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FIG. 815b.

A usual subdivision of a one-microfarad standard condenser
and the manner of using it in a circuit like that of Fig. 815a is
given in I and II, Fig. 815b, where the lettering of the two dia-
grams corresponds. This last method of measuring a high resist-
ance by leakage has advantages over the others described as
follows :

The method is a zero method and hence independent of the


proportionality of a galvanometer. A ballistic galvanometer is
not required, as any type of galvanometer of moderate sensibility
will serve as the indicating instrument. The sensibility of the
method may be made anything desired by simply increasing or
decreasing the E.M.F. of the source Ba (Fig. 815a). The final
value of R m is given in terms of quantities all of which can be very


precisely determined. Thus ^ is given as the ratio of two resist-
ances, and likewise the ratio can be far more precisely determined

r z

than the ratio of two deflections. Lastly, if the two mica con-
densers Ci and C-2, are precisely alike and mounted in the same
box any diminution of the charge of one due to its own leakage can
be assumed as practically the same as the diminution of the charge
of the other due to its own leakage, hence the insulation resistance
of the two condensers does not require consideration. But if
there is a difference in the insulation resistance of each it is readily

The method permits the easy determination of the capacity C p
without any change in the circuits. It may be objected that the
method requires several adjustments of the interval of leak to
secure a balance and hence an undue expenditure of time. In
practice this objection hardly holds because an exact balance is
not required as the precise time that would be required for an
exact balance may be obtained by a simple calculation from the
small deflection which finally remains after two time-adjustments
have been made.

The above method was applied to the measurement of the specific
resistance at room temperature of some samples of red fiber.
The samples were in sheets 0.35 cm thick. In the middle and
upon opposite sides of a sheet, square pieces of tin foil (much
smaller than the sheets) were fastened. In one case the tin-foil
sheets were fastened down with thin glue and in the second case
they were simply pressed down with weights. The tin-foil sheets
were 6.28 cms X 10 cms. The results were
pi = 13.7 X 10 3 megohms between opposite faces of a centimeter
cube when the tin foil was glued down, and
p 2 = 616 X 10 3 megohms when the tin foil was merely pressed on

the fiber. (Compare Appendix IV, 5.)
To make these determinations the following values were used for


the quantities (their meaning being given in Fig. 815a) :
ri = 3672 ohms, r z = 3000 ohms.
Ci = Cz = 0.5 microfarad.

With the electrodes glued on, the time of leak for a balance
within 4 scale-divisions was 8 seconds, and with the electrodes
pressed on, it was 300 seconds for a balance within +10 scale-
divisions. With corrections in the time made for the small de-
flections obtained, the above values for the resistivity of fiber,
expressed in megohms, were obtained. The ratio of about 45 to 1
between the resistivity obtained with electrodes pressed upon the
fiber and electrodes glued upon the fiber shows how the apparent
resistivity of a substance like fiber is affected by apparently slight
changes in the conditions under which the test is conducted.



900. Introductory Note. In the manufacture and installa-
tion of long cables, especially those of the submarine type, the
insulation resistance per mile or per kilometer of the cables is
tested. This, however, is only one of several tests which are made
upon such cables. The phenomena observed in testing the insula-
tion resistance are complicated and not well understood and a full
treatment of the subject would not only be too extended for this
work but it belongs rather to the subject of fault location and the
study of the electrical properties of dielectrics. We shall, there-
fore, confine our treatment of insulation-resistance measurements
of long cables to a brief outline of the standard methods employed
and merely state the phenomena observed, requesting the reader
to refer to special publications upon the subject for a fuller treat-
ment, and for the explanations of the phenomena, which have
been attempted.

90 1 . Formula for Calculating
the Insulation Resistance of a
Cable. If the specific resist-
ance p of the insulation of a
cable is known, the insulation
resistance per kilometer of the
cable may be calculated as fol-

In Fig. 901, which represents
the cross-section of an insulated
cable, let r\ radius of metal
core, r z = radius of outside sur-
face of insulation, r = radial FIG. 901.
distance from center of core

to any point p within the insulation, dr = the radial depth of an
infinitely thin annulus of insulation and I = the length of the



Then the resistance of the annulus is

Integrating between the limits r 2 and ri we have

Expressing in common logarithms and combining the constants
we obtain

0.3664 p r,
R= i log - (3)

Example. Assume p = 4.5 X 10 14 . Take I = 1 kilometer =
10 5 cms, TI = 0.13 cm and r z = 0.53 cm. These constants
apply, approximately, to a No. 10 B. & g. wire insulated with
rubber ^ inch thick.

^ 0.37 X 4.5 X 10 14 0.53

Then R = - - log ia ^^5 = 1.016 X 10 9 ohms per

JL \J vJ JLo

kilometer or, approximately, 1000 megohms per kilometer

902. Theorem upon the General Relation Between Capacity
and Resistance.

(1) From a unit charge of electricity in a medium of constant

4 7T

specific inductive capacity K, ^ lines of electrostatic force issue.


This is well established but may be easily proved as follows: If
two point charges e and e' are located at a distance r from each
other in space, the specific inductive capacity of which is K, then
the force in dynes between these charges is, by the law of Coulomb,


F =


Now by definition the force at any point in space is equal to the
rate of fall of the potential in the direction of the line of force at
that point. If we take the potential to decrease as the distance
n measured along the line of force increases, we have

Or if ds is an element of surface taken normal to the lines of force
at any point in the space,

-^-ds = ^- 2 ds. (3)

dn Kr 2 ^ '



If we imagine one of the charges surrounded by a sphere of radius
r and we integrate over the surface of this sphere, the area of
which is 4 irr 2 , we have



Let the charge e = e' = I, then


Eq. (5) states that the total induction, namely, the total number of
lines of force which issue from a unit charge in space of specific

4 TT 4

, is -^ - If the charge is e then


lines of

inductive capacity

force issue from it.

(2) If eris the surface density of electricity upon any surface,
namely, the number of electrostatic units of charge per unit area,
then for the unit of area we have the electric force or induction,

*__*=!!?. (6 )

This states that the electric force or fall of potential from

4 7T

the surface in the direction of the field is -^ times the surface

density of the electricity.
From Eq. (6) we obtain


K dv

4?r dn


(3) Now let Fig. 902 represent an element of space. Let a
current of electricity enter the ele-
ment at the face dxdy, and nor-
mal to this face. If Id is the
current density, then the current
which enters the face of the ele-
ment will be

di = Id dx dy. (8)

Suppose the difference of potential


FIG. 902.

between the two ends of the element is v
length of the element. Then,

i, and that dn is the

di =



where dR is the resistance in ohms of the element parallel to dn.

But - dR = r y p >


,. T , , v vi , ,
, di = Id dx dy = : - dx dy,


an p dn p dn

where - =K', the conductivity of the medium (assumed constant).


If we compare Eq. (7) with Eq. (9) we see that in the electro-

static case corresponds with K f in the electromagnetic case.
Thus any formula for lines of electrostatic induction becomes a
formula for lines of current flow when we make 4x0- = I d and
change K into K'. Or one can say, by comparing Eq (7) and
Eq. (9), that

pl d =j?<r. (10)

Eq. (10) leads to the important conclusion that, any formula which
gives the electrostatic induction thru a surface will express the value
of the current density multiplied by the specific resistance of the
medium when the medium of specific inductive capacity K is replaced
by a medium of specific resistance p.

(4) As an example of the above take the general case of the
relation between electrostatic capacity and ohmic resistance. In
general the capacity of any two electrodes will be the total charge
upon the surface of one of them divided by the difference of poten-
tial between them. Or if a is the surface density at any point of
one electrode and ds is an element of the surface of one electrode,
their electrostatic capacity is

f fads

C 8t - ii- (ii)

v Vi

Now multiply both sides of (11) by -^, and we have


n I I ~l? a ds I I Id ds
4TrC 8t J J pK ./ /

pK v vi v



the conductance from one electrode to the other. In making
this statement we conceive the medium of which the specific
inductive capacity is K to be replaced by a medium of which the
specific resistance is p, or we conceive the same medium to have

this specific resistance.

ance between the two electrodes, then

If we write G = -^ , where R is the resist-


= J5 , or RCst =



Eq. (13) shows that in every circuit where the electrostatic lines
and the lines of current flow pass thru the same medium the
product of the resistance and the capacity of the circuit is constant

and equal to

A very simple case will make this physically clear. Suppose
we have two parallel plates, each of area A, and separated by a
distance d. Suppose that between these plates there is a slab of
dielectric (much larger than the plates) and that the specific
inductive capacity of this slab is K, and its specific resistance is p.
Then the resistance between the plates is

The capacity of the plates is

C at =




and we have

pd AK
A 4ird

P _K


Namely, we cannot increase the electrostatic
capacity of the plates by increasing the area
without decreasing the resistance between
them by a like amount, nor can we diminish
the distance between them, thereby increasing
their capacity, without equally diminishing
the resistance between them.

903. Application of Theorem to the Meas-
urement of a High Resistance by Leakage.
Let it be required to measure the resist-

i- c ; J

FIG. 903.

ance of any condenser, as C, Fig. 903, by the method of leakage,


and assume first that the only capacity used is that of the
condenser itself. By Eq. (3), par. 811, the time of leak is

T = RC\og e ^ (1)

Now we have shown, Eq. (6), par. 812, that for the best results,
the capacity, which has been charged to the potential V lt should

be allowed to leak until this potential has fallen to . Hence,


in this case,

T = RC log e e or, as log e e = 1,

T = RC. (2)

Since the product RC will remain constant however we change the
thickness or area of the dielectric, it follows that the time of leak

required for the potential to fall to - of its value is the same for a

condenser of any form, size or number of plates, provided the
quality of the dielectric remains the same. We may express the
value of this time as follows: In Eq. (2) C is expressed in farads
and R in ohms. If we express C in electrostatic units, we have

T RC 8t
9 X 10 11 '

But by Eq. (13), par. 902,


An ordinary case would be one in which p = 4.5 X 10 14 and
K = 5, which values placed in Eq. (3) give

T = 199 seconds or about 3J minutes.

The conclusion to draw from this result is, that (in measuring the
insulation resistance of a cable where the capacity of the cable
is the only capacity which leaks) it will require the same time for

the charge to leak away so - of the original charge remains what-


ever dimensions are given to the cable either in length or in cross-
section. By using a high charging potential the charge will give


a sensitive galvanometer a full-scale deflection, even tho the
cable is very short. Hence, there will be no gain in this case in
using a long length of cable over a short one.

We may, however, use an auxiliary capacity C a as indicated
in dotted line in Fig. 903. Then the total capacity which leaks
will be

C t = C a + C s t = C a -j- T p >

the capacity in this relation being expressed in electrostatic units.
By Eq. (3) we shall then have,

77 = RC a pK . .

9X 10 11 " r 47r9X 10 11 '
or T t = RCmf 10- 6 + P K 0.885 X 10~ 13 (6)

where C m / is the capacity of the auxiliary condenser expressed in

Eq. (6) shows -that, if C m / is taken large the time of leak is in-
creased, but as C m f may be an accurate high-resistance mica con-
denser the capacity of which can be accurately determined, while
the capacity of the resistance under measurement may not be
determinable with exactness, it may be very advantageous for pre-
cision to use an auxiliary condenser. Furthermore, it will not in
this case be necessary to submit the resistance under measurement
to the high potential which might otherwise be required to secure
the necessary galvanometer deflections.

904. Insulation Resistance of a Long Cable by Deflection
Methods. When the insulation resistance of a long cable, such
as a section of a submarine cable, is to be tested, it is more cus-
tomary to use a direct deflection method than any other. A
systematic plan of procedure is usually followed, which may be
described as follows:

The apparatus used generally consists of a sensitive galvanom-
eter of high resistance, a galvanometer shunt, a short-circuit key
for the galvanometer, and a Rymer-Jones key, also a standard
high resistance for calibrating the galvanometer. The resistances
commonly measured in practice may range from 1 to 40,000
megohms. The value of the resistance is interpreted in terms of
galvanometer deflections.

In making the test three operations are performed.



1st. The negative pole of the battery is joined to the cable
core, the galvanometer being in circuit after the first rush of
current is over. The positive pole of the battery is put to earth.
The cable being in a tank of water, its outside sheath is earthed.

2d. The cable is allowed to discharge itself for a certain time,
being disconnected from the battery. The deflections produced
by the discharge current, after the first rush of current is over,
are noted.

3d. The positive pole of the battery is joined to the cable core
and the negative pole to the earth, and after the first rush of cur-
rent is over the galvanometer deflections are again noted.

In these three operations a record of the time, as well as the
galvanometer deflections, is carefully kept.

FIG. 904a.

For carrying out these three operations the apparatus may be
connected as given in Fig. 904a. K is the Rymer-Jones key, and
it is to be noted that the levers of the key cannot be placed in any
position which will short-circuit the battery. S is the galvanom-
eter shunt, which may or may not be required, depending upon
the relation which the galvanometer sensibility bears to the resist-
ance being measured and to the E.M.F. of the battery employed.
k is the short-circuit key. The cable C is usually coiled up in a
tank of water.

At the point where the wire from the galvanometer is attached
to the cable core, care must be exercised to arrange matters, as
far as possible, so no current will leak from the core over the out-


side surface of the insulation to the water in the tank. A leakage
path of this kind will be a resistance in parallel with the resistance
being measured and its unrecognized existence may lead to en-
tirely incorrect results. Two methods are employed to prevent
this leak. The first is to carefully pare the insulation at the end
of the cable into a conical shape and then, being careful not to
touch, moisten or otherwise contaminate the surface, plunge the
end of the cable into hot paraffin wax. This will give the surface
a high insulation. The other method is to employ a guard wire.
This wire is shown in Fig. 904a in dotted line. Two or three turns
of a fine wire are taken about the conical end of the insulation and
then carried to the terminal of the galvanometer which is not
attached to the cable core.

When the cable core is being charged negatively or positively
there will be no leak over the surface of the insulation which will
pass thru the galvanometer, because the conical surface of the
insulation is maintained by the guard wire at practically the same
potential as the core. In the second test, where the cable is
allowed to discharge itself for a certain time, being disconnected
from the battery, the guard wire will only serve to increase the
rate of leak and hence is of doubtful advantage for this part of
the test.

It is seen from the connections that with the levers 1 and 2 on a
and 6, respectively, the core of the cable is put to the positive pole
and the tank to the negative pole of the battery. Putting levers
1 and 2 on b and a, respectively, puts the negative pole to the core
and the positive pole to the tank. Putting both levers on b
connects the cable core and tank thru the galvanometer without
the battery being in circuit.

In the first operation, testing with negative current, the short-
circuit key is kept closed while levers 1 and 2 are thrown to b and
a until the first rush of current is over, this rush of current being
due to the rapid charging of the capacity of the cable.

This rush of current is usually over, even in very long cables,
in a few seconds. After about five seconds, the short-circuit
key is opened. The galvanometer will now deflect to a maximum
deflection, more or less rapidly, depending upon its natural period,
and when it has obtained this maximum deflection, which will at
once begin to decline, a record should be made of the deflection
and the time, counting the time zero when the negative pole of


the battery is put to the core. The deflection of the galvanom-
eter will steadily decrease, rapidly at first and less rapidly as the
time advances, gradually reaching a minimum deflection after
several minutes. It reaches its minimum or asymptotic value in
perhaps 30 minutes. The test may be continued with advantage
for this period, reading the deflections every minute.

The second operation is now begun. The key k is first closed
and the levers of K are thrown to 6. A few seconds thereafter k
is opened again and the deflections of the galvanometer are now
noted as in the first operation, again counting the time zero when
the levers of K are changed. These deflections will be large at first
and then gradually die away as in the first operation. This is
due to the fact that the electricity, which has been stored in the
dielectric, is given out, part of it with a rush, as a condenser dis-
charges itself, while, thereafter, the remainder discharges slowly
and at a decreasing rate.

This second part of the test may be continued for five minutes,
the deflections being read every minute.

The third operation is performed exactly like the first except
that the positive pole of the battery is put to the cable core.
When the short-circuit key is opened it will be noted that the
direction of the deflection is opposite to that obtained when
charging the cable negatively and the same as that obtained upon
discharging the cable. This part of the test may be continued for
five minutes, the deflections being recorded every minute. It is
called testing with a positive current and concludes the observa-
tions. The following curves, Fig. 904b, drawn from data given
in " Kempe's Handbook of Electrical Testing," will exhibit the
general character of the phenomena.

Curve A exhibits the decline of the deflection with the time,
the electrification being negative, in the interval 1 minute to 15
minutes. The course of the curve in the interval to 1 minute is
not known. Beyond 15 minutes it may be studied and is found
to assume an asymptotic value, as suggested by the dotted line.

Curve B exhibits the deflections, where the core and sheath of
the cable are joined, or the cable is " earthed," in the interval
1 minute to 5 minutes. The course of the curve between and
1 minute is not known. The deflection after the fifth minute is
known to continue to decline gradually to a zero value, as sug-
gested by the dotted line. In some instances it may take many



hours for the cable to become quite neutral; that is, for the
deflection to become sensibly zero. In a cable of 10 or 15 miles
length the deflection practically reaches zero in the course of 30

Curve C exhibits the deflections, which gradually decline with
the time, when the core of the cable is put to the positive pole of
the battery, immediately upon the removal of the earth con-
nection. The course of this curve is like that of curve A, and the
same remark holds, that between and 1 minute the curve is not
accurately known, at least not from galvanometric observations.

FIG. 904b.

In cables without defects or " faults " in their insulation the
course of the curves will be regular and of the general character
shown in Fig. 904b. Unless both ends of the cable core are
joined to the galvanometer, as indicated in Fig. 904a, irregularities
in the curves may be produced by inductive effects which would
result, on shipboard, by the rolling of the ship, or, in factories, by
induction from neighboring currents. With both ends of the core
joined to the galvanometer these effects are avoided. Defective
insulation of the lead wires may also produce irregularities in the
curves, so one must not too hastily conclude that a cable is defec-
tive when the curves are seen to be irregular.


The quality of the insulation may be judged from the curves
which in a perfect cable exhibit the following relations: If the
current in the earth-reading (curve B) at the end of the first
minute be added to the, current at the end of the negative electri-
fication (curve A) the sum should equal the current for the nega-
tive electrification at the end of 1 minute. Or in the case shown
by the curves, 59 + 142 = 201, which is not very different from

Again, if the last negative electrification-reading be added to
the recorded earth-reading at any period, the sum should equal
the negative electrification-reading at the end of the same period.
Thus the last electrification-reading is 142, the earth-reading at
the end of the fourth minute is 25, and the negative electrifica-
tion-reading at the end of the fourth minute is 164. We have
25 + 142 = 167, which is approximately the correct sum.

Again, if from the deflection at the end of the first minute of
positive electrification (curve C) we take the last earth-reading,
it should equal the deflection at the end of the first minute of
negative electrification. Thus, 227 - 22 = 205.

The accuracy of these relations, the general smoothness of the
curves, and the rate at which the deflections decline give
the necessary information, which enables those accustomed to the
requirements to judge of the perfection of the insulation of the

The tests necessary for merely determining the specific resist-
ance of the dielectric of the cable are not, of course, as elaborate
as those given above, and in ordinary practice, when land cables
or marine cables of moderate length are tested, only the first
operation of testing with negative electrification is undertaken.

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