the current flows for t seconds, the total quantity conveyed
between the two points is Q = It, therefore, the total work done
is IRxIt, or PRt, this energy being spent solely in heating the
conductor. To reduce this to ergs, I and R must be expressed in
absolute units. Since one ampere = 10" 1 absolute units of current
and one ohm = 10 9 absolute units of resistance (Par. 427), we have
the total energy expended = / 2 ^Xl0 7 ergs. In Par. 11 it was
shown that the small calorie is equivalent to 4.2 XlO 7 ergs. To
reduce the above expression to calories, we must, therefore,
divide it by this number, hence
H *JT 2 #* XlO 7 ) -5- (4.2 XlO 7 ) = PRt/ '4.2 = PRt X0.24
which is IstieVame as the expression in the preceding paragraph.
480. Electric Heating of Wires. When a current flows through
a wire, the wire is heated. The heat generated in the wire is con-
veyed away, mainly by radiation and convection. The rate at
which this heat is dissipated increases as the temperature of the
wire exceeds that of the surrounding medium. The temperature
of the wire continues to rise until the loss of heat by radiation, etc.,
exactly balances the amount generated by the current. Reflection
will show that since the heated air in a room ascends, a wire upon
the ceiling will radiate its heat more slowly than if lower down,
also, since the insulation upon a wire hinders the escape of the
heat, the temperature of an insulated wire carrying a current will
exceed that of the same sized bare wire. If the escape of heat be
still further impeded by enclosing the wire in a wooden moulding,
as is sometimes done, its temperature may reach a point where
the insulation becomes charred or even where the woodwork is
set on fire. For this reason, most insurance companies forbid
the use of these wooden ceiling strips and specify that wiring
must either be exposed or enclosed in non-combustible conduits,
and must be so proportioned that its temperature shall never
exceed a certain allowable maximum.
481. Calculation of Temperature. The dissipation of heat
by a wire varies with the material of which the wire is composed
and with the nature of its surface, with the extent of this surface,
with the excess of its temperature over that of the surrounding
medium and with the nature of this medium. If, when its tem-
perature is 1 C above that of the surrounding medium it emits e
calories per second per square centimeter of surface, it will emit
Te calories per square centimeter per second when its temperature
is T C above. If its length be I centimeters and its diameter be d
centimeters, its surface is irdl square centimeters and its emission
per second is Teirdl calories. During this time, the calories
generated per second by the current are I 2 .Rx0.24, hence when
the temperature becomes constant,
Teirdl = 7 2 #X0.24
Substituting for R its value (Par. 285)
and solving for 7, we have
o / T />
Applying this to wires of the same material, p is constant, and
if the wires attain the same temperature, T is constant, hence,
the current to raise these wires to the same temperature varies
as the square root of the cube of the diameter of the wires. This
formula enables us to calculate the size of the fuse wires (Par. 306)
which will melt when the current reaches a certain maximum. If
the fuse wire be of tin, its specific resistance p is 13X10- 6 ohms,
and e is about .00025. Its melting point being 230 C, T is 230
minus the temperature (Centigrade) of the surrounding air.
482. Localizing the Heating Effect of a Current. If a current
passes through two portions of a circuit, each of the same resist-
ance, the amount of heat developed in each will be the same. If
380 ELEMENTS OF ELECTRICITY.
one of these portions be a large wire, several hundred yards long,
and the other be a small wire, only a few inches in length, the heat
will still be the same in amount but in the case of the large wire
it will be distributed over its entire length and, on account of the
great radiating surface, there will be no perceptible rise in tem-
perature. On the other hand, the heat is concentrated in the
small wire, which can not dispose of it by radiation, and the tem-
perature of the small wire therefore rises. Such is the principle
upon which the employment of electricity for heating and for
lighting is based. The current is brought to the required spot
through wires of but little resistance and is then passed through
a short length of high resistance, the development of heat being
thereby localized. If the portion of the circuit is to be heated to
incandescence, as for example the filament in an incandescent
lamp, its length must be short and its resistance high. If it is
merely to be warmed, its length must be greater and its resistance
less. The following examples will make this clear.
483. Electric Fuzes. Electric fuzes are of many kinds. Fig.
235 represents in section an ordinary blasting fuze, which is also
variously designated as a primer, a cap, or a detonator. It con-
sists of a copper case A, which contains the explosive, usually
mercuric fulminate, and which is closed by a plug of wood, or wax,
or sulphur or some similar cementing material. Through this plug
pass the lead wires which come of various lengths to suit the
depth of the drill holes in which the blast is to be fired. The inner
ends of the lead wires are connected by a fine platinum "bridge" B,
about .001 inch in diameter and one quarter of an inch long.
About this bridge there is usually wrapped a wisp of gun-cotton.
The passage of the current heats the platinum bridge and ignites
the gun-cotton; this, in turn, ignites the fulminate and causes the
main charge to explode. These fuzes afford the simplest and
safest method of firing high explosives, and the only certain
method of blasting under water and of causing a number of charges
to explode simultaneously. They are fired from a safe distance,
the current usually being supplied from a hand magneto, although
it may be furnished by a battery or taken from any other con-
venient source. In the military service, they are used to explode
submarine mines and to fire heavy artillery. For this latter use
they are charged with black powder instead of with the fulminate.
484. Electric Welding. If two metal bars connected to the
terminals of a generator be touched together, the current flowing
through the resistance along the surface of contact will cause the
local production of great heat. Such is the principle of the
electric welding process devised by Elihu Thomson. The bars to
be welded are brought together, the necessary current is turned
on and in a very short time the metal softens. If now the bars
be pressed together, a weld results. In this manner steel axles
two inches square are joined in a little over a minute and a half.
Alternating current is used almost exclusively. It was shown
above (Par. 477) that the heating effect varies as the square of
the current. By a simple step down transformer (Par. 431) an
alternating current may be transformed into another whose
voltage is low but whose amperage is great. Thus, in welding the
rails of trolley lines, the current is taken from the line itself but
is transformed down, currents as great as 25,000 amperes being
employed, and the rails in the mean time being squeezed together
with a pressure of thirty-five tons.
485. The Electric Arc. If the wires attached to the terminals
of a battery or of a generator be touched together, completing the
circuit, there will be a rush of current which, on account of the
localized resistance, will, as we have just seen (Par. 484), develop
great heat at the point of contact. If the wires be now separated
about an eighth of an inch and if the E. M. F. between them be
not less than about forty volts, the current will continue to flow,
being conveyed by the vapor of the metal volatilized by the intense
heat, and brilliant light will be emitted by the glowing ends of
the wires and by the incandescent vapor between. This will
continue for only a few seconds for the ends of the wires will
rapidly melt off. If the terminal wires be attached to carbon
rods which are then touched together and separated, the same
brilliant light will be produced but in this case it will last much
longer since the carbon is infusible. The flame, or rather the
stream of incandescent vapor between the carbons, is really a
382 ELEMENTS OF ELECTRICITY.
flexible conductor composed of volatilized carbon and has the prop-
erties of any other conductor carrying a current. For instance,
it is surrounded by a magnetic field of its own and if placed in
another magnetic field will tend to move off to one side (Par. 356).
Because of the interaction of its field with that of the earth, it is
generally somewhat curved, and on this account it was named the
electric arc. If the field be strong enough, the arc may be pushed
so far to one side as to be extinguished. A form of apparatus
utilizing this principle to prevent accidental arcs when switches
are opened is called a "magnetic blow-out."
As long as the arc is maintained, the carbons consume away
slowly but at different rates, the positive carbon wasting much
more rapidly than the negative. The tip of the positive carbon
becomes hollowed out into a little pit, called the crater; on the
other hand, the tip of the negative carbon seems to receive the
particles torn away from the positive carbon and assumes a rather
The chief source of the light of the arc is the crater of the
positive carbon, the arc itself emitting but little. The maximum
temperature, however, exists in the arc. This temperature, the
highest yet attained, is said to be about 3500 C, or twice that
required to fuse platinum. In this arc the most infusible sub-
stances are promptly melted and even vaporized.
486. The Electric Furnace. Although the light and the intense
heat produced by the electric arc have been known for over one
hundred years, it was not until the development within the last
thirty years of machines for supplying continuously the required
current that the use of the arc for illuminating purposes became
commercially practicable, and its utilization on a large scale as a
source of heat dates from the still more recent development of
such great sources of power as Niagara Falls.
Electric furnaces may be divided into two general classes ac-
cording as the body to be heated is or is not a conductor. If it be
not a conductor, it must either be placed beneath the arc, the
heat of which is both radiated and reflected down upon it, or it
must be intimately mixed with powdered carbon or other conduct-
ing substance, the passage of the current through which produces
enough heat to raise the temperature of the body to the required
point. If it be a conductor, it may be made one electrode of an
immense arc and be heated both by the heat radiated from the
remaining electrode and by that produced by the passage of the
current, or it may be heated by the passage of the current alone.
Of this last class there are two subdivisions according as the cur-
rent is conveyed directly through the body or is produced in it
The intense heat of the electric furnace, 3500 C or more, has
made it possible to fuse silica and to produce therefrom utensils
of great use in the laboratory; has permitted the reduction of the
most refractory ores, notably those of aluminum; has enabled
the chemist to manufacture graphite, silicon, etc.; and finally has
led to the production of chemical compounds hitherto unknown.
487. Moissan's Furnace. One of the earliest electric furnaces
was that devised by Moissan. It is shown in section in Fig. 236
and consists of a chamber scooped in a block of lime and covered
by a lid made from a second block. Lime is used since when either
hot or cold it does not conduct appreciably. The carbons enter
through grooves on opposite sides. The body to be heated is
placed in the cavity in the lower block and the heat produced by
the arc is reflected down upon it, that is, the furnace is in principle
a reverberatory furnace.
Furnaces of this kind can not be made on a large scale. They
are quite small and are used for fusing small amounts of refractory
substances, as in the production of artificial gems.
488. Manufacture of Carborundum. In 1890 Acheson made
in a small electric furnace a crystalline substance which he sup-
posed to be a compound of carbon and corundum, or emery, and
he accordingly named it carborundum. It is now known to be
the carbide of silicon, or SiC. It is of great hardness and has come
into extensive use as an abrasive, displacing emery in the various
wheels, grindstones, whetstones, polishing cloths and powders.
ELEMENTS OF ELECTRICITY.
It is made on a large scale at Niagara Falls. The furnaces, built
of brick without mortar, are some fifteen feet long by seven feet
wide and high. At each end (Fig. 237) there are built into the
wall heavy copper terminals to each of which are attached the
electrodes proper, sixty carbon rods, three inches in diameter and
two feet long. These electrodes are connected by a core of crushed
coke about nine feet long and two feet in diameter. Around this
core there is packed about ten tons of an intimate mixture of
34% coke, 54% sand, 10% sawdust, and 2% salt. The salt acts
as a flux; the sawdust keeps the mass porous. An alternating
current of 4000 amperes at 185 volts is turned on. This, as will
be shown in the next chapter, represents about 1000 horsepower.
In a short while a large amount of carbon monoxide is produced
and burns as it emerges from the crevices between the bricks. In
twelve hours the furnace becomes red hot but the current continues
to flow for twenty-four hours before it is turned off. When it has
cooled sufficiently the furnace is dismantled. The interior core
of coke is found to be converted into graphite. This is surrounded
by a sixteen inch layer of iridescent purplish crystals of carbo-
rundum. Outside of this layer there are slag-like clinkers.
In a somewhat similar manner calcium carbide, CaC 2 , is made
by heating a mixture of lime and powdered coke, the reaction
CaO+3C = CaC 2 +CO
Calcium carbide is used for the production of acetylene gas for
489. Manufacture of Aluminum. Although very widely dis-
tributed, the ores of aluminum are most refractory and until
recently their reduction was one of the difficult processes in
metallurgy. The metal is now obtained from bauxite, a mineral
containing over sixty per cent of aluminum oxide, A1 2 3 . Alone,
this is practically infusible but dissolves readily in fused cryolite,
a double fluoride of aluminum and sodium. The current is passed
through this fused mass, aluminum is released at the cathode and
oxygen at the anode. The aluminum being liquid settles to the
bottom and is drawn off from time to time, fresh supplies of
bauxite being continually added. The cryolite is not affected.
The action in this case being electrolytic as well as thermal,
direct current must be used. Aluminum which ten years ago sold for
eight dollars a pound can now be produced with profit at twenty-
490. Electric Iron Furnaces. There is an increasing use of
electric furnaces for the treatment of pig iron by a process similar
to the ordinary open-hearth process. The fused metal is one of
the electrodes, the other consists of large carbons which penetrate
^the dome of the furnace. The arc plays between these carbons
and the metal beneath. Suitable linings are used and the proper
ingredients are added to the molten metal to remove the sulphur,
phosphorus and other objectionable substances. Such furnaces
are now made of a capacity of fifteen tons.
491. The Induction Furnace. The induction furnace, recently
introduced for the manufacture of high-grade steel, is a special
application of the principle of the transformer. It is shown dia-
grammatically in Fig. 238. P is the primary and S is an annular
trough of non-conducting fire-brick. Into this trough is placed
the metal which is to be treated and this mass of steel constitutes
386 ELEMENTS OF ELECTRICITY.
a short-circuited secondary of a single turn. The alternating cur-
rent in P is stepped down in S to a current of large amperage
sufficient to bring the steel to a molten state. At the proper time
the required amount of spiegeleisen or other material is added.
These furnaces have been made large enough to handle ten tons
of steel at a charge.
492. Power Defined. If a certain hoisting engine raises a
weight from the ground to the top of a building in two minutes,
and a second engine raises the same weight the same height in one
minute, the work in each case is the same but the second engine
does its work twice as rapidly as the first and is therefore said to
be twice as powerful. Power may be defined as the rate of doing
work. It would ordinarily, therefore, be measured in foot-pounds
493. Horse-Power. About one hundred and fifty years ago,
the mine owners in Cornwall employed horses to operate the pumps
which kept their mines free from water. As the mines sunk deeper,
the difficulty and expense of removing the water increased so that
many were abandoned as no longer profitable. It was at this
time that Watt perfected his steam engine and began to introduce
it in the mines. The miners knew how many horses were required
to lift so much water but had no notion of the capabilities of the
new-fangled engine; they therefore required that before purchas-
ing an engine they should be told how many horses it could sup-
plant. In order to be able to furnish this information, Watt
carried out a series of tests with the powerful horses used in the
London breweries, as a result of which he concluded that such a
horse working eight hours a day could perform work at a rate
equivalent to raising 33,000 pounds one foot per minute. This
figure has ever since been accepted as the measure of a horse-power.
The unit of time is, however, commonly taken as one second, the
corresponding foot-pounds being 550.
In electrical measurements, it is desirable to express this in
absolute units. Remembering that the pound is about 445,000
dynes (Par. 11), and that the foot =30.48 centimeters, the horse-
power is in round numbers 7,460,000,000 (or 746 XlO 7 ) ergs per
494. Expression for Electric Power. There are a number of
ways in which an expression for electric power may be deduced.
388 ELEMENTS OF ELECTRICITY.
It is superfluous to say that in every case the results must be the
same, yet, several of these methods will now be explained, for each
presents the matter from a slightly different view-point and the
student will thus get a broader grasp of the subject. We shall
begin with the simplest.
(a) In Par. 477 we saw that the heat developed by a current of
strength / flowing for t seconds through a resistance R is I 2 Rt.
This represents energy expended, or work, and if divided by t it
will give the rate at which the work is done, or the power (Par.
492). Hence, the power developed by a current I in heating a
resistance R is PR.
This last expression may be factored as follows: I 2 R = Ix!R.
But IR is the drop of potential E between the two points A and B
(Fig. 234), hence for I 2 R we may write IE, or the power expended
in heating any portion of an electric circuit is measured by the
product of the current flowing in the circuit by the difference in
potential between the ends of the portion.
(b) In Par. 358 it was proven that the work done by a current
I flowing around a coil is I N, N being the change in the number
of lines of force embraced by the coil. If this work be done in time
t, the power = IN/t. But (Par. 425) N/t = E, and the foregoing
expression also reduces to IE, or, as above, the power developed in
a coil, a portion of a circuit, is measured by the product of the cur-
rent flowing through the circuit by the difference in potential
between the ends of the coil. In this case, the heating effect is
(c) Finally, taking the most general case of a portion of a circuit
of any shape whatsoever, and placing no restriction upon the
nature of the work performed by the current, if E be the difference
of potential between the ends of the portion and if during the time
under consideration Q units are transferred around the circuit, the
work done in the portion is QE (Par. 72). But Q = lxt, hence the
work is I. t. E. Dividing this by t to obtain the power, we again
arrive at IE, or, in general, the power expended in any portion of
an electric circuit is measured by the product of the current by the
difference in potential between the ends of the portion.
495. Development of Power in a Battery. Since the source of
the energy developed in a single cell is the chemical action result-
ing in the consumption of the zinc by the acid (Par. 192), no matter
how a battery may be grouped, if the same amount of zinc be con-
sumed in the same time, the same power is developed. This may
be illustrated as follows: Suppose N cells, each of an E. M. F. of
e volts and an internal resistance of r ohms be grouped in series
with an external circuit of negligible resistance. The E. M. F. of
the battery is Ne, the current is Ne/ Nr = e/r, and if z be the zinc
consumed in one cell per second, the total amount consumed per
second is Nz.
If these same cells be grouped in parallel, the E. M. F. of the
battery is e, the current through each cell is e/r, the total current
is Ne/r and the total consumption of zinc per second is again Nz.
The power developed in the two groupings should therefore be the
same. In the first case it is NeXe/r or Ne 2 /r; in the second case
it is e X Ne/r or again Ne 2 /r.
496. Units of Electrical Power. From Par. 494 the expression
for electrical power is
P = IE
If in this, / be one absolute unit of current and E be one absolute
unit of E. M. F., P becomes one absolute unit of electric power.
This unit has received no name but represents the expenditure of
energy at the rate of one erg per second.
If in the same expression, we make / one ampere and E one
volt, we again have P = 1. This unit, the practical unit of electric
power, is called the watt. Since the ampere is 1(H absolute units
of current and the volt is 10 8 absolute units of E. M. F. (Par. 427),
the watt= IE= 10 -*X 10 8 = 10 7 absolute units of power, or ten
million ergs per second.
We saw in Par. 493 that the horse-power was 746 XlO 7 ergs per
second. The horse-power is therefore 746 watts. The commercial
unit of electric power is the kilowatt, or one thousand watts. The
kilowatt is 1000/746, or just about Ij horse-power. The com-
mercial unit of electric work, the unit by which it is bought and
sold, is the kilowatt-hour.
497. Measurement of Electric Power. Since the power ex-
pended between two points in an electric circuit is measured by the
product of the current by the difference in potential between the
two points, we may measure the current by an ammeter, and
the difference of potential by a voltmeter, and by multiplication
obtain the watts. As an illustration, suppose we wish to determine
390 ELEMENTS OF ELECTRICITY.
the consumption of power in the 16 candle-power, 100 volt lamp,
AB, Fig. 239. Connections are made as shown. The ammeter
reads the current / flowing through AB, and the voltmeter reads
the difference of potential E between A and B. The product of
these two readings gives the watts consumed. If, for example,
the current be one-half ampere and the difference of potential
between A and B be 100 volts, the power is 50 watts. It requires,
therefore, a kilowatt to run 20 such lamps, or about one horse-
power to run 15.
If, in the above example, the ammeter be read while the volt-
meter is connected up, a slight error will be committed, for exami-
nation of the figure will show that the ammeter reads not the
current through the lamp but the sum of the currents through
both the lamp and the voltmeter. If the resistance of the volt-
meter be 15,000 ohms (Par. 458), the current through it is T M<r
or T^ ampere. The current through the lamp is therefore really
i T fcff = ^ ampere, and the power consumed in the lamp is
100 X T 7 sV = 49-J- watts instead of 50, indicating an error of 1^ per