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just described. In investigating it, however, Cooper Hewitt dis-
covered some remarkable properties. Thus, at the outset, its
resistance is so great as to require several thousand volts to start
the current through it. This resistance seems to be confined to
the surface of the negative electrode, and is temporarily destroyed
by the passage of a current. Although several thousand volts
are required to start the current through a tube twenty inches
long, when once started it may be maintained by a pressure of
50 volts, provided it does not fall below one ampere. If it falls
below this, the negative-electrode resistance re-asserts itself, the
current ceases, and the high voltage is required to start the cur-
rent again.

Various forms of this lamp have been devised, all alike in princi-
ple but differing in the arrangements for starting. A common
form is shown in Fig. 252. This particular lamp, designed for use
in a 100 volt circuit, and taking a current of three and a half
amperes, consists of a one-inch glass tube, AB, 45 inches long and
shaped as shown. It is supported by a frame CD, which carries
the lead wires and which hangs from the suspension bar E. The


canopy F contains the various coils and electro-magnets used in
connection with the lamp. The tube is exhausted to a pressure of
one millimeter. The positive electrode A is df iron, a metal to
which mercury does not adhere, and the negative electrode B is a
small puddle of mercury.

Fig. 252.

To start the lamp, the ring attached to A is pulled down, the
lamp and frame rotating about the point E until A is slightly
below the level of B. The mercury in B flows down the tube
and makes contact at A. This little stream of mercury between
A and B would act as a short circuit were it not for a ballasting
coil (Par. 508) in the canopy F. The ring is now released, the
lamp tips back to its original position and the mercury runs back
into B. In doing so, the thread of mercury breaks at some point
producing a flash-like arc, volatilizing some of the metal and
ionizing the vapor so that the lamp starts. This voltage at break
is aided by an inductance coil in series. In the smaller sizes of
lamps, this tipping is done by electro-magnets. Several other
starting devices are in use.

This form of lamp can be used with direct current only, but
others are made for use with alternating currents. The principle
of these latter will be explained when the subject of the mercury
arc rectifier is reached.

The efficiency of the light is high, being 0.64 watt per candle-
power. It is rich in actinic rays and especially valuable for photog-
raphy, blue printing, etc., but has one very grave objection. It
is devoid of red rays and red objects placed in it appear purple or
black. It imparts to persons a peculiarly ghastly appearance and
can not be used where colors are to be shown in their proper rela-
tion. No way has yet been discovered of adding the needed red.




528. Seebeck's Discoveries. In 1821, in investigating Volta's
contact series (Par. 187), Seebeck discovered that in a circuit com-
posed of two metals, if one of the junctions be at a different tem-
perature from the other, an E. M. F. and current will be produced.
Fig. 253 represents a circuit composed of a strip of copper and one


Fig. 253.

of iron which are joined at the points A and B. The strips may be
welded, or soldered, or simply pressed together. If the junction
A be heated so that its temperature is higher than that of B, a
current will flow around the circuit in the direction indicated by
the arrows, that is, at the cool junction it will flow from the iron
to the copper, and at the hot junction, from the copper to the iron.
The needle placed within the circuit will indicate this current.
The two metals constitute a thermo-couple, and the E. M. F. pro-
duced is called the thermo-electric electro-motive force. Seebeck
found further that this E. M. F. varied (a) with the metals used
and (b) with the difference of temperature of the junctions, and he
was able to arrange the following thermo-electric series in which, in
a thermo-couple composed of any two, the current at the cold
junction flows from the metal higher on the list to the metal which
is lower.



Thermo- Electric Series.
Antimony Tin

Iron Lead

Zinc Copper

Silver Platinum

Gold Bismuth

In accordance with these observations, thermo-couples are
usually made of antimony and bismuth, though certain metallic
sulphides may also be used. The E. M. F. produced is very feeble.
Even for an antimony-bismuth couple, it is only about one ten-
thousandth of a volt per degree Centigrade, or if one junction of
such a couple be placed in boiling water, the other in melting ice,
the E. M. F. will be about one-hundredth of a volt.

529. Thermo-Electric Inversion. In 1823 Gumming added to
the discoveries of Seebeck by showing that the thermo-electric



Fig. 254.

E. M. F. varied not only with the difference of temperature of the
two junctions but also with their actual temperatures, Thus, if
one junction of the copper-iron couple shown in Fig. 253 be kept
at a constant temperature and the other be heated so that its tem-
perature increases at a uniform rate, the E. M. F. will at first also
increase uniformly but finally will slacken and will reach a maxi-
mum at 275 C, after which it will decrease. This is shown
graphically by the curve in Fig. 254, in which the abscissae repre-
sent temperatures and the ordinates the corresponding E. M. F.
The temperature Ot, at which the E. M. F. te is a maximum, is
called the neutral temperature and varies for each different pair of


metals. If the temperature of the junctions be equally distant
from t, the E. M. F. is zero. Thus at OT =2 xOt, the E. M. F. is
zero and beyond T it is negative, hence the current is reversed and
OT is called the temperature of inversion. Had the constant
temperature of one junction been Of instead of 0, the maximum
E. M. F. would have been me, the neutral temperature remaining
unchanged. This thermo-electric curve has been shown by Lord
Kelvin to be a parabola.

530. The Peltier Effect. From what has just been seen, if one
junction of an antimony-bismuth thermo-couple be heated, as




Fig. 255.

shown in Fig. 255, a current will flow around the circuit as indi-
cated by the arrows, that is, flowing at the cold junction B from
the antimony to the bismuth.

If the source of heat be now removed, the current will still con-
tinue to flow so long as the junction A is at a higher temperature
than the junction B. The only conceivable source of this current
is the heat energy at A, and since this heat energy is converted
into electrical energy, there must be at that point an absorption
and disappearance of heat. Also, since the actual current through
the junction B is opposite in direction to the current which would
have been produced by the absorption of heat at that point,
the logical inference is that heat is developed at B. The correct-
ness of this inference was shown by Peltier in 1834. A bar of anti-
mony and one of bismuth were placed crosswise as shown in Fig.
256 and were soldered together. Between the ends C and B were
connected a galvanometer G and a key S. Between A and D were
connected a battery and a key K. K was closed for a while,
allowing a current to flow around the triangular circuit in the
direction DEA, or passing at the junction from the bismuth to


the antimony. K was then opened and S was closed. The gal-
vanometer immediately indicated a current from C to B, showing
that the junction E had been cooled below the temperature of B
and C by the passage of the current from the battery. The battery
was now reversed so that when K was closed the current flowed in
the direction AED, or from the antimony to the bismuth. After
a while, K was again opened and S closed. The galvanometer now
indicated a current from B to C, showing that the junction E had
been heated above the temperature of B and C.

Fig. 256.

We thus see that when a current is passed across the junction
of two dissimilar metals, heat is evolved if the current flows from
the metal that is the higher in the thermo-electric series (Par. 528),
and heat is absorbed if it flows from the metal that is the lower
in this series.

This heating or cooling produced by the passage of a current
across the junction of two dissimilar metals is called the Peltier
effect, and is entirely distinct from the Joule effect discussed in
Chapter 35. The Joule effect varies as the square of the current
and is independent of the direction of flow; the Peltier effect varies
as the first power of the current and is reversed if the direction of
the flow be reversed.

In the manufacture of very delicate electrical measuring instru-
ments, consideration must be given to these various thermo-elec-
tric effects. If in the circuit of such instruments a junction of
different metals occurs, the heating effect of the current may set
up thermo-electric effects which might cause appreciable error in
the indications of the instrument.


531. The Thomson Effect. Sir William Thomson (Lord
Kelvin) showed that when a current flows through a homogeneous
conductor which is heated at one point more than at another, heat
is either developed or absorbed, depending upon the nature of the
conductor and the direction of the current. Thus, in a copper wire
whose center is hotter than the ends, heat is absorbed by the cur-
rent as it flows towards the hot center and evolved as it flows from
this center. With an iron wire, these effects are reversed, heat
being developed in the first half and absorbed in the second. This
Thomson effect has not been observed in lead and consequently lead
is taken as the standard, or is made one of the elements in each
thermo-couple which is tested in order to determine the thermo-
electric power of the various metals.

The subject of thermo-electricity is susceptible of elaborate
mathematical treatment but its importance is not now sufficient
to warrant a more extended discussion. We shall therefore pass
at once to a description of some of its practical applications.

532. The Thermopile. Although, as stated above (Par. 528),
the E. M. F. of a thermo-couple is very feeble, if a number of these
couples arranged in the same order be connected in series and the
alternate junctions be heated, the E. M. F.s will all act in the same
direction and the total E. M. F. will be the sum of the separate
E. M. F.s, in other words, the arrangement is similar to a battery

composed of a number of cells con-
nected in series. Such an arrange-
ment is called a thermopile.

Many forms of thermopiles have
been devised. For example, the
couples may be grouped as shown
in Fig. 257 like the spokes of a
wheel radiating from a central cy-
lindrical opening, and there may
be a number of these groups
placed one above the other and all
connected in series. The interior
Fi 257 cylinder may then be heated by a

small furnace, by gas jets, or by

hot water, the outer ends of the couples being cooled by the air.
At first sight it seems that the thermopile affords a satisfactory

solution of an extremely important problem, the direct conversion



of heat energy into electrical energy without the usual interme-
diate steps of heating water, producing steam, utilizing the expan-
sion of the steam to produce rotation, and by means of this rota-
tion producing electricity as outlined in Par. 423, each of which
steps is accompanied by inevitable loss of energy. Thermopiles
have been constructed to furnish the small currents required in
gold and silver plating, and are used in certain extremely sensitive
heat-measuring instruments (Par. 533), but where electricity is to
be supplied on a large scale, they are a failure. The Joule effect,
the Peltier effect and the heat conductivity of the two metals all
tend to raise the temperature of the cool junctions and thus
decrease the E. M. F., and the couples themselves deteriorate
rapidly with use. Their efficiency is very low, less than one-half
of one per cent of the heat energy being converted into electrical

533. The Radiometer. There has been employed for the com-
parison of radiant heat from different sources, a thermopile con-
sisting of a rectangular bundle of thermo-couples arranged in series
and mounted in a frame as shown in Fig. 258. The contiguous

Fig. 258.

couples and the metal strips of each couple, except at the junctions,
are insulated from each other by sheets of mica. The first and
last strips of the series are connected to terminals T, which are
attached one on each side of the frame. The pile, except the end
which is to receive the radiant heat, is shielded by a protecting
hood. The receiving end is coated with lampblack, the best
absorbent of heat. When in use, a sensitive galvanometer is con-
nected to the terminals, the current through the galvanometer
varying directly as the difference of temperature of the hot and
cold faces of the pile.



Thermometers and pyrometers have been constructed on the
principle of the thermopile. In the pyrometers, the couple is com-
posed of platinum and rhodium.

534. The Radio- Micrometer. An extremely sensitive form of
radiometer, the radio-micrometer, has been devised by Vernon
Boys. It combines the principles of the thermo-couple and the
d'Arsonval galvanometer. As shown diagram-
matically in Fig. 259 it differs from the d'Arsonval
galvanometer (Par. 378) only in that a quartz
fibre is substituted for the phosphor-bronze sus-
pension, and the coil consists of a single vertically-
elongated loop of copper wire. To the lower ends
of this loop there are soldered two small bars of
antimony and bismuth and these bars are con-
nected by a little sheet of lampblack-coated copper
foil, only one-tenth of an inch square. When
the copper foil is heated, the E. M. F. of the
couple is very small but, since the resistance of
the copper loop is also small, the current is ap-
preciable and the loop moves in accordance with
Maxwell's law (Par. 371), the deflection being observed by means
of the mirror M. It is said that a change in the temperature of
the copper foil of one-millionth of a degree will cause a deflection
of one division on the scale, and that the radiant heat of a candle
can be detected at a distance of two miles. Instruments of this
kind, known also as bolometers, have been used to measure the
heat radiated from the stars and to compare the heat emitted
from different portions of the solar spectrum.

Fig. 259.




535. Two Systems of Electric Units. There are two distinct
systems of electric units; one, the electro-static, based upon the
interaction of static charges; the other, the electro-magnetic, based
upon the interaction of a magnetic pole and the field produced
about a conductor carrying a current. The electro-magnetic units,
and the derived practical units, are, on account of their suitability
for practical purposes, used to the exclusion of those of the electro-
static system. Nevertheless, it is desirable for the student to be
acquainted with both systems and to understand the relation ex-
isting between them.

In the electro-static system, the starting point is the unit quan-
tity, which is defined (Par. 56) as that quantity which when placed
at a distance of one centimeter in air from a similar and equal
quantity, repels it with a force of one dyne.

In the electro-magnetic system, the starting point is the unit
pole, or (Par. 133) that pole which, when placed at a distance of one
centimeter from a similar and equal pole, repels it with a force of
one dyne.

536. Units of Current and Quantity. Thus far, there does not
seem to be much to choose between the two systems. In the next
step, however, there is a marked difference.

In the electro-static system the unit current is that current
which conveys unit quantity in unit time.

In the electro-magnetic system, the unit current can not be
defined so simply. We have shown, however (Par. 353), that a
current flowing in a conductor establishes about that conductor
a magnetic field which varies directly with the current. There-
fore, with other conditions constant, we may take the strength of
the field produced as a measure of the strength of the current, and
the simplest way to compare magnetic fields is to compare the
forces which they exert upon the same pole. The electro-magnetic
unit of current is therefore defined (Par. 355) as that current which,


flowing through one centimeter of a conductor bent into the arc of
a circle whose radius is one centimeter, exerts a force of one dyne
upon a unit pole placed at the center of the circle. This current,
we have seen, is ten amperes.

Having thus defined the unit current, we may now define the
electro-magnetic unit of quantity as that quantity conveyed by
unit current in unit time. The ampere flowing for one second
conveys one coulomb; the absolute unit of quantity is therefore
equal to ten coulombs. It is thus seen that in the electro-static
system we pass from unit quantity to unit current; on the other
hand, in the electro-magnetic system, we pass from unit current
to unit quantity.

By experiments and measurements based on widely different
methods, it has been found that the electro-magnetic unit of
quantity is about (2.98+)(10 10 ) times as great as the electro-
static unit of quantity. For round numbers, this is taken as
3X10 10 , or thirty billion. The coulomb, therefore, as has already
been stated (Par. 56), is three billion (3X10 9 ) times as great as
the electro-static unit.

537. Units of Electro -Motive Force. In either system, unit
difference of potential exists between two points when the expendi-
ture of one erg is required to convey a unit of quantity of elec-
tricity from one to the other. The electro-magnetic unit of poten-
tial is therefore ~ TTT^ times the electro-static unit of potential.

o /\ J.U

In Par. 427 it was stated that 10 8 absolute electro-magnetic units
of potential were equal to one volt. The volt is therefore 3 X 10 10 ~ 8
= 3 XlO 2 = 300 times as small as the electro-static unit of potential,
or, as was stated in Pars. 77 and 78, the electro-static difference of
potential in ergs must be multiplied by 300 to reduce it to volts.

538. Primary Electro-Magnetic Units. The units of E. M. F.,
current and resistance are bound together by Ohm's law, I = E/R,
which necessarily is true whatever units be employed, that is,
whether we use the absolute or the practical units. It follows that

absolute unit of E. M. F.

absolute unit of current

absolute unit of resistance

If, therefore, any two of these units be fixed upon, the third follows
as a matter of course; or, it suffices to define any two, and these


definitions fix the third. It was this consideration that led to the
definition of resistance as a ratio, to which definition attention was
called in Par. 307.

The question now arises, which two shall be selected as our
primary units.

In Par. 355, the definition of the absolute unit of current was
given (repeated in the preceding paragraph), and in Par. 374 it was
shown how by means of the tangent galvanometer a current could
be measured in absolute units. The absolute unit of current is
therefore selected as one of the primary units.

Reflection will show that of the three units, resistance is the only
one which could be perpetuated in a material standard, such as a
given length of a certain-sized wire of a specified material. If
resistance could be measured absolutely, it would naturally be
selected as the second primary unit. We shall now explain how
this may be done, but preliminary thereto we must develop an-
other conception of electric resistance.

539. Dimensional Formulae. It has been shown (Par. 10) that
the fundamental units of our system are the centimeter, the gram
and the second, and that all the other units are derived from these.
It is therefore possible to express any derived unit in terms of
length, mass and time. Such expressions are called the dimensional
formulae of the units in question. A study] of these dimensional
formulae will afford a clearer conception of the nature of the units
and will bring to light unexpected relations.

540. Dimensional Formulae of Electro-Magnetic Resistance.

From Ohm's law, R = E/I. E, the difference of potential, is meas-
ured by the work done in moving unit quantity of electricity
through a difference of potential E. If to move Q units the work
done is W, then to move one unit, the work is W/Q, whence


* CD

But work = forceXpath=FxL, and Q = IxT. Substituting

these values in (I) p v r

E = x

Substituting this for E in Ohm's law

= x (II)



Two poles, each of strength m, at a distance L apart exert upon
each other a force F=m?/L 2 , whence

m = V*\Z? (Ill)

A pole of strength m placed in a magnetic field of strength H is
acted upon by a force F=m.H, whence H=F/m. \

The field produced at the center of a circular coil by a current
/ (Par. 354) is proportional to I/L, orH = I/L, L being the radius
of the coil. Equating these two values of H and solving for m, we
have m=F.L/I.

Substituting this value of m in (III), and solving, we have
F = 7 2 , whence (II) becomes

R = L/T

But L is length and T is time, hence resistance is of the nature
of a velocity.

541. Resistance Expressed as Velocity. Why it is possible to
express resistance as a velocity may be shown as follows: Let Fig.


Fig. 260.

260 represent the arrangement of parallel rails and sliding cross
bar which we have already described several times. Suppose the
rails to be of negligible resistance, to be one centimeter apart and
to embrace between them a uniform unit field. AB, moving with
uniform velocity, is slid along towards D, which is at an indefinite
distance to the left. If AB moves V centimeters per second it will
cut V lines of force and will generate V absolute units of E. M. F.,
in direction from A to B (Par. 422). If the resistance of A B be R t
the current through AB will be

I = v

Since the current varies directly with V, the velocity of AB, it
is possible to move AB rapidly enough to make 7 one absolute
unit of current. When 7 becomes 1, the above expression becomes
R = V, or R is expressed as a velocity.


If R be one ohm, in order to drive a current of one absolute unit
through AB, it must be moved with a velocity of 10 9 centimeters
(ten million meters, or one earth's quadrant per second (Par. 4) ).

From the foregoing, knowing the strength of the field between
the rails and the velocity with which AB is moved, we could deter-
mine V. The current in the circuit could be read from an ammeter
at Z). Thus having V and 7, the quotient of the former by the
latter would give R, the resistance of AB. Practically, such a
determination is impossible. A B could not be moved for a suffi-
cient length of time with the desired rapidity; it would not, as it
moved, maintain unvarying contact with the rails; and finally,
the resistance of the rails is not negligible, hence the resistance of
the circuit would continually decrease. However, several methods
have been devised by which these difficulties are obviated and we
shall now explain one, first proposed by Weber and improved by
later investigators.

542. Absolute Measurement of Resistance. In Fig. 261, AB
represents a circular coil of a number of turns of wire, the ends of

Fig. 261.

the coil being joined together. It is mounted upon a vertical axis
about which it may be spun rapidly. Through an opening in the
top there extends a silk fibre from which there hangs at the center
of the coil a needle. The arrows H represent lines of force of the
earth's field. If the coil, viewed from above, be spun in a clock-
wise direction, it will cut the lines H and consequently an E. M. F.
will be induced. Application of the right hand rule (Par. 422) will
show that as the side B moves from B to A, it will generate an
E. M. F. acting upward and during the same time a downward

Online LibraryWirt RobinsonThe elements of electricity → online text (page 33 of 46)