SO 4 )
(\ acid) \
126 x io 10
!
Insulators.
j
Glass (at 2OOc)
2-27 x io 16
less than one
Guttapercha
(at 20c)
3 -5 x io 23
billionth.
It is found that those substances that possess a high
conducting power for electricity are also the best con-
ductors of heat. Liquids are worse conductors than the
metals, and gases are perfect non-conductors, except
when so rarefied as to admit of discharge by convection
through them (Art. 283).
349. Effects of Heat on Resistance. Changes
of temperature affect temporarily the conducting power
of metals. Forbes found the resistance of iron to
increase considerably as the temperature is raised. The
resistances of copper and lead also increase, while that
CHAP, vi.] ELECTRICITY AND MAGNETISM. 311
of carbon appears on the other hand to diminish on
heating. German-silver and other alloys do not show j
so much change, hence they are used in making standard
resistance-coils. Those liquids which only conduct by
being electrolysed (Art. 205), conduct better as the
temperature rises. The effect of light in varying the
resistance of selenium is stated in Art. 389.
35O. Typical Circuit. Let us consider the typical
case of the circuit shown
in Fig. 128, in which a
battery, ZC, is joined up
in circuit with a galvano- StL
meter by means of wires
whose resistance is R.
The total electromotive-
force of the battery we
will call E, and the total Fi s- I28 -
internal resistance of the liquids in the cells r. The
resistance of the galvanometer coils may be called G.
Then, by Ohm's law :
The internal resistance r of the liquids ol the battery
bears a very important relation to the external resistance
of the circuit (including R and G), for on this relation !
depends the best way of arranging the battery cells
for any particular purpose. Suppose, for example,
that we have a battery of 50 small Daniell's cells at
our disposal, of which we may reckon the electro-
motive-force as one volt (or more accurately, 1-079 volt)
each, and each having an internal resistance of two
ohms. If we have to use these cells on a circuit where
there is already of necessity a high resistance, we should /
couple them up "in simple serie's " rather than in /
parallel branches of a compound circuit. For, suppos-
ing we have to send our current through a line of
telegraph 100 miles long, the external resistance R will
312 ELEMENTARY LESSONS ON [CHAP. VL
be (reckoning 13 ohms to the mile of wire) at least
1300 ohms. Through this resistance a single such cell
would give a current of less than one milli-ampere, for
here E = i, R == 1300, r 2, and therefore
C = jJL. = ^^ = ^ of an ampere, a current far
too weak to work a telegraph instrument.
With fifty such cells in series we should have E = 50,
r = 100, and then
C = .300+ .00 = ^ = Ts of an atn P fere > or over 35 mil"-
amperes. In telegraph work, where the instruments
require a current of 5 to 10 milli-amperes to work them,
it is usual to reckon an additional Daniell's cell for every
5 miles of line, each instrument in the circuit being
counted as having as great a resistance as 10 miles of
wire.
If, however, the resistance of the external circuit be
small, such arrangements must be made as will keep the
total internal resistance of the battery small. Suppose,
for example, we wish merely to heat a small piece of
platinum wire to redness, and have stout copper wires
to connect it with the battery. Here the external resist-
ance may possibly not be as much as one ohm. In that
case a single cell would give a current of J of an ampere
(or 333 milli-amperes) through the wire, for here E = i,
R s= i, and r 2. But ten cells would only give half
as much again, or 476 milli-amperes, and fifty cells only
495 milli-amperes, and with an infinite number of such
cells in series the current could not possibly be more
than 500 milli-amperes, because every cell, though it adds
i to E, adds 2 to R. It is clear then that though link-
ing many cells in series is of advantage where there is
the resistance of a long line of wire to be overcome, yet
where the external resistance is small the practical advan-
tage of adding cells in series soon reaches a limit.
But suppose in this second case, where the external
resistance of the circuit is small, we reduce also the
CHAP, vi.] ELECTRICITY AND MAGNETISM. 313
internal resistance of our battery by linking cells to-
gether in parallel branches of a compound circuit, join-
ing several zincs of several cells together, and joining
also their copper poles together (as suggested in Art.
181), a different and better result is attained. Suppose
we thus join up four cells. Their electromotive-force
will be no more, it is true, than that of one cell, but
their resistance will be but J of one such cell, or J an
ohm. These four cells would give a current of 666
milli-amperes through an external resistance of i ohm,
for if E = i, R = i, and the internal resistance be J
of r, or = J, then
C = R = of an ampere, or 666 milli-amperes.
351. Best Grouping of Cells. It is at once
evident that if we arrange the cells of a battery in n
files of m cells in series in each file (there being m x n
similar cells altogether), the electromotive-force of each
file will be m times the electromotive -force E of each
cell, or ;^E ; and the resistance of each file will be m
times the resistance r of each cell, or mr. But there
being n files in parallel branches the whole internal
resistance will be only of the resistance of any one file,
or will be ^r^ hence, by Ohm's law, such a battery would
give as its current
It can be shown mathematically that, for a given battery of cells, the most
effective way of grouping them when they are required to work through a
given external resistance R, is so to choose m and , that the internal (
resistance (^r) shall equal the external resistance. The student should '
verify this rule by taking examples and working them out for different
groupings of the cells. Although this arrangement gives the strongest current
it is not the most economical ; for if the internal and external resistances be
equal to one another, the useful work in the outer circuit and the useless
work done in heating the cells will be equal also, half the energy being
wasted. The greatest economy is attained when the external resistance is
very great as compared with the internal resistance ; only, in this case, the
materials of the battery will be consumed slowly, and the current will not be
drawn off at its greatest possible strength.
314 ELEMENTARY LESSONS ON [CHAP. vi.
352. Long and Short Coil Instruments. The student will
also now have no difficulty in perceiving why a "long-coil"
galvanometer, or a "long-coil" electromagnet, or instrument of
any kind in which the conductor is a long thin wire of high
resistance, must not be employed on circuits where both R and
I rare already small. He will also understand why, on circuits
of great length, or where there is of necessity a high resistance
and a battery of great electromotive force is employed, "short-
coil " instruments are of little service, for though they add little
to the resistances their few turns of wire are not enough with
the small currents that circulate in high-resistance circuits ; and
why " long-coil " instruments are here appropriate as multiplying
the effects of the currents by their many turns, their resistance,
though perhaps large, not being a serious addition to the existing
resistances of the circuit. A galvanometer with a " long-coil "
of high resistance, if placed as a shunt across two points of a
circuit, will draw therefrom a current proportional to the differ-
' ence of potential between those points. Hence such an instru-
ment may be used as a voltmeter (Art. 360 d.)
353. Divided Circuits. If a circuit divides, as in
Fig. 129, into two branches at A, uniting together again
at B, the current will also
be divided, part flowing
through one branch part
through the other. The
relative strengths of cur-
rent in the two branches
will be proportional to
their conductivities, i.e.,
inversely proportional to
their resistances. Thus, if r be a wire of 2 ohms re-
sistance and r' 3 ohms, then current in r: current in
r' = r':r
= 3'2,
or, |- of the whole current will flow through r^ and J- of
the whole current through r'.
The joint resistance of the divided circuit between A
and B will be less than the resistance of either branch
singly, because the current has now choice of either path.
In fact, the joint conductivity will be the sum of the two
CHAP, vi.] ELECTRICITY AND MAGNETISM. 315
separate conductivities. And if we call the joint resist-
ance R, it follows that
JE = I 4- =
R r r' rr' >
whence R = r ^ ^ or, in words, the joint
resistance of a divided conductor is equal to the product
of the two separate resistances divided by their sum.
Kirchhoff has given the following important laws, both of
them deducible from Ohm's law.
(i. ) In any branching network of wires the algebraic sum of
the currents in all the wires that meet in any point is
zero.
(ii.) When there are several electromotive -forces acting at
different points of a circuit, the total electromotive -force
round the circuit is equal to the sum of the resistances
of its separate parts multiplied each into the strength of
the current that flows through it.
354. Current Sheets. When a current enters a
solid conductor it no longer flows in one line but spreads
out and flows through the mass of the conductor. When
a current is led into a thin plate of conducting matter it
spreads out into a " current sheet " and flows through
the plate in directions that depend upon the form of the
plate and the position of the pole by which it returns to
the battery. Thus, if wires from the two poles of a
battery are brought into contact with two neighbouring
points A and B in the middle of a very large flat sheet
of tinfoil, the current flows through the foil not in one
straight line from A to B, but in curving " lines of flow,"
which start out in all directions from A, and curl round to
meet in B, in curves very like those of the " lines of force "
that run from the N.-pole to the S.-pole of a magnet
(Fig. 50). When the earth is used as a return wire to
conduct the telegraph currents (Fig. 160), a similar
spreading of the currents into current sheets occurs.
316 ELEMENTARY LESSONS ON [CHAP. vi.
LESSON XXX. Electrical Measiirements.
355. The practical electrician has to measure electri-
cal resistances, electromotive -forces, and the capacities
of condensers. Each of these several quantities is
measured by comparison with ascertained standards, the
particular methods of comparison varying, however, to
meet the circumstances of the case. Only a few simple
cases can be here explained.
356. Measurement of Resistance. Resistance
is that which stops the flow of electricity. Ohm's law
shows us that the strength of a current due to an electro-
motive force falls off in proportion as the resistance in
the circuit increases.
(a) It is therefore possible to compare two resistances
with one another by finding out in what proportion each
of them will cause the current of a constant battery to
fall off. Thus, suppose in Fig. 128 we have a standard
battery of a few Daniell's cells, joined up in circuit with
a wire of an unknown resistance R, and with a galvan-
ometer, we shall obtain a current of a certain strength,
as indicated by the galvanometer needle experiencing a
certain deflection. If we remove the wire R, and sub-
stitute in its place in the circuit wires whose resistances
we know, we may, by trying, find one which, when inter-
posed in the path of the current, gives the same deflection
on the galvanometer. Hence we shall know that this
wire and the one we called R offer equal resistance to
the current. Such a process of comparison, which we
< may call a method of substitiition of equivalent resistances,
was further developed by Wheatstone, Jacobi, and others,
when they proposed to employ as a standard resistance
a long thin wire coiled upon a wooden cylinder, so that
any desired length of the standard wire might be thrown
into the circuit by unwinding the proper number of turns
of wire off the cylinder, or by making contact at some
point at any desired distance from the end of the wire.
CHAP, vi.] ELECTRICITY AND MAGNETISM. 317
Such an instrument was known as a Rheostat, but it is
now superseded by the resistance 'coils explained below.
(b) The method explained above can be used with
any galvanometer of sufficient sensitiveness, but if a
tangent galvanometer is available the process may be
shortened by calculation. Suppose the tangent galvano-
meter and an unknown resistance R to be included in
the circuit, as in Fig. 128, and that the current is strong
enough to produce a deflection of d degrees : Now sub-
stitute for R any known resistance R', which will alter the
deflection to d' ; then (provided the other resistances of
the circuit be negligibly small) it is clear that since the
strengths of the currents are proportional to tan d and
tan d' respectively, the resistance R can be calculated by
the inverse proportion.
tan d : tan 3' = R' : R.
(c) With a differential galvanometer (Art. 203), and a
set of standard resistance coils, it is easy to measure the
resistance of a conductor. Let the circuit divide into two
branches, so that part of the current flows through the
unknown resistance and round one set of coils of the
galvanometer, the other part of the current being made
to flow through the known resistances and then round
the other set of coils in the opposing direction. When
we have succeeded in matching the unknown resistance
by one equal to it from amongst the known resistances,
the currents in the two branches will be equal, and the
needle of the differential galvanometer will show no
deflection. With an accurate instrument this null method
is very reliable.
(d) The best of all the ways of measuring resistances
is, however, with a set of standard resistance coils and
the important instrument known as Wlieatstone's Bridge,
described below in Art. 358.
(e) To measure very high resistances the plan may be
adopted of charging a condenser from a standard battery
for a definite period through the resistance, and then
3i8 ELEMENTARY LESSONS ON FCHAP. vi.
ascertaining the accumulated charge by discharging it
through a ballistic galvanometer (Art. 204).
357. Fall of Potential along a Wire. To under-
stand the principle of Wheatstone's Bridge we must
explain a preliminary point. If the electric potential of
different points of a circuit be examined by means of an
electrometer, as explained in Art. 263, it is found to de-
crease all the way round the circuit from the + pole of
the battery, where it is highest, down to pole, where
it is lowest. If the circuit consist of one wire of uniform
thickness, which offers, consequently, a uniform resistance
to the current, it is found that the potential falls uniformly ;
if, however, part of the circuit resists more than another,
it is found that the potential falls most rapidly along the
conductor of greatest resistance. But in every case the
fall of potential between any two points is proportional to
the resistance between those two points ; and we know, for
example, that when we have gone round the circuit to
a point where the potential has fallen through half its
value, the current has at that point gone through half
the resistances.
358. Wheatstone's Bridge. This instrument,
invented by Christie, and applied by Wheatstone to
measure resistances, consists of a system of conductors
shown in diagram in Fig. 130. The circuit of a constant
battery is made to branch at P into two parts, which
re-unite at Q, so that part of the current flows through
the point M, the other part through the point N. The
four conductors D, C, B, A, are spoken of as the " arms "
of the "balance" or "bridge;" it is by the proportion
subsisting between their resistances that the resistance
of one of them can be calculated when the resistances of
the other three are known. When the current which
starts from C at the battery arrives at P, the potential
will have fallen to a certain value. The potential of the
current in the upper branch falls again to M, and
continues to fall to Q. The potential of the lower
CHAP, vi.] ELECTRICITY AND MAGNETISM.
319
branch falls to N, and again falls till it reaches the value
at Q. Now if N be the same proportionate distance
Fig. 130.
along the resistances between P and Q, as M is along
the resistances of the upper line between P and Q, the
potential will have fallen at N to the same value as it
has fallen to at M ; or, in other words, if the ratio of the
resistance C to the resistance D be equal to the ratio
between the resistance A and the resistance B, then M
and N will be at equal potentials. To find out whether
they are at equal potentials a sensitive galvanometer is
placed in a branch wire between M and N ; it will show
no deflexion when M and N are at equal potentials ; or
when the four resistances of the arms " balance " one
another by being in proportion, thus :
A : C : : B : D.
If, then, we know what A, B, and C are, we can calculate
D, which will be
D = SL
BxC
A~
EXAMPLE. Thus if A and C are (as in Fig. 133) loohms
and 100 ohms respectively, and B be 15 okms t D will
be 15 x 100 -T- 10 = 150 ohms.
320
ELEMENTARY LESSONS ON [CHAP. vr.
359. Resistance Coils. Wires of standard resist-
ance are now sold by instrument makers under the name
of Resistance Coils. They consist of coils of german-
[ silver (see Art. 349) (or sometimes silver-iridium alloy),
wdund with great care, and adjusted to such a length as
to have resistances of a definite number of ohms. In order
to avoid self-induction,
and the consequent sparks
(see Art. 404) at the
opening or closing of the
circuit, they are wound
in the peculiar manner
indicated in Fig. 131,
each wire (covered with
Fig. I3I silk or paraffined- cotton)
being doubled on itself
before being coiled up. Each end of a coil is soldered
to a solid brass piece, as coil I to A and B, coil 2 to
B and C ; the brass pieces being themselves fixed to a
block of ebonite (forming the top of the " resistance
box "), with sufficient room between them to admit of
the insertion of stout well-fitting plugs of brass. Fig.
132 shows a complete resistance -box, as fitted up for
Fig. 132.
electrical testing, with the plugs in their places. So
long as the plugs remain in, the current flows through
CHAP, vi.] ELECTRICITY AND MAGNETISM.
321
the solid brass pieces and plugs without encountering
any serious resistance ; but when any plug is removed,
the current can only pass from the one brass piece to
the other by traversing the coil thus thrown into circuit.
The series of coils chosen is usually of the following
numbers of ohms* resistance i, 2, 2, 5 ; 10, 20, 20,
50; 100, 200, 200, 500 ; up to 10,000 ohms.
By pulling out one plug any one of these can be thrown
into the circuit, and any desired whole number, up to
20,000, can be made up by pulling out more plugs ; thus
a resistance of 263 ohms will be made up as 200 -f 50
+ 10 + 2 + I.
It is usual to construct Wheatstone's bridges with some
resistance coils in the arms A and C, as well as with a
complete set in the arm B. The advantage of this
Fig- 133
arrangement is that by adjusting A and C we determine
the proportionality between B and D, and can, in certain
cases, measure to fractions of an ohm. Fig. 133 shows
a more complete scheme, in which resistances of 10, 100,
and 1000 ohms are included in the arms A and C.
Y
322 ELEMENTARY LESSONS ON [CHAP. vi.
EXAMPLE. Suppose we had a wire, whose resistance we
knew to be between 46 and 47 ohms, and wished to
measure the fraction of an ohm, we should insert it at D,
and make A 100 ohms and C 10 ohms ; in that case D
would be balanced by a resistance in B I o times as great
as the wire D. If, on trial, this be found to be 464 ohms
we know that D = 464 x 10 -j- 100 = 46*4 ohms.
In practice the bridge is seldom or never made in the
lozenge -shape of the diagrams. The resistance -box of
Fig. 132 is, in itself, a complete "bridge," the appropriate
connections being made by screws at various points. In
using the bridge the battery circuit should always be
completed by depressing the key Kj before the key
K 2 of the galvanometer circuit is depressed, in order
to avoid the sudden violent " throw " of the galvanometer
needle, which occurs on closing circuit in consequence of
self-induction (Art. 404).
36O. Measurement of Electromotive-Force.
There being no easy absolute method of measuring
electromotive-forces, they are usually measured relatively -,
by comparison with the electromotive-force of a standard
cell, such as that of Daniell (Art. 170), or better still
that of Latimer Clark (Art. 177). The methods of
comparison are various ; only three can here be men-
tioned.
(a) Call E the electromotive-force of the battery to be
measured, and E' that of a standard battery. Join E
with a galvanometer, and let it produce a deflection of
d 1 degrees through the resistances of the circuit ; then
add enough resistance r to bring down the deflection to
d. 2 degrees say 10 degrees less than before. Now
substitute the standard battery in the circuit and adjust
the resistances till the deflection is 5 X as before, and then
add enough resistance /, to bring down the deflection
to 5 2 . Then
r 1 : r = E' : E,
since the resistances that will reduce the strength of the
current equally will be proportional to the electromotive-
forces.
CHAP, vi.] ELECTRICITY AND MAGNETISM. 323
(b) If the poles of a standard battery are joined by a long
thin wire, the potential will fall uniformly from the + to
the pole. Hence, by making contacts at one pole
and at a point any desired distance along the wire, any
desired proportional part of the whole electromotive-force
can be taken. This proportional part may be balanced
against the electromotive-force of any other battery, or
used to compare the difference between the electromotive-
forces of two different cells.
(c) The electromotive-force of a battery may be measured
directly as a difference of potentials by a quadrant electro-
meter. In this case the circuit is never closed, and no
current flows.
(d) If a galvanometer be constructed so that the resistance
of its coils is several thousand ohms, in comparison with
which the internal resistance of a battery or dynamo
machine is insignificant, such a galvanometer will serve
to measure electromotive-forces ; for, by Ohm's law, the
strength of current which such a battery or dynamo can
send through it will depend only on the electromotive-
force between the ends of the coil. Such a galvanometer,
suitably graduated, is sometimes called a " Volt-meter"
or " Potential galvanometer." It can be used to determine
the difference of potential between any two points of a
circuit by connecting its terminals as a shunt to the
circuit between these two points.
361. Measurement of Internal Resistance of
Battery. This may be done in three ways.
(a) Note by a tangent galvanometer the strength of the
current, first, when the resistance of the external circuit
is small ; and secondly, when a larger known external
resistance is introduced. From this the proportion
between the internal resistance and the introduced ex-
ternal resistance can be calculated.
(3) (Method of Opposition}. Take two similar cells and
join them in opposition to one another, so that they send
no current of their own. Then measure their united
resistance just as the resistance of a wire is measured.
The resistance of one cell will be half that of the two.
(c) (MancSs Method). Place the cell itself in one arm of
the Wheatstone's bridge, and put a key where the battery
usually is, adjust the resistances till the permanent galvano-
324 ELEMENTARY LESSONS ON [CHAP. vi.
meter deflection is the same whether the key be depressed
or not. When this condition of things is attained the
battery resistance is balanced by those of the other three
arms. (Not a reliable method. )
362. Measurement of Capacity of a Con-
denser. The capacity of a condenser may be measured
by comparing it with the capacity of a standard con-
denser such as the \ microfarad condenser shown in
Fig. 1 06, in one of the following ways :
(a) Charge the condenser of unknown capacity to a
certain potential ; then make it share its charge \v ith the
condenser of known capacity, and measure the potential
to which the charge sinks ; then calculate the original
capacity, which will bear the same ratio to the joint
capacity of the two as the final potential bears to the
original potential.
(b) Charge each condenser to equal differences of
potential, and then discharge each successively through
a ballistic galvanometer (Art. 204), when the sine of half
the angle of the first swing of the needle will be propor-
tional in each case to the charge, and therefore to the
capacity.
(c) Charge the two condensers simultaneously from
one pole of the same battery, interposing high resistances
in each branch, and adjusted so that the potential rises
at an equal rate in both ; then the capacities are inversely
proportional to the resistances through which they are
respectively being charged.
(d) Another method, requiring no standard condenser,
is as follows : Allow the condenser, whose capacity is to
be measured, to discharge itself slowly through a wire of
very high resistance. The time taken by the potential
to fall to any given fraction of its original value is pro-
portional to the resistance, to the capacity, and to the
logarithm of the given iraction.
363. Resistance Expressed as a Velocity. It will be
seen, on reference to the table of "Dimensions" of electro-
magnetic units (Art. 324), that the dimensions of resistance are
CHAP, vi.] ELECTRICITY AND MAGNETISM. 325
given as LT~ l , which are the same dimensions (see Art. 258) as
those of a velocity. Every resistance is capable of being
expressed as a velocity. The following considerations may
assist the student in forming a physical conception of this :
Suppose we have a circuit composed of two horizontal rails
Fig. 134-
(Fig. 134), CS and DT, I centim. apart, joined at CD, and
completed by means of a sliding piece AB. Let this variable
circuit be placed in a uniform magnetic field of unit .intensity,
the lines of force being directed vertically downwards through
the circuit. If, now, the slider be moved along towards ST
with a velocity of n centimetres per second, the number of
additional lines of force embraced by the circuit will increase at
the rate n per second ; or, in other words, there will be an
induced electromotive - force (Art. 394) impressed upon the
circuit, which will cause a current to flow through the slider
from A to B. Let the rails have no resistance, then the
strength of the current will depend on the resistance of AB.
Now let AB move at such a rate that the current shall be of
unit strength. If its resistance be one "absolute" (electro-
magnetic) unit it need only move at the rate of I centim. per
second. If its resistance be greater it must move with a pro-
portionately greater velocity ; the velocity at which it must
move to keep up a current of unit strength being numerically
equal to its resistance. The resistance known as " one ohm" is
intended to be io 9 absolute electromagnetic ttnits, and therefore is
represented by a velocity of I o 9 centimetres, or ten million metres
(one earth-quadrant) per second.
364. Evaluation of the Ohm. The value of the ohm in absolute measure
was determined by a Committee of the British Association in London in 1863.
It being impracticable to give to a horizontal sliding -piece so high a velocity
as was necessitated, the velocity which corresponded to the resistance of a
wire was measured in the following way : A ring of wire (of many turns),
pivoted about a vertical axis, as in Fig. 135, was made to rotate very rapidly
and uniformly. Such a ring in rotating cuts the lines of force of the earth's
magnetism. The northern half of the ring, in moving from west toward east,
326 ELEMENTARY LESSONS ON [CHAP. vi.
will have (see Rule Art. 395) an upward current induced in it, while the
southern half, in crossing .from east toward west, will have a downward
current induced in it. Hence the
rotating ring will, as it spins, act
as its own galvanometer if a small
magnet be hung at its middle ; the
magnetic effect due to the rotating
j / -x % j coil being proportional directly to
, L.L fcU^.. jjj ^ t | ie horizontal component of the
earth's magnetism, to the velocity
of rotation, and to the number of
turns of wire in the coil, and in-
versely proportional to the resist-
ance of the wire of the coils. Hence,
all the other data being known, the
resistance can be calculated and
Fig. 135- measured as a velocity. ^Our
present practical ohm was constructed by comparison with this rotating coil ;
but there being some doubt as to whether the existing ohms really represent
io9 centims. per second, a re-determination of the ohm was suggested in 1880
by the British Association Committee. At the International Congress of
Electricians in Paris 1881, the necessity of further evaluations was indorsed.
It was also agreed that the practical standards should no longer be con-
structed in German silver wire, but that they should be made upon the plan
originally suggested by Siemens, by defining the -practical ohm as the
resistance of a column of pure mercury of a certain length, and of one
millimetre of cross-section. The original " Siemens' unit" was one metre in
length, and was rather less than an ohm (o'94is ohm). The most recent
careful determinations by Lord Rayleigh and by Mr. Glazebrook show that
the standard coil of German silver prepared by the British Association
(hitherto called " one ohm") is only 0*986 of the true theoretical ohm (== 10^
absolute units). The mercury column representing the true ohm. should
therefore be io6'2i centimetres in length.
NOTE ON THE RATIO OF THE ELECTROSTATIC
TO THE ELECTROMAGNETIC UNITS.
365. If the student will compare the Table of Dimensions of
Electrostatic Units of Art. 258 with that of the Dimensions of
Electromagnetic Units of Art. 324, he will observe that the dimen-
sions assigned to similar units are different in the two systems.
Thus, the dimensions of "Quantity" in electrostatic measure are
M * L * T , and in electromagnetic measure are M^ L L "
Dividing the former by the latter we get LT" 1 , a quantity
CHAP, vi.] ELECTRICITY AND MAGNETISM.
327
which we at once see is of the nature of a velocity. This
velocity occurs in every case in the ratio of the electrostatic to
the electromagnetic measure of every unit. It is a definite
concrete velocity, and represents that velocity at which two
electrified particles must travel along side by side in order that
their mutual electromagnetic attraction (considered as equivalent
in moving to two parallel currents) shall just equal their mutual
electrostatic repulsion, see Art. 337. This velocity, "z/," which
is of enormous importance in the electromagnetic theory of light
(Art. 390), has been measured in several ways.
UNIT.
ELECTROSTATIC.
ELECTROMAGNETIC.
RATIO.
Quantity .
Potential .
Capacity .
M^ L$ T- 1
M^ L* T-?
L
M^ L2
L -1 T 2
LT- 1 = v
L ~ IT = lr
L 2 T~ 2 = ^ 2
Resistance .
L ~ 1T
LT- 1
~~ z;2
(a) Weber and Kohlrausch measured the electrostatic unit of
quantity and compared it with the electromagnetic unit of
quantity, and found the ratio v to be = 3-1074 x io 10 centims.
per second.
(b) Sir W. Thomson compared the two units of potential
and found 1ft
v 2-825 x I0
and later, =2-93 x io 10 .
(c) Professor Clerk Maxwell balanced a force of electrostatic
attraction against one of electromagnetic repulsion, and found
v = 2-88 x io 10 .
(d) Professors Ayrton and Perry measured the capacity of a
condenser electromagnetically by discharging it into a ballistic
galvanometer, and electrostatically by calculations from its size,
and found
v 2-980 x io 10 ,
The velocity of light is believed to be
= 2-9992 x io 10 ;
or, according to G. Forbes's latest determination,
the velocity of red light is 2-9826 x io 10 .
328 ELEMENTARY LESSONS ON [CHAP. vn.
CHAPTER VI l.
HEAT, LIGHT, AND WORK, FROM ELECTRIC CURRENTS.
LESSON XXXI. Heating Effects of Currents.
366. Heat and Resistance. A current may do
work of various kinds, chemical, magnetic, mechanical,
and thermal. In every case where a current does work
that work is done by the expenditure of part of the energy
of the current. We have seen that, by the law of Ohm,
the current produced by a given battery is diminished in
strength by anything that increases the external resistance.
But the strength of the current may be diminished, in
certain cases, by another cause, namely, the setting up
of an opposing electromotive force at some point of the
circuit. Thus, in passing a current through a voltameter
(Art. 214) there is a diminution due to the resistance of
the voltameter itself, and a further diminution due to the
opposing electromotive -force (commonly referred to as
" polarisation ") which is generated while the chemical
work is being done. So, again, when a current is used to
drive an electromagnetic motor (Art. 375), the rotation
of the motor will itself generate a back- current, which
will diminish the strength of the current. Whatever
current is, however, not expended in this way in external
work, is frittered down into heat, either in the battery or
in some part of the circuit, or in both. Suppose a
quantity of electricity to be set flowing round a closed
circuit. If there were no resistance to stop it it would
CHAP, vii.] ELECTRICITY AND MAGNETISM.
329
circulate for ever ; just as a waggon, set rolling along a
circular railway should go round for ever if it were not
stopped by friction. When matter in motion is stopped
by friction the energy of its motion is frittered down by
the friction into heat. When electricity in motion is
stopped by resistance the energy of its flow is frittered
down by the resistance into heat. Heat, in fact, appears
wherever the circuit offers a resistance to the current.
If the terminals of a battery be joined by a short thick
wire of small resistance, most of the heat will be de-
veloped in the battery ; whereas, if a thin wire of con-
siderable resistance be interposed in the outer circuit, it
will grow hot, while the battery itself will remain com-
paratively cool.
367. Laws of Development of Heat: Joule's
Law. To investigate the
development of heat by a
current, Joule and Lenz used
instruments on the prin-
ciple of Fig. 136, in which
a thin wire joined to two
stout conductors is enclosed
within a glass vessel con-
taining alcohol, into which
also a thermometer dips.
The resistance of the wire
being known, its relation to
the other resistances can
be calculated. Joule found
that the number of units of heat developed in a con-
ductor is proportional
(i.) to its resistance ;
(ii.) to the square of the strength of the current ;
and
(iii.) to the time that the current lasts.
The equation expressing these relations is known as
Joule's Law, and is
Fig. 136.
330 ELEMENTARY LESSONS ON [CHAP. vn.
H = C 2 Rt x 0-24
where C is the current in amperes, R the resistance in
ohms, / the time in seconds, and H the heat in the usual
unit of heat-quantities, viz. the amount of heat that will
raise i gramme of water through iC of temperature
(Art. 255).
Joule's law may be arrived at by the following calculation.
The work W done by a current in moving Q units of electricity
through a difference of potential V 2 V l is
W^QtV.-VJ;
and since Q -= Ct, and V 2 - V x = E, and W = JH, (where J is
Joule's equivalent = 4*2 x io 7 , and H the heat in water-gramme-
centigrade degree units), we have
JH = CtE (and E = CR).
= C 2 Rt
, TT
whence H
But as C and R are here in " absolute " units, they must be
multiplied by 10 2 X io 9 = io 7 , to reduce to the ordinary case
of ampb-es and ohms ; whence
H = C 2 Rt -^ 4-2
= C 2 Rt x 0-24.
This is equivalent to the statement that a current of
one ampere flowing through a resistance of one ohm
developes therein 0-24 heat-units per second.
Dr. Siemens proposes to call this quantity of heat (or its
mechanical equivalent in work) by the name of one joule. If
this suggestion be adopted, the electric unit of heat, the joule,
will be only 0*24 of an ordinary heat-unit or calorie (Art. 255),
and I calorie will be equal to 4-2 joules.
The second of the above laws, that the heat is, c&teris paribus, propor-
tional to the square of the strength of the current, often puzzles young
students, who expect the heat to be proportional to the current simply.
Such may remember that the consumption of zinc is, ceeteris paribus> also
proportional to the square of the current ; for, suppose that in working
through a high resistance (so as to get all the heat developed outside the
battery) we double the current by doubling the number of battery cells, there
will be twice as much zinc consumed as before in each cell, and as there are
twice as many cells as at first the consumption of zinc is four times as great
as before.
368. Favre's Experiments. Favre made a series of most ^
important experiments on the relation of the energy of a current
CHAP, vii.] ELECTRICITY AND MAGNETISM. 331
to the heat it developes. He ascertained that the number of
heat-units evolved when 33 grammes (i equivalent) of zinc are
dissolved in dilute sulphuric acid (from which it causes hydrogen
to be given off) to be 18,682. This figure was arrived at by
conducting the operation in a vessel placed in a cavity of his
calorimeter, an instrument resembling a gigantic thermometer
filled with mercury, the expansion of which was proportional to
the heat imparted to it. When a Smee's cell was introduced
into the same instrument, the solution of the same amount of"
zinc was observed to be accompanied by the evolution of 18,674
units of heat (i.e. an amount almost identical with that observed
before), and this amount was the same whether the evolution
took place in the battery-cell when the circuit was closed with a
short thick wire, or whether it took place in a long thin wire
placed in the external circuit. He then arranged 5 Smee's cells
in series, in cavities of the calorimeter, and sent their current
round a small electromagnetic engine. The amount of heat
evolved during the solution of 33 grammes of zinc was then
observed in three cases ; (i. ) when the engine was at rest ; (ii. )
when the engine was running round and doing no work beyond
overcoming the friction of its pivots ; (iii. ) when the engine was
employed in doing 13,124,000 gramme-centimetres (= 12,874
x io 6 ergs) of work, by raising a weight by a cord running over
a pulley. The amounts of heat evolved in the circuit in the
three cases were respectively, 18,667, I 8,657, and 18,374 units.
In the last case the work done accounts for the diminution in
the heat frittered down in the circuit. If we add the heat-
equivalent of the work done to the heat evolved in the latter
case, we ought to get the same value as before. Dividing the
12,874 x io 6 ergs of work by Joule's equivalent, expressed in
"absolute" measure (42 x io 6 ), we get as the heat-equivalent of
the work done 306 heat units. Now 18,374 + 306 = 18,680,
a quantity which is almost identical with that of the first
observation, and quite within the limits of unavoidable experi-
mental error.
369. Rise of Temperature. The elevation of
temperature in a resisting wire depends on the nature of
the resistance. A veiy short length of a very thin wire may
resist just as much as a long length of stout wire. Each
will cause the same number of units of heat to be evolved,
but in the former case, as the heat is spent in warming a
332 ELEMENTARY LESSONS ON [CHAP. vn.
short thin wire of small mass, it will get very hot, whereas
in the latter case it will perhaps only warm to an imper-
ceptible degree the mass of the long thick wire. If the
wire weigh w grammes, and have a specific capacity for
heat s, then H = swQ, where 8 is the rise of tempera-
ture in degrees (Centigrade). Hence
C 2 R/
6 = 0-24 x
SW
Since the resistance of metals increases as they rise in
temperature, a thin wire heated by the current will resist
more, and grow hotter and hotter until its rate of loss of
heat by conduction and radiation into the surrounding
air equals the rate at which heat is supplied by the
current.
The following pretty experiment illustrates the laws of
heating. The current from a few cells is sent through a
chain made of alternate links of silver and platinum
wires. The platinum links glow red-hot while the silver
links remain comparatively cool. The explanation is
that the specific resistance of platinum is about six times
that of silver, and its capacity for heat about half as
great ; hence the rise of temperature in wires of equal
thickness traversed by the same current is roughly twelve
times as great for platinum as for silver.
Thin wires heat much more rapidly than thick, the
rise of temperature in different parts of the same wire
(carrying the same current), being^ for different thick-
nesses, inversely proportional to the fourth power of the
diameters.
Thus, suppose a wire at any point to become reduced to half
its diameter, the cross -section will have an area J as great as in
the thicker part. The resistance here will be 4 times as great,
and the number of heat units developed will be 4 times as great
as in an equal length of the thicker wire. But 4 times the
amount of heat spent on the amount of metal will warm it to
a degree 16 times as great, and 1 6 = 2 4 .
For surgical purposes a thin platinum wire, heated
white-hot by a current, is sometimes used instead of a
CHAP. VIL] ELECTRICITY AND MAGNETISM. 333
knife, as, for example, in the operation of amputating the
tongue for cancer. Platinum is chosen on account of its
infusibility, but even platinum wires are fused by the
current if too strong. Carbon alone, of conductors, resists
fusion.
37O. Blasting by Electricity. In consequence of
these heating effects, electricity can be applied to fire
blasts and mines, stout conducting wires being carried
from an appropriate battery at a distance to a special
fuze, in which a very thin platinum wire is joined in the
circuit. This wire gets hot when the current flows, and
being laid amidst an easily combustible substance to
serve as a priming, ignites this and sets fire to the charge
of gunpowder. Torpedoes can thus be exploded beneath
the water, and at any desired distance from the battery.
The special case of heat developed or abstracted by a
current passing through a junction of dissimilar metals,
known as Peltier's effect, is mentioned in Art. 380.
LESSON XXXII. The Electric Light.
371. The Voltaic Arc. If two pointed pieces of
carbon are joined by wires to the terminals of a power-
ful voltaic battery or other generator of electric currents,
and are brought into contact for a moment and then
drawn apart to a short distance, a kind of electric flame
called the voltaic arc is produced between the points
of carbon, and a brilliant light is emitted by the white
hot points of the carbon electrodes. This phenomenon
was first noticed by Humphry Davy in 1800, and its ex-
planation appears to be the following : Before contact
the difference of potential between the points is insufficient
to permit a spark to leap across even ^-^ of an inch of
air-space, but when the carbons are made to touch, a
current is established. On separating the carbons the
momentary extra -current due to self-induction of the
334 ELEMENTARY LESSONS ON [CHAP. vn.
circuit (Art. 404), which possesses a high electromotive-
force, can leap the short distance, and in doing so
volatilises a small quantity of carbon between the points.
Carbon vapour being a partial conductor allows the
current to continue to flow across the gap, provided it be
not too wide ; but as the carbon vapour has a very high
Fig. 137.
resistance it becomes intensely heated by the passage
of the current, and the carbon points also grow hot.
Since, however, solid matter is a better radiator than
gaseous matter, the carbon points emit far more light
CHAP, vii.] ELECTRICITY AND MAGNETISM. 335
than the arc itself, though they are not so hot. In the
arc the most infusible substances, such as flint and
diamond, melt ; and metals such as gold and platinum
are even vapourised readily in its intense heat. When
the arc is produced in the air the carbons slowly burn
away by oxidisation. It is observed, also, that particles
of carbon are torn away from the + electrode, which be-
comes hollowed out to a cup-shape, and some of these
are deposited on the electrode, which assumes a
pointed form, as shown in Fig. 137. The resistance of
the arc may vary, according to circumstances, from 0-5
ohm to nearly 100 ohms. It is also found that the arc
exerts an opposing electromotive-force of its own, and
tends to set up a counter-current.
To produce an electric light satisfactorily a minimum
electromotive-force of 40-50 volts is necessary ; and as
the current must be at least from 5 to 10 or more
amperes, it is clear that the internal resistance of the
battery or generator must be kept small. With weaker
currents or smaller electromotive-forces it is impracticable
to maintain a steady arc. The internal resistance of
the ordinary Daniell's or Leclanche's cells (as used in
telegraphy) is too great to render them serviceable for
producing electric lights. A battery of 40-60 Grove's
cells (Art. 171) is efficient, but will not last more than
2 or 3 hours. A dynamo-electric machine (such as M
described in Art. 407 to 411), worked by a steam-engine, '
is the best generator of currents for practical electric
lighting. The quantity of light emitted by an electric
lamp is disproportionate to the strength of the current ;
and is, within certain limits, proportional to the square |
of the heat developed, or to the fourth power of the
strength of the current.
372. Electric Arc Lamps. Davy employed wood
charcoal for electrodes to obtain the arc light. Pencils
of hard gas-carbon were later introduced by Foucault.
In all the more recent arc lamps, pencils of a more
336
ELEMENTARY LESSONS ON [CHAP. vn.
dense and homogeneous artificial coke-carbon are used.
These consume away more regularly, and less rapidly,
but still some contrivance is necessary to push the
points of the carbons forward as fast as
needed. It is requisite that the mechan-
ism should start the arc by causing the
pencils to touch and then separate them
to the requisite distance for the produc-
tion of a steady arc ; the mechanism
should also cause the carbons not only
to be fed into the arc as fast as they
consume, but also to approach or recede
automatically in case the arc becomes
too long or too short ; it should further
bring the carbons together for an instant
to start the arc again if by any chance
the arc goes out. Electric Arc Lamps
or Regulators, fulfilling these
conditions, have been invented
by a number of persons. These
may be classified as follows :
(a) Clockwork Lamps. Fig.
138 shows the regulator of Fou-
cault as constructed by Duboscq;
in this lamp the carbon-holders
are propelled by a train of
clockwork wheels actuated by
a spring. An electromagnet
at the base, through which the
current runs, attracts an arma-
ture and governs the clock-
work. If the current is too
strong the armature is drawn down, and the clockwork
draws the carbons further apart. If the current is
weakened by the resistance of the arc, the armature is
drawn upwards by a spring, and a second train of wheels
comes into play and moves the carbons nearer together.
138.
CHAP. VIL] ELECTRICITY AND MAGNETISM. 337
Clockwork arc lamps have also been devised by Serrin
and by Crompton, in which the weight of the carbon-
holders drive the clockwork mechanism.
(b) Break-wheel Lamps. Jaspar and Crompton have
devised mechanism for regulating the rate of feeding
the carbon into the arc by adding to the train of
wheels a break-wheel ; the break w r hich stops the wheel
being actuated" by a small electromagnet which allows
the wheel to run forward a little when the resistance of
the arc increases beyond its normal amount.
(c) Solenoid Lamps. In this class of arc lamp one
of the carbons is attached to an iron plunger capable of
sliding vertically up or down inside a hollow coil or
solenoid, which, being traversed by the current, regulated
the position of the carbons and the length of the arc.
Siemens employed two solenoids acting against one
another differentially, one being a main-circuit coil, the
other being a shunt-circuit. If the resistance of the arc
became too great, more of the current flowed past the
lamp through the shunt-circuit, and caused the carbon-
holders to bring the carbons nearer together. Shunt-
circuits to regulate the arc have also been used by
Lontin, Brush, Lever, and others.
(d) Clutch Lamps. A somewhat simpler device is
that of employing a clutch to pick up the upper carbon
holder, the lower carbon remaining fixed. In this kind
of lamp the clutch is worked by an electromagnet,
through which the current passes. If the lamp goes
out the magnet releases the clutch, and the upper carbon
falls by its own weight and touches the lower carbon.
Instantly the current starts round the electromagnet,
causes it to act on the clutch which grips the carbon-
holder and raises it to the requisite distance. Should
the arc grow too long the lessening attraction on the
clutch permits the carbon -holder to advance a little.
Hart, Brush, Weston, and Lever employ clutch lamps.
373. Electric Candles. To obviate the expense
z
338 ELEMENTARY LESSONS ON [CHAP. vn.
and complication of such regulators, electric candles have
been suggested by JablochkofF,
Wilde, and others. Fig. 139
depicts Jablochkoff 's candle,
consisting of two parallel pen-
cils of hard carbon separated
by a thin layer of plaster of
Paris and supported in an up-
right holder. The arc plays
across the summit between the
two carbon wicks. In order
that both carbons may consume
at equal rates, rapidly alternat-
ing currents must be employed,
which is disadvantageous from
an economical point of view.
374. Incandescent Elec-
tric Lamps. Voltaic arcs of
an illuminating power of less
than 100 candles cannot be
Fi ^ maintained steady in practice,
and are uneconomical. For
small lights it is both simpler and cheaper to employ a
thin continuous wire or filament of some infusible con-
ductor, heated to whiteness by passing a current through
it. Thin wires of platinum have repeatedly been sug-
gested for this purpose, but they cannot be kept from
risk of fusing. Iridium wires and thin strips of carbon
have also been suggested by many inventors. Edison in
1878 devised a lamp consisting of a platinum spiral com-
bined with a short-circuiting switch to divert the current
from the lamp in case it became overheated. More recently
thin filaments of carbon have been employed by Swan,
Edison, Lane-Fox, Maxim, Crookes, and others for the
construction of little incandescent lamps. In these lamps
the carbon filament is mounted upon conducting wires,
usually of platinum, which pass into a glass bulb, into
CHAP, vii.] ELECTRICITY AND MAGNETISM. 339
which they are sealed, the bulbs being afterwards ex-
hausted of air and other gases, the vacuum being made
very perfect by the employment of special mercurial
air-pumps. Carbon is better for this purpose than
platinum or any other metal, partly because of its
superior infusibility and higher resistance, and partly
because of the remarkable property of carbon of offering
a lower resistance when hot than when cold. This
property, which is the reverse of that observed in metals,
renders it less
liable to become
overheat e d.
The forms of
several incan- ,
descent lamps
are shown in
Fig. 1 40. Sv&n '
(i) prepares his
filament from
cotton thread
parchmentised
in sulphuric
acid and after-
wards carbon-
ised ; such a
filament be-
coming remark-
ably elastic and
metal-like in the process. Edison (2) now uses a thin
flat strip of carbonised bamboo instead of a filament.
Maxim (3) uses a preparation of paper. Lane-Fox (4)"
and Akester (6) use prepared and carbonised vegetable
fibres. Crookes (5) employs a filament made from animal
or vegetable matter parchmentised by treatment with
cuprammonic chloride. The resistance of such lamps
varies according to size and length of the filament from
3 to 200 ohms. The current necessary to heat the
Fig. 140.
340 ELEMENTARY LESSONS ON [CHAP. vn.
filaments white-hot is usually from I to 1-3 ampere. To
produce this current the electromotive force that must
be applied is dependent on the resistance of the lamp.
Suppose a lamp the resistance of which is 60 ohms when
cold and 40 ohms when hot : the requisite current will
be obtained by applying an electromotive force of about
50 volts, because 50 ~- 40 = 1-25 ampere. The best
economy is obtained with very thin cylindrical filaments
of high resistance. Flat strips of carbon which expose
a disproportionate amount of surface, and thick filaments
in which the mass of carbon is considerable, are open
to objection. Well-made lamps, if not overheated, will
last 1000 to 1 200 hours before the filament disintegrates.
It is usual to group these lamps in parallel arc between
the leading main conductor and the return main, so that
each lamp is independent of the others if the electro-
motive force of the supply is constant. The light
emitted varies according to the size of lamp from 2 to
50 candles. There appears to be some difficulty in
obtaining durable filaments that will bear being made
incandescent to a higher candle power.
LESSON XXXIII. Electromotors (Electromagnetic
Engines).
375. Electromotors. Electromagnetic engines, or
electromotors, are machines in which the motive power
is derived from electric currents by means of electro-
magnets. In 1821 Faraday showed a simple case of
rotation produced between a magnet and a current of
electricity. In 1831 Henry, and in 1833 Ritchie, con-
structed electromagnetic engines producing rotation by
electromagnetic means. Fig. 141 shows a modification
of Ritchie's electromotor. An electromagnet DC, is
poised upon a vertical axis between the poles of a fixed
magnet (or electromagnet) SN. A current, generated
by a suitable battery, is carried by wires which terminate
CHAP. VIL] ELECTRICITY AND MAGNETISM. 341
in two mercury-cups, A, B, into which dip the ends of
the coil of the movable electromagnet CD. When a
current traverses the coil of
CD it turns so as to set itself
in the line between the poles
NS, but as it swings round,
the wires that dip into the mer-
cury-cups pass from one cup
to the opposite, so that, at the
moment when C approaches S,
the current in CD is reversed,
and C is repelled from S and
attracted round to N, the cur-
rent through CD being thus
reversed every half turn. In
larger electromotors, the mer- -
cury-cup arrangement is replaced jjj
by a commutator, consisting of
a. brass ring, slit into two or
more parts, and touched at
opposite points by a pair of metallic springs or " contact
brushes."
In another form of electromotor, devised by Froment,
bars of iron fixed upon the circumference of a rotating
cylinder are attracted up towards an electromagnet, in
which the current is automatically broken at the instant
when each bar has come close up to its poles. In a third
kind, an electromagnet is made to attract a piece of soft
iron alternately up and down, with a motion like the
piston of a steam-engine, which is converted by a crank
into a rotatory motion. In these cases the difficulty
occurs that, as the attraction of an electromagnet falls off
nearly in inverse proportion to the square of the distance
from its poles, the attracting force can only produce
effective motion through very small distances.
The dynamo-electric machines of Gramme, Siemens,
and others, described in Arts. 407 to 411, will also work
Fig. 141.
342 ELEMENTARY LESSONS ON [CHAP. vn.
as electromotors, and, indeed, are the most efficient of
electromagnetic engines.
In 1839 Jacobi propelled a boat along the river Neva
at the rate of 2^ miles per hour with an electromagnetic
engine of about one horse-power, worked by a battery of
64 large Grove's cells.
In 1882 an iron screw-boat capable of carrying 12
persons, and driven by two Siemens' dynamos, with a
power of about 3 horse-power, the electricity being fur-
nished by 45 accumulators of the Sellon-Volckmar type,
has been worked upon the Thames at a speed of 8 miles
per hour.
Electric railways on which trains are propelled by
power furnished by dynamo-electric generators stationed
at some fixed point, and communicating with the electro-
magnetic machinery of the train either by the rails or by
a special conductor, have been constructed by Siemens
in Berlin, and by Edison in Menlo Park.
376. Electric Transmission of Power to a
distance. The increasing use of dynamo -electric
machines for electric lighting has revived the problem of
transmitting power to a distance by electrical means,
and so utilising waste water-power. A mountain stream
may be made to turn a water-wheel or turbine, and
drive a dynamo -electric machine, thereby generating
currents which can be conveyed by wires to an electro-
motor at a distant point, and there reconverted into
mechanical power. Whether such transmission is profit-
able or not depends on the efficiency of the machines
employed.
377. Theory of Efficiency of Electromotors.
If a galvanometer be included in a circuit with a battery
and an electromotor, it is found that the current is weaker
when the electromotor is working than when the electro-
motor is standing still, and that the faster the electromotor
runs the weaker does the battery current become. This
is due to electromagnetic induction (Art. 391) between the
CHAP, vii.] ELECTRICITY AND MAGNETISM. 343
moving and fixed parts of the electromotor, which, as it
spins round, generates a back-current. The electromotive-
force due to this inductive action increases with the speed
of the electromotor, so that the back-current is strongest
when it runs fastest. If the motor be loaded so as to
do work by moving slowly against considerable forces, the
back-current will be small, and only a small proportion
of the energy of the current will be turned into useful
work. If it be set to run very quickly, so as to generate
a considerable back-current, it will utilise a larger pro-
portion of the energy of the direct current, but can only
run fast enough to do this if its load be very light.
Jacobi calculated that the practical efficiency lay between
these two extremes, and that an electromotor would turn
the energy of a battery into work in the most effective
way when it was allowed to do its work at such a speed
that the battery current was thereby reduced to half its
strength. This is indeed true if it be desired to do the
work at the quickest possible rate. But where economy
in working is desired, and when it is not needful to get
through the work as rapidly as possible, or to consume
materials in the battery at a great rate, then a higher
economic efficiency will be attained by making the electro-
motor do lighter work and spin at a greater speed ; for
if the electromotive-force of the battery be E volts , and
the counter electromotive-force of the motor while running
be e volts, then the efficiency of the motor (that is to
say, the ratio which the work it takes up from the cur-
rent bears to the whole energy of the current) will be
equal to -~ Now if the motor be allowed to run more
quickly e will increase proportionately, and if it runs
very quickly e may become very nearly equal to E ; that
is to say, the motor will utilise very nearly all the energy
of the current. But since, by Ohm's law, the current is
= ^-^, it follows that if e is very nearly as great as E,
the current will be reduced to a small fraction of its
original strength. The materials of the battery will be
344 ELEMENTARY LESSONS ON [CHAP. vn.
more slowly used, and it will take a longer time to do
the total amount of the work, but the percentage of
energy of the current turned into work will be higher.
A Siemens' dynamo-electric machine (Art. 409) used as
a motor can attain an efficiency of over 8 5 per cent.
378. Cost of Working. The cost of working
electromotors by batteries is great. A pound of zinc
contains only about -J- as much potential energy as a
pound of coal, and it costs more than twenty times as
much : the relative cost for equal amounts of energy is
therefore about 120 : i. But, as shown above, an elec-
tromagnetic engine will turn 85 per cent of the electric
energy into work, while even good steam-engines only
turn about 10 to 20 per cent of the energy of their fuel
into work, small steam-engines being even less efficient.
But, reckoning electromagnetic engines as being 5 times
as "efficient" as steam-engines of equal power, the
necessary zinc is still 24 times as dear as the equivalent
amount of coal. This calculation does not take into
account the cost of acids of the batteries. In fact,
where strong currents are wanted, batteries are aban-
doned in favour of dynamo-electric machines, worked by
steam or water power, or by gas-engines.
In the case of transmission of power, as in the preced-
ing paragraph, the expense may be far smaller if the
original water-power costs little. The dynamo-machine
may turn 90 per cent of the mechanical power into the
energy of electric currents, and the electromotor may
convert back 85 per cent of the current energy (or 76
per cent of the original power) into work.
378. (bis) Calculation of Electric Power. The
mechanical work of a current may be calculated as
follows : A current whose strength is C conveys through
the circuit in / seconds a quantity of electricity = C/.
But the number of ergs of work W, done by a current
is equal to the product of the quantity of electricity into
the difference of potentials E through which it is trans-
CHAP, vii.] ELECTRICITY AND MAGNETISM. 345
ferred (Art. 367), provided these latter are expressed in
"absolute" C.G.S. units; or
C/E=W
Now if W ergs of work are done in / seconds, the rate of
working is got by dividing W by tj whence
If C and E are expressed in amperes and volts respec-
tively, and it is desired to give the rate of working in
horse -power, it must be remembered that i ampere
icr 1 C.G.S. units of current; that i volt = io 8 C.G.S.
units of E.M.F. ; and that i horse-power (as defined by
Watt) =550 foot-pounds per second = 76 kilogramme-
metres per second = 76 x io 5 gramme-centimetres per
second = 746 x io 7 ergs per second, whence
For example, to find the rate at which actual work is
consumed in an electric lamp : measure the whole current
in amperes j measure the difference of potential between
the terminals of the lamp in volts; multiply them to-
gether and divide by 746 ; the result will be the number
of horse-power used up in the lamp : or the rule may be
written thus :
H-P = CE x 0-00134.
A convenient " electric power-meter " may be made of
an electrodynamometer (Art. 336) having the fixed coil
of thick wire to receive the whole current, and having
the movable coil of many turns of thin wire arranged
as a shunt to the lamp or dynamo whose power is to be
measured.
It has been proposed by Preece and by Siemens to
call the unit of electric power (i.e. one ampere working
through one volt) a watt. One horse-power will equal
746 watts.
34<5 ELEMENTARY LESSONS ON [CHAP, vin
CHAPTER VIII.
THERMO-ELECTRICITY.
LESSON XXXIV. Thermo-Electric Currents.
379. In 1822 Seebeck discovered that a current may
be produced in a closed circuit by heating a point of
contact of two dissimilar metals. Thus, if a piece of
bismuth and a piece of antimony be soldered together,
and their free ends be connected with a short -coil
galvanometer, it is found that if the junction be warmed
to a temperature higher than that of the rest of the
circuit, a current flows whose direction across the heated
point is from bismuth to antimony, the strength of the
current being proportional to the excess of temperature.
If the junction is cooled below the temperature of the
rest of the circuit a current in the opposite direction is
generated. The electromotive -force thus set up will
maintain a constant current so long as the excess of
temperature of the heated point is kept up, heat being
all the while absorbed in order to maintain the energy of
the current. Such currents are called Thermo-electric
currents, and the electromotive -force producing them
is known as Thermo-electr emotive-force.
380. Peltier Effect. In 1834 Peltier discovered
a phenomenon which is the converse of that discovered
by Seebeck. He found that if a current of electricity
from a battery be passed through a junction of dissimilar
metals the junction is either heated or cooled, according
CHAP. VIIL] ELECTRICITY AND MAGNETISM. 347
to the direction of the current. Thus a current which
passes through a bismuth-antimony pair in the direction
from bismuth to antimony absorbs heat in passing the
junction of these metals, and cools it ; whereas, if the
current flow from antimony to bismuth across the
junction it evolves heat, and the junction rises in tem-
perature.
This phenomenon of heating (or cooling) by a current,
where it crosses the junction of two dissimilar metals
(known as the " Peltier effect," to distinguish it from the
ordinary heating of a circuit where it offers a resistance
to the current, which is sometimes called the "Joule
effect "), is utterly different from the evolution of heat in
a conductor of high resistance, for (a) the Peltier effect
is reversible, the current heating or cooling the junction
according to its direction, whereas a current meeting
with resistance in a thin wire heats it in whichever
direction it moves ; and (b) the amount of heat evolved
or absorbed in the Peltier effect is proportional simply
to the strength of the current, not to the square of that
strength as the heat of resistance is.
The complete law of the heat developed in a circuit will
therefore require to take into account any Peltier effects which
may exist at metal junctions in the circuit. If the letter P
stand for the difference of potential due to the heating of the
junction, expressed as a fraction of a volt, then the complete
law of heat is
H = 0-24 x (C?R/ + Pa)
which the student should compare with Joule's law in Art. 367.
The quantity called P is also known as the coefficient of the
Peltier effect ; it has different values for different pairs of metals,
and is numerically equal to the number of ergs of work which
are the dynamical equivalent of the heat evolved at a junction
of the particular metals by the passage of one amptre of electricity
through the junction.
381. Thermo-electric Laws. The thermo-electric
properties of a circuit are best studied by reference to
the simple circuit of Fig. 142, which represents a
ELEMENTARY LESSONS ON [CHAP. vm.
bismuth-antimony pair united by a copper wire. Volta's
law (Art. 72) concerning the difference of potentials
due to contact would tell us that when all are at one
temperature the dif-
ference of poten-
tials between bis-
muth and copper
in one direction
is equal to the sum
of the differences
between bismuth
and antimony, and
between antimony
and copper in the
other direction, and that hence there would be equilibrium
between the opposing and equal electromotive -forces.
But when a junction is heated this equilibrium no longer
exists and Volta's law ceases to be true. The new
electromotive-force set up at the heated junction is found
to obey the following laws :
(i.) The thermo- electromotive -force is, for the same
pair of metals, proportional (even through con-
siderable ranges of temperature) to the excess of
temperature of the junction over the rest of the
circuit.
(ii.) The total thermo-electromotive- force in a circuit
is the sum of all the separate thermo -electromotive-
forces at the various junctions.
It follows from this law that the various metals can be
arranged, as Seebeck found, in a series, according to
their thermo-electric power, each one in the series being
thermo-electrically positive (as bismuth is to antimony)
toward one lower down. The following is the thermo-
electric series of metals, together with the differences
of potentials (in microvolts) which they exhibit with a
difference of temperature of iC, lead being regarded as
the standard zero metal.
CHAP, viii.] ELECTRICITY AND MAGNETISM. 349
+ Bismuth . . . . 89 to 97
German-silver . . . 1 1 '75
Lead .... o
Platinum . . . . 0*9
Zinc . . . . - 3*7
Copper . . . . - 3-8
Iron . ... - 17-5
Antimony . . . . 22-6 to 26*4
A very small amount of impurity may make a great
difference in the thermo-electric power of a metal, and
some alloys, and some of the metallic sulphides, as
galena, exhibit extreme thermo-electric power.
The electromotive -forces due to heating single pairs
of metals are very small indeed. If the junction of a
copper-iron pair be raised iC above the rest of the
circuit its electromotive-force is only 13*7 millionths of a
volt (i.e. 13-7 microvolts). That of the more powerful
bismuth-antimony pair is for iC, about 117 microvolts.
382. Thermo-electric Inversion. Gumming dis-
covered that in the case of iron and other metals an
inversion of their thermo-electric properties may take
place at a high temperature. In the case of the copper-
iron pair the temperature of 280 is a neutral point ;
below that temperature the current flows through the
hotter junction from the copper to the iron ; but when
the circuit is above that temperature iron is thermo-
electrically positive to copper.
383. Thermo-electric Diagram. The facts of
thermo-electricity are best studied by means of the
diagrams suggested by Sir W. Thomson and constructed
by Professor Tait. In that given in Fig. 143, the
horizontal divisions represent the temperatures, the
vertical distances indicating the differences of potential
on a scale of millionths of volts. These differences are
measured with respect to the metal lead, which is
taken as the standard of zero at all temperatures, because,
while with other metals there appears to be a difference
of potentials between the metal hot and the same metal
35
ELEMENTARY LESSONS ON [CHAP. vin.
cold, hot lead brought into contact with cold lead shows
no perceptible difference of potential.
100
200
300
Fig. 143.
An example will illustrate the usefulness of the diagram. Let
a circuit be made by uniting at both ends a piece of iron and a
piece of copper ; and let the two junctions be kept at o and
1 00 respectively by melting ice and boiling water. Then the
total electromotive-force round the circuit is represented by the
area a, o, -15, b. The slope of the lines for the various metals
represents the property referred to above, of an electromotive-
force between differently heated portions of the same metal
accompanied by an absorption or evolution of heat when the
current flows from a hotter to a colder portion of the same
metal. This effect, known as the Thomson effect from its
discoverer Sir W. Thomson, is opposite in iron to what it is
in copper or zinc. In copper, when a current of electricity flows
from a hot to a cold point, it evolves heat in the copper, and it
absorbs heat when it flows from a cold point to a hot point in
the copper. In iron a current flowing from a hot point to a
cold point absorbs heat.
384. Thermo-electric Piles. In order to increase
CHAP, viii.] ELECTRICITY AND MAGNETISM. 351
the electromotive-force of thermo-electric pairs it is usual
to join a number of pairs of metals (preferably bismuth
and antimony) in series, but so bent that the alternate
junctions can be heated as shown in Fig. 144 at B B B,
Fig. 144.
whilst the other set A A A are kept cool. The various
electromotive-forces then all act in the same direction,
and the current is increased in proportion to the number
of pairs of junctions. Powerful thermo-electric batteries
have been made by Clamond, an iron-galena battery
of 1 20 pairs affording a strong current; but it is
extremely difficult to maintain them in effective action
for long, as they fail after continued use, probably
owing to a permanent molecular change at the junctions.
In the hands of Melloni the thermo-electric pile or
thermopile, constructed of many small pairs of anti-
mony and bismuth united in a compact form, proved an
excellent electrical thermometer when used in conjunction
with a sensitive short-coil astatic galvanometer like that
of Fig. 88. For the detection of excessively small
differences of temperature the thermopile is an invaluable
instrument, the currents being proportional to the differ-
352
ELEMENTARY LESSONS ON [CHAP. vin.
ence of temperature between the hotter set of junctions
on one face of the thermopile and the cooler set on the
other face. The arrangement of the thermopile and
galvanometer for this purpose is shown in Fig. 145.
Fig. 145-
CHAP, ix.] ELECTRICITY AND MAGNETISM. 353
CHAPTER IX.
ELECTRO-OPTICS.
LESSON XXXV. General Relations between Light
and Electricity.
385. Of late years several important relations have
been observed between electricity and light. These
relations may be classified under the following heads :
(i.) Production of double refraction by dielectric stress.
(ii.) Rotation of plane of polarisation of a ray of light
on traversing a transparent medium placed in a
magnetic field, or by reflection at the surface of a
magnet.
(iii.) Change of electric resistance, exhibited by
selenium and other bodies during exposure to light.
(iv.) Relation between refractive index and dielectric
capacity of transparent bodies.
It was announced by Mrs. Somerville, by Zantedeschi, and
others, that steel needles could be magnetised by exposing
portions of them to the action of violet and ultra-violet rays
of light ; the observations were, however, erroneous.
386. Electrostatic Optical Stress. In 1875 Dr.
Kerr of Glasgow discovered that glass when subjected to
a severe electrostatic stress undergoes an actual strain,
which can be observed by the aid of a beam of polarised
light. In the original experiment two wires were fixed
into holes drilled in a slab of glass, but not quite meeting,
354 ELEMENTARY LESSONS ON [CHAP. ix.
so that when these were placed in connection with the
terminals of an induction coil or of a Holtz machine the
accumulating charges on the wires subjected the inter-
vening dielectric to an electrostatic stress. The slab
when placed between two Nicol prisms as polariser and
analyser 1 exhibited double refraction. The behaviour of
the glass was as if it had been subjected to a pull along
the direction of the electric force, i.e., as if it had ex-
panded along the lines of electrostatic induction. Later,
he found that bisulphide of carbon and other insulating
liquids exhibit similar phenomena, but that of these the
fatty oils of animal and vegetable origin exhibited an
action in the negative direction, as if they had contracted
along the lines of induction. It is found that the
quantity of optical effect (i.e., the difference of retardation
between the ordinary and extraordinary rays) per unit
thickness of the dielectric is proportional to the square of
the resultant electric force. The axis of double refraction
is along the line of the electric force. Quincke has
pointed out that these phenomena can be explained by
the existence of electrostatic expansions and contractions,
stated in Art. 273.
387. Magneto-optic Rotation of the Plane of
Polarisation of a Bay of Light. A ray of light
is said to be polarised if the vibrations take place in one
plane. Ordinary light can be reduced to this condition
by passing it through a suitable polarising apparatus
(such as a Nicol prism, a thin slice of tourmaline crystal,
etc.) In 1845 Faraday discovered that a ray polarised
in a certain plane can be twisted round by the action
of a magnet, so that the vibrations are executed in a
different plane. The plane in which a ray is polarised
can be detected by observing it through a second Nicol
prism (or tourmaline), for each such polariser is opaque
to rays polarised in a plane at right angles to that plane
*
1 The student is referred to Prof. Balfour Stewart's Lessons on Element-
ary Physics for further information concerning the properties of polarised light.
CHAP. ix.J ELECTRICITY AND MAGNETISM. 355
in which it would itself polarise light. Faraday caused
a polarised ray to pass through a piece of a certain
" heavy glass " (consisting chiefly of borate of lead),
lying in a powerful magnetic field, between the poles
of a large electromagnet, through the coils of which a
current could be sent at pleasure. The emerging ray
traversed a second Nicol prism which had been turned
round until all the light was extinguished. In this posi-
tion its own plane of symmetry was at right angles to the
plane of polarisation of the ray. On completing the cir-
cuit, light was at once seen through the analysing Nicol
prism, proving that the ray had been twisted round into
a new position, in which its plane of polarisation was no
longer at right angles to the plane of symmetry of the
analyser. But if the analysing Nicol prism was itself
turned round, a new position could be found (at right
angles to the plane of polarisation of the ray) at which
the light was once more extinguished. The direction of
the magneto-optic rotation of the plane of polarisation is
the same (for diamagnetic media) as that in which the
current flows which produces the magnetism. Verdet,
who repeated Faraday's experiments, using powerful
electromagnets of the form shown in Fig. 127, dis-
covered the important law that, with a given material,
the amount of rotation is proportional to the strength of
the magnetic force H. In case the rays do not pass
straight along the direction of the lines of force (which
is the direction of maximum effect), the amount of rota-
tion is proportional to the cosine of the angle /3 between
the direction of the ray and the lines of force. It is also
proportional to the length I of the material through
which the rays pass. These laws are combined in the
equation for the rotation & ;
6 = w H cos )8 /,
where w is a coefficient which represents the specific
magnetic rotatory power of the given substance, and is
known as " Verdefs constant" Now, H -cos Q is the
356
ELEMENTARY LESSONS ON [CHAP. ix.
resolved part of the magnetic force in the direction of
the ray ; and H cos /3 / is the difference of magnetic
potential 1 between the point A where the ray enters and
B where it leaves the medium. Hence /, the coefficient
of specific magnetic rotatory power, is found by divid-
ing the observed angular rotation by the difference of
magnetic potential between the points where the ray
enters and leaves the medium ; or
Different substances possess different magnetic rotatory
powers. For diamagnetic substances the coefficient is
usually positive ; but in the case of many magnetic
substances, such as solutions of ferric chloride, has a
negative value ; (i.e. in these substances the rotation is
in the opposite direction to that in which the magnetising
current flows). The phenomenon discovered by Hall
(Art. 337) appears to be intimately related to the
phenomenon of magneto-optic rotation.
Bisulphide of Carbon
Water ....
Heavy glass .
Coefficient of Specific
Magnetic Rotation,
(Verdet's Constant in C. G. S.)
Magnetic
Rotatory
Power.
3-047 x io~ 5
9386 x io~ 5
4-33 x io~ 5
I '000
308
I '422
It is convenient, for purposes of reference, to take the
rotatory power of bisulphide of carbon as unity. Careful
measurements executed by J. E. H. Gordon have shown
that the rotatory power of bisulphide of carbon, thus
assumed as a standard, must be multiplied by 3-047 x
i o~ 6 to reduce it to C. G. S. measure ; for he finds that
1 For force X length = -work ; and the work done in bringing a unit
magnetic pole from A to B against the magnetic force measures the
difference of magnetic potential. See Art. 310 (e).
CHAP, ix.] ELECTRICITY AND MAGNETISM. 357
this is the number of degrees through which a polarised
ray of green light (of thallium flame) will be rotated by
traversing unit difference of potential. For rays of
different colours the rotation is not equal, but varies
(very nearly) inversely as the square of the wave-length ;
the rotation by bisulphide of carbon of red, green, and
blue light (rays "C," "E," and "G"), being respectively
as -60, i -oo, and i -65. H. Becquerel, who gave this law,
also found that for substances of similar nature the rota-
tion depends on the refractive index, but in rather a com-
plicated relation, being proportional to ^ 2 (fj? i) ;
where ^ is the refractive index.
Gases also rotate the plane of polarisation of light in
a magnetic field with varying amounts ; coal-gas and
carbonic acid being more powerful than air or hydrogen ;
oxygen and ozone being negative. The rotation is in all
cases very slight, and varies for any gas in proportion to
the density that is to the quantity of gas traversed. H.
Becquerel has lately shown that the plane of the natural
polarisation of the sky does not coincide with the plane
of the sun, but is rotated by the influence of the earth's
magnetism through an angle which, however, only reached
59' of arc at a maximum on the magnetic meridian.
388. Dr. Kerr showed in 1877 that a ray of polarised
light is also rotated when reflected at the surface of a
magnet or electromagnet. When the light is reflected
at a pole the plane of polarisation is turned in a direction
contrary to that in which the magnetising current flows.
If the light is reflected at a point on the side of the
magnet it is found that when the plane of polarisation is
parallel to the plane of incidence the rotation is in the
same direction as that of the magnetising current ; but
that, when the plane of polarisation is perpendicular to
the plane of incidence, the rotation is in the same
direction as that of the magnetising current only when
the incidence exceeds 75, being in the opposite direc-
tion at lesser angles of incidence.
35** ELEMENTARY LESSONS ON [CHAP. ix.
389. Photo-voltaic Properties of Selenium.
In 1875 Willoughby Smith discovered that the metal
selenium possesses the abnormal property of changing
its electric resistance under the influence of light.
Ordinary fused or vitreous selenium is a very bad
conductor ; its resistance being nearly forty -thousand-
million (3-8 x io 10 ) times as great as that of copper.
When carefully annealed (by keeping for some hours at
a temperature of about 22OC, just below its fusing
point, and subsequent slow cooling), it assumes a crystal-
line condition, in which its electric resistance is consider-
ably reduced. In the latter condition, especially, it is
sensitive to light. Prof. W. G. Adams found that green-
ish-yellow rays were the most effective. He also showed
that the change of electric resistance varies directly as
I the square root of the illumination, and that the resist-
ance is less with a high electromotive-force than a
low one. Lately, Prof. Graham Bell and Mr. Sumner
Tainter have devised forms of " selenium cells," in which
the selenium is formed into narrow strips between the
edges of broad conducting plates of brass, thus securing
both a reduction of the transverse resistance and a large
amount of surface-exposure to light. Thus a cell, whose
resistance in the dark was 300 ohms, when exposed to
sunlight had a resistance of but 150 ohms. This pro
perty of selenium the latter experimenters have applied
in the construction of the Photophone, an instrument
which transmits sounds to a distance by means of a
beam of light reflected to a distant srJot from a thin
mirror thrown into vibrations by the voice ; the beam
falling, consequently, with varying intensity upon a re-
ceiver of selenium connected in circuit with a small
battery and a Bell telephone (Art. 435) in which the
sounds are reproduced by the variations of the current.
Similar properties are possessed, to a smaller degree,
by tellurium. Carbon is also sensitive to light.
About the middle of the present century Becquerel
showed that when two plates of silver, coated with
CHAP, ix.] ELECTRICITY AND MAGNETISM. 359
freshly deposited chloride of silver, are placed in a cell
with water and connected with a galvanometer, a current
is observed to pass when light falls upon one of the two
plates, the exposed plate acting as a negative pole.
39O. Electromagnetic Theory of Light. Clerk
Maxwell proposed a theory of the relation between
electromagnetic phenomena and the phenomena of light,
based upon the assumption that each of these are due to
certain modes of motion in the all-pervading " ather " of
space, the phenomena of electric currents and magnets
being due to streams and whirls, or other bodily move-
ments in the substance of the aether, while light is due
to vibrations to and fro in it.
We have seen (Arts. 115, 338, and 387) what evidence there
is for thinking that magnetism is a phenomenon of rotation,
there being a rotation of something around an axis lying in the
direction of the magnetisation. Such a theory would explain
the rotation of the plane of polarisation of a ray passing through
a magnetic field. For a ray of plane-polarised light may be con-
ceived of as consisting of a pair of (oppositely) circularly-polarised
waves, in which the right-handed rotation in one ray is periodi-
cally counteracted by an equal left-handed rotation in the other
ray ; and if such a motion were imparted to a medium in which
there were superposed a rotation (such as we conceive to take
place in every magnetic field) about the same direction, one of
these circularly-polarised rays would be accelerated and the other
retarded, so that, when they were again compounded into a
single plane-polarised ray, this plane would not coincide with the
original plane of polarisation, but would be apparently turned
round through an angle proportional to the superposed rotation.
It was pointed out (Art. 337) that an electric dis-
placement produces a magnetic force at right angles to
itself; it also produces (by the peculiar action known as
induction) an electric force which is propagated at right
angles both to the electric displacement and to the mag-
netic force. Now it is known that in the propagation of
light the actual displacements or vibrations which con-
stitute the so-called ray of light are executed in directions
at right angles to the direction of propagation. This
ELEMENTARY LESSONS ON [CHAP. ix.
analogy is an important point in the theory, and
immediately suggests the question whether the respective
rates of propagation are the same. Now the velocity
of propagation of electromagnetic induction is that
velocity "z/" which was shown (Art. 365) to represent
the ratio between the electrostatic and the electro-
magnetic units, and which (in air) is believed to be
2-9857 x io 10 centimetres per second.
And the velocity of light (in air) has been repeatedly
measured (by Fizeau, Cornu, Michelson, and others)
giving as the approximate value
2-9992 x io 10 centimetres per second.
The close agreement of these figures is at least re-
markable. Amongst other mathematical deductions
from the theory may be mentioned the following : (i.)
all true conductors of electricity must be opaque 1 to light;
(ii.) for transparent media the specific inductive capacity
ought to be equal to the square of the index of refraction.
Experiments by Gordon, Boltzmann, and others, show
this to be approximately true for waves of very great
wave-length. The values are shown below. For gases
the agreement is even closer.
K.
M 2 .
Flint Glass
3-162
2-796
Bisulphide of Carbon
1-812
2-606
Sulphur (mean)
4-151
4-024
Paraffin . . 2-32
2'33
1 The author of these Lessons has found that in some crystalline bodies
which conduct electricity better in one direction than in another, the opacity
to light differs correspondingly. Coloured crystals of Tourmaline conduct
electricity better across the long axis of the crystal than along that axis.
Such crystals are much more opaque to light passing along the axis than
to light passing across it. And, in the case of rays traversing the crystal
across the axis, the vibrations across the axis are more completely absorbed
than those parallel to the axis : whence it follows that the transmitted light
will be polarized.
CHAP, x.] ELECTRICITY AND MAGNETISM. 361
CHAPTER X.
INDUCTION CURRENTS (Magneto-Electricity).
LESSON XXXVI. Currents produced by Induction.
391. In 1831 Faraday discovered that currents can
be induced in a closed circuit by moving magnets near
it, or by moving the circuit across the magnetic field,
and he followed up this discovery by finding that a
current whose strength is changing may induce a
secondary current in a closed circuit near it. Such
currents, whether produced by magnets or by other
currents, are known as Induction Currents. And
the action of a magnet or current in producing such
induced currents is termed electromagnetic induc-
tion.i
392. Induction Currents produced by a Mag-
net. If a coil of insulated wire be connected in circuit
with a delicate (long- coil) galvanometer, and a magnet
be inserted rapidly into the hollow of the coil (as in Fig.
l The student must not confuse this electromagnetic induction with the
phenomenon of the electrostatic induction of one charge of electricity by
another charge, as explained in Lesson III., and which has nothing to do
with currents. Formerly, before the identity of the electricity derived from
different sources was understood (Art. 218), electricity derived thus from the
motion of magnets was termed magneto-electricity. For most purposes the
adjectives magneto-electric and electro --magnetic are synonymous. The
production of electricity from magnetism, and of magnetism from electricity,
are, it is true, two distinct operations ; but both are included in the branch
of science denominated Electromagnetics.
362
ELEMENTARY LESSONS ON [CHAP. x.
146), a momentary current is observed to flow round
the circuit while the magnet is being moved into the
coil. So long as the magnet lies motionless in the coil
it induces no currents. But if it be rapidly pulled out of
the coil another momentary
current will be observed to
flow, and in the opposite direc-
tion to the former. The in-
duced current caused by in-
serting the magnet is an
inverse current^ or is in the
opposite direction to that
which would magnetise the
magnet with its existing polar-
ity. The induced current
caused by withdrawing the
magnet is a direct current.
Precisely the same effect is
produced if the coil be moved
towards the magnet as if the
magnet were moved toward
the coil. The more rapid the motion is, the stronger
are the induced currents.
393. Induction Currents produced by Cur-
rents. Faraday also showed that the approach or
recession of a current might induce a current in a closed
circuit near it. This may be conveniently shown as an
experiment by the apparatus of Fig. 147.
A coil is joined up to a sensitive galvanometer as
before. A smaller coil of stout wire is connected to the
poles of a battery (a single Bunsen's cell in Fig. 147), so
as to be traversed by a current. On approaching or
inserting the smaller or "primary " coil into the larger
or "secondary" coil, a momentary inverse current is
produced ; and on removing it a momentary direct
current (*>., one which runs the same way round the
outer secondary coil as the primary current which
Fig. 146.
CHAP, x.] ELECTRICITY AND MAGNETISM.
363
circulates in the inner coil) is observed. Breaking the
battery circuit while the primary coil lies still within the
secondary outer coil produces the same effect as if the
primary coil were suddenly removed to an infinite dis-
tance. Making the battery circuit while the primary
3 6 4
ELEMENTARY LESSONS ON [CHAP. x.
coil lies within the secondary produces the same effect
as plunging it suddenly into the coil.
So long as a steady current traverses the primary
circuit there are no induced currents in the secondary
circuit, unless there is relative motion between the two
circuits : but moving the secondary circuit towards the
primary has just the same effect as moving the primary
circuit towards the secondary, and vice versa.
We may tabulate these results as follows :
By
means
of
Momentary Inverse
currents are induced
in the secondary circuit
Momentary Direct
currents are induced
in the secondary circuit
Magnet
while approaching.
while receding.
Current
while approaching,
or beginning^
or increasing in strength.
while receding,
or ending^
or decreasing in strength.
394. Fundamental Laws of Induction. When
we reflect that every circuit traversed by a current has a
field of magnetic force of its own in which there are lines-
of-force running through the circuit (Art. 192), and that a
coil of many turns has a field in which the lines-of-force
are distributed almost identically as those of a magnet
are, we shall see that the facts tabulated in the preceding
paragraph may be summed up in the following funda-
mental laws :
(i.) A decrease in the number of lines-of-force which
pass through a circuit produces a current round
the circuit in the positive direction (i.e.) produces
a "direct" current); while an increase in the
number of lines-of-force which pass through the
CHAP, x.] ELECTRICITY AND MAGNETISM. 365
circuit produces a current in the negative direction
round the circuit.
Here we suppose the positive direction along lines-of-force to
be the direction^along which a free N. -pole would tend to move,
and positive direction round the circuit to be the same as the
direction in which the hands of a clock move. (See also p. 275.)
(ii.) The total induced electromotive -force acting
round a closed circuit is equal to the rate of
decrease in the number of lines-of-force which
pass through the circuit.
Suppose at first the number of lines-of-force passing through
the circuit to be N I} and that after a very short interval of time,
/, they are N 2 , then the total induced electromotive-force E is
F _ Ni-N 2
/ :
By Ohm's law, C = E -r- R, therefore
r - N i- N 2
R*
If N 2 is greater than N 1} and there is an increase in the number
of lines-of-force, then N t N 2 will be a negative quantity, and
C will have a negative sign, showing that the current is an
inverse one.
A reference to Fig. 134 will make this important law clearer.
Suppose ABCD to be a wire circuit of which the piece AB can
slide along DA and CB towards S and T. Let the vertical
arrows represent vertical lines of force in a uniform magnetic
field, and show (as is the case with the vertical components
of the earth's lines-of-force in the northern hemisphere) the
direction in which a N. -pointing pole would move if free. The
positive direction of these lines of force is therefore vertically
downwards through the circuit. Now if AB slide towards ST
with a uniform velocity it will cut a certain number of lines-of-
force every second, and a certain number will be added during
every second of time to the total number passing through the
circuit. If Nj be the number at the beginning, and N 2 that at
the end of a circuit, N x N 2 will be a negative quantity, and
there will be an electromotive - force round the circuit whose
direction through the sliding piece is from A towards B.
395. The following adaptation of Ampere's rule to the case
of induction may be useful : Suppose a figure swimming in any
conductor to turn so as to look along the (positive direction of the)
366 ELEMENTARY LESSONS ON [CHAP. x.
lines-of-force, then if he and the conductor be moved toivards his
right hand he will be swimming with the ctirrent induced by this
motion ; if he be moved towards his left hand, the current will
be against him.
396. Lenz's Law. In Art. 320 it was laid down that a
circuit traversed by a current experiences a force tending to
move it so as to include the greatest possible number of lines-
of-force in the embrace of the circuit. But if the number of
lines-of-force be increased, during the increase there will be an
opposing (or negative) electromotive -force set up, which will
tend to stop the original current, and therefore tend to stop the
motion. If there be no current to begin with, the motion will
generate one, which being in a negative direction will tend to
diminish the number of lines-of-force passing through the
circuit, and so stop the motion. Lenz, in 1834, summed up
the matter by saying that in all cases of electromagnetic induction
the induced currents have such a direction that their reaction
tends to stop the motion which produces them. This is known
as Lenz's Law.
397. Mutual Induction of Two Circuits. In
Art. 3 20 it was shown that when two circuits, in which
currents of unit strength are flowing, are placed near
together, they have a mutual potential whose value we
called M. This symbol M, upon investigation, was
found to represent the number of lines-of-force which
each circuit induced through the other circuit, or was
" the number of each other's lines -of- force mutually
intercepted by both circuits when each carries unit
current." This number depended upon the form and
position of the circuits, and was greatest when they
were brought as near together as possible. Hence
we may regard this quantity M as the "coefficient
of mutual induction " of the two circuits ; and any
movement of either circuit which alters the number
of lines-of-force passing mutually through them, will
be accompanied by the production of induced cur-
rents in each. It can be shown mathematically that,
in the case of two simple circular circuits of equal size,
enclosing area S, the greatest number of lines-of-force
CHAP, x.] ELECTRICITY AND MAGNETISM.
367
each can induce through the other, when each carries
unit current, is 4?rS, which is the maximum value of
M. If the circuits are not simple, but have respectively
m turns and n turns, then the value of M will be
4?rS x mn, when the circuits coincide with each other.
398. The Induction Coil. Induced currents have
in general enormously high electromotive-forces, and are
able to spark across spaces that ordinary battery cur-
rents cannot possibly cross. In order to observe these
effects a piece of apparatus invented by Mason, and im-
proved by Ruhmkorff, and termed the Induction Coil or
Inductorium (Fig. 148), is used. The induction coil con-
sists of a cylindrical bobbin having a central iron core
Fig. ,48.
surrounded by a short inner or " primary " coil of stout
wire, and by an outer " secondary" coil consisting of many
thousand turns of very fine wire, very carefully insulated
between its different parts. The primary circuit is joined
to the terminals of a few powerful Grove's or Bunsen's
cells, and in it are also included an interrupter, and a
commutator or key. The object of the interrupter is
368 ELEMENTARY -LESSONS ON [CHAP. x.
to make and break the primary circuit in rapid suc-
cession. The result of this is at every " make " to induce
in the outer " secondary " circuit a momentary inverse
current, and at every " break " a powerful momentary
direct current. The currents at " make " are sup-
pressed, as explained below : the currents at " break "
manifest themselves as a brilliant torrent of sparks
between the ends of the secondary wires when brought
near enough together. The primary coil is made of
stout wire, that it may carry strong currents, and produce
a powerful magnetic field at the centre, and is made of
few turns to keep the resistance low, and to avoid self-
induction of the primary current on itself. The central
iron core is for the purpose of increasing, by its great
coefficient of magnetic induction, the number of lines-
of- force that pass through the coils : it is usually made
of a bundle of fine wires to avoid the induction currents,
which if it were a solid bar would be set circulating in
it, and which would retard its rapidity of magnetisation
or demagnetisation. The secondary coil is made with
many turns, in order that the coefficient of mutual
induction may be large ; and as the electromotive-force
of the induced currents will be thousands of volts, its
resistance will be immaterial, and it may be made of the
thinnest wire that can conveniently be wound. In Mr.
Spottiswoode's giant Induction Coil (which yields a
spark of 42^ inches' length in air, when worked with 30
Grove's cells), the secondary coil contains 280 miles of
wire, wound in 340,000 turns, and has a resistance of
over 100,000 ohms.
The interrupters of induction coils are usually self-
acting. That of Foucault, shown with the coil in Fig.
148, consists of an arm of brass L, which dips a platinum
wire into a cup of mercury M, from which it draws the
point out, so breaking circuit, in consequence of its
other end being attracted toward the core of the coil
whenever it is magnetised ; the arm being drawn back
CHAP, x.] ELECTRICITY AND MAGNETISM. 369
again by a spring when, on the breaking of the circuit,
the core ceases to be a magnet. A more common
interrupter on small coils is a " break," consisting of a
piece of thin steel which makes contact with a platinum
point, and which is drawn back by the attraction of the
core on the passing of a current ; and so makes and
breaks circuit by vibrating backwards and forwards just
as does the hammer of an ordinaiy electric bell.
Associated with the primary circuit of a coil is usually
a small condenser^ made of alternate layers of tinfoil and
paraffined paper, into which the current flows whenever
circuit is broken. The object of the condenser is, firstly,
to make the break of circuit more sudden by preventing
the spark of the "extra -current" (due to self-induction
in the primary circuit) (Art. 404) from leaping across
the interrupter ; and, secondly, to store up the electricity
of this self-induced extra-current in order that, when
circuit is again made, the current shall attain its full
strength gradually instead of suddenly, thereby causing
the inductive action in the secondary circuit at " make "
to be comparatively feeble.
399. Ruhmkorff's Commutator. In order to
cut off or reverse the direction of the battery current at
will, Ruhmkorff invented the commutator or current-
reverser, shown in Fig. 149. In this instrument the
battery poles are connected through the ends of the
axis of a small ivory or ebonite cylinder to two cheeks
of brass V and V, which can be turned so as to place
them either way in contact with two vertical springs B
and C, which are joined to the ends of the primary coil.
Many other forms of commutator have been devised ;
one, much used as a key for telegraphic signalling, is
drawn in Fig. I 59.
400. Luminous Effects of Induction Sparks.
The induction coil furnishes a rapid succession of sparks
with which all the effects of disruptive discharge may be
studied. These sparks differ only in degree from those
2 B
370 ELEMENTARY LESSONS ON [CHAP. x.
furnished by friction machines and by Leyden jars (see
Lesson XXIII. on Phenomena of Discharge).
V
Fig. 149.
For studying discharge through glass vessels and tubes
from which the air has been partially exhausted, the
coil is very useful. Fig. 1 50 illustrates one of the
many beautiful effects which can be obtained, the spark
expanding in the rarefied gas into flickering sheets of
light, exhibiting striae and other complicated phenomena.
4O1. Currents Induced in Masses of Metal.
A magnet moved near a solid mass or plate of metal
induces in it currents, which, in flowing through it from
one point to another, have their energy eventually
frittered down into heat, and which, while they last,
produce (in accordance with Lenz's law) electromagnetic
forces tending to stop the motion. Several curious
instances of this are known. Arago discovered that
when a disc of copper is rotated in its own plane under
a magnetic needle the needle turns round and follows
the disc ; and if a magnet is rotated beneath a balanced
metal disc the disc follows the magnet. Attempts were
made to account for these phenomena known as
CHAP, x.] ELECTRICITY AND MAGNETISM.
Arago's rotations by supposing there to be a sort of
magnetism of rotation, until Faraday proved them to
be due to induction. A
magnetic needle set swing-
ing on its pivot comes to
rest sooner if a copper disc
lies beneath it, the induced
currents stopping it. If a
cube or disc of good con-
ducting metal be set spin-
ning between the poles of
such an electromagnet as
that drawn in Fig. 127,
and the current be suddenly
turned on, the spinning metal
stops suddenly. If, by sheer
force, a disc be kept spin-
ning between the poles of
a powerful electromagnet it
will get hot in consequence
of the induced currents flow-
ing through it. In fact,
any conductor moved forc-
ibly across the lines -of-
force of a magnetic field
experiences a mechanical
resistance due to the in-
duced currents which op-
pose its motion.
4O2. Induction - cur-
rents from Earth's Mag- Fig. 150.
netism. It is easy to ob-
tain induced currents from the earth's magnetism. A
coil of fine wire joined to a long-coil galvanometer, when
suddenly inverted, cuts the lines -of- force of the earth's
magnetism, and is traversed accordingly by a current.
Faraday, indeed, applied this method to investigate
372 ELEMENTARY LESSONS ON [CHAP. x.
the direction and number of lines -of -force. If a small
wire coil be joined in circuit with a long- coil galvan-
ometer having a heavy needle, and the little coil be sud-
denly inverted while in a magnetic field, it will cut all
the lines-of-force that pass through its own area, and
the sine of half the angle of the first swing (see Art.
204) will be proportional to the number of lines of
force cut ; for with a slow-moving needle, the total quan-
tity of electricity that flows through the coils will be the
integral whole of all the separate quantities conveyed
by the induced currents, strong or weak, which flow
round the circuit during the rapid process of cutting
the lines-of-force ; and the little coil acts therefore as a
magnetic pro of -plane.
If the circuit be moyed parallel to itself across a uni-
form magnetic field there will be no induction currents,
for just as many lines-of-force will be cut in moving
ahead in front as are left behind. There will be no cur-
rent in a wire moved parallel to itself along a line-of-force ;
nor if it lie along such a line while a current is sent
through it will it experience any mechanical force.
403. Earth Currents. The variations of the
earth's magnetism, mentioned in Lesson XII., alter the
number of lines-of-force which pass through the tele-
graphic circuits, and hence induce in them disturbances
which are known as " earth currents." During magnetic
storms the earth currents on the British lines of telegraph
have been known to attain a strength of 40 milli-amperes,
which is stronger than the usual working currents.
Feeble earth currents are observed every day, and are
more or less periodic in character.
404. Self-induction: Extra .Currents. In Art.
397 the induction of one circuit upon another was ex-
plained, and was shown to depend upon the number of
lines-of-force due to one circuit which passed through
the other, the coefficient of mutual induction M being
the number of mutual lines-of-force embraced by both
CHAP, x.] ELECTRICITY AND MAGNETISM. 373
circuits when each carried unit current. Now, if two
such circuits approach one another so as actually to
coincide, the mutual induction becomes a self-induc-
tion of the circuit on itself. For every circuit there is a
coefficient of self-induction^ whose value depends upon the
form of the circuit, and which will be greater if the
circuit be coiled up into many turns, so that one loop of
the circuit can induce lines-of-force through another loop
of the same. Let L represent the coefficient of self-in-
duction of one circuit, and L' that of a second circuit
equal to the first. When these two circuits coincide with
one another their coefficient of mutual induction (/.*., the
number of lines-of-force running through both circuits,
each carrying unit current) M will be equal to -L + L';
or, L = ^ M. Now for two coincident circuits having
n turns each, and each of area S (by Art. 397),
j M = 4?rS
hence the coefficient of self-induction for one circuit
of n turns coiled up in one plane,
L = 4irS
The existence of self-induction in a circuit is attested by
the so-called extra-current, which makes its appear-
ance as a bright spark at the moment of breaking circuit.
If the circuit be a simple one, and consist of a straight
wire and a parallel return wire, there will be little or no
self-induction ; but if the circuit be coiled up, especially if
it be coiled round an iron bar, as in an electromagnet,
then on breaking circuit there will be a brilliant spark, and
a person holding the two ends of the wires between which
the circuit is broken may receive a slight shock, owing
to the high electromotive-force of this self-induced extra
current. The extra - current due to self-induction on
"making" circuit is an inverse current, and gives no spark,
but it prevents the battery current from rising at once to
its full value. The extra-current on breaking circuit is
a direct current, and therefore increases the strength of
the current just at the moment when it ceases altogether.
374 ELEMENTARY LESSONS ON [CHAP. x.
4O5. Helmholtz's Equations. Helmholtz, who
investigated mathematically the effect of self-induction
upon the strength of a current, deduced the following
important equations to express the relation between the
self-induction of a circuit and the time required to
establish the current at full strength :
The current of self-induction at any moment will be
proportional to the rate at which the current is increasing
in strength. Let r represent a very short interval of
'time, and let the current increase during that short
interval from C to C + c. The actual increase during
the interval is c, and the rate of increase in strength is
Hence, if the coefficient of self-induction be L, the
electromotive-force of self-induction will be - L-, and, if
T
the whole resistance of the circuit be R, the strength of
the opposing extra-current will be . - during the short
interval r ; and hence the actual strength of current flow-
ing in the circuit during that short interval instead of
being (as by Ohm's Law it would be if the current were
steady) C = E -i- R, will be
r - E L c
c - R ~ RT
To find out the strength at which the current will have
arrived after a time / made up of a number of such small
intervals added together requires an application -of the
integral calculus, which at once gives the following
result :
(where e is the base of the natural logarithms).
Put into words, this expression amounts to saying that
after a lapse of / seconds the self-induction in a circuit
on making contact has the effect of diminishing the
strength of the current by a quantity ', the logarithm of
whose reciprocal is inversely proportional to the coefficient
CHAP, x.] ELECTRICITY AND MAGNETISM. 375
of self -induction , and directly proportional to the resist-
ance of the circuit and to the time that has elapsed since
making circuit.
A very brief consideration will show that in those
cases where the circuit is so arranged that the coefficient
of self-induction, L, is small as compared with the resist-
ance R, the fraction ^- will have a high value, and the
R \
term ( g - jff will vanish from the equation for all appre-
ciable values of/.
Where, however, L is large as compared with R, as
in long coils, long lines of telegraph cable, etc., the value
of this term, which stands for the retardation due to self-
induction^ may become considerable.
4O6. Induced Currents of Higher Orders.
Professor Henry discovered that the variations in the
strength of the secondary current could induce tertiary
currents in a third closed circuit, and that variations in
the tertiary currents might induce currents of a fourth
order, and so on. A single sudden primary current pro-
duces therefore two secondary currents (one inverse and
one direct), each of these produces two tertiary currents,
or four tertiary currents in all. But where the primary
current simply varies in strength in a periodic rise and
fall, as when a musical note is transmitted by a micro-
phone or telephone (Art. 435), there will be the same
number of secondary and tertiary fluctuations as of
primary, each separate induction involving, however, a
retardation of a quarter of the full period.
LESSON XXXVII. Magneto-electric and Dynamo-
electric Generators.
4O7. Faraday's discovery of the induction of currents
in wires by moving them across a magnetic field sug-
gested the construction of magneto-electric machines
376 ELEMENTARY LESSONS ON [CHAP. x.
to generate currents in place of voltaic batteries. In
the early attempts of Pixii (1833), Saxton, and Clarke,
bobbins of insulated wire were fixed to an axis and spun
rapidly in front of the poles of strong steel magnets.
But, since the currents thus generated were alternately
inverse and direct currents, a commutator (which rotated
with the coils) was fixed to the axis to turn the successive
currents all into the same direction. The little magneto-
electric machines, still sold by opticians, are on this
principle. Holmes and Van Malderen constructed more
powerful machines, the latter getting a nearer approach
to a continuous current by combining around one axis
sixty -four separate coils rotating between the poles of
forty powerful magnets.
In 1856 Siemens devised an improved armature, in
which the coils of wire were wound lengthways along
a spindle of peculiar form, thereby gaining the advantage
of being able to cut a greater number of lines - of- force
when rotated in the powerful " field " between the poles
of a series of adjacent steel magnets. The next im-
provement, due to Wilde, was the employment of elec-
tromagnets instead of steel magnets for producing the
" field " in which the armature revolved ; these electro-
magnets being excited by currents furnished by a small
auxiliary magneto-electric machine, also kept in rotation.
4O8. Dynamo-electric Machines. In 1867 the
suggestion was made simultaneously, but independently,
by Siemens and by Wheatstone, that a coil rotating
between the poles of an electromagnet might from the
feeble residual magnetism induce a small current, which,
when transmitted through the coils of the electromagnet,
might exalt its magnetism, and so prepare it to induce
still stronger currents. Magneto-electric machines con-
structed on this principle, the coils of their field-magnets
being placed in circuit with the coils of the rotating
armature, so as to be traversed by the whole or by a
portion of the induced currents, are known as dynamo-
CHAP, x.] ELECTRICITY AND MAGNETISM. 377
electric machines or generators, to distinguish them
from the generators in which permanent steel magnets
are employed. In either case the current is due to
magneto-electric induction ; and in either case also the
energy of the currents so induced is derived from the
dynamical power of the steam-engine or other motor
which performs the work of moving the rotating coils
of wire in the magnetic field. Of the many modern
machines on this principle the most famous are those of
Siemens, Gramme, Brush, and Edison. They differ
chiefly in the means adopted for obtaining practical con-
tinuity in the current. In all of them the electromotive-
force generated is proportional to the number of turns
of wire in the rotating armature, and (within certain
limits) to the speed of revolution. When currents of
small electromotive-force, but of considerable strength,
are required, as for electroplating, the rotating armatures
of a generator must be made with small internal resist-
ance, and therefore of a few turns of stout wire or ribbon
of sheet copper. For producing currents of high electro-
motive-force for the purpose of electric lighting, the
armature must be driven very fast, and must consist of
many turns of wire, or, where very small resistance is
necessary (as in a system of lamps arranged in parallel
arc), of rods of copper suitably connected.
There are several ways of arranging the coils upon the rotating
armature, and the methods adopted may be classified as follows :
i. Drum Armatures, in which the coils are wound longitudinally upon
the surface of a cylinder or drum. Examples : the Siemens (Alteneck)
and Edison machines.
2 Ring Armatures, in which the coils are wound around a ring. Ex-
amples : the Pacinotti, Gramme, Brush, Giilcher, and Biirgin
machines.
3. Pole Armatures, in which the coils are arranged radially with their
poles pointing outwards. Example : Lontin machine.
4. Disc Armatures, having coils arranged in or on a disc. Examples :
Niaudet, Wallace, Hopkinson, and Gordon. In an early machine by
Faraday a simple copper disc rotating between the poles of a magnet
generated a continuous current.
378 ELEMENTARY LESSONS ON [CHAP. x.
There are also several ways of arranging the coils of
the field-magnets, giving rise to following classification :
1. Series-Dynamo, wherein the coils of the field-magnets are in series
with those of the armature and the external circuit.
2. Shunt- Dynamo, in which the coils of the field-magnets form a shunt
or shunts to the main circuit ; and being made of many turns of
thinner wire, draw off only a fraction of the whole current.
3. Separately-excited Dynamo : one in which the currents used to excite
the field-magnets are derived from a separate machine.
All these varieties have their appropriate uses according to the conditions
under which they are applied. The shunt-dynamo is best for arc lamps
driven in series ; the series-dynamo or separately-excited dynamo for incan-
descent lamps worked in parallel arc.
4O9. Siemens' Machine. The dynamo -electric
generator, invented by Siemens and Von Hefner Alteneck,
usually called the Siemens' machine, is shown in Fig.
151. Upon a stout frame are fixed four powerful flat
electromagnets, the right pair having their N. -poles
facing one another and united by arched pieces or
cheeks of iron. The two S. -poles of the left pair are
similarly united. In the space between the right and
left cheeks, which is, therefore, a very intense magnetic
field, lies a horizontal axis, upon which rotates an
armature consisting of fifty -six separate longitudinal
coils, each end of each coil being connected with a
copper bar forming one segment of the collector or
commutator at the anterior end of the axis. This
armature differs from the earlier simple longitudinal
armature of Siemens only in the multiplication and
arrangement of its parts, the division into so many paths
giving a current which is practically continuous. The
collector, made up, as said, of copper bars or segments
fixed upon a cylinder of insulating material, may be
regarded as a split-tube. The current cannot pass from
one segment to the next without traversing one of
the fifty-six coils of the armature ; and, as the end of
one coil and the beginning of the next are both con-
nected to the same commutator bar, there is a continuous
communication round the whole armature. Against the
CHAP, x.] ELECTRICITY AND MAGNETISM. 379
commutator press a pair of metallic brushes or springs,
as contact pieces, which touch opposite sides at points
Fig. 151
above and below, and so lead away into the circuit the
current generated in the coils of the rotating armature.
Suppose the lines-of-force in the field to run from right
to left, 1 and the armature to rotate left-handedly, as seen
in Fig. 151, then, by the rule given in Art. 395, in all
1 Their direction is not .exactly thus when the generator is working, as
the magnetic force due to the currents in the coils, which is nearly horizontal
in direction, changes the resultant magnetic force to an oblique direction
across the field. It is for this reason that the commutator "brushes " have
to be displaced with a certain angular "lead." A similar displacement of
the brushes occurs in the Gramme and all other dynamo-ekctric generators,
the degree of displacement to get maximum strength of current varying with
the resistances in the external circuit and with the work done by the current.
380 ELEMENTARY LESSONS ON [CHAP. x.
the separate wires of the coils, moving upwards on the
right, there will be currents induced in a direction from
the back toward the front. In all the separate wires of
the coils moving downwards on the left of the axis, the
induced currents will be in a direction from the front
toward the back. Hence, if the coils are joined as
described to the commutator bars all the currents thus
generated in one half of the coils will be flowing into
the external circuit at one of the commutator brushes ;
and all the reverse currents of the other half of the coils
will be flowing out of the other brush. The terminal
screws connected by wires to the commutator brushes
correspond to the + and poles of a galvanic battery,
the coils of the field -magnets being included in the
external circuit.
41O. Gramme's Machine. In 1864 Pacinotti in-
vented a magneto-electric machine, its armature being a
toothed ring of iron with coils wound between the pro-
jections. In 1870 Gramme invented a dynamo-electric
machine having a ring armature differing only in being
completely overwound with coils of insulated copper
wires. The principle of this generator is shown in
diagram in Fig. 152. The ring itself, made of a bundle
of annealed iron wires, is wound in separate sections,
the ends of each coil being joined to strips of copper
which are insulated from each other, and fixed sym-
metrically as a commutator around the axis, like a split
tube. Their actual arrangement is shown again in Fig.
153. The coils of the separate sections of the ring are
connected together in series, each strip of the commu-
tator being united to one end of each of two adjacent
coils. Against the split -tube collector press metallic
brushes to receive the current. When this ring is rotated
the action is as follows : Suppose (in Fig. 152) the ring
to rotate in the opposite direction to the hands of a clock
in the magnetic field between the N and S-poles of a
magnet (or electro-magnet), and that the positive direc-
CHAP, x.] ELECTRICITY AND MAGNETISM. 381
tion of the lines of force is from N to S. As a matter
of fact the lines will not be straight across from N to S,
because the greater part of them will pass into the ring
near N and traverse the iron of the ring to near S, where
they emerge ; the space within the ring being almost
entirely destitute of them. Consider one single coil of
the wire wrapped round the ring at E" which is ascending
Fig. 152.
toward S ; the greatest number of lines-of-force will pass
through its plane when it lies near E", at right angles to
the line NS. As it rises toward S and comes to E the
number of lines-of-force that traverse it will be steadily
diminishing, and will reach zero when it comes close to
S and lies in the line NS, edgeways to the lines-of-force.
As it moves on toward E' it will again enclose lines-of-
force, which will, however, pass in the negative direction
through its plane, and at E' the number of such negative
lines-of-force becomes a maximum. Hence, through all
its journey from E" to E' the number of (positive) lines-
of-force embraced by a strand of the coils has been
diminishing ; during its journey round the other half from
E' to E" again, the number will be increasing. There-
fore, by the rule given in Art. 395, in all the coils moving
round the upper half of the ring direct currents are being
382 ELEMENTARY LESSONS ON [CHAP. x.
generated, while in the coils of the lower half of the ring
inverse currents are being generated. Hence there is a
constant tendency for electricity to flow from the left side
at E' both ways round towards the right side at E", and
E" will be at a higher potential than E'. A continuous
Fig. 153-
current will therefore be generated in an external wire,
making contact at F and'F by means of brushes, for as
each successive coil moves up towards the brushes the
induced current in it increases in strength, because the
coils on each side of this position are sending their
induced currents also toward that point. Fig. 153 shows
the little Gramme machine, 21 inches high, suitable for
CHAP, x.] ELECTRICITY AND MAGNETISM. 383
producing an electric arc light when driven by a 2^
horse-power engine. Above and below are opposite
pairs of powerful electro-magnets, whose iron pole-pieces
project forwards and almost embrace the central ring-
armature, which, with the commutator, is fixed to the
horizontal spindle.
411. (a) Brush's Machine. In Brush's dynamo-
electric generator, a ring-armature is also used, identical
in form with that invented by Pacinotti, the iron ring
being enlarged with protruding cheeks, with spaces be-
tween, in which the coils are wound, the coils themselves
being also somewhat differently joined, each coil being
united with that diametrically opposite to it, and having
for the pair a commutator consisting of a collar slit into
two parts. For each pair of coils there is a similar
collar, the separate collars being grouped together and
communicating to two or more pairs of brushes that rub
against them the currents which they collect in rotating.
The electromotive-force of these machines is very high,
hence they are able to drive a current through a long
row of arc lamps connected in one series. The largest
Brush machines capable of maintaining 40 arc lights
have an electromotive -force exceeding 2000 volts.
Dynamo machines having modifications of the ring-
armature have also been invented by Giilcher, Schuckert,
and others. In Giilcher's and Schuckert's machines
the ring -armature takes the form of a flattened disk,
thereby reducing the amount of " idle " wire on the
inner side of the ring. In Biirgin's machine the armature
is made up of eight or ten rings, each constructed upon
a very simple hexagonal core of iron wire, and placed
side by side upon one spindle, each ring being set
slightly in advance of its neighbour.
Siemens and others have devised another class of
dynamo-electric machines, differing entirely from any of
the preceding, in which a coil or other movable con-
ductor slides round one pole of a magnet and cuts the
384 ELEMENTARY LESSONS ON [CHAP. x.
CHAP, x.] ELECTRICITY AND MAGNETISM. 385
lines of force in a continuous manner without any reversals
in the direction of the induced currents. Such machines,
sometimes called " uni-polar " machines, have, however,
very low electromotive-force.
All and any of the continuous-current magneto-electric
and dynamo-electric machines can be used as electro-
motors, the armature rotating with considerable power
when a current from an independent source is led into
the machine.
411. (b) Edison's Machine. The largest dynamo -electric
generators hitherto made are those constructed by Edison for
his system of electric lighting. This machine (as shown in Fig.
154) is built upon the same bed-plate as the steam-engine (of
1 20 H-P) which drives it, and is called by its designer the
steam-dynamo. The field-magnets are placed horizontally, and
consist of 1 2 cylindrical iron bars overwound with wire, united to
solid iron pole-pieces weighing many tons. Between the upper
and lower pole-pieces rotates the armature, which is a modifica-
tion of the drum-armature of Siemens, and is made up of 98
long rods of copper connected by copper discs at the ends instead
of coils of wire. The commutator or collector consists of 49
parallel bars of copper, like the split-tube commutator of the
other machines. The circuit of the armature runs from one bar
of the commutator along one of the copper rods into a copper
disc at the far end, crosses by this disc to the opposite rod,
along which it comes back to the front end to another copper
disc connected to the next bar of the commutator, and so on all
round. This arrangement greatly reduces the wasteful resistance
of the armature, and adds to the efficiency of the machine. The
interior of the armature is made up of thin discs of iron strung
upon the axis to intensify the magnetic action while avoiding
the currents which would be generated wastefully (see Art. 401)
in the mass of the metal were the iron core solid. There are
also 5 pairs of brushes at the commutator to diminish sparking.
This machine has a very high efficiency, and turns 90 per cent
of the mechanical power into electrical power. It is capable of
maintaining 1300 of Edison's incandescent lamps (Art. 374)
alight at one time. When driven at 300 revolutions per minute
the current generated is about 900 amperes, and the electro-
motive-force 105 volts.
411. (c) Alternate-Current Machines. In some dynamo-
2 C
386 ELEMENTARY LESSONS ON [CHAP. x.
electric machines the alternately-directed currents generated by
the successive approach and recession of the coils to and from
the fixed magnet-poles are never commuted, but pass direct to
the circuit. In a typical machine of this class invented by
Wilde, the armature consists of a series of bobbins arranged
upon the periphery of a disk which rotates between two sets of
fixed electromagnets arranged upon circular frames, and pre-
senting N and S- poles alternately inward. The alternate-
current machine of Siemens is similar in design. Such
machines cannot excite their own field-magnets with a constant
polarity, and require a small auxiliary direct-current dynamo to
excite their magnets. In another machine, devised by De
Meritens, a ring - armature, resembling those of Pacinotti and
Brush, moves in front of permanent steel magnets? In this
machine the current induced in the circuit in one direction
while the coils approach one set of poles is immediately followed
by a current in the other direction as the coils recede from this
set of poles and approach the set of poles of contrary sign.
Alternate-current machines have also been devised by Lontin,
Gramme, and others, for use in particular systems of electric
lighting; as, for example, the Jablochkoff candle (Art. 374).
In Lontin's machine, as in the more recent and much larger
disk-dynamo of Gordon, the field-magnet coils rotate between
two great rings of fixed coils in which the currents are in-
duced. The latest form of alternate-current machine, designed
by Ferranti, differs from the machines of Wilde and Siemens in
the substitution of copper strips wound in zig-zag, for the set
of rotating bobbins in the armature. This construction had
previously been applied by Hopkinson and Muirhead.
411. (d) Combination Machines. The field -magnets of
a dynamo-electric machine are sometimes wound with two sets
of coils, so that it can be used as a combined shunt- and-series
machine (see Art. 408). Such machines, when run at a certain
"critical" speed, may be made to yield a constant current, or
to work at a constant electromotive- force whatever the resistances
in circuit. It is possible to attain either of these ends by com-
bining, in one case a shunt-winding, in the other case a series-
winding, with an independent magnetisation derived either from
a permanent magnet or from a separately-excited field magnet.
CHAP. XL] ELECTRICITY AND MAGNETISM. 387
CHAPTER XL
ELECTRO-CHEMISTRY.
LESSON XXXVI 1 1 . Electrolysis and Electrometallurgy.
412. In Lessons XIV. and XVIII. it was explained
that a definite amount of chemical action in a cell
evolves a current and transfers a certain quantity of
electricity through the circuit, and that, conversely, a
definite quantity of electricity, in passing through an
electrolytic cell, will perform there a definite amount of
chemical work. The relation between the current and
the chemical work performed by it is laid down in the
following paragraphs.
413. Electromotive - force of Polarisation.
Whenever an electrolyte is decomposed by a current,
the resolved ions have a tendency to reunite, that
tendency being commonly termed " chemical affinity."
Thus, when zinc sulphate (Zn SO 4 ) is split up into Zn
and SO 4 the zinc tends to dissolve again into the solution
by reason of its " affinity " for oxygen and for sulphuric
acid. But zinc dissolving into sulphuric acid sets up an
electromotive-force of definite amount ; and to tear the
zinc away from the sulphuric acid requires an electro-
motive-force at least as great as this, and in an opposite
direction to it. So, again, when acidulated water is*
decomposed in a voltameter, the separated hydrogen
388 ELEMENTARY LESSONS ON [CHAP. xi.
and oxygen tend to reunite and set up an opposing
electromotive -force of no less than 1*45 volts. This
opposing electromotive-force, which is in fact the measure
of their " chemical affinity " is termed the electromotive-
force of polarisation. It can be observed in any water-
voltameter (Art. 208), by simply disconnecting the
wires from the battery, and joining them to a galvan-
ometer, when a current will be observed flowing back
through the voltameter from the hydrogen electrode,
toward the oxygen electrode. The polarisation in a
voltaic cell (Art. 163) produces an opposing electro-
motive-force in a perfectly similar way.
Now, since the affinity of hydrogen for oxygen is
represented by an electromotive-force of i *4 5 volts, it is
clear that no cell or battery can decompose water unless
it has an electromotive -force at least of 1-45 volts.
With every electrolyte there is a similar minimum
electromotive-force necessary to produce complete con-
tinuous decomposition.
414. Theory of Electrolysis. Suppose a current
to convey a quantity of electricity Q through a circuit
in which there is an opposing electromotive -force E :
the work done in moving Q units of electricity against
this electromotive-force will be equal to E x Q. (If E
and Q are expressed in "absolute" C.G.S. units, E-Q
will be in ergs.) The total energy of the current, as
available for producing heat or mechanical motion, will
be diminished by this quantity, which represents the
work done against the electromotive-force in question.
But we can arrive in another way at an expression
for this same quantity of work. For the quantity of
electricity in passing through the cell will deposit a
certain amount of metal : this amount of metal could be
burned, or dissolved again in acid, giving up its potential
energy as heat, and, the mechanical equivalent of treat
toeing known, the equivalent quantity of work can be
calculated. Q units of electricity will cause the depo-
CHAP. XL] ELECTRICITY AND MAGNETISM. 389
sition of Q^ grammes of an ion whose absolute electro-
chemical equivalent is z. [For example, z for hydrogen
is -000105 gramme, being ten times the amount (see table
in Art. 2 1 2) deposited by one coulomb, for the coulomb
is T V of the absolute C.G.S. unit of quantity.] If H
represent the number of heat units evolved by one
gramme of the substance, when it enters into the com-
bination in question, then Q^H represents the value (in
heat units) of the chemical work done by the flow of the
Q units ; and this value can immediately be translated
into ergs of work by multiplying by Joule's equivalent J
( = 42 x io 6 ). [See Table on page 400.]
We have therefore the following equality :
EQ = Q*HJ ; whence it follows that
E = zH] ; or, in words, the electromotive-
force of any chemical reaction is equal to the product of
the electro-chemical equivalent of the separated ion into
its heat of combination, expressed in dynamical units.
EXAMPLES. (i) Electromotive-force of Hydrogen tending to
unite with Oxygen. For Hydrogen z -000105 5 H
(heat of combination of one gramme) = 34000 gramme-
degree-units ; J 42 x io 6 .
000105 x 34,000 x 42 x io 6 1-45 x io 8 "absolute"
units of electromotive-force, or = 1-45 volts.
(2) Electromotive-force of Zinc dissolving into Sulphuric Acid.
z -003412 ; H = 1670 (according to Julius Thomsen) ;
J = 42 x io 6 .
003412 x 1670 x 42 x io 6 = 2-394 x io 8 .
or = 2*394 volts.
(3) Electromotive-force of 'Copper dissolving into Szdphuric Acid.
z = -003307 ; H = 909-5 ; J = 42 x io 6 .
003307 x 909-5 x 42 x io 6 = i -2633 x io 8 .
or = I '2633 volts.
(4) Electromotive-force of a Daniell's Cell. Here zinc is dissolved
at one pole to form zinc sulphate, the chemical action setting
up a + electromotive-force, while at the other pole copper
is deposited by the current out of a solution of copper
sulphate, thereby setting up an opposing (or - ) electro-
390
ELEMENTARY LESSONS ON [CHAP. XL
motive-force. That due to zinc is shown above to be
+ 2*396 volts, that to deposited copper to be - 1-263.
Hence the net electromotive-force of the cell is (neglecting
the slight electromotive -force where the two solutions
touch) 2 '394 - 1*263 = 1*131 volts. This is nearly what
is found (Art. 170) in practice to be the case. It is less
than will suffice to electrolyse water, though two DanielFs
cells in series electrolyse water easily.
415. Secondary Batteries : Storage of Electric Currents.
A voltameter, or series of voltameters, whose electrodes are
thus charged respectively with hy-
drogen and oxygen, will serve as
secondary batteries, in whi f ch the
energy of a current may be stored up
(as chemical work) and again given
out. Ritter, who in 1803 con-
structed a secondary pile, used elec-
trodes of platinum. Gaston Plante,
in 1860, devised a secondaiy cell
consisting of two pieces of sheet
lead rolled up (without actual con-
tact) as electrodes, dipping into
dilute sulphuric acid, as in Fig.
155 ; the lead becoming with re-
peated charges in alternate directions
coated with a semi -porous film of
brown dioxide of lead on the anode
plate, and on the kathode plate
assuming a spongy metallic state
presenting a large amount of surface
and holding the gases well. When
such a battery, or accumulator of
currents, is charged by connecting it
with a dynamo-electric machine or
other powerful generator of currents,
the anode plate becomes peroxidised,
while the kathode plate is deoxidised by the hydrogen that
is liberated. The plates may remain for many days in this
condition, and will furnish a current until the two lead surfaces
are reduced to a chemically inactive state. The electromotive-
force of such cells may even attain from 2*10 to 2*25 volts.
Plante has ingeniously arranged batteries of such cells so that
they can be charged in parallel arc, and discharged in series,
Fig. 155-
CHAP. XL] ELECTRICITY AND MAGNETISM.
giving (for a short time) currents of extraordinary strength.
Faure, in 1881, improved the Plante accumulator by giving the
two lead plates a preliminary coating of red-lead (or minium).
When a current is passed through the cell to charge it, the red-
lead is peroxidised at the anode, and reduced, first to a con-
dition of lower oxide, then to the spongy metallic state, at the
kathode, and thus a greater thickness of the working substance
is provided, and takes far less time to form than is the case in
Plante's cells. For electric lighting, Faure's cells are made up
Fig. 156.
with flat plates in the form shown in Fig. 156. In Sellon's
and Volckmar's accumulators the minium is packed into inter-
stices in the lead plates. A secondary cell resembles a Leyden
jar in that it can be charged and then discharged. Its time-
rate of leakage is also similar. The residual charges of Leyden
jars, though small in quantity and transient in their discharge,
yet exactly resemble the polarisation charges of voltameters.
416 Grove's Gas Battery. Sir W. Grove devised a cell
in which platinum electrodes, in contact respectively with hy-
drogen and oxygen gas, replaced the usual zinc and copper plates.
Each of these gases is partially occluded by the metal platinum,
which, when so treated, behaves like a different metal. In Fig.
157 one form of Grove's Gas Battery is shown, the tubes O
and H containing the + and - electrodes, surrounded with
oxygen and hydrogen respectively.
392
ELEMENTARY LESSONS ON [CHAP. xi.
417. General Laws of Electrolytic Action. In
addition to Faraday's quantitative laws given in Art. 211,
f / the following are
important :
(a.) Every
electrolyte is de-
composed into
two portions, an
anion and a ka~
tion, which may
be themselves
either simple or
compound. In
the case of simple
binary com-
pounds, such as
fused salt (Na
Cl), the ions are
simple elements.
In other cases
the products are
often complicat-
ed by secondary
actions. It is
even possible to
deposit an alloy
of two metals
brass for example
from a mix-
ture of the cya-
nides of zinc and
of copper.
(<.) In binary compounds and most metallic solutions,
the metal is deposited by the current where it leaves the
cell, at the kathode.
(c.) Aqueous solutions of salts of the metals of the
alkalies and alkaline earths deposit no metal, but evolve
Fig. 157.
CHAP. XL] ELECTRICITY AND MAGNETISM. 393
hydrogen owing to secondary action of the metal upon
the water. From strong solutions of caustic potash and /
soda Davy succeeded in obtaining metallic sodium and \
potassium, which were before unknown. If electrodes of \
mercury are employed, an amalgam of either of these
metals is readily obtained at the kathode. The so-
called ammonium-amalgam is obtained by electrolysing a
warm, strong solution of salammoniac between mercury
electrodes.
(d.) Substances can be arranged in a definite series
according to their electrolytic behaviour ; each substance
on the list behaving as a kathion (or being " electroposi-
tive ") when electrolysed from its compound with any
other on the list. In such a series the oxidisable metals,
potassium, sodium, zinc, etc., head the list ; after which
come the less oxidisable or "electronegative" metals ; then
carbon, oxygen, phosphorus, iodine, chlorine, sulphur,
and lastly ozone.
(e.) From a solution of mixed metallic salts the least
electropositive metal is deposited first, unless the current
be very strong.
(f.) The liberated ions appear only at the elec-
trodes.
(g) For each electrolyte a minimum electromotive-
force is requisite, without which complete electrolysis
cannot be effected. (See Art. 413.)
(h.) If the current be of less electromotive-force than
the requisite minimum, electrolysis may begin, and a
feeble current flow at first, but no ions will be liberated,
the current being completely stopped as soon as the
opposing electromotive-force of polarisation has risen to
equality with that of the electrolysing current.
(/.) There is no opposing electromotive-force of polar-
isation when electrolysis is effected from an anode of the
same metal that is being deposited at the kathode. The
feeblest cell will suffice to deposit copper from sulphate of
copper if the anode be a copper plate.
394 ELEMENTARY LESSONS ON [CHAP. XL
(/.) Where the ions are gases, pressure affects the
conditions. Under a pressure of 300 atmospheres acid-
ulated water is not electrolysed, and behaves as an
insulator.
(/.) The chemical work done by a current in an
electrolytic cell is proportional to the minimum electro-
motive-force of polarisation.
(/.) Although the electromotive-force of polarisation
may exceed this minimum, the work done by the current
in overcoming this surplus electromotive-force will not
appear as chemical work, for no more of the ion will be
liberated ; but it will appear as an additional quantity of
heat (or " local heat ") developed in the electrolytic cell.
(m.) Ohm's law holds good for electrolytic conduction
as well as for metallic conductors.
(n.) Amongst the secondary actions which may occur
the following are the chief: (i.) The ions may them-
selves decompose ; as SO 4 into SO 3 + O. (2.) The ions
may react on the electrodes ; as when acidulated water
is electrolysed between zinc electrodes, no oxygen being
liberated, owing to the affinity of zinc for oxygen. (3.)
The ions may be liberated in an abnormal state. Thus
oxygen is frequently liberated in its allotropic condition
as ozone, particularly when permanganates are electro-
lysed. The " nascent " hydrogen liberated by the elec-
trolysis of dilute acid has peculiarly active chemical
properties. So also the metals are sometimes deposited
abnormally : copper in a black pulverulent film ; anti-
mony in roundish gray masses (from the terchloride
solution) which possess a curious explosive property, etc.
418. Hypotheses of Grotthuss and of Clau-
sius. A complete theory of electrolysis must explain
firstly, the transfer of electricity, and, secondly ', the transfer
of matter, through the liquid of the cell. The latter
point is the one to which most attention has been
given, since the " migration of the ions " (i.e. their trans-
fer through the liquid) in two opposite directions, and
CHAP, xi.] ELECTRICITY AND MAGNETISM.
395
their appearance at the electrodes only, are salient
facts.
The hypothesis put forward in 1805 by Grotthuss
serves fairly, when stated in accordance with modern
terms, to explain these facts. Grotthuss supposes that,
when two metal plates at different potentials are placed
in a cell, the first effect produced in the liquid is that
the molecules of the liquid arrange themselves in in-
numerable chains, in which every molecule has its
constituent atoms pointing in a certain direction ; the
atom of electropositive substance being attracted toward
the kathode, and the fellow atom of electronegative
substance being attracted toward the anode. (This
assumes the constituent atoms grouped in the molecule
to retain their individual electric properties.) The
diagram of Fig. 158 shows, in the case of Hydrochloric
Fig. 158.
Acid, a row of molecules i, i, at first distributed at
random, and secondly (as at 2, 2,) grouped in a chain
as described. The action which Grotthuss then sup-
poses to take place is that an interchange of partners
goes on between the separate atoms all along the line,-
396 ELEMENTARY LESSONS ON [CHAP. xi.
each H atom uniting with the Cl atom belonging to the
neighbouring molecule, a + half molecule of hydrogen
being liberated at the kathode, and a half molecule
of chlorine at the anode. This action would leave the
molecules as in 3, 3, and would, when repeated, result
in a double migration of hydrogen atoms in one direc-
tion and of chlorine atoms in the other, the free atoms
appearing only at the electrodes, and every atom so
liberated discharging a certain definite minute charge of
electricity upon the electrode where it was liberated. 1
Clausius has sought to bring the ideas of Grotthuss
into conformity with the modern kinetic hypothesis of
the constitution of liquids. Accordingly, we are to
suppose that in the usual state of a liquid the molecules
are always in movement, gliding about amongst one
another, and their constituent atoms are also in move-
ment, and are continually separating and recombining
into similar groups, their movements taking place in all
possible directions throughout the liquid. But under
the influence of an electromotive-force these actions are
controlled in direction, so that when, in the course of the
usual movements, an atom separates from a group it
tends to move either toward the anode or kathode ;
and if the electromotive force in question be powerful
enough to prevent recombination, these atoms will be
permanently separated, and will accumulate around the
electrodes. This theory has the advantage of account-
ing for a fact easily observed, that an electromotive force
less than the minimum which is needed to effect com-
plete electrolysis may send a feeble current through an
1 Mr. G. J. Stoney has lately reckoned, from considerations founded on
the size of atoms (as calculated by Loschmidt and Sir W. Thomson), that
for every chemical bond ruptured, a charge of 10 2O of a coulomb is trans-
ferred. This quantity would appear therefore to be the natural atomic
charge or unit. To tear one atom of hydrogen from a hydrogen compound
this amount of electricity must be sent through it. To liberate an atom of
zinc, or any other di-valent metal from its compound, implies the transfer
of twice this amount of electricity.
CHAP. XL] ELECTRICITY AND MAGNETISM. 397
electrolyte for a limited time, until the opposing electro-
motive force has reached an equal value. Helmholtz,
who has given the name of electrolytic convection to this
phenomenon of partial electrolysis, assumes that it takes
place by the agency of uncombined atoms previously
existing in the liquid. This assumption is virtually in-
cluded in the kinetic hypothesis of Clausius.
419. Electrometallurgy. The applications of elec-
tro-chemistry to the industries are threefold. Firstly,
to the reduction of metals from solutions of their ores,
a process too costly for general application, but one
useful in the accurate assay of certain ores, as, for
example, of copper ; secondly, to the copying of types,
plaster casts, and metal -work by kathode deposits of
metal ; thirdly, to the covering of objects made of baser
metal with a thin film of another metal, such as gold,
silver, or nickel. All these operations are included
under the general term of electrometallurgy.
420. Electrotyping". In 1836 De La Rue ob-
served that in a Daniell's cell the copper deposited out
of the solution upon the copper plate which served as a
pole took the exact impress of the plate, even to the
scratches upon it. In 1839 Jacobi in St. Petersburg,
Spencer in Liverpool, and Jordan in London, independ-
ently developed out of this fact a method of obtaining,
by the electrolysis of copper, impressions (m^reversed
relief) of coins, stereotype plates, and ornaments. A
further improvement, due to Murray, was the employment
of moulds of plaster or wax, coated with a film of plum-
bago in order to provide a conducting surface upon
which the deposit could be made. Jacobi gave to the
process the name of galvano-plastic, a term generally
abandoned in favour of the term electrotyping 1 or
electrotype process.
Electrotypes of copper are easily made by hanging a
suitable mould in cell containing a saturated solution of
sulphate of copper, and passing a current of a battery
398 ELEMENTARY LESSONS ON [CHAP. XL
through the cell, the mould being the kathode ; a plate
of copper being employed as an anode, dissolving gradu-
ally into the liquid at a rate exactly equal to the rate of
deposition at the kathode. This use of a separate
battery is more convenient than producing the electro-
types in the actual cell of a Daniell's battery. The
process is largely employed at the present day to repro-
duce repouss and chased ornament and other works of
art in facsimile, and to multiply copies of wood blocks
for printing. Almost all the illustrations in this book,
for example, are printed from electrotype copies, and not
from the original wood blocks, which would not wear so
well.
421. Electroplating. In 1801 Wollaston observed
that a piece of silver, connected with a more positive
metal, became coated with copper when put into a
solution of copper. In 1805 Brugnatelli gilded two
silver medals by making them the kathodes of a cell
containing a solution of gold. Messrs. Elkington, about
the year 1840, introduced the commercial processes of
electroplating. In these processes a baser metal, such
as German silver (an alloy of zinc, copper, and nickel)
is covered with a thin film of silver or gold, the solutions
employed being, for electro -gilding^ the double cyanide
of gold and potassium, and for electro -silvering the
double cyanide of silver and potassium.
Fig. 159 shows a battery and a plating- vat containing
the silver solution. From the anode is hung a plate of
metallic silver which dissolves into the liquid. To the
kathode are suspended the spoons, forks, or other
articles which are to receive a coating of silver. The
addition of a minute trace of bisulphide of carbon to the
solution causes the deposited metal to have a bright
surface. If the current is too strong, and the deposition
too rapid, the deposited metal is grayish and crystalline.
In silvering or gilding objects of iron it is usual first
to plate them with a thin coating of copper. In gilding
CHAP. XL] ELECTRICITY AND MAGNETISM. 399
base metals, such as pewter, they are usually first
copper-coated. The gilding of the insides of jugs and
cups is effected by filling the jug or cup with the gilding
solution, and suspending in it an anode of gold, the vessel
itself being connected to the pole of the battery.
Fig. 159-
Instead of a battery a thermo-electric generator (Art.
384), or a dynamo-electric generator (Art. 408), is now
frequently employed.
422. Metallo-cnromy. In 1826 Nobili discovered that when
a solution of lead is electrolysed a film of peroxide of lead forms
upon the anode. If this be a sheet of metal, a plate of
polished steel, for instance, placed horizontally in the liquid
beneath a platinum wire as a kathode, the deposit takes place
in symmetrical rings of varying thickness, the thickest deposit
being at the centre. These rings, known as Nobili's rings,
exhibit all the tints of the rainbow, owing to interference of
the waves of light occurring in the film causing rays of different
wave-length and colour to be suppressed at different distances
from the centre. The colours form, in fact, in reversed order,
the " colours of thin plates" of Newton's rings. According
to Wagner this production of chromatic effects by electrolysing
a solution of lead in caustic soda, is applied in Nuremberg to
ornament metallic toys. The author of these Lessons has
observed that when Nobili's rings are made in a magnetic
400
ELEMENTARY LESSONS ON [CHAP. xi.
field they are no longer circular, the depositing currents being
drawn aside in a manner which could be predicted from the
observed action of magnets on conductors carrying currents.
422 (bis). Electro - Chemical Power of Metals. The
following Table gives the electromotive - force of the different
metals as calculated by the method of Art. 414 from their
electro - chemical equivalents (Art. 212), and from the heat
evolved by the combination with oxygen of a portion of the
metal equivalent electro-chemically in amount to one gramme
of hydrogen. The electromotive - forces (in volts) as observed
(in dilute sulphuric acid) are added for comparison.
Substance.
Heat of
Equivalent.
E. M. F. calculated.
E. M. F.
observed.
Relatively
to Oxygen.
Relatively
to Zinc.
Potassium
69,800
3^5
+ ri8
+ 1*14
Sodium
67,800
2-95
+ 1*09
Zinc . . . ".
42,700
1-86
O
Iron ....
34,120
i '57
-0'29
Hydrogen
34,000
1-49
-0-37
Lead ....
25,100
1-13
-073
-o*55
Copper . . .
18,760
0-81
- '05
-1-079
Silver ....
9,000
0-39
- '47
Platinum .
7,500
o'33
- '53
-i'55
Carbon
2,000
0*09
- 75
Oxygen . . .
o
0'
- -86
- i' ; 873
(Nitric Acid) .
- 6,000
-0*26
-2'12
-1-96
(Black Oxide of )
Manganese) (
(Peroxide of Lead)
- 6,500
-12,150
-0*29
-o'53
-2-15
-2'39
-2-25
-2-55
(Ozone)
- 14,800
-0*64
-2'50
-2-67
The order in which these metals are arranged is in fact nothing else than
the order of oxidisability of the metals (in the presence of dilute sulphuric
acid) ; for that metal tends most to oxidise which can, by oxidising, give out
the most energy. It also shows the order in which the metals stand in their
power to replace one another (in a solution containing sulphuric acid.) In
this order too, the lowest on the list first, are the metals deposited by an
electric current from solutions containing two or more of them : for that
metal comes down first which requires the least expenditure of energy to
separate it from the elements with which it was combined.
CHAP. XIL] ELECTRICITY AND MAGNETISM. 401
CHAPTER XII.
TELEGRAPHS AND TELEPHONES.
LESSON XXXIX. Electric Telegraphs.
423. The Electric Telegraph. It is difficult to assign the
invention of the Telegraph to any particular inventor. Lesage
(Geneva, 1774), Lomond (Paris, 1787), and Sir F. Ronalds
(London, 1816), invented systems for transmitting signals
through wires by observing at one end the divergence of a pair
of pith-balls when a charge of electricity was sent into the other
end. Cavallo (London, 1795) transmitted sparks from Leyden
jars through wires "according to a settled plan." Soemmering
(Munich, 1808) established a telegraph in which the signals
were made by the decomposition of water in voltameters ; and
the transmission of signals by the chemical decomposition of
substances was attempted by Coxe, R. Smith, Bain, and others.
Ampere (Paris, 1821) suggested that a galvanometer placed at
a distant point of a circuit might serve for the transmission of
signals. Schilling and Weber (Gottingen, 1833) employed the
deflections of a galvanometer needle moving to right or left to
signal an alphabetic code of letters upon a single circuit.
Cooke and Wheatstone (London, 1837) brought into practical
application the first form of their needle telegraph. Henry
(New York, 1831) utilised the attraction of an electromagnet
to transmit signals, the movement of the armature producing
audible sounds according to a certain code. Morse (New York,
1837) devised a telegraph in which the attraction of an arma-
ture by an electromagnet was made to mark a dot or a dash
upon a moving strip of paper. Steinheil (Munich, 1837)
discovered that instead of a return-wire the earth might be used,
contact being made to earth at the two ends by means of earth -
2 D
402
ELEMENTARY LESSONS ON [CHAP. xn.
plates (see Fig. 160) sunk in the ground. Gintl (1853) and
Stearns (New York, 1870) devised methods of duplex signalling.
Stark (Vienna) and Bosscha (Leyden, 1855) invented dipkx
signalling, and Edison (Newark, N. J., 1874) invented quad-
ruplex telegraphy. For fast-speed work Wheatstone devised his
automatic transmitter, in which the signs which represent the
letters are first punched by machinery on strips of paper ; these
are then run at a great speed through the transmitting instru-
ment, which telegraphs them off at a much greater rate than if
the separate signals were telegraphed by hand. Hughes devised
a type-printing telegraph. Wheatstone invented an ABC tele-
graph in which signals are spelled by a hand which moves over
a dial. For cable- working Sir W. Thomson invented his mirror
galvanometer and his delicate siphon-recorder. It is impossible
in these Lessons to describe more than one or two of the
simpler and more frequent forms of telegraphic instruments.
Students desiring further information should consult the excel-
lent manuals on Telegraphy by Messrs. Preece and Sivewright,
and by Mr. Culley.
424. Single -Needle Instrument. The single^
needle instrument (Fig. 160) consists essentially of a
vertical galvan-
ometer, in which
a lightly hung
magnetic needle
is deflected to
right or left
when a current
is sent, in one
direction or the
other, around a
coil surrounding
the needle ; the
needle visible in
front of the dial
is but an index,
the real magnetic needle being behind. A code of
movements agreed upon comprises the whole alphabet
in combinations of motions to right or left. In order
Fig. 1 60.
CHAP, xii.] ELECTRICITY AND MAGNETISM. 403
to send currents in either direction through the circuit,
a " signalling-key " or " tapper " is usually employed.
The tapper at one end of the line works the instru-
ment at the other ; but for the sake of convenience it
is fixed to the receiving instrument. In Fig. 160 the
two protruding levers at the base form the tapper, and
by depressing the right hand one or the left hand one,
currents are sent in either direction at will.
The principle of action will be made more clear by
reference to Fig. 161, which shows a separate signalling
key. The two
horizontal levers
are respectively
in communica-
tion with the
'Mine," and with
the return - line
through "earth."
When not in use
they both spring Fig- l6l .
up against a cross
strip of metal joined to the zinc pole of the battery.
Below them is another cross strip, which communicates
with the copper (or- + ) pole of the battery. On
depressing the " line " key the current runs through the
line and back by earth, or in the positive direction.
On depressing the " earth " key (the line key remaining
in contact with the zinc-connected strip), the current
runs through the earth and back by the line, or in the
negative direction. Telegraphists ordinarily speak of
these as positive and negative currents respectively.
As it is necessary that a line should be capable of
being worked from either end, a battery is used at each,
and the wires so connected that when at either end a
message is being received, the battery circuit at that end
shall be open. Fig. 162 shows the simplest possible
case of such an arrangement. At one end is a battery
404
ELEMENTARY LESSONS ON [CHAP. xn.
zc, one pole of which is put to earth, and the other com-
municates with a key K. This key is arranged (like that
in Fig. 164), so that when it is depressed, so as to send
a signal through the line, it quits contact with the
receiving instrument at its own end. The current
flowing through the line passes through K' and enters a
Fig. 162.
receiving instrument G' at the distant end, where it pro-
duces a signal, and returns by the earth to the battery
whence it started. A similar battery and key at the
distant end suffice to transmit signals in the opposite
direction to G when K is not depressed. The diagram
is drawn as if G were a simple galvanometer ; but the
arrangement would perfectly suit the Morse instrument,
in which it is only required at either end to send long
and short currents without reversing the direction.
425. The Morse Instrument. The most widely
used instrument at the present day is the Morse. The
Morse instrument consists essentially of an electro-
magnet, which, when a current passes through its coils,
draws down an armature for a short or a long time.
CHAP. XIL] ELECTRICITY AND MAGNETISM. 405
It may either be arranged as a "sounder" in which
case the operator who is receiving the message listens
to the clicks and notices whether the intervals between
them are long or short; or it may be arranged as an
" embosser" to print dots and dashes upon a strip of paper
drawn by clockwork through the instrument. In the
most modern form, however, the Morse instrument is
arranged as an "ink-writer" in which the attraction of
the armature downwards lifts a little inky wheel and
pushes it against a ribbon of paper. If the current is
momentary it prints a mere dot. If the current con-
tinues to flow for a longer time the ribbon of paper moves
on and the ink-wheel marks a dash. The Morse code,
or alphabet of dots and dashes, is as follows :
A . K . U . .
B ... L . . . V . . . -
C . . M W. -
D . . N . X . . -
J ^ Q Y .
F ! . . P . . Z . .
G . Q . Full stop
H . . . . R . , Repetition . . - - . .
I . . S . . . Hyphen ....-
J . T Apostrophe . . .
426. Relay. In working over long lines, or where
there are a number of instruments on one circuit, the
currents are -often not strong enough to work the
recording instrument directly. In such a case there is
interposed a relay or repeater. This instrument con-
sists of an electromagnet round which the line current
flows, and whose delicately poised armature, when
attracted, makes contact for a local circuit in which a
local battery and the receiving Morse instrument are
included. The principle of Jhe relay is, then, that a
current too weak to do the work itself may set a strong
local current to do its work for it.
406
ELEMENTARY LESSONS ON [CHAP. xn.
In Fig. 163 is shown a Morse instrument (an "em-
bosser ") M, joined in circuit with a local battery B, and
Earth
Line, Battery
Fig 163.
a relay. Whenever a current in the line circuit moves
the tongue of the relay it closes the local circuit, and
causes the Morse to record either a dot or a dash upon
the strip of paper. The key K is shown in an enlarged
K
Fig. 164.
view in Fig. 164. The line wire is connected with the
central pivot A. A spring /keeps the front end of the
key elevated when not in use, so that the line wire is in
CHAP, xii.] ELECTRICITY AND MAGNETISM. 407
communication through the rear end of the key with the
relay or receiving instrument, Depressing the key breaks
this communication, and by putting the line wire in com-
munication with the main battery transmits a current
through the line.
427. Faults in Telegraph Lines. Faults may
occur in telegraph lines from several causes : either from
the breakage of the wires or conductors, or from the
breakage of the insulators, thereby short-circuiting the
current through the earth before it reaches the distant
station, or, as in overhead wires, by two conducting
wires touching one another. Various modes for testing
the existence and position of faults are known to telegraph
engineers ; they depend upon accurate measurements of
resistance or of capacity. Thus, if a telegraph cable part
in mid-ocean it is possible to calculate the distance from
the shore end to the broken end by comparing the resist-
ance that the cable is known to offer per mile with the
resistance offered by the length up to the fault, and divid-
ing the latter by the former.
428. Duplex Telegraphy. There are two distinct
methods of arranging telegraphic apparatus so as to
transmit two messages through one wire, one from each
end, at the same time. The first of these, known as
the differential method, involves the use of instruments
wound with differential coils, and is applicable to special
cases. The second method of duplex working, known
as the WheatstonJs Bridge Method, is capable of much
more general application. The diagram of Fig. 165
will explain the general principle. The first require-
ment in duplex working is that the instrument at each
end shall only move in response to signals from the
other end, so that an operator at R may be able to.
signal to the distant instrument M' without his own
instrument M being affected, M being all the while in
circuit and able to receive signals from the distant
operator at R'. To accomplish this the circuit is
408 ELEMENTARY LESSONS ON [CHAP. xn.
divided at R into two branches, which go, by A and
B respectively, the one to the line, the other through
a certain resistance P to the earth. If the ratio
between the resistances in the arms RA and RB is
equal to the ratio of the resistances of the line and of
P, then, by the principle of Wheatstone's Bridge, no
current will pass through M. So M does not show any
currents sent from R ; but M' will show them, for the
current on arriving at C will divide into two parts, part
flowing round to the earth by R', the other part flowing
Fig. 165.
through M' and producing a signal. If, while this is
going on, the operator at the distant R' depresses his
key and sends an equal current in the opposite direction,
the flow through the line will cease ; but M will now
show a signal, because, although no current flows
through the line, the current in the branch RA will
now flow down through M, as if it had come from the
distant R', so, whether the operator at R be signalling
or not, M will respond to signals sent from R'.
The Diplex method of working consists in sending
two messages at once through a wire in the same direc-
tion. To do this it is needful to employ instruments
which work only with currents in one given direction.
The method involves the use of " relays " in which the
armatures are themselves permanently magnetised (or
" polarised "), and which therefore respond only to
currents in one direction.
The Quadruplex method of working combines the
CHAP, xii.] ELECTRICITY AND MAGNETISM. 409
duplex and the diplex methods. On one and the same
line are used two sets of instruments, one of which
(worked by a "polarised" relay) works only when the
direction of the current is changed, the other of which
(worked by a non-polarised relay adjusted with springs
to move only with a certain minimum force) works only
when the strength of the current is changed and is inde-
pendent of their direction.
429. Submarine Telegraphy. Telegraphic corn-
Fig. 1 6 6.
munication between two countries separated by a strait
or ocean is carried on through cables, sunk to the
410 ELEMENTARY LESSONS ON [CHAP. XH.
bottom of the sea, which carry conducting wires care-
fully protected by an outer sheath of insulating and
protecting materials. The conductor is usually of purest
copper wire, weighing from 70 to 400 Ibs. per nauti-
cal mile, made in a sevenfold strand to lessen risk
of breaking. Fig. 166 shows, in their natural size,
portions of the Atlantic cables laid in 1857 and 1866
respectively. In the latter cable, which is of the usual
type of cable for long lines, the core is protected first by
\ a stout layer of guttapercha, then by a woven coating of
jute, and outside all an external sheath made of ten iron
wires, each covered with hemp. The shore ends are even
more strongly protected by external wires.
43O. Speed of Signalling through Cables.
Signals transmitted through long cables are retarded, the
retardation being due to two causes.
Firstly, The self-induction of the circuit may prevent
the current from rising at once to its height, the retarda-
tion being expressed by Helmholtz's equations, given in
Art. 405.
Secondly, The cable in its insulating sheath, when
immersed in water, acts like a Leyden jar of enormous
capacity (as explained in Art. 274), and the first portions
of the current, instead of flowing through, remain in the
cable as an electrostatic charge. For every separate
signal the cable must be at least partially charged and
then discharged. Culley states that when a current is
sent through an Atlantic cable from Ireland to New-
foundland no effect is produced on the most delicate
instrument at the receiving end for two-tenths of a
second, and that it requires three seconds for the current
to gain its full strength, rising in an electric wave which
travels forward through the cable. The strength of the
current falls gradually also when the circuit is broken.
The greater part of this retardation is due to electrostatic
charge, not to electromagnetic self-induction ; the re-
tardation being proportional to the square of the length
CHAP. XIL] ELECTRICITY AND MAGNETISM. 411
of the cable. The various means adopted to get rid of
this retardation are explained in Art. 275.
431. Receiving Instruments for Cables. The
mirror-galvanometer of Sir W. Thomson (Art. 202) was
devised for cable signalling, the movements of the spot
of light sweeping over the scale to a short or a long
distance sufficing to signal the dots and dashes of the
Morse code. The Siphon Recorder of Sir W. Thomson
is an instrument which writes the signals upon a strip of
paper by the following ingenious means : The needle
part of a powerful and sensitive galvanometer is replaced
by a fine siphon of glass suspended by a silk fibre, one
end of which dips into an ink vessel. The ink is spurted
without friction upon a strip of paper (moved by clock-
work vertically past the siphon), the spurting being
accomplished electrically by charging the ink vessel by
a continuous electrophorus, which is itself worked by a
small electromagnetic engine.
LESSON XL. Electric Bells, Clocks, and Telephones.
432. Electric Bells. The common form of Electric
Bell or Trembler consists of an electromagnet, which
moves a hammer backward and forward by alternately
attracting and releasing it, so that it beats against a bell.
The arrangements of the instrument are shown in Fig.
167, in which E is the electromagnet and H the hammer.
A battery, consisting of one or two Leclanch cells placed
at some convenient point of the circuit, provides a current
when required. By touching the " push " P, the circuit
is completed, and a current flows along the line and
round the coils of the electromagnet, which forthwith
attracts a small piece of soft iron attached to the lever,
which terminates in the hammer H. The lever is itself
included in the circuit, the current entering it above and
quitting it at C by a contact-breaker, consisting of a
spring tipped with platinum resting against the platinum
412
ELEMENTARY LESSONS ON [CHAP. xn.
tip of a screw, from which a return wire passes back to
the zinc pole of the battery. As soon as the lever is
attracted forward the circuit is broken at C by the spring
moving away from contact with the screw ; hence the
current stops, and the electromagnet ceases to attract the
armature. The lever and hammer therefore fall back,
Fig. 167.
again establishing contact at C, whereupon the hammer
is once more attracted forward, and so on. The push
P is shown in section on the right of Fig. 167. It
usually consists of a cylindrical knob of ivory or porcelain
capable of moving loosely through a hole in a circular
support of porcelain or wood, and which, when pressed,
forces a platinum-tipped spring against a metal pin, and
so makes electrical contact between the two parts of the
interrupted circuit.
433. Electric Clocks. Clocks may be either driven
or controlled by electric currents. Bain, Hipp, and
others, have devised electric clocks of the first kind, in
which the ordinary motive power of a weight or spring is
CHAP, xii.] ELECTRICITY AND MAGNETISM. 413
abandoned, the clock being driven by its pendulum, the
" bob " of which is an electromagnet alternately attracted
from side to side. The difficulty of maintaining a perfectly
constant battery current has prevented such clocks from
coming into use.
Electrically controlled clocks, governed by a standard
central clock, have proved a more fruitful invention. In
these the standard timekeeper is constructed so as to
complete a circuit periodically, once every minute or half
minute. The transmitted currents set in movement the
hands of a system of dials placed at distant points, by
causing an electromagnet placed behind each dial to
attract an armature, which, acting upon a ratchet wheel
by a pawl, causes it to move forward through one tooth
at each specified interval, and so carries the hands round
at the same rate as those of the standard clock.
Electric chronographs are used for measuring very small in-
tervals of time. A style fixed to the armature of an electro-
magnet traces a line upon a piece of paper fixed to a cylinder
revolving by clockwork. A current sent through the coils of
the electromagnet moves the armature and causes a lateral notch
in the line so traced. Two currents are marked by two notches ;
and from the interval of space between the two notches the in-
terval of time which elapsed between the two currents may be
calculated to the ten-thousandth part of a second if the speed
of rotation is accurately known. The velocity with which a
cannon ball moves along the bore of the cannon can be measured
thus.
434. Electric Telephones. The first successful
attempt to transmit sounds electrically was made in
1 86 1 by Reis, who succeeded in conveying musical and
other tones by an imperfect telephone. In this instru-
ment the voice was caused to act upon a point of loose
contact in an electric circuit, and by bringing those parts
into greater or less intimacy of contact (Art. 346), thereby
varied the resistance offered to the circuit. The trans-
mitting part of Reis's telephone consisted of a battery
and a contact-breaker, the latter being formed of a tym-
414 ELEMENTARY LESSONS ON [CHAP. xn.
panum or diaphragm of stretched membrane, capable of
taking up sonorous vibrations, and having attached to
it a thin elastic strip of platinum, which, as it vibrated,
beat to and fro against the tip of a platinum wire, so
making and breaking contact wholly or partially at each
vibration in exactly the same manner as is done with the
carbon contacts in the modern transmitters of Blake,
Berliner, etc. The receiving pa# of the instrument
consisted of an iron wire fixed upon a sounding-board
and surrounded by a coil of insulated wire forming part
of the circuit. The rapid magnetisation and demag-
netisation of such an iron core will produce audible
sounds (Art. 1 1 3), which, since the pitch of a note
depends only on the frequency and not on the form or
amplitude of the vibrations, will reproduce the pitch of a
note sung into the transmitting part. If the current vary
less abruptly, the iron wire is partially magnetised and
demagnetised, giving rise in turn to vibrations of varying
amplitudes and forms ; hence such a wire will serve
perfectly as a receiver to reproduce speech if a good
transmitter is used. Reis himself transmitted speech
with his instrument, but only imperfectly, for the tones
of speech cannot be transmitted by abrupt interruptions
of the current, to which Reis's transmitter is prone when
spoken into, owing to the extreme lightness of the con-
tact : they require gentle undulations, sometimes simple,
sometimes complex, according to the nature of the sound.
The vowel sounds are produced by periodic and complex
movements in the air ; the consonants being for the most
part non-periodic. If the parts in contact be not too
light, and speech be not too loud, Reis's transmitter
works fairly as a transmitter, the platinum contacts when
clean serving as a satisfactory current-regulator to vary
the current in proportion to the vibrations of the voice.
Reis also devised a second receiver, in which an electro-magnet
attracted an elastically-supported armature of iron, which vibrated
under the attraction of the more or less interrupted current.
CHAP, xii.] ELECTRICITY AND MAGNETISM. 415
435. Graham Bell's Telephone. In 1876 Graham
Bell invented the magneto-telephone. In this instrument
the speaker talks to an elastic plate of thin sheet iron,
which vibrates and transmits its every movement electric-
ally to a similar plate in a similar telephone at a distant
station, causing it to vibrate in an identical manner, and
therefore to emit identical sounds. The transmission of i
the vibrations depends upon the principles of magneto- ;
electric induction explained in Lesson XXXVI. Fig. '
1 68 shows Bell's Tele-
phone in its latest form,
and its internal parts in
section. The disc D is
placed behind a conical
mouthpiece, to which the
speaker places his mouth
or the hearer his ear.
Behind the disc is a mag-
net A A running the length
of the instrument ; and
upon its front pole, which
nearly touches the disc,
is fixed a small bobbin,
Fig. 168.
1 on which is wound a coil C of fine insulated wire, the
ends of the coil being connected with the terminal screws
F F. One such instrument is used to transmit, and one
to receive, the sounds, the two telephones being con-
nected in simple circuit. No battery is needed, for the
transmitting instrument itself generates the induced
currents as follows : The magnet AA induces a certain
number of lines-of-force through the coil C. Many of
these pass into the iron disc. When the iron disc in
vibrating moves towards the magnet-pole, more lines-of
force meet it ; when it recedes, fewer lines-of-force meet
it. Its motion to and fro will therefore alter the number
of lines-of-force which pass through the hollow of the coil
C, and will therefore (Art. 394) generate in the wire of
416 ELEMENTARY LESSONS ON [CHAP. xn.
the coils currents whose strength is proportional to the
rate of change in the number of the lines-of-force which
pass through the coil. Bell's telephone, when used as
a transmitter, may therefore be regarded as a sort of
magneto-electric generator, which, by vibrating to and
fro, pumps currents in alternate directions into the wire.
At the distant end the currents as they arrive flow round
the coils either in one direction or the other, and there-
fore either add momentarily to or take from the strength
of the magnet. When the current in the coils is in such
a direction as to reinforce the magnet, the magnet attracts
the iron disc in front of it more strongly than before. If
the current is in the opposite direction the disc is less
attracted and flies back. Hence, whatever movement is
imparted to the disc of the transmitting telephone, the
disc of the distant receiving telephone is forced to repeat,
and it therefore throws the air into similar vibrations,
and so reproduces the sound. Bell's Telephone, used
as a receiver, differs only from the second receiver of
Reis in having as its armature a thin elastic iron plate
instead of an iron bar oscillating on an elastic support,
and in having its central magnet of steel instead of
iron.
436. Edison's Telephone. Edison constructed a
telephone for transmitting speech, in which the vibrations
of the voice, actuating a diaphragm of mica, made it
exert more or less compression on a button of prepared
lamp-black placed in the circuit. The resistance of this
is affected by pressure of contacts ; hence the varying
pressures due to the vibrations cause the button to offer
a varying resistance to any current flowing (from a battery)
in the circuit, and vary its strength accordingly. This
varying current may be received as before in an electro-
magnetic receiver of the type described above, and there
set up corresponding vibrations. Edison has also in-
vented a Telephone Receiver of singular power, which
depends upon a curious fact discovered by himself, namely,
CHAP, xii.] ELECTRICITY AND MAGNETISM. 417
that if a platinum point presses against a rotating cylinder
of moist chalk, the friction is reduced when a current
passes between the two. And if the point be attached
to an elastic disc, the latter is thrown into vibrations
corresponding to the fluctuating currents coming from
'the speaker's transmitting instrument.
Fig. 169.
436 (bis). Dolbear's Telephone. Telephone Re-
ceivers have also been invented by Varley and Dolbear,
in which the attraction between the oppositely-electrified
armatures of a condenser is utilised in the production of
sounds. The transmitter is placed in circuit with the
primary wire of a small induction-coil ; the secondary
wire of this coil is united through the line to the receiving
condenser. In Dolbear's telephone the receiver consists
merely of two thin metal discs, separated by a very thin
air-space, and respectively united to the two ends of the
secondary coil. As the varying currents flow into and
out of this condenser the two discs attract one another
more or less strongly, and thereby vibrations are set
2 E
418 ELEMENTARY LESSONS ON [CHAP. xn.
up which correspond to the vibrations of the original
sound.
437. Hughes' Microphone. Hughes, in 1878,
discovered that a loose contact between two conductors,
forming part of a circuit in which a small battery and a
receiving telephone are included, may serve to transmit
sounds without the intervention of any specific tympanum
or diaphragm like those of Reis and Edison, because the
smallest vibrations will effect the amount of the resistance
at the point of loose-contact, if the latter be delicately
set. The Microphone (Fig. 169) embodies this prin-
ciple. In the form shown in the figure, a small thin
pencil of carbon is supported loosely between two little
blocks of the same substance fixed to a sounding-board
of thin pine-wood, the blocks being connected with one
or two small cells and a Bell telephone as a receiver.
The amplitude of the vibrations emitted by this telephone
may be much greater than those of the original sounds,
and therefore the microphone may serve, as its name
indicates, to magnify minute sounds, such as the ticking
of a watch or the footfalls of an insect, and render them
audible. The less sensitive carbon -transmitters, used
frequently in conjunction with the telephone, are some-
times regarded as varieties of the microphone. In some
of these instruments Blake's, for instance there is a
tympanum like that of Edison's and of Reis's tele-
phone.
438. Hughes' Induction Balance. The extreme
sensitiveness of Bell's telephone (Art. 435) to the feeblest
currents has suggested its employment to detect currents
too weak to affect the most delicate galvanometer. The
currents must, however, be intermittent, or they will not
keep the disc of the telephone in vibration. Hughes
applied this property of the telephone to an instrument
named the Induction Balance (Fig. 170). A small
battery B, connected with a microphone M, passes
through two coils of wire P 15 P 2 , wound on bobbins fixed
CHAP, xii.] ELECTRICITY AND MAGNETISM. 419
on a suitable stand. Above each of these primary coils
are placed two secondary coils, Si, S 2 , of wire, of the
same size, and of exactly equal numbers of turns of wire.
The secondary coils are joined to a telephone T, and
are wound in opposite directions. The result of this
arrangement is that whenever a current either begins or
stops flowing in the primary coils, PI induces a current
in S 1? and P 2 in S 2 . As Si and S 2 are wound in opposite
ways, the two currents thus induced in the secondary
wire neutralise one another, and, if they are of equal
strength, balance one another so exactly that no sound
Fig. 170.
is heard in the telephone. But a perfect balance cannot
be obtained unless the resistances and the co-efficients of
mutual induction and of self-induction are alike. If a flat
piece of silver or copper (such as a coin) be introduced
between S x and P 1; there will be less induction in Si than
in S 2 , for part of the inductive action in Pj is now spent
on setting up currents in the mass of the metal (Art. 401),
and a sound will again be heard in the telephone. But
balance can be restored by moving S 2 farther away from
P 2 , until the induction in S 2 is reduced to equality with
Si, when the sounds in the telephone again cease. It is
possible by this means to test the relative conductivity of
different metals which are introduced into the coils. It
is even possible to detect a counterfeit coin by the indi-
4 2o ELEMENTARY LESSONS. [CHAP. xn.
cation thus afforded of its conductivity. The induction
balance has also been applied in surgery to detect the
presence of a bullet in a wound, for a lump of metal may
disturb the induction when some inches distant from the
coils.
PROBLEMS AND EXERCISES. 421
PROBLEMS AND EXERCISES.
QUESTIONS ON CHAPTER I.
1. From what is the word "electricity" derived?
2. Name some of the different methods of producing electri-
fication.
3. A body is charged so feebly that its electrification will not
perceptibly move the leaves of a gold-leaf electroscope. Can
you suggest any means of ascertaining whether the charge of the
body is positive or negative ?
4. Describe an experiment to prove that moistened thread
conducts electricity better than dry thread.
5. Why do we regard the two electric charges produced
simultaneously by rubbing two bodies together as being of
opposite kinds ?
6. Explain the action of the electrophorus. Can you suggest
any means for accomplishing by a rotatory motion the operations
of lifting up and down the cover of the instrument so as to obtain
a continuous supply instead of an intermittent one.
7. Explain the Torsion Balance, and how it can be used to
investigate the laws of the distribution of electricity.
8. Two small balls are charged respectively with + 24 and
8 units of electricity. With what force will they attract one
another when placed at a distance of 4 centimetres from one
another? Ans. 12 dynes.
9. If these two balls are then made to touch for an instant
422 PROBLEMS AND EXERCISES.
and then put back in their former positions, with what force
will they act on each other ?
Ans. They repel one another with a force ot 4 dynes.
10. Zinc filings are sifted through a sieve made of copper wire
upon an insulated zinc plate joined by a wire to an electroscope.
What will be observed ?
1 1. Explain the principle of an air-condenser ; and state why
it is that the two oppositely charged plates show less signs of
electrification when placed near together than when drawn apart
from one another.
12. There are four Leyden jars A, B, C, and D, of which A,
B, and D, are of glaVs, C of guttapercha. A, B, and C, are of
the same size, D being just twice as tall and twice as wide
as the others. A, C, and D, are of the same thickness of
material, but B is made of glass only half as thick as A or D
Compare their capacities. Ans. Take capacity of A as I
that of B will be 2
that of C will be |
and that of D will be 4.
13. How would you prove that there is no electrification
within a closed conductor ?
14. What prevents the charge of a body from escaping away
at its surface ?
15. Explain the action of Hamilton's mill.
1 6. Two brass balls mounted on glass stems are placed half
an inch apart. One of them is gradually charged by a machine
until a spark passes between the two balls. State exactly what
happened in the other brass ball and in the intervening air up
to the moment of the appearance of the spark.
17. Define electric density. A charge of 248 units of elec-
tricity was imparted to a sphere of 4 centims. radius. What is
the density of the charge ? Ans. 1-23 nearly.
QUESTIONS ON CHAPTER II.
I. A dozen steel sewing-needles are hung in a bunch by
threads through their eyes. How will they behave when hung
over the pole of a strong magnet ?
PROBLEMS AND EXERCISES. 423
2. Six magnetised sewing-needles are thrust vertically through
six little floats of cork, and are placed in a basin of water with
their N. -pointing poles upwards. How will they affect one
another, and what will be the effect of holding over them the
S. -pointing pole of a magnet ?
3. What distinction do you draw between magnets and
magnetic matter ?
4. On board an iron ship which is laying a submarine tele-
graph cable there is a galvanometer used for testing the continuity
of the cable. It is necessary to screen the magnetised needle of
the galvanometer from being affected by the magnetism of the
ship. How can this be done ?
5. How would you prove two magnets to be of equal
strength ?
6. The force which a magnet-pole exerts upon another
magnet-pole decreases as you increase the distance between
them. What is the exact law of the magnetic force, and how
is it proved experimentally ?
7. What force does a magnet-pole, the strength of which is
9 units, exert upon a pole whose strength is 16 units placed
6 centimetres away ? Ans. 4 dynes.
8. A pole of strength 40 units acts with a force of 32 dynes
upon another pole 5 centimetres away. What is the strength
of that pole ? Ans. 20 units.
9. It is desired to compare the magnetic force at a point 10
centimetres from the pole of a magnet with the magnetic force
at 5 centimetres' distance. Describe four ways of doing this.
10. Explain the phenomenon of Consequent Poles.
11. In what direction do the lines of magnetic induction (or
"lines of force") run in a plane in which there is a single
magnetic pole ? How would you arrange an experiment by which
to test your answer ?
12. What is a Magnetic Shell 1 What is the law of the/
potential due to a magnetic shell ?
13. A steel bar magnet suspended horizontally, and set to
oscillate at Bristol, made no complete oscillations in five
424 PROBLEMS AND EXERCISES.
minutes ; the same needle when set oscillating horizontally at
St. Helena executed 112 complete oscillations in four minutes.
Compare the horizontal component of the force of the earth's
magnetism at Bristol with that at St. Helena.
Ans. H at Bristol : H at St. Helena : : 484 : 784.
14. Supposing the dip at Bristol to be 70 and that at St.
Helena to be 30, calculate from the data of the preceding
question the total force of the earth's magnetism at St. Helena,
that at Bristol being taken as '48 unit. Ans. "307.
[N.B. The student should see Footnote i, on p. 116.]
15. A small magnetic needle was placed magnetically north
of the middle point of a strong bar-magnet which lay (magneti-
cally) east and west. When the magnet was 3 feet away from
the needle the deflexion of the latter was 2 ; when moved up
to a distance of 2 feet the deflexion was 6 30' ; and when only
I foot apart the deflexion was 43. Deduce the law of the total
action of one magnet on another.
1 6. Describe how the daily irregularities of the earth's mag-
netism are registered at different stations for comparison.
QUESTIONS ON CHAPTER III.
1. Show that the total of the differences of potential by con-
tact in three simple voltaic cells joined in series is three times as
great as the difference of potential in one cell, the materials
being the same in each.
2. How can local action and polarisation be prevented in a
voltaic cell ?
3. Supposing the length of spark to be proportional to the
difference of potential, calculate from the data of Arts. 291 and
178 how many DanielPs cells would be required to yield a
sufficient difference of potential to produce a spark one mile long
through air. Ans. 1092 million cells.
4. On what does the internal resistance of a batteiy depend ?
Is there any way of diminishing it ?
5. Twenty -four similar cells are grouped together in four
rows of six cells each ; compare the electromotive-force and the
PROBLEMS AND EXERCISES. 425
resistance of the battery thus grouped, with the electromotive-
force and the resistance of a single cell.
Ans. The E.M.F. of the battery is six times that of
one cell. The total internal resistance is one and
a half times that of one cell.
6. A piece of silk-covered copper wire is coiled round the
equator of a model terrestrial globe. Apply Ampere's rule to
determine in which direction a current must be sent through the
coil in order that the model globe may represent the condition
of the earth magnetically.
Ans. The current must flow across the Atlantic from
Europe to America, and across the Pacific from
America toward India ; or, in other words, must
flow always from east toward west.
7. A current of "24 amperes flows through a circular coil of
seventy-two turns, the (average) diameter of the coils being 20
centimetres. What is the strength of the magnetic field which
the current produces at the centre of the coil ?
Ans. I -08.
8. Suppose a current passing through the above coil produced
a deflection of 35 upon a small magnetic needle placed at its
centre (the plane of the coils being in the magnetic meridian),
at a place where the horizontal component of the earth's
magnetic force is -23 units. Calculate the strength of the
current in amperes. (Art. 200.) Ans. 0*035.
9. The current generated by a dynamo-electric machine was
passed through a large ring of stout copper wire, at the centre'
of which hung a small magnetic needle to serve as a tangent
galvanometer. When the steam engine drove the armature of
the generator at 450 revolutions per minute the deflection of the
needle was 60. When the speed of the engine was increased
so as to produce 900 revolutions per minute the deflection was
74. Compare the strength of the currents in the two cases.
Ans. The current was twice as great as before, for tan
74 is almost exactly double of tan 60.
10. The current from two Grove's cells was passed through
a sine -galvanometer to measure its strength. When the con-
ducting wires were of stout copper wire the coils had to be
turned through 70 before they stood parallel to the needle.
But when long thin wires were used as conductors the coils
426 PROBLEMS AND EXERCISES.
only required to be turned through 9. Compare the strength
of the current in the first case with that in the second case
when flowing through the thin wires which offered considerable
resistance. Ans. Currents are as I to ^, or as 6 to I.
11. A plate of zinc and a plate of copper are respectively
united by copper wires to the two screws of a galvanometer.
They were then dipped side by side into a glass containing
dilute sulphuric acid. The galvanometer needle at first showed
a deflection of 28, but five minutes later the deflection had
fallen to 11. How do you account for this falling off?
12. Classify liquids according to their power of conducting
electricity.
13. Name the substances produced at the anode and kathode
respectively during the electrolysis of the following substances :
Water, dilute sulphuric acid, sulphate of copper (dissolved in
water), hydrochloric acid (strong), iodide of potassium (dissolved
in water), chloride of tin (fused).
14. A current is sent through three electrolytic cells, the first
containing acidulated water, the second sulphate of copper, the
third contains a solution of silver in cyanide of potassium. How
much copper will have been deposited in the second cell while
2-268 grammes of silver have been deposited in the third cell?
And what volume of mixed gases will have been given off at the
same time in the first cell ?
Ans. -6614 grammes of copper and 352-8 cubic centi-
metres of mixed gases.
15. A current passes by platinum electrodes through three
cells, the first containing a solution of blue vitriol (cupric
sulphate), the second containing a solution of green vitriol
(ferrous sulphate), the third containing a solution of ferric
chloride. State the amounts of the different substances evolved
at each electrode by the passage of 1000 amperes of electricity.
,, ( Anode -0840 grammes of oxygen gas.
Ans. First cell, \ ^ ofll ^ . OTQmmM rt f i^Jr
Second cell,
Third cell,
grammes <
Anode -0840 grammes of oxygen.
Kathode -2940 grammes of iron.
Anode -3727 grammes of chlorine.
Kathode '1470 grammes of iron.
1 6. A tangent galvanometer, whose "constant" in absolute
units was O'oSo, was joined in circuit with a battery and an
PROBLEMS AND EXERCISES. 427
electrolytic cell containing a solution of silver. The current
was kept on for one hour ; the deflection observed at the begin-
ning was 36, but it fell steadily during the hour to 34. Sup-
posing the horizontal component of the earth's magnetic force
10 be "23, calculate the amount of silver deposited in the cell
during the hour, the electro-chemical equivalent of silver being
croii34O. Ans. '0526 gramme.
17. A piece of zinc, at the lower end of which a piece of
copper wire is fixed, is suspended in a glass jar containing a
solution of acetate of lead. After a few hours a deposit of
lead in a curious tree -like form ("Arbor Saturni") grows
downwards from the copper wire. Explain this.
1 8. Explain the conditions under which electricity excites
muscular contraction. How can the converse phenomenon of
currents of electricity produced by muscular contraction be
shown ?
QUESTIONS ON CHAPTER IV.
1 . Define the unit of electricity as derived in absolute terms
from the fundamental units of length, mass, and time.
2. At what distance must a small sphere charged with 28
units of electricity be placed from a second sphere charged with
56 units in order to repel the latter with a force of 32 dynes ?
Ans. 7 centimetres.
3. Suppose the distance from the earth to the moon to be (in
round numbers) 383 x io 8 centimetres ; and that the radius of
the earth is 63 x io 7 centimetres, and that of the moon 15 x
io r centimetres ; and that both moon and earth are charged
until the surface density on each of them is of the average value
of io units per square centimetre. Calculate the electrostatic
repulsion between the moon and the earth.
4. A small sphere is electrified with 24 units of + electricity.
Calculate the force with which it repels a unit of + electricity at
distances of I, 2, 3, 4, 5, 6, 8, and io centimetres respectively.
Then plot out the " ctirve of force" to scale; measuring the
respective distances along a line from left to right as so many
centimetres from a fixed point as origin ; then setting out as
428 PROBLEMS AND EXERCISES.
vertical ordinates the amounts you have calculated for the
corresponding forces ; lastly, connecting by a curved line the
system of points thus found.
5. Define electrostatic (or electric) "potential y" and calculate
(by the rule given in italics in Art. 238) the potential at a point
A, which is at one corner of a square of 8 centimetres' side,
when at the other three corners B, C, D, taken in order,
charges of + 16, +34, and +24 units are respectively placed.
Ans. 8, very nearly exactly.
6. A small sphere is electrified with 24 units of + electricity.
Calculate the potential due to this charge at points I, 2, 3, 4, 5,
6, 8, and 10 centimetres' distance respectively. Then plot out
the "curve of potential" to scale, as described in Question 4.
7. What are equipotential surfaces ? Why is the surface of
an insulated conductor an equipotential surface ? Is it always
so?
8. A sphere whose radius is 14 centimetres is charged until
the surface density has a value of 10. What quantity of
electricity is required for this? Ans. 24,630 units (nearly).
9. In the above question what will be the potential at the
surface of the sphere? (See last sentence of Art. 246.)
Ans. 1760 (very nearly).
10. In the case of question 8, what will be the electric force at
a point outside the sphere and indefinitely near to its surface ?
(Art. 251.) Ans. 1257 (very nearly).
11. Suppose a sphere whose radius is 10 centimetres to be
charged with 6284 units of electricity, and that it is then caused
to share its charge with a non-electrified sphere whose radius is
15 centimetres, what will the respective charges and surface-
densities on the two spheres be when separated ?
Ans. Small sphere, q 2513*6, Q = 2 :
Large sphere, q = 377O'4, 9 = 1-33.
12. A charge of + 8 units is collected at a point 20 centi-
metres distant from the centre of a metallic sphere whose radius
is 10 centimetres. It induces a negative electrification at the
nearest side of the sphere. Find a point inside the sphere such
that if 4 negative units were placed there they would exercise
PROBLEMS AND EXERCISES. 429
a potential on all external points exactly equal to that of the
actual negative electrification. (See Art. 250.)
Ans. The point must be on the line between the outside
positive charge and the centre of the sphere and at
5 centims. from the surface.
13. Two large parallel metal plates are charged both
positively but unequally, the density at the surface of A being
+ 6, that at the surface of B being + 3. They are placed 2
centimetres apart. Find the force with which a + unit of
electricity is urged from A towards B. Find also the work
done by a + unit of electricity in passing from A to B.
Ans. Electric force from A towards B = 1 8 '85 dynes; work
done by unit in passing from A to B = 37*5 ergs.
14. What is meant by the dimensions of a physical quantity?
Deduce from the Law of Inverse Squares the dimensions of
electricity ; and show by this means that electricity is not a
quantity of the same physical dimensions as either matter, energy,
or force.
15. Explain the construction and principles of action of the
quadrant electrometer. How could this instrument be made
self-recording ?
1 6. One of the two coatings of a condenser is put to earth,
to the other coating a charge of 5400 units is imparted. It is
found that the difference of potential thereby produced between
the coatings is 15 (electrostatic) units. What was the capacity
of the condenser ? Ans. 360.
17. What is the meaning of specific inductive capacity '? Why
does hot glass appear to have a higher specific inductive capacity
than cold glass ?
1 8. Compare the phenomenon of the residual charge in a
Leyden jar with the phenomenon of polarisation in an electro-
lytic cell.
19. A condenser was made of two flat square metal plates,
the side of each of them being 35 centimetres. A sheet of
indiarubber *4 centim. thick was placed between them as a
dielectric. The specific inductive capacity of indiarubber
being taken as 2-25, calculate the capacity of the condenser.
Ans. 548-8 electrostatic units.
430 PROBLEMS AND EXERCISES.
20. Calculate (in electrostatic units) the capacity of a mile of
telegraph cable the core being a copper wire of -18 centim.
diameter, surrounded by a sheathing of guttapercha "91 centim.
thick. \k for guttapercha = 2-46; one mile = 160,933
centims.] Ans. 1,879,130 units.
21. A Leyden jar is made to share its charge with two other
jars, each of which is equal to it in capacity. Compare the
energy of the charge in one jar with the energy of the original
charge. Ans. One ninth as great.
22. A series of Leyden jars of equal capacity are charged
"in cascade." Compare the total energy of the charge of the
individual jars thus charged, with that of a single jar charged
from the same source.
23. Classify the various modes of discharge, and state the
conditions under which they occur.
24. Suppose a condenser, whose capacity is 10,000 charged
to potential 14, to be partially discharged so that the potential
fell to 5. Calculate the amount of heat produced by the
discharge, on the supposition that all the energy of the spark
is converted into heat. Ans. -020357 of a unit of heat.
25. How do changes of pressure affect the passage of electric
sparks through air ?
26. Why are telegraphic signals through a submerged cable
retarded in transmission, and how can this retardation be
o.bviated ?
27. How is the difference of potential between the earth and
the air above it measured ? and what light do such measure-
ments throw on the periodic variations in the electrical state of
the atmosphere ?
28. What explanation can be given of the phenomena of a
thunderstorm ?
29. What are the essential features which a lightning-con-
ductor must possess before it can be pronounced satisfactory ?
And what are the reasons for insisting on these points ?
30. How can the duration of an electric spark be measured ?
PROBLEMS AND EXERCISES. 431
QUESTIONS ON CHAPTER V.
1. Define magnetic potential ', and find the (magnetic) potential
due to a bar magnet 10 centimetres long, and of strength 80,
at a point lying in a line with the magnet poles and 6 centi-
metres distant from its N. -seeking end. Ans. 8*3.
2. A N. -seeking pole and a S. -seeking pole, whose strengths
are respectively +120 and 60, are in a plane at a distance
of 6 centimetres apart. Find the point between them where
the potential is = o ; and through this point draw the curve of
zero potential in the plane.
3. Define "intensity of the magnetic field." A magnet
whose strength is 270 is placed in a uniform magnetic field
whose intensity is *i66. What are the forces which act upon
its poles ? Ans. + 45 dynes and 45 dynes.
4. Define "intensity of magnetisation." A rectangular bar-
magnet, whose length was 9 centimetres, was magnetised until
the strength of its poles was 164. It was 2 centimetres broad
and -5 centimetre thick. Supposing it to be uniformly magnet-
ised throughout its length, what is the intensity of the magnet-
isation? Ans. 164.
5. Poisson suggested a two -fluid theory of magnetism, the
chief point of the hypothesis being that in the molecules of iron
and other magnetic substances there were equal quantities of
two opposite kinds of magnetic fluid ; and that in the act of
magnetisation the two fluids were separated. What facts does
this theory explain ? What facts does it fail to explain ?
6. A current whose strength in "absolute" electromagnetic
units was equal to 0*05 traversed a wire ring of 2 centimetres
radius. What was the strength of field at the centre of the
ring? What was the potential at a point P opposite the
middle of the ring and 4 centimetres distant from the circum-
ference of the ring. Ans. f= "1571 ; V = 0*0421.
7. What limits are there to the power of an electromagnet ?
8. What is the advantage of the iron core in an electro-
magnet ?
9. Assuming the effective coefficient of magnetisation of iron
432 PROBLEMS AND EXERCISES.
to be 20, calculate the strength of the pole of an electromagnet
whose coils consist of 50 turns of wire of an average radius of
I centimetre, when a current of 2 amperes passes through the
coils, the core consisting of a bar 5 centimetres long and of I
square centimetre of area in its cross section [see Art. 328 (rf)].
Ans. 528 units.
10. Enunciate Maxwell's rule concerning magnetic shells,
and from it deduce the laws of parallel and oblique currents
discovered by Ampere.
1 1 . A circular copper dish is joined to the zinc pole of a
small battery. Acidulated water is then poured into the dish,
and a wire from the carbon pole of the battery dips into the
liquid at the middle. A few scraps of cork are thrown in to
render any movement of the liquid visible. What will occur
when the N. -seeking pole of a strong bar-magnet is held above
the dish ?
1 2. Rogef hung up a spiral of copper wire so that the lowei
TSnd/wj/ dipped into a cup of mercury. When a strong current
was sent through the spiral it started a continuous dance, the
lower end producing bright sparks as it dipped in and out of
the mercury. Explain this experiment.
13. It is believed, though it has not yet been proved, that
ozone is more strongly magnetic than oxygen. How could this
be put to proof?
QUESTIONS ON CHAPTER VI.
1. The resistance of telegraph wire being taken as 13 ohms
per mile, and the E. M. F. of a Leclanche cell as 1-5 volt,
calculate how many cells are needed to send a current of 12
mitti-amptres through a line 120 miles long ; assuming that the
instruments in circuit offer as much resistance as 20 miles of
wire would do, and that the return-current through earth meets
with no appreciable resistance. Ans. 1 5 cells.
2. 50 Grove's cells (E. M. F. of a Grove = I '8 volt} are
united in series, and the circuit is completed by a wire whose
resistance is 1 5 ohms. Supposing the internal resistance of each
cell to be 0-3 ohm, calculate the strength of the current.
Ans. 3 amperes.
PROBLEMS AND EXERCISES. 433
3. The current running through an incandescent filament of
carbon in a lamp was found to be exactly I ampere. The
difference of potential between the two terminals of the lamp
while the current was flowing was found to be 30 volts. What
was the resistance of the filament ?
4. Define specific resistance. Taking the specific resistance
of copper as 1642, calculate the resistance of a kilometre of
topper wire whose diameter is I millimetre. Ans. 20*9 ohms.
5. On measuring the resistance of a piece of No. 30 B. W. G.
(covered) copper wire, 18-12 yards long, I found it to have a
resistance of 3 -02 ohms. Another coil of the same wire had a resist-
ance of 22-65 h ms w ^ at length of wire was there in the coil ?
Ans. 135-9 yards.
6. Calculate the resistance of a copper conductor one square
centimetre in area of cross- section, and long enough to reach
from Niagara to New York, reckoning this distance as 480
kilometres. Ans. 78-8 ohms.
7. You have given an unlimited number of Telegraph Daniell's
cells (Fig. 77), their E. M. F. being i'i volt each, and their
average internal resistance being 2 '2 ohms each. What will be
the strength of the current when five such cells, in series, are
connected through a wire whose resistance is 44 ohms ?
f Ans. O'l ampere.
8. Show in the preceding case that with an infinite number
of cells in series, the current could not possibly exceed 0*5
ampere.
9. The specific resistance of guttapercha being 3-5 x io 23 ,
calculate the number of coulombs of electricity that would leak
in one century through a sheet of guttapercha one centimetre
thick and one metre square, whose faces were covered with
tinfoil and joined respectively to the poles of a battery of 100
Daniell's cells. Ans. 9-7 coulomb.
10. Six Daniell's cells, for each of which E = 1-05 volts, r
0-5 ohm, are joined in series. Three wires, X,Y, and Z, whose
resistances are severally 3, 30, and 300 ohms, can be inserted
between the poles of the battery. Determine the current (in
amperes] which flows when each wire is inserted separately ; also
determine that which flows when they are all inserted at once
in parallel arc.
2 F
434 PROBLEMS AND EXERCISES.
Ans. Through X 1-05 amperes per sec.
Through Y 0*1909 ,,
Through Z 0-0207
Through all three 1-105
11. Calculate the number of cells required to produce a
current of 50 milli-amperes, through a line 114 miles long, whose
resistance is 1 2 J ohms per mile, the available cells of the battery
having each an internal resistance of I *5 ohm, and an E. M. F. of
1 *5 volt. Ans. 50 cells.
12. You have 20 large Leclanche cells (E.M.F. = 1-5 volt,
7'=O'5 ohm each) in a circuit in which the external resistance is
10 ohms. Find the strength of current which flows (a) when
the cells are joined in simple series ; (b) all the zincs are united,
and all the carbons united, in parallel arc ; (c) when the cells are
arranged two abreast (i.e. in two files of ten cells each) ; (d]
when the cells are arranged four abreast.
Ans. (a) i 5 ampere.
(b) 0-1496 ,,
(c) i'2
(d) 0-702
13. With the same battery how would you arrange the cells
in order to telegraph through a line 100 miles long, reckoning
the line resistance as 12 J ohms per mile?
14. I have 48 cells, each of 1-2 volt E.M.F., and each of
2 ohms internal resistance. What is the best way of grouping
them together when it is desired to send the strongest possible
current through a circuit whose resistance is 12 ohms?
Ans. Group them three abreast.
15. Show that, if we have a battery of n given cells each of
resistance r in a circuit where the external resistance is R, the
strength of the current will be a maximum when the cells are
coupled up in a certain number of rows equal numerically to
V nr ~- R.
1 6. Two wires, whose separate resistances are 28 and 24, are
placed in parallel arc in a circuit so that the current divides,
part passing through one, part through the other. What resist-
ance do they offer thus to the current ? Ans. 12-92 ohms.
17. Using a large bichromate cell of practically no internal
resistance, a deflection of 9 was obtained upon a tangent
PROBLEMS AND EXERCISES. 435
galvanometer (also of small resistance) through a wire whose
resistance was known to be 435 ohms. The same cell gave a
deflection of 5 upon the same galvanometer when a wire of
unknown resistance was substituted in the circuit. What was
the unknown resistance ? Ans. 790 ohms.
1 8. In a Wheatstone's bridge in which resistances of 10 and
100 ohms respectively were used as the fixed resistances, a wire
whose resistance was to be determined was placed : its resist-
ance was balanced when the adjustable coils were arranged to
throw 28 1 ohms into circuit. What was its resistance ?
Ans. 28*1 ohms.
19. A battery of 5 Leclanche cells was connected in simple
circuit with a galvanometer and a box of resistance coils. A
deflection of 40 having been obtained by adjustment of the
resistances, it was found that the introduction of 150 additional
ohms of resistance brought down the deflection to 29. A battery
of ten Darnell's cells was then substituted in the circuit and
adjusted until the deflexion was 40 as before. But this time it
was found that 216 ohms had to be added before the deflection
was brought down to 29. Taking the E.M.F. of a single
Daniell's cell as 1-079 volt, calculate that of a single Leclanche
cell. Ans. i '499 volt.
20. How are standard resistance coils wound, and why?
What materials are they made of, and why ?
21. Three very small Daniell's cells gave, with a sine galvan-
ometer (itself of no appreciable resistance), a reading of 57. On
throwing 20 ohms into the circuit the galvanometer reading fell
to 25. Calculate the internal resistance of the cells.
Ans. 6'6 ohms each.
22. A knot of telegraph cable was plunged in a tub of water
and then charged for a minute from a battery of 120 Daniell's
cells. The cable was then discharged through a long -coil
galvanometer with a needle of slow swing. The first swing
was 40. A condenser whose capacity was \ microfarad was
then similarly charged and discharged ; but this time the first
swing of the needle was only over 14. What was the capacity
of the piece of cable ? Ans. 0*934 microfarad.
23. Using an absolute electrometer, Sir W. Thomson found
the difference of potential between the poles of a Daniell's cell
436 PROBLEMS AND EXERCISES.
to be "00374 electrostatic units (C.G.S. system). The ratio of
the electrostatic to the electromagnetic unit of potential is given
in Art. 365, being = v . The volt is defined as io 8 electromag-
netic units. From these data calculate the E. M. F. of a
Daniell's cell in volts. Ans. 1*115 volt.
24. The radius of the earth is approximately 63 x io r centi-
metres. The ratio of the electrostatic to the electromagnetic
unit of capacity is given in Art. 365. The definition of the
farad is given in Art. 323. Calculate the capacity of the earth
(regarded as a sphere) in microfarads.
Ans. 700 microfarads (nearly).
25. The electromotive-force of a Daniell's cell was determined
by the following process : Five newly-prepared cells were set
up in series with a tangent galvanometer, whose constants were
found by measurement. The resistances of the circuit were also
measured, and found to be in total 16*9 ohms. Knowing the
resistance and the absolute strength of current the E. M. F. could
be calculated. The deflection obtained was 45, the number of
turns of wire in the coil io, the average radius of the coils n
centimetres, and the value of the horizontal component of the
earth's magnetism at the place was 0*18 C.G.S. units. Deduce
the E.M.F. of a Daniell's cell.
Ans. I -0647 x io 8 C.G.S. units, or 1-0647 wfa
QUESTIONS ON CHAPTER VII.
1. I have seen a small chain in which the alternate links
were of platinum and silver wires. When an electric current
was sent through the chain the platinum links grew red hot
while the silver links remained cold. Why was this ?
2. Calculate by Joule's law the number of heat units developed
in a wire whose resistance is 4 ohms when a steady current of
14 ampere is passed through it for io minutes.
Ans. 1 1 "2 units of heat.
3. What sort of cells ought to be the best for providing
currents to fire torpedo shots ?
4. Explain why a regulator like that of Duboscq is employed
in obtaining a steady voltaic arc.
PROBLEMS AND EXERCISES. 437
5. I once tried to obtain an electric light by using a battery
of 3000 telegraph Daniell's cells in series, but without success.
Why did this enormous battery power fail for this purpose?
Could it have been made to give a light by any different arrange-
ment of the cells ?
6. A battery of 2 Grove's cells, a galvanometer, and a little
electromagnetic engine, were connected in circuit. At first the
engine was loaded, so that it could only run slowly ; but when
the load was lightened it spun round at a tremendous speed.
But the faster the little engine worked the feebler was the
current indicated by the galvanometer. Explain this.
7. A current of 9 amperes worked an electric arc light, and on
measuring the difference of potential between the two carbons
by an electrometer it was found to be 140 volts. What was
the amount of horse-power absorbed in this lamp ?
Ans. 1-69 H.-P.
8. You have a lathe in your workshop which requires power
to turn it. There is a stream of water tumbling down the hill-
side, two miles off, with power enough to turn twenty lathes.
How can you bring this power to the place where you want to
use it ?
9. What is the use of the electro-dynamometer ? Assum-
ing that the moment of the force acting on the movable coil of
the electro-dynamometer is proportional to the product of the
strengths of the currents in the two coils, show that the work
performed by a current is really measured by the electro-
dynamometer of Marcel Deprez, in which one set of coils has a
very small resistance and the other a very high resistance (con-
sisting of many turns of fine wire), the latter being arranged as
a shunt to the lamp, motor, or other instrument, in which the
work to be measured is being done, the former having the
whole current passed through it.
QUESTIONS ON CHAPTER VIII.
I. A strong battery - current is sent, for a few moments,
through a bar made of a piece of antimony soldered to a piece
of bismuth. The battery is then disconnected from the wires
and they are joined to a galvanometer which shows a deflection.
Explain this phenomenon.
43 8 PROBLEMS AND EXERCISES.
2. A long strip of zinc is connected to a galvanometer by
iron wires. One junction is kept in ice, the other is plunged
into water of a temperature of 5OC. Calculate, from the table
given in Art. 381, the electromotive-force which is producing
the current. Ans. 690 microvolts.
3. When heat is evolved at a junction of two metals by the
passage of a current, how would you distinguish between, the
heat due to resistance and the heat due to the Peltier effect ?
4. Sir W. Thomson discovered that when a current flows
through copper it absorbs heat when it flows from a hot point
to a cold point ; but that when a current is flowing through
iron it absorbs heat when it flows from a cold point to a hot
point. From these two facts, and from the general law that
energy tends to run down to a minimum, deduce which way a
current will flow round a circuit made of two half-rings of iron
and copper, one junction of which is heated in hot water and the
other cooled in ice.
QUESTIONS ON CHAPTER IX.
1. Give the reasons which exist for thinking that light is an
electromagnetic phenomenon.
2. How is the action of magnetic forces upon the direction
of the vibrations of light shown? and what is the difference
between magnetic and diamagnetic media in respect of their
magneto-optic properties ?
3. It was discovered by Willoughby Smith that the resistance
of selenium is less when exposed to light than in the dark.
Describe the apparatus you would employ to investigate this
phenomenon. How would you proceed to experiment if you
wished to ascertain whether the amount of electric effect was
proportional to the amount of illumination ?
QUESTIONS ON CHAPTER X.
i. The ends of a coil of fine insulated wire are connected
with terminals of a long-coil galvanometer. A steel bar-magnet
PROBLEMS AND EXERCISES. 439
is placed slowly into the hollow of the coil, and then withdrawn
sttddenly. What actions will be observed on the needle of the
galvanometer ?
2. Round the outside of a deep cylindrical jar are coiled two
separate pieces of fine silk-covered wire, each consisting of many
turns. The ends of one coil are fastened to a battery, those of
the other to a sensitive galvanometer. When an iron bar is
poked into the jar a momentary current is observed in the
galvanometer coils, and when it is drawn out another moment-
ary current, but in an opposite direction, is observed. Explain
these observations.
3. A casement window has an iron frame. The aspect is
north, the hinges being on the east side. What happens when
the window is opened?
4. Explain the construction of the induction coil. What
are the particular uses of the condenser, the automatic break,
and the iron wire core ?
5. It is desired to measure the strength of the field between
the poles of an electromagnet which is excited by a current from
a constant source. How could you apply Faraday's discovery
of induction currents to this purpose ?
6. What is meant by the term "extra-currents?" A small
battery was joined in circuit with a coil of fine wire and a
galvanometer, in which the current was found to produce a
steady but small deflection. An unmagnetised iron bar was
now plunged into the hollow of the coil and then withdrawn.
The galvanometer needle was observed to recede momentarily
from its first position, then to return and to swing beyond it
with a wider arc than before, and finally to settle down to its
original deflection. Explain these actions.
7. In what respect do dynamo - electric machines differ from
magneto-electric machines ? Where does the magnetism of the
field -magnets come from in the former? Where does the
dynamical energy of the currents come from in the latter ?
8. The older magneto - electric machines produced only
intermittent currents, and these were usually alternating in
direction. By what means do the more modern magneto-electric
generators produce currents which are continuous and direct ?
440 PROBLEMS AND EXERCISES.
9. A compass needle, when set swinging, comes to rest
sooner if a plate of copper is placed beneath it than if a plate of
glass or wood lies beneath it. Explain this fact.
10. Explain how it is that on making circuit the current
rises only gradually to its full strength, especially if there are
large electromagnets in the circuit.
11. Foucault set the heavy bronze wheel of his gyroscope
spinning between the poles of a powerful electromagnet, and
found that the wheel grew hot, and stopped. What was the
cause of this ? Where did the heat come from ?
12. The strength of the field between the poles ot a large
electromagnet was determined by the following means : A
small circular coil, consisting of 40 turns of fine insulated wire,
mounted on a handle, was connected to the terminals of a long-
coil galvanometer having a heavy needle. On inverting this coil
suddenly, at a place where the total intensity of the earth's mag-
netic force was '48 unit, a deflection of 6 was shown as the first
swing of the galvanometer needle. The sensitiveness of the
galvanometer was then reduced to -3^ by means of a shunt. The
little coil was introduced between the poles of the electromagnet
and suddenly inverted, when the first swing of the galvan-
ometer needle reached 40. What was the strength of the field
between the poles? Ans. 3157 units.
QUESTIONS ON CHAPTER XI.
1. It is found that a single Daniell's cell will not electrolyse
acidulated water, however big it may be made. It is found, on
the other hand, that two Daniell's cells, however small, will
suffice to produce continuous electrolysis of acidulated water.
How do you account for this ?
2. When a gramme of zinc combines with oxygen it gives
out 1301 heat-units. When this zinc oxide is dissolved in
sulphuric acid 369 more units are evolved. To separate an
equivalent amount of copper sulphate into sulphuric acid and
copper oxide requires 588 heat -units to be expended. To
separate the copper from the oxygen in this oxide requires 293
more heat-units. The absolute electro -chemical equivalent of
zinc is 0-0034 1 2 (see Art. 212), and Joule's dynamical equivalent
PROBLEMS AND EXERCISES: 441
of heat is 42 x io 6 . From these figures calculate the electro-
motive force of a DanielPs cell.
Ans. 1-1306 x io 8 C.G.S. units, or
1.1306. volt.
3. Explain the operation of charging a secondary battery.
What are the chemical actions which go on during charging and
during discharging ?
4. Most liquids which conduct electricity are decomposed
(except the melted metals) in the act of conducting. How do
you account for the fact observed by Faraday that the amount
of matter transferred through the liquid and deposited on the
electrodes is proportional to the amount of electricity trans-
ferred through the liquid ?
5. Describe the process for multiplying by electricity copies
of engravings on wood-blocks.
6. How would you make arrangements for silvering spoons
of nickel-bronze by electro-deposition ?
QUESTIONS ON CHAPTER XII.
1. Sketch an arrangement by which a single line of wire can
be used by an operator at either end to signal to the other ; the
condition of working being that whenever you are not sending
a message yourself your instrument shall be in circuit with the
line wire, and out ^/"circuit with the battery at your own end.
2. What advantages has the Morse instrument over the
needle instruments introduced into telegraphy by Cooke and
Wheatstone ?
3. Explain the use and construction of a relay.
4. It is desirable in certain cases (diplex and quadruplex
signalling) to arrange telegraphic instruments so that they will
respond only to currents which come in one direction through
the line. How can this be done ?
5. A battery is set up at one station. A galvanometer needle
at a station eighty miles away is deflected through a certain
number of degrees when the wire of its coil makes twelve turns
round the needle ; wire of the same quality being used for
both line and galvanometer. At 200 miles the same deflection
is obtained when twenty -four turns are used in the gal van-
442 PROBLEMS AND EXERCISES.
ometer-coil. Show by calculation (a] that the internal resist-
ance of the battery is equal to that of 40 miles of the line- wire ;
(b] that to produce an equal deflection at a station 360 miles
distant the number of turns of wire in the galvanometer -coil
must be 40.
6. Suppose an Atlantic cable to snap off short during the
process of laying. How can the distance of the broken end
from the shore end be ascertained ?
7. Suppose the copper core of a submarine cable to part at
some point in the middle without any damage being done to
the outer sheath of guttapercha. How could the position of
the fault be ascertained by tests made at the shore end ?
8. Explain the construction and action of an electric bell.
9. Describe and explain how electric currents are applied in
the instruments by which very short intervals of time are
measured.
10. Explain the use of Graham Bell's telephone (i) to
transmit vibrations ; (2) to reproduce vibrations.
11. Describe a form of telephone in which the vibrations of
sound are transmitted by means of the changes they produce in
the resistance of a circuit in which there is a constant electro-
motive-force.
12. Two coils, A and B, of fine insulated wire, made exactly
alike, and of the same number of windings in each, are placed
upon a common axis, but at a distance of 10 inches apart. They
are placed in circuit with one another and with the secondary wire
of a small induction-coil of Ruhmkorff 's pattern, the connections
being so arranged that the currents run round the two coils in
opposite directions. A third coil of fine wire, C, has its two
ends connected with a Bell's telephone, to which the experi-
menter listens while he places this third coil between the other
two. He finds that when C is exactly midway between A and
B no sound is audible in the telephone, though sounds are
heard if C is nearer to either A or B. Explain the cause of this.
He also finds that if a bit of iron wire is placed in A silence is
not obtained in the telephone until C is moved to a position
nearer to B than the middle. Why is this ? Lastly, he finds
that if a disc of brass, copper, or lead, is interposed between A
and C, the position of silence for C is now nearer to A than the
middle. How is this explained ?
INDEX.
443
INDEX.
N.B. The Figures refer to the Numbered Paragraphs.
ABSOLUTE Electrometer, 261
Galvanometer, 200
Measurements, 325a, 363, 364
Units of Measurement, 255
Accumulator, 47, 48, 266
of currents (see Secondary
Batteries)
Action at a distance, 21, 56, 272
Air condenser, 48, 267
Air, resistance of, 291, 325^
Alclini, Giovanni, Experiments on
Animals, 229
Amalgam, electric, 41
Amalgamating zinc plates, 162
Amber, i
Amoeba, the sensitiveness of, 230
Am-meter, 200 (bis)
Ampere, Andre, Theory of Electro-
dynamics, 331, 334
"Ampere's Rule," 186
Laws of Currents, 332
suggests a Telegraph, 423
Table for Experiments, 333
Theory of Magnetism, 338
Ampere, the, 323
Angles, "Way 5 of Reckoning, 129
Solid, 133
Animal Electricity, 68, 231
Anion, 210
Annual variations of magnet, 143
Anode, 207
Arc, voltaic, 371
Arago, Franfois Jean,
classification of lightning, 304
magnetisation by current, 326
on magnetic action of a voltaic
current, 191
on magnetic rotations, 401
Armature of magnet, 101
of dynamo - electric machine,
407, 409, 410
Armstrong; Sir Wm., his Hydro-
electric Machine, 44
Astatic magnetic needles, 190
Galvanometer, 190
Atmospheric Electricity, 64, 301, 306
Attracted-disc Electrometers, 261
Attraction and repulsion of elec-
trified bodies, i, 3, 18, 20,
66, 236
and repulsion of currents, 331,
and repulsion of magnets, 76, 80
332
Aurora, the, 144, 145, 309
Ayrton (W. E.) and Perry (John)
on contact electricity, 72
on dielectric capacity, 271
value of "v," 365
am-meter, 200 (fa's)
voltmeter, 360 (d)
Azimuth Compass, 134, 136
B. A. UNIT (or ohm), 323, 363, 364
Back Stroke, 26, 304
Bain's Chemical Writing Telegraph,
218
Balance, Wheatstone's, 358
Ballistic Galvanometer, 204
Bancalariou diamagnetism of flames,
Battery of Leyden Jars, 54
Batteries, voltaic, 154, 167, 182
list of, 178
secondary, 415
Beccaria, Fatfier G., on electric
distillation, 223
444
INDEX.
Beccaria, Father G., on atmospheric
electricity, 306
Becquerel, Antoine Cesar, on atmo-
spheric electricity, 307
on diamagnetism, 339
Becquerel, Edmond, on photo-voltaic
currents, 389
Becquerel, Henri, on magneto-optic
rotation, 387
Bell, Alexander Graham, his Tele-
phone, 435
The Photophone, 389
Bells, electric, 432
JBennet's Doubler, 23
Electroscope, 13, 25
Bertsctis Electric Machine, 45
Best grouping of cells, 351
Bichromate Battery, 165
Bifilar Suspension, 118, 262^ 336
Biot, Jean Baptiste, Experiment with
hemispheres, 30
Law of magnetic distribution,
138
on atmospheric electricity, 307
Bismuth, diamagnetic properties of,
87, 313, 339
Blasting by electricity, 286, 370
Blood, diamagnetism of, 339
Boracite, 67
"Bound" electricity, 24, 149 {foot-
note)
Boltzmann, on Dielectric capacity,
270, 271, 390
Boyle, Hon. Robert, on electrical
attraction, 2
Branched circuit, 353
Breaking a magnet, 106
Breath-figures, 297
Bridge, Wheatstpne's, 358
British Association Unit, 323, 364,
365-
Brugmans discovers magnetic repul-
sion of bismuth, 339
Brush discharge, 290
Brush's dynamo-electric machine, 411
Btmsen's Battery, 172
CABLE, Atlantic, 274 (footnote), 275,
296, 429
submarine, 429
,, as condenser, 274,
296, 430
,Cabot, Sebastian, on magnetic de-
clination, 136
Cailletet on resistance of air, 291
Calibration of Galvanometer, 198
Callan's Battery, 172
Callaud's Battery, 176
Canton, John, discovers Electrostatic
Induction, 18
on Electric Amalgam, 41
Candle, electric, 373
Capacity, definition of, 246
measurement of, 362
of accumulator or condenser,
50, 267, 277
of conductor, 37, 47, 247, 277
of Leyden Jar, 50, 267
specific inductive, 21, 49, 268,
272
unit of (electrostatic), 247
unit of (practical), 276
Capillary Electrometer, 225, 265
Carnivorous Plants, sensitive to elec-
tricity, 230
Carre", P., Dielectric machine, 45
on magnets of cast metal, 97
Cascade arrangement of Jars, 279
Cautery by electricity, 369
Cavallo Tiberius, his attempt to
telegraph, 423
his pith-ball electroscope, 3
on a fireball, 304
on atmospheric electricity, 302,
306
Cavendish, Hon. H., on Specific
Inductive capacity, 268, 269
on nitric acid produced by
sparks, 286
Ceca, Father, on atmospheric elec-
tricity, 306
Cell, voltaic, 152
Charge, electric, 7
resides on surface, 27
residual of Leyden Jar, 53, 272
Chart, magnetic, 136, 169
Chemical actions in the battery, 159
laws of, 166, 211, 417
of spark discharge, 286
outside the battery, 205, 412
Chemical test for weak currents, 218,
286
Chimes, electric, 43
Chronograph, electric, 433
Circuit, 152
simple and compound, 181
Clark's(Latimer) standard cell, 177
Clausius, R., theory of Electrolysis,
418
Cleavage, electrification by, 60
Clocks, electric, 433
Cobalt, magnetism of, 86
Coefficient of Magnetic induction, 89
313
of mutual induction, 397
INDEX.
445
Coercive force, 89
Colour of spark, 289
Columbus, Cristofero, on magnetic
variation, 136
Combustion a source of electrification,
62
Commutator, 375, 399, 407
Compass (magnetic), Mariner's, 79,
X 34
Compound circuit, 181
Condensation, 48
Condensers, 48, 267
standard, 276
use of, 275
Condensing electroscope, 71, 149
Conduction, 27, 158
by liquids, 205
of gases, 158
Conductivity, 158, 346, 348
Conductors and Non-conductors, 8, 27
Consequent Poles, 104, 109
Contact Electricity, 71, 149
Series of metals, 72
Continuous electrophorus, 23, 45
Convection of Electricity, 45, 337
Convection-currents, properties of, 337
Convection-induction machines, 45
Convection-streams at points, 35 (a),
43 2 49
Cooling and heating of junction by
current, 380
Cost of power derived from electricity,
378
Coulomb, Torsion Balance, 15, 119
Law of Inverse Squares, 16,
117, 119, 235, 245
on distribution of charge, 35, 248
Coulomb, the, 323
Couple, magnetic, 123
Crookes, William, on shadows in
electric discharge, 293
on repulsion from negative
electrode, 300
Crown of cups, 151
Cruickshank 's Trough Battery, 169
Crystals, electricity of, 66
dielectric properties of, 270
magnetism of, 343
Crystallisation, 61
Cummings phenomenon, 382
Cuneus' discovery of Ley den Jar, 52
Current, effects due to, 153
Current Electricity, 147
strength of, 158, 179
,, unit of, 196
Current -re verser (see Commutator)
Current sheets, 340
Curvature affects surface-density, 35,
249
Curves, magnetic (see Magnetic
Figures)
Cuthbertson's Electric machine, 38,
289
Cylinder Electrical machine, 39
DAILY variations of magnet, 142
Dalibard's lightning-rod, 302
Darnell's Battery, 170
Davy's (Marie) Battery, 175
Davy, Sir Humphrey, magnetisation
by current, 326
discovers electric light, 371
electrolyses caustic alkalies,
4i7 (*)
De Haldat, magnetic writing, in
De la Rive's Floating Battery, 194
DelaR^te, Chloride of Silver Battery,
174, 291
on electrotypmg, 420
on length of spark, 291
Declination, Magnetic, 136
variations of, 136, 141
Decomposition of water, 206, 413
of alkalies, 417
Deflections, method of, 118, 123, 3253
Dellmanris electrometer, 260
Density (surface) of charge, 35, 248
magnetic, 127, 311
Dewar, James, on currents generated
by light in the eye, 231
his capillary electrometer, 225
Diagram, thermo-electric, 383
Diamagnetic polarity, 342
Diamagnetism, 87, 339
of flames, 344
of gases, 340
Diaphragm currents, 224
Dielectric capacity (see Specific In-
ductive Capacity)
strain, 56, 272
strength, 284
Dielectrics, 8, 49, 270
Differential Galvanometer, 203
Dimensions of Units (see Units)
Dip, or Inclination, 137
variation of, 141
Diplex signalling, 428
Dipping Needle, 137
Discharge affected by magnet, 294
brush, 43
by evaporation, 223
by flame, 7, 291
conductive, 282
convective, 43, 283
disruptive, 281
/
446
INDEX.
Discharge affected by points, 43, 290,
effects of, 43, 284, 286
electrical, 7, 280
glow, 290, 302 (footnote)
limit of, 248
sensitive state of, 294
velocity of, 296
Discharger, Discharging-tongs, 51
Universal, 54
Disruption produces electrification, 60
Dissectable Leyden Jar, 55
Dissipation of Charge, 299
Distillation, electric, 223
Distribution of Electricity, 28, 35,
248, 249
of Current, 240
of Magnetism, 104, 122
Divided Circuit, 353
Touch, 93
Dolbear's Telephone, 436
Doubler, 23, 45
Double Touch, 94
Dry-Pile, 182, 264
Duboscq's Lamp, 372
Du Fay's experiments, 4, 27
Duplex Telegraphy, 275, 428
Duration of Spark, 296
Duter on Electric Expansion, 273
Dynamic Electricity (see Current
Electricity)
Dynamo-electric machines, 408
Dyne, the (unit of force), 255
E
EARTH, the, a magnet, 88
currents, 275, 403
electrostatic capacity'of, 32 $b
intensity of magnetisation, 313
magnetic moment of, 325b
used as return wire, 423
Earth's magnetism (see Terrestrial
Magnetism)
Edison, Thomas A Iva, electric lamp,
374 ; stearn-dynamo, 411 (6)
carbon telephone, 436
meter for currents, 216
quadruplex telegraphy, 428
Edlund on galvanic expansion, 221
Eel, electric (Gymnotus), 68
Electrics, i
Electric Air-Thermometer, 288
Cage, 34
Candle, 373
Clocks, 433
Distillation, 223
(Frictional) machines, 39
Electric Egg, the, 292
Expansion, 273
Force, 155 (footnote), 241
Fuze, 286, 370
Images, 250
Kite, 302
Lamps, 372
Light, 371
Mill or Fly, 43
Oscillations, 295
Osmose, 222
Pistol, 286
Shadows, 293
Shock, 226
Wind, 43
Electricity, theories of, 6, 300
Electro-capillary phenomena, 225
Electro-chemical equivalents, 211, 212
Electro-chemistry, 412
Electrodes, 207
unpolarisable, 231
Electrodynamics, 331
Electrodynamometer, 336,378 (bis.)
Electrolysis, 208
laws of, 211, 414, 417
of copper sulphate, 209
of water, 207, 413
theory of, 414
Electrolytes, 207, 417
Electrolytic convection, 418
Electromagnets, 98, 326
laws of, 328
Electromagnetic engines (motors), 375
Electromagnetics, 310
Electromagnetic theory of Light, 390
Electromagnetism, 326
Electrometallurgy, 419
Electrometer, absolute, 261
attracted-disc, 261
capillary, 225, 265
Dellmanns, 260
divided-ring, 71
Peltier's, 260, 307
portable, 261
quadrant (Sir W. Thomson' s} t
262
repulsion, 260
torsion, 15
trap-door, 261
Electromotive-force, 155
measurement of, 360
unit of, 322, 323
Electromotors, 375
Electro-Optics, 385
Electrophorus, 22
continuous, 23, 45
Electroplating, 421
Electroscopes, n
Bohnenberger's, 13, 264
INDEX.
447
Electroscopes, Bcnnefs gold-leaf, 13,
25
Fechner's, 264
Gaugain's discharging, 259
Gilberts straw-needle, 12
Ha-tikel's, 264
Henley's quadrant, 14
Pith-ball, 2, 3
Voltes condensing, 71, 149
Electrostatics, 7, 233
Electrotyping, 420
Energy of charge of Leyden Jar, 270
of electric current, 378
Equator, Magnetic, 78
Equipotential surfaces, 242, 310 (f)
magnetic, 310
Equivalents, electro-chemical, 212
Erg, the (unit of work), 255
Evaporation produces electrification,
63,303
discharge by, 223
Everett, James D., on atmospheric
electricity, 307
on exact reading of galvan-
ometer, 202 (footnote)
on intensity of magnetisation
of earth, 313
Expansion, electric, 273, 386
Extra-current (self-induced), 404
FAILURE and exhaustion of batteries,
1 60
Fall of Potential along a wire, 263, 357
Farad, the (unit of capacity), 276, 323
Faraday, Michael, molecular theory
of electricity, 6
chemical theory of cell, 166
dark discharge, 290
Diamagnetism, 339, 340, 344
discovered inductive capacity,
2i, 269, 271
Discovery of magneto - induc-
tion, 391
Electro-magnetic rotation, 375
experiment on dielectric polar-
isation, 272
gauze-bag experiment, 31
hollow-cube experiment, 31
ice-pail experiment, 34
laws of electrolysis, 211, 214
Magnetic lines-of-force, 108, 402
on Aragrfs rotations, 401
on dissipation of charge, 291
on identity of different kinds of
electricity, 217, 218, 286
Voltameter, 214
Faraday, Michael, Magneto -optic
discovery, 387
predicted retardation in cables,
2 74
Faure's Secondary Battery, 415
Favre^s experiments on Heat of Cur-
rents, 368
Fechner's electroscope, 264
Feddersen, W., on electric oscilla-
tions, 296
Ferromagnetic substances, 339
Field, magnetic, 105, 191, 312
Figures, magnetic (see Magnetic
figures)
electric, 297
Fire of St. Elmo, 302 (footnote)
Flame, currents of, 291
diamagnetism of, 344
discharge by, 7, 291
produces electrification, 62
Fleming's Battery, 182
Fontana on electric expansion, 273
Force, electric, 155 (footnote), 241,
251* 252
magnetic, 83, 155 (footnote),
electromotive, 155
Foucaults Regulator Lamp, 372
Interrupter, 398
Franklin, Benjamin, discovered
action of points, mentioned
in, 35 (c), 43, 32
cascade arrangement of Leyden
Jars, 279 ^
Electric Chimes, 43
Electric Kite, 302
Electric portraits, 288
his charged pane of glass, 47
invents Lightning Conductors,
kills turkey by electric shock,
226
One-fluid theory of Electricity,
6
on seat of charge, 55
theory of the Aurora, 309
" Free" electricity, 24, 149 (footnote)
Friction produces electrification, i, 10
Frog's legs, contractions of, 148, 229
Froment's Electromotor, 375
Fuze, electric, 286, 370
Galvani, Aloysins, observed move
ments of frog's leg, 148
448
INDEX.
Galvani, Aloystus, on preparation of |
frog's limbs, 229
on Animal Electricity, 231
Galvanic Batteries (see Voltaic
Batteries)
Electricity (see Current Elec-
tricity}
Taste, 227
Galvanism (see Current Electricity)
Galvanometer, 197
absolute, 200
astatic, 198, 231
ballistic, 204
constant of, 200
differential, 203
Du Bois Reymond's, 231
Helmholtz's, 199
reflecting (Sir IV. Thomson's),
or mirror, 202
sine, 201
tangent, 199
Galvanoplastic (see Electrotyping)
Galvanoscopej 188
Gas Battery, 416
Gases, resistance of, 158
Gassiot, J. P , on striae, 294, 300
Gaugain, Jean Mothee, discharging
electroscope, 259
on Pyroelectricity, 66
Tangent Galvanometer, 199
Gauss, F., invented absolute measure-
ment, 325a
magnetic moment of earth,
3250
magnetic observations, 313
Gay, Lussac, on atmospheric elec-
tricity, 307
Geissler's tubes, 291
Gernez on electric distillation, 223
Gibson and Barclay on dielectric
capacity of paraffin, 270
Gilbert, Dr. William, discovers
electrics, i
discovered magnetic reaction,
. 8 3
discovers that the earth is a
magnet, 88, 135
heat destroys magnetism, 99
his balanced - needle electro-
scope, 12
observation of moisture, 9
observations on magnets, 78
on de - electrifying power of
flame, 291
on magnetic figures, 108
on magnetic substances, 85
on magnetic permeability, 84
on methods of magnetisation,
96,97
Gilding by Electricity, 431
Globular lightning, 304
Glow Discharge, 290, 302 (footnote]
Glowing of wires, 369
Gold-leaf Electroscope (see Electro-
scope)
Gordon,}. E. H., on magneto-optic
rotatory power, 387
on dielectric capacity, 270, 271
on length of spark, 291
Gramme's dynamo-electric machine,
410
Gravitation Battery, 176
Gray, Stephen, discovers conduction,
27
on lightning, 302
Grotthnss' theory, 160, 418
Grove, Sir William R., his Gas
Battery, 416
Grove's Battery, 171
magnetic experiment, 113
on electric property of Flame,
291
Guard-ring, Guard-plate, 248, 261
Guericke, Otto von, discovered elec-
tric repulsion, 3
invents electric machine, 38
observes electric sparks, 9
Gunpowder fired by electricity, 286,
288, 370
Gymnotus (electric eel), 68, 218
Halts phenomenon, 337
Hankel's electroscope, 264
Harris, Sir W. Snow, his unit
Leyden jar, 259
attracted - disc electrometer,
261
on length of spark, 291
Heat, effect of, on magnets, 99, 100
,, batteries, 183
,, conductivity, 349
Heating effects of currents, 171, 366,
380
due to magnetisation, 113, 401
effect of^sparks, 288
,, dielectric stress, 272
local, at electrodes, 417
Helmholtz, Hermann L. F., on
effect of current on sight, 228
Electrolytic convection, 418
Equations of Self-induction,
405
Galvanometer, 199
Henry, Joseph, invented the
" sounder," 423
INDEX.
449
Henry, Joseph, on induced currents of
higher orders, 406
Holtz, W., his electric machine, 46
on electric shadows, 293 (foot-
note]
on tubes having unilateral re-
sistance, 300
Hopkinson, John, on dielectric cap-
acity of glass, 270
on residual charge and its
return, 53, 272
Horizontal component of magnetism,
123, 138
Hughes, David Edward, the Print-
ing Telegraphers
the Microphone, 437
Humboldt, Alexander von, on elec-
tric eels, 68
discovers galvanic smell, 228
produced electric contractions
in fishes, 229
Hunter, Dr. John, on effect of
current on sight, 228
Hydroelectric machine, 44
IMAGES, electric, 250
Incandescent electric lights, 374
Inclination (or Dip), 137
variation of, 141
Index Notation, 3250
Induced charges of electricity, 18
currents, 391
Induction (electrostatic) of charges,
18
(magnetic) lines of, 89
(magnetic) of magnetism, 89,
3i3
coefficient of, 342
(magneto-electric) of currents,
. 39i
Induction-coil or Inductorium, 398
Induction-convection machines, 45
Inductive-capacity, specific, 21, 49,
268, 272
Insulators, 8, 27
Intensity of current, 179
ef earth's magnetic force, 138,
3 2 5a
of magnetic field, 312
of magnetisation, 313
Inverse Squares, Law of, 16, 117, 235,
245 .
Inversion, Thermo-electric, 382
Ions, 210
Isoclinic lines, 139
Isogonic lines, 139
Jacoot, Moritz Hermann, on local
action, 162
discovers galvanoplastic pro-
cess, 420
his boat propelled by electricity,
theory of electromotors, 377
Jallochkofi, Paul, his battery, 182
electric candle, 373
Jar, Ley den, 51
capacity of, 50, 267, 277
cascade arrangement of,
279
discharge of, 51, 295
discovery of, 52
,, energy of charge of, 278
seat of charge of, 55
spark of, 289, 296
theory of, 267
^ Unit, 259
Jenkin, Fleeming, on cable as con-
denser, 274
on magnetic saturation, 328
on retardation in cables, 296
Joule, James Prescott, on effects of
magnetisation, 113
Law of Heat of Current, 367
. Mechanical equivalent of Hea
eat,
. 4*4
on atmospheric electricity, 306
on lifting - power of electro-
magnet, 330
./<7#/-effect, the, 380, 367
KATHODE, 207
Kation, 210
Keeper, 101
Kerr, Dr. John, Electro - optic dis-
coveries, 273, 386
Magneto-optic discoveries, 114,
388
Kinnersley, Elijah, Electric Ther-
mometer, 288
Kirchhoff, Gustav, Laws of Branched
Circuits, 353 ^
Kite, the electric, 302
Kohlrausch, F., on residual charge,
272
on electro-chemical equivalent,
211 (footnote)
LAMELLAR magnetisation, 107
2 G
45
INDEX.
Laminated magnets, 95 i
Law of Inverse squares, 16, 117, 235, !
245
Leakage, rate of, 299
Leclctnchl's Battery, 173
Le Baillif on diamagnetism of
antimony, 339
Lemonnier discovers atmospheric
electricity, 306
Length of spark, 291
Lenz's Law, 396
alcohol calorimeter, 367
Leyden Jar (see Jar)
Lichtenberg 's figures, 297
Lifting-power of magnets, 103
of electromagnets, 330
Light affects resistance, 389
Electric, 371
Electromagnetic theory of, 365,
390
polarised, rotated by magnet,
. 114, 387, 388
Lightning, 9, 302, 304
conductors, 32, 305
duration of, 296, 304
Lines-of-force, electric, 243
due to currents, 191, 327, 334
magnetic, 89, 108, 310, 312
Lippmann, G., Capillary Electro-
meter, 225, 265
Liquids as conductors, 205
resistance of, 348
" Local Action " in batteries, 161
Lodestone, 76, 340
"Long-coil" instruments, 352
Loss of Charge, 15, 299
Louis XV. electrifies 700 monks, 226
Lullin's experiment, 285
Luminous effects of spark, 289, 400
M
MACHINE, Electric, 38
convection-induction, 45
cylinder, 39
dynamo-electric, 408
Holtzs, 46
hydro-electrical, 44
invention of, 38
magneto-electric, 407
plate, 44
Winter's, 40
Magne-crystallic action, 343
Magnet, breaking a, 106
Magnets, natural and artificial, 76,
77, 326
Magnetic actions of current, 184, 318,
326, 327, 334
Magnetic attraction and repulsion, 80,
no
cage, 84
curves, 108, 191
field, 105, 191, 312, 327
figures, 108, 109, no, 191
,, theory of, 126
fluids, alleged, 91
force, 83, 310 (e)
measurement of, 118,
32$a
induction, 89
coefficient of, 342
iron ore, 76
lines-of-force, 89, 108, 109, no,
316
lines-of-force of current, -191,
320, 327
maps, 139
meridian, 136
metals, 86, 339
moment, 123 (footnote), 313,
3 25a
needle, 79, 134
oxide of iron, 76, 172 (footnote)
paradox, a, 128
pole, unit, 125
potential, 310, 314, 315
proof-plane, 402
saturation, 102
, , Beetz, on, 1 1 5 ( foot-
note), 328 ()
screen, 84
shell, 107, 192, 311 (Jt)
,, force due to, 127
,, potential due to, 127, 315
storms, 145, 309
substances, 85, 339
units, 321
writing, in
Magnetisation, coefficient of, 89, 313,
340
intensity of, 313
lamellar, 107
mechanical effects of, 113
methods of, 92-98, 326
solenoidal, 107
sound of, 113, 434
time needed for, 324 (e)
Magnetism, 76
action of, on light, 114, 387
caused by heat, 98
destruction of, 99
distribution of, 104
of gases, 339, 387
lamellar, 107
laws of, 81, 116, 310
permanent, 90, 313
residual, 102
INDEX.
451
Magnetism, solenoidal, 107, 314
temporary, 90, 102, 313
terrestrial, 88, 135
theories of, 91, 115, 338
unit of, 125
Magnetite, 76
Magneto-electricity, 74, 391
Magneto-electric induction, 391
machines, 407
Magnetographs, 146
Magnetometer, 124
self-registering, 146
Magneto-optic Rotations, 387
Magnets, artificial, 77
compound, 95
forms of, 101
lamellar, 107
laminated, 95
methods of making, 92-98
natural, 76, 101
power of, 103
Mance's method, 361
Maps, magnetic, 139
Mariner's Compass, 134
Marked pole, 80
Mascart, E., on self - registering
apparatus, 288
on atmospheric electricity, 308
Matteiicci, Carlo, on physiological
effects, 68, 230
on electromotive - force in
muscle, 231
Maynooth Battery (see Callaris
Battery)
Maxwell, James Clerk, Electro-
magnetic theory of Light,
337, 365, 390
on ii,iectric Images, 250
on protection from Lightning,
3 2 > 35
on residual charge of jar, 272
on self-repulsion of circuit, 334
rule for action of current on
magnet, 193, 317
Theorem of equivalent Mag-
netic shell, 192, 318
Theory of Magnetism, 115
Measurements, electrical, 355-363
magnetic, 118, 325a
Mechanical effects of Discharge, 284,
effects of magnetisation, 113
in dielectric, 272
Medical Applications of Electricity,
232,369
Megohm, 323
Meidinger's Battery, 176
Meridian, Magnetic, 136
Metallo-chromy, 432
Microfarad condenser, 276
Microphone, the, 437
Milli-ampere, 323
Mimosa, the, electric behaviour of, 230
Minotto's Battery, 176
Mirror Galvanometer, 203
Moisture, effect of, i, 8, 299
Molecular theory of Electric action, 6
actions of current, 221
Moment of Couple, 123
of inertia, 325a
magnetic, 123 {footnote), 32sa
Morse Telegraph instrument, 425
Mouse-mill (see Replenisher)
Miiller, Johannes, on strength of
electromagnets, 328
Multiplier, Schweigger's, 189
Muscular contractions, 229, 231
Musschenbroek, Peter van, dis-
covery of Ley den Jar, 52
on Magnetic Figures, no
Mutual Induction, coefficient of, 320,
397
Mutual Potential, coefficient of, 320
N
Napoleon III.'s Battery, 182
Needle, magnetic, 79
Needle Telegraph, 424
Negative electrification, 4, 300
Newton, Sir Isaac, observations on
action and reaction, 83
his lodestone, 103
suggests electric origin of light-
ning, 9, 302
suggests glass for electric
machines, 38
Niaiidefs Battery, 173
Nobili t LeopoldOi on muscular con-
tractions, 68
on currents of animal electricity,
231
discovers NobiWs rings, 422
Non-conductors, 8
Non-electrics, 2
North and south, 81, 135
North magnetic pole, the, 81, 135
Null methods, 263
Oerstedt, Hans Christian, discovers
magnetic action of current, 184,
185, 191
Ohm, Dr. G. S., 179
" Ohm's Law," 180, 345
452
INDEX.
Ohm, the, or unit of resistance, 323
,, determination of, 364
One-fluid theory of electricity, 6
Optical strain, electrostatic, 386
electromagnetic, 387
Oscillations, electric, 295
method of (for electrostatics),
120 (footnote), 235
method of (for magnetic mea-
surement), 120, 121, 122, 32$a
Osmose, electric, 222
Other sources of electricity than fric-
tion, 10, 57
Ozone, 208, 298, 302 (footnote)
Page, Charles G., discovers magnetic
sounds, 113
Parallel currents, laws of, 332
Paramagnetic, 339
" Passive" state of iron, 172 (footnote]
Peltier, Atfianase, his electrometer,
260, 307
heating effect at junctions, 380
theory of thunderstorms, 303
Penetrative power of discharge, 284
Periodicity of aurora and magnetic
storms, 144, 145, 309
Perry and Ayrton (see Ayyton and
Perry)
Pile, Voltaic, 150
Pith-ball electroscope, 2, 3
Phosphorescence caused by discharge,
292
Photo -voltaic property of selenium,
389
Photophone, 389
Physiological actions, 226, 287
Plane, the proof-, 29
,, For magnetism, 402
PlantS, Gaston, his secondary bat-
teries, 415
on globular lightning, 304
Plants, electricity of, 69, 230
Plate condenser, 48, 268, 277
electrical machine, 40
Plilcker, Julius, on magne-crystallic
action, 343
Poggendorff,J. C., his battery, 165
Pouits, density of charge on, 35, 249
discharge at, 39, 42, 43, 249
Polarity, diamagnetic, 342
magnetic, 82, 106, 115
Polarisation (electrolytic) in battery
cells, 163, 414
of Voltameter, 272, 413, 415
remedies for, 165
i Polarised light rotated by magnetic
forces, 387
relay, 428
j Poles of magnets, 78, 122
of pyroelectric crystals, 66
of Voltaic battery, 154
j Porrefs phenomenon, 222
Portable electrometer, 261
j Portative force, 103
i Positive and negative electrification.
! 4 3?
j Potential, electric, 37, 237
zero, 37, 239
magnetic, 310, 314, 315
due to current, 318
mutual, of two circuits, 319,
320
Pouillet, Claude S. M., sine galvan-
ometer, 201
tangent galvanometer, 199
Power, transmission of, 376
Practical Units, 323
Preece t William Henry, on space
protected from lightning, 305
Pressure produces electrification, 65
Priestley, Joseph,, on electric expan-
sion, 273
Prime conductor, 39
Printing telegraphs, 423
Proof-plane, 29
,, (magnetic), 402
Poisson on magnetism in crystals
Protoplasm, electric property of, 231
Pyroelectricity, 66
Q
Quadrant electrometer (Sir W.
Thomson's), 262
electroscope (Henley s), 14
Quadruplex telegraphy, 428
"Quantity" arrangement of cells,
etc., 181
of electricity, unit of, 17, 236
Quetelet, ., on atmospheric elec-
tricity, 308
Quincke, Georg, on diaphragm cur-
rents, 224
on electric expansion, 273
on electro - optic phenomena,
386
Ray, electric (torpedo), 68
Recovery, elastic, 272
INDEX.
453
Redistribution of charge, 36
Reflecting galvanometer, 202
Registering magnetographs and elec-
trometers, 146, 307^
Reis, Philip t invention of telephone,
434
Relation between currents and mag-
nets, 184, 318, 326, 391
between current and energy,
378
between current and heat and
light, 366
Relays, 426
Replenisher, 45, 261, 262
Repulsion and attraction of electrified
bodies, i, 3, 18, 20, 66, 236
and attraction, experiments on,
43
and attraction of currents, 331
and attraction of magnets, 76,
80
Repulsion electrometers, 260
Residual charge of Leyden jar, 53, 272
,, of cable, 274, 430
of Voltameter, 272,
4i5
magnetism, 102
Resinous electricity, 4
Resistance, 27, 158, 179, 346
absolute unit of, 363, 364
affected by temperature, 349
light, 389
,, sound, 436
as a velocity, 363
bridge or balance, 358
coils, 359
internal, of cell, 181, 350
,, measurement
of, 361
laws of, 347
measurement of, 356
of gases, 158, 348
of liquids, 158, 349
specific, 348
Retardation of currents through
cables, 274, 296, 430
Retentivity (magnetic), 90, 313
Return shock or stroke, 26, 304
Reymond, D^l Bois, his galvanometer,
231
on animal electricity, 231
unpolarisable electrodes, 231
Rheocord, 356
Rheostat, 356
Rheometer, \
Rheoscope, > see footnote to 197
Rheotrope, )
Riess, Peter, on electric distribution,
35
Riess, Peter, on length of spark, 291
electric thermometer, 288 {foot-
note}
Ritchie s electromotor, 375
Ritter, Johann IVilhelm, on action
of current on sight, 228
his secondary pile, 415
on subjective galvanic sounds,
230
on the sensitive plant (Mimosa),
230
Rolling friction, 10
Romagnosi, Dr., discovers magnetic
action of current, 184
Romas, De, his electric kite, 302
Ronalds, Sir Francis, invented a
telegraph, 423
Rotations, electromagnetic, 335
Arago's, 401
Rowland, Harry A ., on magnetic
effect of electric convection, 337
on intensity of magnetisation,
3*3
Ruhmkorff's induction coil, 398
commutator, 399
electromagnet, 339
St. Elmo's fire, 502 (footnote)
Salts, electrolysis of, 417
Sanderson, J. Burdon, on electric
sensitiveness of carnivorous plants,
231
Sawdust battery, 158, 176
Schiveigger's multiplier, 189
Secondary batteries, 178, 415
Secular variations of magnetic ele-
ments, 141
Seebeck's discovery of thermo-elec-
tricity, 379
Selenium, photo-voltaic properties of,
Self-induction of circuit, 404
Self-recording apparatus, 146, 288, 307
Self-repulsion of current, 334
Sensitive plant, behaviour of, 230
Series, union of cells in, 171
Shadows, electric, 293
Sheet conductor, flow of electricity
in, 354
Shell, magnetic (see Magnetic Shell)
Shock, electric, 226
of current, 226
"Short-coil" instruments, 352
Shunt, 202
Siemens, Carl ]Vilheltn t on heating
effect in Leyden jar, 272
454
INDEX.
Siemens, Carl Wilhelm, his dynamo- j Tatty Peter Guthrie, thermo-electric
electric machine, 409 ! diagram, 383
his longitudinal armature, 407 j Tangent galvanometer, 199
! Taste affected by current, 227
Sight affected by current, 228
Silurus, the, 68
Sine galvanometer, 201
Single touch, 92
Single-fluid cells, 169
Siphon-recorder, 431
Smee's Battery, 165, 169
Soap-bubble, electrified, 3
Solenoid, 327
magnet, 314
Solid angles, 133
Solidification, 61
Sound of magnetisation, 113
Sounder, the, 425
Sources of electricity, 10, 57
Spark, 9, 43, 281
duration of, 296
length of, 44, 291, 302
Specific resistance, 348
inductive capacity, 21, 49, 268,
272
Speed of signalling, 274, 275, 296, 430
Sphere, distribution of charge over
35 (a), 248, 249
Spottiswoode, William, on stnse, 294
Stewart, Balfoiir, on atmospheric
electricity, 308
on magnetic storms, 144
Storms, magnetic, 145
Standards of resistance (see Resist- \
ance Coils)
Strain, dielectric, 56
Strength of current, 158, 179
,, in magnetic mea-
sure, 195, 196
Strength of magnet pole, 102
of magnetic shell, 315
Striae in vacuum tubes, 292, 294
Sturgeon, W., invents the electro-
magnet, 326
Submarine telegraphs, 429
Sulzer^s experiment, 227
Symmer, on two kinds of electrifica-
tion, 4
Surface-density of charge, 35, 248
limit of, 248
of magnetism, 127, 311
Swammerdam 's frog experiment, 229
Swans electric lamp, 374
T
Tatty Peter Guthrie, electrification
by evaporation of sulphate of copper
solution, 63
Telegraph, electric, 423
Bain's chemical, 218
Morse's^ instrument, 425
needle instrument, 424
Telegraphy, diplex, 428
duplex, 428
quadruplex, 428
submarine, 429
Telephone, Philip Reis's, 434
currents of, 229
Dolbears, 436
Edison's (carbon), 436
Graham Bell's (articulating),
Varley's (condenser), 272
Temperature affects resistance, 183
affected by resistance, 369
Tension of electrostatic forces, 248
(footnote)
Terquem, A. y parrot-cage experi-
ment, 31
Terrestrial Magnetism, 88, 135
Test for weak currents (chemical), 218,
286
for weak currents (physiologi-
cal), 229
Testing for faults, 427
Tetanisation produced by interrupted
currents, 230
Theories of Electricity, 6, 300, and
preface, ix.
Theories of Magnetism, 91, 115
,, Ampere's, 338
Maxwell's, 115
Theory of Electrolysis, Joule's, 414
Grotthuss's and Clausiuss, 418
Thermo-electric currents, \
Thermo-electricity,
7, 379
Thermo-electric Diagram, 383
Thermo-electromotive Series, 382
j Thermo-pile, 384
Thompson, Silvamts Phillips, on
magnetic figures due to cur-
rents, 334
on Magnetic wntmg, in
on Nobili's rings, 422
on Positive and Negative
states, 300
on opacity of Tourmaline, 390
(footnote)
Thomson, Joseph, /., on Contact
Electricity, 73
Thomson, Sir William, the Re-
plenisher (or Mouse-Mill), 45, 261,
262
INDEX.
455
Thomson, Sir William, Proof of
Contact Electricity, 71
Attracted - disc Electrometers,
261
Divided-ring Electrometer, 71
Electric convection of Heat
(the " Thomson-effect"), 383
Mirror Galvanometer, 202, 431
Modified Daniel? s Battery, 176
on atmospheric electricity, 306
on Electric Images, 250
on length of spark, 291
on nomenclature of Magnet
Poles, 81 (footnote)
on sounds in condensers, 272
predicts electric oscillations,
295 (footnote)
Quadrant Electrometer, 262
Siphon Recorder, 431
Thermo-electric Diagram, 383
Water-dropping Collector, 307
Thunder, 9, 304
Thunderstorms, 302
Theory of, 303
Tinfoil Condensers, 47, 275
Tongs, Discharging-, 51
Torpedo (electric fish), 68, 218
Torpedoes, fuzes for firing, 286, 370
Torsion affected by magnetisation, 113
Torsion Balance, or \ (Coulomb's)
Torsion Electrometer ) 15, 119
Total action of magnet, 32$a
Tourmaline, 66, 297, 390 (footnote)
Transmission of Power by Electricity,
376
Tubes offeree, 243, 311
Two-fluid cells, 170
Two-fluid theory, 6
Two kinds of Electrification, 4, 5
,, Magnetic poles, 81
Tyndall, John, on diamagnetic polar-
ity, 342
on magne-crystallic action, 343
UNIT Jar, 259
Unit (Electrostatic) of Electricity, 17,
236
Electrostatic) of Capacity, 247
lagnetic Pole, 125
of difference of potential, 242
322, 323
of Electromotive-force, 322, 323
of Resistance, 322, 323
of Strength of Current, 196,
322, 323
Units, Fundamental and Derived,
.254. 255
dimensions of, 258, 324
Electrical (Electrostatic), 257
Electromagnetic, 322, 323
Magnetic, 321
Physical Dimensions of, 258,
324, 35i
Practical, 323
Universal Discharger, 54
Ure t Dr., on Animal Electricity, 229
" v" values of, 365, 390
Vacuum, induction takes place
through, 56, 84, 89
partial, spark in, 9, 292
spark will not pass through,
291
Vacuum-tubes, 292
"Variation," the (see Declination)
Variation of Declination and Dip,
secular, 141 ; annual, 143 ; diurnal,
142 ; geographical, 136
Varley, C. F. , his Telephone, 272
Vegetables, Electricity of, 69
carnivorous, sensitiveness of,
230
Velocity of Discharge, 296
of Electricity (alleged), 296
of Light, 365, 390
Verdetjs Constant, 387
Vibration produces Electrification, 59
Vitreous electricity, 4
Volt, the, 323
Volta, A lessandro, his Electrophorus,
22
Condensing Electroscope, 71,
149
Contact Senes, 72
Crown of Cups, 151
on Atmospheric Electricity, 307
on Contact Electricity, 71, 148
on Electric Expansion, 273
on Electrification due to com-
bustion, 62
Subjective Sounds due to
Current, 228
Volta's Law, 72, 148, 156
Voltaic Pile, 150
Voltaic Electricity (see Current Elec-
tricity)
Arc, 371
Battery, 154, 167; Pile, 150
Cell, simple, 152
Voltameter, 214, 215, 216
Voltmeter, 360 (d)
45 6
INDEX.
W
WATER, Electrolysis of, 206, 413
Weber, the 323
Weber, Wilhelm, the Electro-dyna-
mometer, 336
on diamagnetic polarity, 342
Wheat 'stone, Sir Charles t on the
brush discharge, 290
Automatic Telegraph, 423
Dynamo-electric Machines, 408
on supposed velocity of elec-
tricity, 296
Wheatstone's Bridge or Bal-
ance, 358
Wiedemann, Gustav, on effect of
magnetism on torsion, 113
Wiedemann, Gustav, on diamag-
netism of platinum, 339
Wilde, Henry, Electric Candle, 373
Magneto-electric Machine, 407
Wind, Electric, 43
Wdhler^s Cell, 182
Wollastoris Battery, 169
Wiillner on dielectric capacity, 270
z
ZambonVs Dry Pile, 13, 182, 264
Zanotti, experiment on grasshopper,
229
Zero Potential, 37, 239
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