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which constitutes its " mate." If both wires of a pair are open at
both ends, then the two constitute a condenser; the two con-
ductors, in this case, being the condenser plates, and the double
thickness of insulation which separates the conductors being the
dielectric.

Now, the capacity of a combination of this kind is quite approxi-
mately proportional to the length of the conductor and, therefore,
if the capacity of a conductor (which is the broken conductor) of
unknown length is compared with the capacity of a conductor of
known length, then the distance to the open point is determined.

The comparison of two capacities may be made very simply with
circuits arranged in the manner of a
Wheatstone bridge.

In Fig. 1214a, r\ and r 2 are two
ohmic resistances. These should be
as free as possible from electrostatic
capacity or self-induction and pref-
erably should be fairly high resist-
ances, of the order of 1000 ohms.
Ci and 02 are the two capacities to
be compared. D is some form of
detector, usually a telephone, which
is responsive to an alternating, interrupted, or rapidly varying
current of any kind, This bridge arrangement is supplied with a

FIG. 1214a.

286 MEASURING ELECTRICAL RESISTANCE [ART. 1214

current of this character. By varying the ratio of the two resist-
ances ri and r 2 a value of the ratio may be found such that at all
times the potential at point 1 is the same as the potential at point 2.
This equality of potentials will be indicated by the detector D; in
the case of a telephone, by silence in the telephone.
The condition for a balance is

* = , (1)

T 2 Ci

Note that the capacities are in reciprocal relation to the resistances.
In the application of this principle to fault location a telephone
is invariably used as the detector. The source of variable current
is a battery and a buzzer, or a battery and a small hand commu-
tator for quickly reversing the current. In an emergency the
current may be rapidly interrupted by drawing a metal piece over
the surface of a coarse file.

>j&l

FIG. 1214b.

(a) Good wires available.

To locate an open, say, in a conductor in a telephone cable which
contains the mate of the broken wire and another good pair, the
connections are made as in Fig. 1214b.

Here the capacities of the pair a, b (wire a broken) and a 1} bi
are indicated by the hypothetical condensers drawn in dotted line.
ri and r 2 are varied together, or either of them alone, until the
telephone P is silent, or nearly so.

Then,

As d, the distance to the fault, is proportional to Ci, and as Z, the
length of the good pair, is proportional to c 2 ,

d-=L (2)

ART. 1214]

PRINCIPLES OF FAULT LOCATION

287

If the wires a and 61 are aerials, as a telegraph or electric light
wire, then p, the point of attachment to 6 and 01, would be joined
to the earth or to another good wire on the same poles, which 'runs
the full length of, and is separated the same distance from, both
the good and the faulty conductor.

For this location to be successful the conductors must not be
grounded or crossed and their far ends must be completely open.

(b) When no good wire is available.

In this case.it is necessary to make a test, first at one end of the
line and then at the other end. Also an auxiliary condenser must
be used. The capacity of this need not be known and its value
may be chosen between wide limits, but the same condenser must
be used thruout the test. A suitable value would be one half

t _

4==*.

FIG. 1214c.

Referring to Fig. 1214c the connections are made first as in I.

Here ci, shown in dotted line, represents the capacity to ground
of the open section a to o of the conductor ab. c is the capacity
of the auxiliary condenser. For a balance,

r 2

kd

or

(3)

where d is the distance from the end a to the open, and k is a
constant of proportionality. The connections are made next at
the other end of the line as in II. Here c%, shown in dotted lines,
represents the capacity to ground of the open section b to o.

288 MEASURING ELECTRICAL RESISTANCE [ART. 1215

For a balance, in this case,

ri_ _ c_ _ c

r% c% k (I d)

or c = k (I d) .1 (4)

n

where / is the length of the open wire ab.
From Eqs. (3) and (4),

J Wl 1 fK\

(5)

(c) Another test, used by the Bell Telephone Company, which
is said' to be extremely useful and exceedingly simple to apply, is
the following: A telephone cable which is carried into a building
and is not covered with a lead sheath may have a break in a wire
underneath the insulation. The exact position of this break,
within an inch or two, is located by the use of a telephone, a buzzer,
and a battery. The buzzer has one terminal put to earth and the
other to the wires in the cable at a free end. The tester attaches
one terminal of a telephone to the earth and the other terminal to
his body. He then places his hand upon the cable containing the
broken wire. If he is on the side of the break to which the buzzer
is attached he will hear a sound in the telephone. He moves his
hand along the cable and when he has passed the break the sound
ceases. In this way the position of the break is narrowed down
and finally located within an inch or two of its exact position.
The cause of the sound in the telephone is the condenser current
which flows thru the telephone. The wire of the cable forms one
plate of the condenser and the tester's hand, which grasps the
insulated conductor, forms the other plate of the condenser.
This test is very much used.

1215. Location of Inductive Crosses. An inductive cross
(denned in par. 1201) may be located by a procedure similar to
that employed in locating an open. It is necessary in applying
the test to have in the same cable sheath a pair of good con-
ductors. The method requires a comparison of capacities, when
the conductors used for the test are connected, first in one manner
and then in another. A setting of the ratio arms to give a bal-
ance is made for each connection, and from these two settings
the necessary data are obtained for calculating the distance to
the fault or inductive cross. The method is carried out as follows:

ART. 1215] PRINCIPLES OF FAULT LOCATION

289

Connections are made first as in I, Fig. 1215. The hypothetical
condensers, represented in dotted line, are drawn to indicate the

' 1 Good
2 Pair

~l^.-c

'd

- i^<-*-

/ \ I 4

J G

>\

II

FIG. 1215. .

capacity per unit length of conductor between the pair of good
wires 1, 2; a good wire and its mate 3, 4; and this same good
wire and the wire 4, mated beyond the fault with wire 6 of another
pair.

A balance is obtained with these connections, by varying the
resistances r\ and r 2 . Connections are then made as in II, Fig.
1215, the dotted lines indicating an equally good alternative
arrangement. The hypothetical condensers drawn in dotted line
show the capacities per unit length of conductor as they would be-
come with these connections. A balance is again obtained, the
ratio arms taking the values r/ and r 2 '. The distance to the
fault, by an approximate formula, is now calculated as follows:
Let I = the length of the cable,
d = the distance to the fault,
c = the capacity per unit length of a conductor and its

mate and

GI = the capacity per unit length of a conductor and a con-
ductor of another pair.

290 MEASURING ELECTRICAL RESISTANCE [ART. 1216

In case I,

713 c ^ n\

T_ ~ ~ J i .. n j\' \*)

In case II,

*** d /^\

T77 ~^' (2)

For brevity let

T V '

= a. and -^ = 6.
ri ri'

Then, from Eq. (1),

C ^ C ai-d)' (3)

and from Eq. (2)

_ c [Z - b (I - d)]
Cl ~ bd

Hence,

I a d _ I b (I d) , .

a(l-d) ~ ~bdT
From Eq. (5) we find

d = b a _ 1 \ _. a l - ( 6 )

If in Eq (6) we replace a by its value and 6 by its value , ,

we obtain for the distance to the fault,

f f >\
7 _ ^2 (/ 2 ri ) 1 . .

r 2 / (2r 2 -r 1 )-r 2 r/ t<

Eq. (7) is not rigidly true, because all of the capacity relations
between different conductors were not taken into account. It is,
however, sufficiently exact for practical purposes.

1216. Comments on Practice and Accuracy in Fault Location.
Tho the principles of fault location and the formulae used are
relatively quite simple, difficulties are apt to arise in their appli-
cation in the field. The chief cause of these difficulties is that
conditions, which are assumed to be constant in deducing the
formulae, prove variable in practice. Thus in settled districts no
two widely separated points upon the surface of the earth are at
exactly the same potential. For this reason, if a conductor makes
contact with the earth at two points, stray currents will flow in the
line. Then also the proximity of other lines carrying currents
which alternate or large direct currents which vary will often
induce stray currents in the testing circuit. These may cause

ART. 1216] PRINCIPLES OF FAULT LOCATION 291

erratic movements of the galvanometer which seriously interfere
with the measurement.

The resistance of a fault, especially a ground, may vary greatly
while the test is in progress. A ground may be due to a moist
condition of the insulation which the testing current dries out, and
the ground will disappear while the test is in progress. This is
known as a disappearing ground.

Then another serious cause of trouble, which may become very
puzzling and exasperating, is a bad contact resistance at some
unknown point in the loop circuit. If this contact resistance is
constant false results will be obtained, but if, as often happens, the
bad contact is variable, it becomes impossible to obtain a balance
while the cause of the difficulty is misjudged.

Again two faults may be present on a conductor. The location
then will only give some intermediate point between the faults.
If the resistance of one of the two faults is steady while that of
the other varies, the point of balance on the bridge will shift in a
puzzling way. The cause of this would be difficult to distinguish
from the effects of a poor contact. The best procedure, when
there are two faults, is to cut the wire between the faults and locate
each one separately. The existence of two faults may be dis-
proved by testing from each end of the line. If both locations
place the fault at the same point there is only one.

Any method which gives only the resistance to the fault is in-
ferior to one which gives the distance to the fault as a fraction of
the total length of the cable. In calculating distances from resist-
ances it should be remembered that copper wire varies in resist-
ance about 0.4 of 1 per cent per degree C., and the temperature of a
long conductor may vary considerably from one point to another.
Then also a small variation from standard gauge in the conductor
may mislead one in calculating the distance from the resistance.

Experience shows that copper wire in telephone cables laid under
ground will run about 10 per cent higher in resistance in summer
than in winter in the State of Pennsylvania.

The most important error, however, is likely to arise from the
fact that the conductors are usually longer than the cable sheath,
since pairs of conductors are twisted together in telephone cables.
Even aerials will be longer, due to the sag of the wire, than the
distance measured along the pole line.

It will be noted that in the methods which have been given, the

292 MEASURING ELECTRICAL RESISTANCE [ART. 1216

first two excepted, the resistance of a fault, a cross or a ground,
does not enter into any of the measurements. Also that the gal-
vanometer is so placed that neither the potential differences existing
in the earth, nor any electromotive force at the fault itself, can send
a current thru the galvanometer. Many methods which might
be given for locating crosses or grounds have not been mentioned
because they involve measuring the resistance of the fault itself
or expose the galvanometer to possible earth currents or electro-
motive forces. Such methods, some of which are well known in
connection with fault locations upon marine cables, work well with
artificial lines in the laboratory, but they give uncertain and
unsatisfactory results when used upon land lines in the field. For
this reason we have omitted giving them, but the interested student
will find the standard methods of this character fully explained in
Kempe's " Hand Book of Electrical Testing," and in other works
upon marine cable testing.

If a helper has been instructed to make a connection at the far
end, it is possible for the tester to prove or disprove that he has
done so. One method of ascertaining whether a connection has
been made at the far end, to a wire which can be connected to the
testing set, is carried out as follows : Prepare for a test of the elec-
trostatic capacity of the conductor in question by the deflection
method. Take a deflection before and after the supposed con-
nection has been made. If upon closing the circuit, the latter de-
flection is the larger the connection has been made.

Another and preferable method is to join the two wires,
which are to be connected by the helper at the far end, to the
X posts of the testing set. The switches of the set are arranged
for making a loop resistance measurement. A resistance is un-
plugged in the rheostat which is greater than the resistance of the
loop can possibly be. Before the two wires are joined at the far
end the pointer of the galvanometer will deflect to one end of the
scale corresponding to infinite resistance for X. As soon as the
helper makes the connection the pointer will deflect to the opposite
end of the scale corresponding to a resistance less than that un-
plugged in the rheostat.

In giving the precision with which a fault is located it is cus-
tomary to give not the relative, or per cent, value but the absolute
precision expressed in feet or meters. In measurements of this
character the important matter is the actual distance in feet or

ART. 1217] PRINCIPLES OF FAULT LOCATION 293

meters that the location is out, regardless of the length of line.
It is well, however, to state this latter as giving additional infor-
mation regarding the circumstances under which the location was

1217. A Word on Fault-locating Apparatus. Fault locations
upon land lines can be made, if necessary, with comparatively

FIG. 1217a.

simple apparatus which a skillful tester can devise and assemble
from material usually to be found about an electric station.
However, in connection with the work of a large telephone
equipment, the locating of faults is an important and frequent
operation. It is economy, therefore, to use fault-locating apparatus
devised especially for portability, speed and precision.

It is impossible to give the space here required to describe, even
in outline, the many different forms of fault-locating and cable-
testing apparatus which instrument makers, here and abroad,
have placed upon the market. We shall merely mention two
which have had an extensive use in this country. One is the well-
known portable cable-testing set designed by Henry W. Fisher.
With this set, which is robust and complete in every respect, the

Location of crosses and grounds.

Location of breaks or opens in cables.

Conductor resistance measurements.

Liquid resistance measurements.

Insulation resistance measurements.

Capacity measurements.

294

MEASURING ELECTRICAL RESISTANCE [ART. 1217

The outside appearance of this set is shown in Fig. 121 7a. The
other apparatus referred to, with the design of which the author
was largely connected, is the " Lineman's Fault Finder." This is
shown in Fig. 1217b.

FIG. 12175.

The essential feature of the apparatus is a uniform resistance,
which lies in a circle and is about 100 ohms. By a special con-
struction, it is arranged so that contact can be made at any point
along it, and it is therefore equivalent to a very high resistance
slide wire. It has a moving contact and a uniform scale of 1000
divisions. In series with this, there are two resistances, which
may be short-circuited by switches. One has exactly the same
resistance as the wire. There is a resistance of 100 ohms, and it
is the fixed resistance of the bridge arrangement for resistance
measurements. Resistances of 1000 ohms and 9000 ohms are
connected to the battery post to protect the battery and the
apparatus from excessive current. The 9000 ohms may be short-
circuited by a switch, Other features are a self-contained battery

ART. 1217] PRINCIPLES OF FAULT LOCATION 295

and a galvanometer of the type described in par. 1501, and three
switches which permit the connections to be quickly and unmis-
takably made for the following uses:

Measurement of conductor resistances.

Murray and Varley-loop tests, and, when a telephone and buzzer
are used as accessories, the location of opens.

Both of the above sets are manufactured by The Leeds and

CHAPTER XIII.

MEASUREMENT OF TEMPERATURE BY THE
MEASUREMENT OF RESISTANCE.*

1300. Remarks on Temperature and Thermometry. The

measurement of a physical quantity implies, generally, the numeri-
cal comparison of the quantity with a certain selected quantity
of the same kind taken as a unit. Temperature, however, can-
not be treated as a quantity in the same sense. It is rather to be
considered as a state in which matter is found, and all temperature
measurements are made by comparing the changes in some form
of matter produced by heat. As shown by Lord Kelvin as early
as 1848, temperature may be expressed on a scale which is inde-
pendent of any particular form of matter, but this thermodynamic
scale cannot be used in actual temperature measurements, which,
in practice, consist in comparing the change in some particular
form of matter produced by changes in temperature.

Certain gases change in volume under constant pressure or
change in pressure under constant volume in a nearly regular
manner with equal increments of temperature, as estimated on
the thermodynamic scale. Gas thermometers have, therefore,
naturally been chosen as standards with which to compare the
changes in various forms of matter, which changes may then serve
as a convenient means of temperature measurement. The present
upward range of the gas thermometer scale is 1550 C., with a
probable error of plus or minus 2 C.,f and the melting-point of
pure platinum is known within plus or minus 5 C. and is assigned
the value 1755 C. The melting-points of many other metals are
known with varying degrees of accuracy,! and these melting-points
of the metals constitute fixed temperatures which may be used
for the calibration of various temperature-measuring devices.

The science of thermometry, especially its extension into high-
temperature pyrometry, is far too extensive to be even touched

* Portions of this chapter are taken from an article by the author in the
Proc. of the A. I.E. E., 1906.

f Dr. A. L. Day, Trans, of the Faraday Soc., Nov., 1911, pages 142 and 144.

296

ART. 1301] MEASUREMENT OF TEMPERATURE 297

upon here, and its consideration does not belong to a work of this
kind, but the resistance thermometer, which is one of the best
devices for the measurement of temperature, may with propriety
be briefly described as well as the methods employed for deter-
mining temperature by its use.

1301. Electrical-resistance Thermometry.* Electrical resist-
ance thermometry is possible because very many electrical con-
ductors change in resistance with change of temperature in a
perfectly definite manner.

The percentage change in resistance of the pure metals with
temperature is larger than that in the volume of gases, and over
twenty times as great as the volume change in mercury. Thus,
the coefficient of expansion of nitrogen gas is 0.00367 + , and of
mercury 0.00018 -f, while the coefficient of increase of resistance
of pure nickel is about 0.0041 per degree C. between and 100 C.

A change in electrical resistance can be measured with greater
ease and far greater precision than a change in volume of a liquid
or a gas. A change, in either a high or a low electrical resistance,
can be measured when it is one part in a hundred thousand. Thus,
the sensitiveness of the electrical-resistance method of measuring
temperature is very great. In the use of the bolometer, where the
electrical-resistance method of measuring temperature is carried
to its greatest sensitiveness, temperature changes as small as one
ten-millionth of a degree C. are said to be detectable.

For the electrical-resistance method of measuring temperature
to be of utility the resistance which is measured must always return
to the same value when brought back to the same temperature.
Fortunately, experience has shown that when the proper resistance
materials are chosen, and due precautions in their treatment have
been used, the reliability of the method in this respect is very
satisfactory. A properly constructed resistance thermometer, if
not exposed to too high a temperature, will maintain its calibration
better and longer than the best mercury thermometer, which is
usually subject to small alterations and irregularities due to elastic
after-effects in the glass.

* A valuable treatment of this subject may be found in the Bulletin
of the Bureau of Standards, Vol. 6, Nov., 1909, page 149. Article by C. W.
Waidner and G. K. Burgess. A bibliography of the subject is given there,
and Le Chatelier, 1912 edition.

298 MEASURING ELECTRICAL RESISTANCE [ART. 1301

As the pure metals are greatly elevated in temperature, the
rate of increase in resistance with temperature generally changes.
Thus, over extensive temperature ranges there are no metals of
which the resistance is even approximately a linear function of
temperature. Small impurities in the pure metals affect also the
amount as well as the law of their change.

These facts make it unlikely that an electrical-resistance tem-
perature scale will be found bearing such definite relations to the
absolute-temperature scale that it will serve conveniently for a
standard scale of reference in the same manner as does the scale of
the gas thermometer. When, however, the means are available, it
is relatively easy to determine experimentally the relation between
the electrical resistance of any particular specimen of wire and the
temperature for a working range of the gas thermometer of 900
or 1000 C. An electrical-resistance thermometer can then be
made of this specimen of wire, and it will serve as a standard with
which other resistance thermometers may be very simply and
easily compared.

The law of variation of electrical resistance with temperature
in the case of platinum has been investigated by Callendar and
Griffiths, and several others. It has been shown that in the
case of platinum the following relation exists between the. tem-
perature t, as measured on the air thermometer, and the resistance
of platinum:

Let p t be a so-called " platinum temperature " as defined by the
relation r> r>

' ~

.tiioo -fi/o

where R is the resistance of a given specimen of platinum at 0,
Rioo at 100, and R t at t, all measured on the centigrade scale.
It has been shown that placing

t p t = 5 \ :r 7 rp: + r^

expresses the difference between the " platinum temperature "
and the temperature as measured on the air thermometer. This
" difference formula," as it is called, holds to within 0.1 C. up to
500 C. and within 0.5 C. up to 1000 C. In this formula 5 is a
coefficient which varies with the particular specimen of platinum
used. For very pure platinum it is about 1.5, and larger for im-
pure specimens. To determine 5 the resistance of the thermometer

ART. 1301]

MEASUREMENT OF TEMPERATURE

299

is measured at the three known temperatures, C., 100 C., and
444.6 C., the boiling-point of sulphur. The authors referred to
give convenient methods of using the difference formula to con-
vert the temperatures as given by the platinum-resistance tem-
perature scale to degrees centigrade as given on the scale of the air
thermometer.

In the relation (1) above the quantity Ri OQ RQ is called F i}
the fundamental interval. It is a constant quantity for any par-
ticular thermometer.

F-
The quantity C = nn * is called the fundamental coefficient.

100 R<

As
we have

p t = 100

t RO

Cp t =

Rt-

(3)

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