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The energy lost during a complete cycle
is proportional to the entire shaded area
enclosed by the loop. It will be seen from
this that the lost energy is much less in the
case of soft iron than it is in the case of
steel. This lost energy reveals itself in the
form of heat, the temperature of the core
rising. It represents waste which in the
case of certain alternating-current ma-
chines may assume serious proportions . It
is largely on this account that the best and
softest iron is used in the cores of trans-
Fig. 18 1. formers (Par. 431). Ewing has shown that

the energy consumed in subjecting one ton of soft iron to 100
cycles of strong magnetization per second is about sixteen horse-
power and the energy loss for a very hard tungsten steel is twenty
times greater.

400. Law of Magnetic Circuit. In Par. 387 it was shown that
the intensity of the field at the center of an indefinitely long sole-
noid is

in which N is the number

of turns per centimeter and 7 is the current in absolute units.
Actually it is impracticable to employ very long magnetizing coils
but by substituting the proper values in the integral in the para-
graph referred to, it can be shown that in applying the above
formula to coils whose length is not less than six times their diam-
eter, the error committed does not exceed one per cent. If the


length of the magnetizing coil be I and if the total number of turns
be n, the above expression can be written

ff = ^ ':",.; (I)

Suppose this coil to be wrapped uniformly around an iron ring
whose length is I and whose permeability is /*. The flux or induc-
tion per square centimeter (the word " induction" being used in the
sense of "crop of lines of force produced") is

If the cross-section of the core be A, the total induction is

This may be put in the following form

In Par. 391 it was shown that reluctance is the reciprocal of
permeability, therefore representing 1/V by (ft, the above becomes


Ohm's law may be written (Par. 285)


The similarity of these two expressions is striking. In the case
of electricity, the current varies directly as the electro-motive
force and inversely as the resistance; in the case of the magnetic
field, the flux varies directly as the magneto-motive force and
inversely as the reluctance.

From (I) 47r%7, the magneto-motive force, is equal to H.I in
which H is force in dynes and I is length in centimeters, therefore
this magneto-motive force is measured in work, or ergs. It will be
recalled that the electro-motive force between two points is also
measured (Par. 72) by the work expended in moving a unit charge
from one point to the other.



From (II) it is seen that, like resistance, the reluctance varies
directly as the length and inversely as the cross-section of the
magnetized body, and also as the factor (R, which may be called
the specific reluctance or the reluctivity of the body. It can be
shown by the method used in Par. 288 that specific reluctance is
measured by the reluctance of a centimeter cube of the substance.

The foregoing analogy is not complete. The resistance of a
conductor kept at a constant temperature does not vary with the
current; on the other hand, the permeability, and hence the
reluctance, does vary with the flux.

401. Calculation of Flux. It is seldom that the magnetic cir-
cuit is a complete iron path as assumed in the preceding para-
graph. It most frequently is intersected by air gaps and is
composed of portions which differ in permeability. In such a
case the total reluctance is the sum of the separate reluctances
in series. As an illustration, suppose we are required to calculate

the flux through a magnetic
circuit as shown in Fig. 182
consisting of an iron horseshoe-
shaped portion M whose length
is h, cross-section AI and per-
meability jui, and a cylindrical
iron armature B, whose average
length is 4, cross-section A 2 ,
and permeability ju 2 , the arma-
ture being separated on either
side from the horseshoe frame
by an air gap of length 4, cross-
section A 3 and permeability
unity. The flux, if / be in amperes, is





~> \ \
Vi \ \



1 1 !

i i i

i i '

i i

J^ i






1 1 1

1 1 1


ifo- -//- -<-ii- H

Jjj -

Fig. 182.

A 1M1 ' A 2M2 '

As an alternative problem we may be required to calculate the
ampere turns to produce a required flux in a given circuit. This
involves the solution of the above equation for nl but is com-
plicated by the decrease in permeability with increase in flux.
The permeability under the conditions of the problem is best
obtained from tables or from the corresponding curves of mag-



netization (Par. 394). It may also be necessary to make allow-
ance for a certain amount of leakage of flux which occurs at the
air gaps.

The foregoing calculations are not exact but they enable the
designer of electrical machinery to approximate very closely to.
the solution of his problems.

402. Diamagnetism. In Par. 122 reference was made ta
diamagnetism, or the property possessed by certain bodies,
notably bismuth, which causes them to be feebly repelled from the
poles of a magnet. Various attempts have been made to account
for this phenomenon, the explanation now accepted being based
upon the theory that the permeability of these diamagnetic
substances is less than that of the surrounding medium. Fig. 183
represents a block of bismuth placed in a
magnetic field. The bismuth being less per-
meable than the surrounding air, it crowds off
to the right and left a portion of the field. The
tension along the lines of force causes the
bismuth to move from the stronger into the
weaker field, or away from the magnet.

This hypothesis is corroborated by the fact
that a glass tube filled with a solution of an
iron salt is paramagnetic when suspended in

Fig. 183.

air between the poles of an electro-magnet, but becomes diamag-
netic when surrounded by a denser or more concentrated (and
hence more permeable) solution of the same salt.




403. Electro-Magnets. The combination of a coil with a core
-of a magnetic substance, usually soft iron, which is made a magnet
by the passage of a current through the coil is called an electro-
magnet. The first electro-magnets were made in 1824 by the
English scientist Sturgeon. At that time insulated wire had not
been invented and his magnets were made by insulating the core
by a thick coating of varnish and wrapping the wire on top of this,
the successive turns being so spaced that they did not touch each
other. In 1826, Joseph Henry of Albany discovered how to
insulate wire by a silk covering. This enabled him to wrap the
wire more closely and to put on several layers and he soon pro-
duced electro-magnets remarkable for their power. In 1831 he
constructed one whose iron core weighed less than sixty pounds
yet could support over a ton.

404. Rules for Polarity of Electro -Magnets. After the facts
brought out in the preceding chapters it is perhaps unnecessary
to give a rule for determining the polarity of an electro-magnet.
Should such be needed, the simplest is the right hand rule, which
is merely a variation of the rule given in Par. 345. Place the
palm of the right hand upon the coil, the fingers pointing in the
direction of the flow of the current (Fig. 173) ; the extended thumb
will point to the north pole of the magnet. Another rule frequently
used is the following. Face the pole of the manget; if the mag-
netizing current flows around it in a clockwise direction it is
a south pole; if in a counter-clockwise direction it is a north

405. Value of Electro-Magnets. Electro-magnets are used
extensively and for very varied purposes, their value depending
upon the three following characteristics. j

(1) Their great power. They can be made very much more
powerful than the strongest permanent magnets and they can
also be made of much greater size.


(2) Control of magnetism. The magnetism is perfectly under
the control of the operator and, like an electric light, may be
turned off or on at pleasure.

(3) Control from a distance. The control can be exerted even
at distances of several hundred miles.

406. Tractive Power of Magnets. In Par. 66 it was shown
that a unit charge placed near a plane charged to a uniform sur-
face density 5 is acted upon by a force of 2ird dynes. A frequently
employed conception of magnetism is that the intensity of
magnetization is due to the number of unit poles spread over the
polar or terminal surface of the magnet (Par. 133). If AT" (Fig.
184) be the pole of a bar magnet and if S be a bar of soft iron or
other magnetic substance placed so near N that all the lines of
force which emerge from N enter S, then there will be as many

Fig. 184.

unit poles upon S as there are upon N. The force between N
and S will be one of attraction. If we consider that the magnetism
upon N is uniformly distributed and equivalent to 6 unit poles
per square centimeter, then the same course of deduction as
followed in Par. 66 will show that a unit pole at P is attracted
with a force of 2-n-d dynes. If the sectional area of AT" be A, there
are upon AT", Ad unit poles. There are an equal number upon S,
each of which is acted upon by a force of 2?r5 dynes, therefore,
the total attraction between N and S is

F = 2<Tr5XA5=2Tr.A.5 2 dynes (I)

Since from each unit pole there radiate 4?r lines of force (Par.
145), the total number per square centimeter between N and S
is H=4ir8, whence 8 = H/^TT.

Substituting in (I) above we have


or the tractive force

exerted by a magnet is proportional to the square of the number of
lines of force per square centimeter of pole surface.


Ewing states that by using very high magnetizing lorce a
magnetic pull of over 225 pounds per square inch has been

A curious consequence follows from the above. By decreasing
the pole area we increase the tractive power of the magnet. This
is because as we decrease the area we increase the number of lines
of force per square centimeter and the tractive power varies as
the square of this number. This is the explanation of the fact
referred to in Par. 124, namely, that if one end of a bar magnet
be square and the other end be rounded, the rounded end will
exert the greater pull. The powerful electro-magnets used in
hospitals to extract particles of iron from the eye have long
conical poles.

The above expression for the tractive power seems to indicate
that this power is independent of the distance between the pole
and the body, but actually the force does fall off very rapidly as
we recede from the pole. The explanation is that as we increase
the air gap we increase very greatly the reluctance of the magnetic
circuit and this in turn decreases the flux or H. (Par. 401.)

407. Shape of Electro -Magnets. Since the pull of a magnet
varies as the square of the flux per square centimeter and since
this flux varies inversely as the reluctance of the magnetic circuit,
electro-magnets, as a rule, are designed so that the air gaps in the
circuit are as small as possible. The majority therefore are either
of the horseshoe pattern or bent to three sides of a rectangle.
The magnetizing coil may be wrapped over the whole length of
the horseshoe, or only on the central part or yoke, but most
frequently two coils are used, one being wrapped on each leg of
the core. In small instruments these coils are called spools or
bobbins. The dimensions and relative proportions of the parts of
these magnets are varied according to the use to which they are
to be put.

408. Use of Electro- Magnets. The uses to which electro-
magnets are put may be classed under two general heads; (a) for
creating the magnetic fields required for the operation of certain
electrical machines and (b) for exerting a tractive effort or pull.
The use for creating fields will be described when the subject of
electrical machinery is reached. The second heading embraces
a most varied class of uses among which are (1) lifting weights.



(2) operating annunciators, call and alarm bells, etc., (3) tel-
egraphy, (4) operating automatic switches, (5) regulating the
feed of the carbons of an arc light, regulating clocks from a master
clock, etc. Only a few of these can be described.

409. Lifting Weights by Electro -Magnets. Electro-magnets
are largely used in handling scrap iron, steel billets, boiler plates,
etc. The magnet employed is shown in section in Fig. 185. The
core is a short and heavy one-
piece casting consisting of an

inner cylindrical core sur-
rounded by an annular space
in which the magnetizing coil
is wound, the whole being called
an iron-dad electro-magnet.
When the current is turned on,
the inner core becomes one
pole and the outer ring the
other. Owing to the large
cross-section and little length
of the iron and to the shortness
of the air gap when a piece of Fig. 185.

iron is in contact with the poles, the pull is very powerful. This
magnet, suspended from a derrick, is lowered upon the pile of
scrap iron that is to be moved, the current is turned on, the magnet
with the clinging mass of iron raised, swung over to where it may
be desired, the current turned off and the iron dropped. In
handling such objects as boiler plate, it avoids the necessity of
using and adjusting hooks, chains or ropes. The coil is thoroughly
protected from accidental injury, a sheet of brass usually being
inserted in the annular space.

410. Electric Bells. A common form of electric bell is shown
diagrammatically in Fig. 186. It consists of the bell or gong G,
the hammer H, the electro-magnet M, the battery C (usually
one or two dry cells), and the push button D. The hammer is a
metal knob on a slender arm pivoted at P and bearing at its
middle the soft iron armature A. A delicate spiral spring S is
attached to the arm and exerts upon it a pull from the magnet.
At the back of the armature there is a slender brass strip which
makes contact at B with an adjustable screw. When the button



D is pressed, closing the circuit, a current flows from C to D,
thence to B, thence to P, thence through the coils of M and back
to C. The cores of M are magnetized by this current, attract the
armature A, causing the hammer to strike the bell, but at the same
time break the circuit at B. The circuit being broken, M is no
longer magnetized, the spring S pulls the armature back to its

Fig. 186.

original position, and the contact at B is restored. This causes the
hammer to strike the bell again and so on, a rapid succession of
blows being given so long as the button is pressed. Arrangements
of this kind for rapidly making and breaking a circuit are called

411. The Electric Telegraph. The word "telegraph" meant
originally to convey messages by exchanging signals at a distance.
During the wars of Napoleon there was developed a system of
semaphore signals by which messages could be transmitted
rapidly from point to point. We read in the contemporary
accounts of the campaign in the Spanish peninsula that Napoleon
telegraphed his instructions from Paris to his corps commanders
in the field.

The sending of signals by means of electricity was tried by
many. An insulated wire between two points was given a static
charge which caused a pith ball at the far end of the wire to stand
out. If a charged body be moved near the other end of the wire
corresponding movements could be produced in the pith ball.



Sparks from a Ley den jar were transmitted over a wire in ac-
cordance with a prearranged code. Use was made of the electro-
lytic effect of a current. Twenty-six separate wires, each marked
to correspond to a certain letter of the alphabet, were stretched
between two points and at the receiving station the ends of these
wires dipped into an acidulated solution. A single wire led from
the solution to the ground. At the sending end a voltaic pile was
used, one pole of which was "grounded." When the other pole
was touched to one of the twenty-five wires, the circuit was com-
plete and bubbles of gas appeared at the corresponding end at
the receiving station. These various methods failed mainly
because of the lack of a steady source of electricity. This difficulty
was overcome by the invention in 1836 of the Daniell cell. In
the following year Congress was induced to make an appro-
priation of $30,000 for the erection between Baltimore and
Washington of a line to test the system invented by Morse. This
proved successful and with minor variations is in operation to-day
over the greater part of the globe. It is estimated that there are
now over five million miles of land telegraph lines in use.

412. The Morse Telegraph. The principle of the Morse
telegraph will be readily understood from the following. In the
diagram (Fig. 187) K is the sending and M the receiving station.

Fig. 187.

R is a roll of paper ribbon which is slowly unwound by clockwork
in the direction shown by the arrow. B is a battery of Daniell
cells, one pole of which is grounded at E. Wh&mjhe key K is
closed the current travels from the battery over^pl line to the
electro-magnet M, thence to the ground at E', thence back
through the earth to E. When M becomes magnetized, the iron
armature A is pulled down. This causes the end P of the lever
to rise and to press a pencil against the moving ribbon at D.
When the key K is opened, the circuit is broken and a little



spring S pulls the pencil away from the ribbon. The length of
the pencil mark on the ribbon varies therefore with the length of
time that K is kept closed and the Morse alphabet is accordingly
made up of a system of dots, dashes and intervals or spaces. If
there be in the face of the drum D a groove, and if P instead of
being a pencil is a hard and smooth stylus which presses above
this groove, there will be produced in the ribbon long and short

While the foregoing gives the principle of the Morse telegraph,
in actual practice certain conditions arise which cause a consider-
able modification in the simple arrangement described above.
These are the following:

(1) Each station must be able both to send and to receive.

(2) The line must be so arranged that intermediate stations
may be operated.

(3) If the key K, Fig. 187, be left open, the circuit is broken
and it would be impossible for an operator at M to send a signal
to K. Accordingly, in the American system the key K is kept
closed when not in use, in other words, there is a current constantly
flowing over the line. This would appear to be a wasteful method
and is avoided in the European system, but actually the current
(and the consequent waste) is very small, and since the European
system requires a greater number of batteries, the cost is about
the same.


Fig. 188.

(4) It was soon discovered that the signals could be read by
and therefore the recording apparatus is now generally



omitted and in its place is substituted a sounder, an instrument
shown in simplest form in Fig. 188. A horizontal brass lever L,
pivoted at P, is pulled down at one end by the spring S until the
other end is pressed up against the adjustable contact B. The
lever carries on its upper side the crosswise soft iron armature A
and below this armature is the electro-magnet M. When a current
flows through M the core is magnetized, A is attracted and the
lever is pulled down until the contact D strikes the brass frame
just below, making a loud click. When the current is broken the
spring S causes the lever to fly up and strike B, making a second
click. The interval between these successive clicks determines
whether the sound be a dot or a dash.

(5) The currents employed are only a few thousandths of an
ampere (not entirely through choice but because of the resistance

Fig. 189.

of the line), and are usually not strong enough to actuate directly
either the recording device or the sounder. Morse overcame this
difficulty by means of a relay, an electro-magnet so placed in the
main circuit that when a current flowed the magnet attracted
an armature which in its movement closed an auxiliary circuit,
thereby throwing in a local battery which supplied the necessary
current to operate the recording apparatus. This arrangement
is shown diagrammatically in Fig. 189 in which M is the electro-
magnet in the main line LL, A is the armature, hinged at P and
drawn up against the adjustable stop K by the feeble tension of
the spring S. When a current passes through M , the armature A



is attracted and makes contact at C, thus throwing in on the
sounder the auxiliary battery B. The armature is therefore
really a switch or key for the local circuit.

413. The American System. The operation of the American
system will be understood from Fig. 190. The operator in Boston,
preparatory to signalling, opens the switch S of his sender. This

Fig. 190.

breaks the circuit and stops the current in the line. When he
closes his key K, the circuit is restored, a current flows, each of
the electro-magnets pulls down its relay armature thus causing
every sounder to click. A signal made at one station is therefore
repeated at every station on the line. Should the New York
operator wish to interrupt, he opens his switch S, thus break-
ing the circuit. The Boston operator is aware of this at once
because his own sounder ceases to click, and he at once closes
his switch and awaits instructions from New York. Whenever
a message is completed, the operator must at once close his

Should a break occur in a line, it is still possible to use the
remainder. Thus, should a break occur between Providence and
Boston, the Providence operator by grounding his line, as shown
by the dotted line, restores communication with New York.
Should the break be between Providence and New York, he must
ground his line to the right of his key.



414. Overload Switch. Should a short circuit occur on an
electric-lighting or on a power circuit, serious injury may result.
Various automatic devices are employed to afford protection in
such cases. We saw in Par. 306 the use of fuses for this purpose.
There have been devised many kinds of switches which auto-,
matically break the circuit when the current exceeds a certain
maximum for which they are set. These are called circuit-breakers
or overload switches, the word "load" in electric parlance meaning
current. They are therefore analogous to safety valves.

One of these is shown diagrammatically in Fig. 191. The
switch A when closed makes
contact through a curved arm
with two points B and C. A
stout spring, S, tends to throw
the switch in the direction
shown by the arrow but is
prevented from doing so by a
hook H which engages in a
corresponding hook on the trig-
ger T. The current enters at
E, passes thence to B, thence
through the switch to C, thence
around the coil G and out by F.
Within the coil G there is a
soft iron core. As the current
increases in strength, the coil
exerts a greater and greater
pull upon this core until finally
it is lifted bodily. As it moves
upward it strikes the trigger T,
releasing the switch which is
then thrown forcibly up, thus
breaking the circuit. The Fig. 191.

farther the core is inserted in the coil, the more easily it is lifted,
therefore, by means of the screw K, the switch may be set to trip
at any desired limit.

415. Underload Switch. Automatic switches are also in use
which trip when the current falls below a certain minimum. One
form is shown diagrammatically in Fig. 192. An arm, pivoted at
P, carries at one end a weight W and at the other end an arc of



wire whose extremities dip into mercury cups. The current, flow-
ing as shown, passes around M, thence to the first mercury cup,
thence across the arc to the second cup and out. The armature A
is attracted and held by the electro-magnet M. When the current
decreases below a certain point, M can no longer hold A, the
weight W falls and lifts the ends of the arc out of the mercury

cups, thus break-
ing the circuit.

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