ordinary sources which is approximately sinusoidal. It is usually
required, however, to obtain the resistivity as well as the resist-
ance of an electrolyte, and to determine this at a very exactly
known temperature. The apparatus and method of working de-
vised by Kohlrausch are, with slight modifications, best adapted for
this determination and may be described as follows:
1 1 20. The Method of Kohlrausch for Measuring the Resis-
tivity of an Electrolyte.
I. Direct determination of resistivity, telephone employed
The vessel to contain the electrolyte must be so shaped and
the electrodes so located that the length and cross-section of the
electrolyte measured can be ascertained with precision. For
this purpose nothing is better than a cylindrical glass tube of,
as nearly as possible, uniform bore. This may, for example, be a
glass tube 20 cms long and 1 cm internal diameter. It may be
open at both ends. In the bottom end is fitted an electrode of
gold or platinum which completely fills and is parallel to a right
cross-section of the tube, but may with advantage have some
very smalf holes thru it to allow liquid to rise in the tube when
this is partly submerged in a vessel of liquid. The other elec-
trode is of the same material and should be arranged to be mov-
able along the length of the tube by means of a rod of metal
(preferably gold plated). The rod or the tube should have a scale
cut upon it so that the distance between the two electrodes may
be read from the scale. Diagrammatically the arrangement would
be as suggested in Fig. 1120a. If this tube is insulated in an elec-
trolyte so that the upper electrode, but not the upper end of the
tube, is submerged, the current will only have the one path, within
the tube, from one electrode to the other.
The accurate calibration of this tube for cross-section and dis-
tance between the two electrodes, for any setting of the upper
electrode, must be made with care. Thus a plug may be turned to
fit accurately into each end of the tube if this is round, and these
plugs may have their diameters determined with a micrometer
caliper. This will give the cross-section where the plugs are fitted.
The distance between the electrodes may be determined with a
cathetometer, or the volume of the tube, for a given length, may be
determined by filling it with mercury and weighing this. From
data so obtained the mean cross-section is readily calculated. It
is unusual to find a tube which is not more or less conical. Assum-
ing that it is conical and that Si is the cross-section at one elec-
trode, Sz the cross-section at the other electrode, and that I is the
distance between the two electrodes, then it can easily be shown
that the expression for the resistance from one electrode to the
other, when the tube is filled with a liquid of specific resistance
is called the resistance capacity of the tube. Call this
quantity r c . Then,
To complete the arrangement the outer vessel, containing the
electrolyte, should be provided with a stirrer for stirring the
electrolyte to insure a uniform temperature throughout. The
242 MEASURING ELECTRICAL RESISTANCE [ART. 1120
temperature may then be read with any type of accurate thermom-
eter placed close to, but outside of, the measuring tube.
To make a measurement the two electrode-terminals are con-
nected in one arm of a Wheatstone bridge, which is preferably of
the slide-wire type. A special form of slide-wire bridge with a
long slide wire wound spirally upon a marble cylinder has been
upon the market for several years. A type of bridge of this kind,
in which the marble cylinder is stationary and the contact made
movable, was designed by the author and is shown in Fig. 1120b.
The cylinder upon which the bridge wire is wound is 15 cms in
diameter. There are ten turns of wire, giving a total length of
wire of 470 cms. The contact point consists of a minute piece of
hardened steel mounted in a short rod of manganin (the same
material as the slide wire, so as to avoid thermal E.M.F.'s where
the apparatus is used for other purposes with direct currents).
This steel piece slides upon the wire without abrading it. It is
not visible in the illustration, being inside the protecting hood.
The hood revolves upon a threaded spindle, the pitch of the thread
being equal to the pitch of the groove in the marble block on which
the manganin wire is wound. The resistance of this wire is
approximately 5 ohms. The position of the contact is read by
means of the vertical glass scale shown in the illustration. Com-
ART. 1120] RESISTANCE MEASUREMENTS 243
plete turns are read upon the horizontal lines of the glass scale and
fractions of a turn are read from the scale upon the lower rim of
the hood. The latter scale is divided into 100 scale divisions,
each of about 0.6 cm. These are divided into halves, so that it is
easily possible to estimate to thousandths of one complete revolu-
tion. The wire is made very uniform in resistance.
The connections to use are diagrammatically shown in Fig.
1120c. It is generally better to join the secondary of the induction
coil K to the sliding contact p and the point between the cell
C and the rheostat r, and join the telephone P to the other two
points 1, 2 of the bridge, than vice versa. A balance can generally
be easily obtained with almost complete silence in the telephone.
The resistance R of the electrolyte is then R = -r r. But as the
scale of the slide wire is divided into 1000 divisions, a + b =
1000 or b = 1000 a, whence
As the fraction - occurs frequently in bridge measurements
a table is given for all values of a from 1 to 1000 (see Appendix 1, 1) .
It is desirable, for precision, to choose r as nearly as possible
equal to the resistance of the electrolyte being measured, and
then, for a balance, p will come near the middle of the slide
wire. This will give greater accuracy to the measurement than
if it came near either end. The resistance r should be, as far as
possible, non-inductive and free from electrostatic capacity. The
specific resistance at a particular temperature is obtained by
MEASURING ELECTRICAL RESISTANCE [ART. 1121
dividing the value of R, found for a given temperature, by the
resistance capacity r c of the tube.
If one is not in possession of the special Kohlrausch bridge
illustrated in Fig. 1120b, very good results may be obtained by
using an ordinary straight wire slide-wire bridge. For accuracy in
reading to not better than 0.1 to 0.2 of 1 per cent the circular
slide wire shown in Fig. 401b, may be used with advantage. As
the scale connected with this slide wire is laid off to read the
resistance directly in per cent of the standard resistance all cal-
culation is avoided by its use.
II. Electrodynamometer employed as detector:
In pla.ce of a small induction coil for the current source and a
telephone for a detector one may use alternating current and a
sensitive electrodynamometer as the detector. The proper way
to connect this instrument in circuit is shown in Fig. 1120d.
The reason for placing the fixed coil G of the electrodynamom-
eter in the main circuit is to increase the sensibility of the appa-
ratus, which would be very small if the fixed and swinging coils
were joined in series and the electrodynamometer then connected
in the bridge in the usual way. In this method the alternating
current may be taken directly from the mains and its value reduced
by a suitable resistance r. The method is otherwise carried out
in the same manner as when a telephone and small induction
coil are used.
The type of deflection electrodynamometer recommended is the
one described in par. 1001.
1 121. Determination of Relative Resistivities of Electrolytes.
For this purpose the methods of making the measure-
ments are not different from those just given. A different
ART. 1121] RESISTANCE MEASUREMENTS 245
form of cell for holding the electrolyte is, however, to be
Suppose the containing cell to have any shape and that it is
filled with an electrolyte of known specific resistance p t at temper-
ature t C. If S is the effective cross-section of the cell and I its
length then R t = -~ p t is the resistance of the electrolyte at tem-
perature t C. Let the resistance be accurately determined at
the temperature t C.
If the cell is now filled with an electrolyte of unknown specific
resistance 7 and the resistance of this electrolyte is measured at
temperature ti C., we have, as before,
Whence, taking the ratio of the two resistances so obtained, we
TH-lf P, (1)
Eq. (1) gives the specific resistance of the electrolyte being meas-
ured at the temperature 1 C., in terms of the two resistance
measurements and the specific resistance p t of the standard
electrolyte at the temperature t C. This last value can be taken
from a table of specific resistances of electrolytes at different
temperatures. But if the specific resistance of the electrolyte
being measured is to be compared at the same temperature
with that of the standard electrolyte it is necessary to adopt
either of two procedures. One, is to arrange that the temperature
at which R is determined shall be the same as the temperature
at which R' is determined; or R' may be measured at two temper-
atures, one a little above the temperature t C. and one a little
below this temperature. Then the resistance that the electrolyte
would have at the temperature at which the standard electrolyte
was measured can be determined by a simple calculation. Assum-
ing that R f has been determined in either of these ways we have,
The form of cell which is found very convenient for determinations
of the above class is shown in Fig. 1121.
MEASURING ELECTRICAL RESISTANCE [ART. 1121
Contact with the platinum or gold electrodes is made perma-
nently with mercury in bent glass tubes as shown in the figure,
and temporary lead wires dip into the mercury. During the
measurements the cell should be suspended in a vessel contain-
ing water which is well stirred and of which the temperature can
be accurately taken.
or Gold ~
The resistivities of a saturated solution of sodium chloride
at various temperatures are given in Appendix IV, 4.
The methods described of measuring resistivities of electrolytes
furnish a means of ascertaining the concentration of a solution.
Tables have been constructed which give the relation which has
been found to exist at some standard temperature between the
resistivity and the concentration of many solutions. Hence, if
the nature but not the concentration of any solution is known,
for which tables exist, the latter can be simply and accurately
found by measuring the resistivity of the solution.
The tables usually give not the resistivity but the conductivity
which is the reciprocal of the resistivity. The standard temper-
ature for which the conductivities are given in most tables is
18 C., and hence measurements should be made as near this
temperature as practicable.
For tables of the electrical conductivity of solutions, the reader
is referred to " Physical and Chemical Constants," by G. W. C.
Kaye and T. H. Laby, pages 86-87. Also to " Physikalisch-
Chemische Tabellen," by Landolt, Bornstein and Meyerhoffer,
page 735 and following, third edition.
It may be remarked here that the resistivity of a saturated
solution of sodium chloride (NaCl) at 20 C. is 4.4248 ohms.
This is the resistance between opposite faces of a centimeter-
ART. 1122] RESISTANCE MEASUREMENTS 247
cube of the solution. The resistivity of 100 per cent conductivity
copper at the same temperature is 1.7215 X 10" 6 ohm. Hence
the salt solution has a resistivity which is 2.570 X 10 6 times that
of copper. In general, electrolytes have, roughly, a million times
the resistivity of metals.
1 122. Bering's Liquid Potentiometer Method for Determining
Electrolytic Resistances. Dr. Carl Hering has shown* that
the principle of the potentiometer may be employed for deter-
mining the resistance, and, if the necessary dimensions of the con-
taining vessel are known, the resistivity of an electrolyte. The
method is said to avoid the errors which in direct-current methods
are ordinarily introduced by polarization of electrodes. This
method permits the resistance to be measured between two se-
lected points of a quantity of electrolyte contained in a tank. It
is applied as follows:
The apparatus employed consists of a tank of rectangular form
built of insulating material. A suitable scale is fastened to the
upper and longer edge of the tank for measuring the distance
between the potential electrodes at the moment a balance is
obtained. Two current electrodes are fitted into each end of the
tank which reach across it, and above the surface of the liquid.
The liquid may fill the tank to any convenient height.
It is important to choose potential electrodes which are as inert
as possible in the electrolyte. Two gold coins or thin strips of gold
are recommended for these electrodes. The instruments required
are an ammeter, a galvanometer or millivoltmeter, and means for
determining the E.M.F. of the small cell which is used as the
standard of E.M.F. Porous diaphragms should be fitted in the
ends of the tank to prevent the products of decomposition at
the current electrodes from entering the main body of the elec-
trolyte. The polarities of the two batteries are arranged as in
the ordinary use of the potentiometer. The " setting " is made
by varying the distance between the two gold electrodes until
the galvanometer shows no deflection. At the final setting one of
the potential electrodes should be oscillated thru a small amplitude
in the direction of the fall of potential so the small galvanometer
deflections are equal on both sides of the zero. This setting
made, the current is read upon the ammeter, also the distance
* Transactions of the American Institute of Electrical Engineers, February
28, 1902, page 827.
MEASURING ELECTRICAL RESISTANCE [ART. 1123
between the electrodes. If E is the E.M.F. of the standard cell
and I the current read on the ammeter then the resistance be-
tween the electrodes is R = -y- If I is the distance between the
electrodes and S the cross-section of the tank the specific resist-
ance of the electrolyte is
P= ~T = 17
The author has not tried this method and so cannot speak from
personal experience as to its accuracy and value. Further details
may be obtained by reference to Dr. Bering's original paper.
1123. The Substitution Method. The principle of this
method has already been described, par. 206, Fig. 206b. The
apparatus shown in Fig. 1120a is the same in principle as that
shown in Fig. 206b and may be used for the measurement. The
substitution method of measuring electrolytic resistances is inferior
to alternating-current methods but may be used with advantage,
perhaps, for quick and rough determinations of the resistivities
of electrolytes in battery jars,
electroplating tanks, etc. The
apparatus required is generally
at hand and the tube or cell
may be submerged in any body
of electrolyte and the measure-
ment be very quickly made in
If the electrolyte is a silver,
copper or nickel solution it is
well to use electrodes of these
metals. For other solutions gold
or platinum electrodes are more
suitable. It is recommended to
make the electrodes of fine wire-
mesh, as bubbles from polariza-
tion will more readily escape
from the electrodes.
1124. Resistance of "Grounds"
(Bell Telephone Method).
-Moulding Strip for
No.GB.W.G. Iron Wire.
Pipe, G' long.
There is used in telephone practice what is termed a " Cable pro-
tector ground." These are ground connections made at tele-
phone poles to afford protection for aerial, as well as underground
cable plants, against lightning. The ground connection is carried
to an " open space cutout," and is made in the manner shown in
Fig. 1124a. It is necessary that the resistance of such grounds
should not exceed a proper limit and tests and reports are fre-
quently made upon such grounds. The method adopted by the
telephone company for measuring the ground resistance is known
as the "-three ground method" the principle of which may be
explained as follows:
Referring to Fig. 1124b, GI, G 2 , G 3 are three ground connections,
having resistances to ground x, y, z, respectively. The ground GI
No. 128 Receivers on
is the permanent ground. It is required to determine the resist-
ance x of this. The grounds G 2 and G 3 are auxiliary or temporary
grounds which are constructed in order to effect the measurement.
First measure (by the principle of the method shown in Fig.
250 MEASURING ELECTRICAL RESISTANCE [ART. 1124
1120c) the resistance between GI and G 2 , then between GI and G 3 ,
and lastly between G 2 and G 3 . Calling a, 6, and c these resistances
respectively, we have
x + y = a,
x + z = b,
and y + z = c.
From these three equations we derive
* = ^p. CD
The exact manner, as applied by the telephone company, of
making the measurements is clearly explained by the diagram
shown in Fig. 1124c. The ground resistance may vary between
such limits as 1 and 1000 ohms.
ELEMENTARY PRINCIPLES OF FAULT LOCATION.
1200. Fault Location. All electric lines, whether used for
the transmission of intelligence or power, are subject to what is
technically designated " faults." These faults consist, in general,
of a complete breaking down or a serious deterioration of the
insulation of the line, or of a break in the conductor. If the defect
develops at a definite point it becomes important to be able to
locate its place, as determined in distance from some station along
the line. If the location of a fault can be quickly and accurately
effected, the time and expense of making a repair is greatly reduced.
The methods which have been developed for locating faults
from a station on the line chiefly embody some form of resistance
measurement and are carried out with resistance-measuring appa-
ratus. A description of these methods properly belongs, therefore,
to a work of this character. The full development and application
of the methods when applied to submarine cables in service is
complex and extensive, and should be confined to works devoted
especially to this phase of the subject. The fundamental prin-
ciples of fault location upon land lines, however, are easily under-
stood and may be properly described here. In many cases their
application is quite simple. In other cases, however, the condi-
tions under which the relatively simple principles have to be
applied are complicated by networks of conductors, multiplicity
of faults, earth currents, variations in the size of wires in the same
circuit, and other causes which become at times very puzzling.
The majority of faults may be located, however, by one familiar
with the fundamental principles and moderately practiced in their
application. We proceed to classify and tersely describe these
fundamental principles. For detailed descriptions of the special
apparatus which instrument makers have developed for fault loca-
tion the reader must be referred to the trade publications which
advertise and often very fully describe this class of apparatus.
252 MEASURING ELECTRICAL RESISTANCE [ART. 1201
1201. Faults Occurring on Land Lines.
(a) Grounds. This is a common fault which is a partial or
complete breaking down of the insulation whereby the conductor
becomes connected to the ground or to the sheath of the cable.
If the ground connection is localized at a single point the fault
may be definitely located, but not infrequently a ground connec-
tion occurs at two or more points. In this event a precise location
of each point where the conductor is grounded is, in general, not
(b) Crosses. These are faults in which two or more conductors
in the same sheath, or on the same pole lines, become connected
together or crossed. As in the case of grounds this fault may
occur at one place or several places. In the former case the
localizing of the fault is easy and locations are usually made by the
same methods as are used for locating grounds.
(c) Opens. An open is produced when the conductor-circuit
becomes broken or open. If the circuit is not at the same time
grounded or crossed, the point at which the circuit is open may
usually be located. The methods differ, however, from those used
for grounds or crosses.
(d) Inductive crosses. These faults consist of a transposition
in telephone cables of single sides of adjacent pairs of conductors.
They result from incorrect cable-splicing. This fault is illustrated
by Fig. 1201.
Here one wire of the pair A is transposed with one wire of the
pair B at the splice S. As there is an electrostatic capacity be-
tween pairs of wires as represented by the condensers C\ and (7 2
shown in dotted line, conversation might be carried on between
T a and t a , likewise between T b and 4, but there will also be bad
cross talk between T b and t a , and T a and t b . Workmen often
attempt to correct this fault by connecting the telephones as indi-
ART. 1204] PRINCIPLES OF FAULT LOCATION 253
cated in dotted line, but the cross talk remains. A special method
will be given for locating the position of an inductive cross.
1202. Problems in Fault Location. The chief problems and
tests, treated under the subject of fault location, may be sum-
marized as follows:
(a) Identification of faulty wires.
(b) Determination of the resistance of conductor loops.
(c) The location, in distance from a station, of grounds, crosses,
opens or inductive crosses, on telephone or telegraph lines.
(d) Fault locations when loops are made up of wires of different
sizes and lengths.
(e) Insulation resistance tests of installed and uninstalled cables.
Here either the insulation may be defective in particular places
or the defective insulation may be distributed along the conductor.
(f) The location of grounds or crosses in heavy power cables,
requiring special apparatus.
(g) The location of grounds or crosses in very heavy, short,
underground cables. A special method is here required.
(h) Location of grounds or crosses in high-tension cables which
are subject to inductive disturbance from parallel alternating-
(i) Location of faults in submarine cables, during manufacture,
test, and after being installed. These problems are special and
are not considered here.
1203. Relation of Principles to Practice in Fault Location.
Fault location depends upon certain fundamental principles which
must be clearly understood for intelligent work. They should
be studied before any consideration is given to the details of specific
apparatus and methods. There are, however, many practical
points which must be considered in the successful application of
the fundamental principles. These practical points and famili-
arity with fault-locating apparatus are best acquired, however,
by practice and experience in the field. The principles of the
subject, therefore, should chiefly concern us here and we proceed
to their elucidation.
1204. Location of a Ground upon a Single Line with Only an
Earth Return. Single lines with only earth return are found
in overhead telephone and telegraph lines in unsettled country
and in single lines laid under water. The two methods to be
given are considered as having more of a theoretical interest than
254 MEASURING ELECTRICAL RESISTANCE [ART. 1204
practical value, altho they work out very well with artificial lines
made up in a laboratory.
(a) By testing from each end of line.
Signal from A to B, Fig. 1204a, to open KI and k\, assuming
that ground is not so bad but that it is possible to drive a signal
through. Measure with resistance-measuring device, k being
closed and K open, the resistance
x + y = R.
Leave K open and open k. From end B, with ki closed and KI
open, measure resistance
z + y = Ri = R t x + y
where R t is the total resistance of the line.
Then the resistance to the fault from end A is