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Edwin F. (Edwin Fitch) Northrup.

# Methods of measuring electrical resistance

. (page 29 of 30)

4.453

19.83

1.915

522.2

38

3.965

15.72

1.519

658.5

39

3.531

12.47

1.204

830.4

40

3.145

9.888

0.9550

1047.0

No. 10 pure copper wire weighs 31.43 pounds per 1000 feet.

WIRE DATA AND FORMULAE 375

(2) The Ohm.

1 international ohm = 1.06300 Siemens units.

1 international ohm = 1.01348 British Association (B.A.) units.

1 international ohm = 1.00283 legal ohms.

1 international ohm = resistance at C. of column of pure

mercury, 106.3 cms long, weighing
14.4521 grams, and of uniform cross-
section.

1 British Association unit (B.A.U.) = 0.986699 international

ohm.

1 legal ohm = 0.997178 international ohm.

(3) Resistance of Wire Wound in a Channel.

The following formula will enable the resistance to be calculated
for any wire with any thickness of insulation when wound to fill
a channel of any given volume. The formula assumes the wire
is wound in square order and in a regular manner. The formula
is approximate to the extent that terms which involve the square
of the thickness of the insulation are neglected We have

1.27 Vp,

R> ' 2F'

In relation (1) R t = ohms at t to which wire winds,

V = total volume of channel filled with wire,
Pt = resistivity of wire at t,
d = diameter of wire,
h = twice the thickness of the insulation.

Example. To what resistance will No. 26 B. & S. copper wire
wind per cubic centimeter, when its temperature is 20 C., and
the double thickness of its insulation is 5 mils?

In this case

V = 1 cu. cm,
P20 = 1.594 X 1.08 X 10-*,
d = 0.0405 cm,
h = 0.0127 cm (5 mils).

These values placed in relation (1) give
R t = 0.499 ohm.

376 APPENDIX

(4) Certain Formulae for Wire.*

The wire is pure copper and at 20 C.; bare.

(Ohms per 1000 feet) = 10354 -^ (area in cir. mils).

(Pounds per 1000 feet) = 0.0030269 X (area in cir. mils).

(Feet per pound) = 330,360 -r- (area in cir. mils).

(Ohms per pound) = 3,420,400 -f- (area in cir. mils) 2 .

(Feet per ohm) = 0.096585 X (area in cir. mils).

2

Area in circular mils = diameter in mils

For approximate calculations it may be easily remembered that

1000 feet No. 10 wire = 1 ohm,

1000 feet No. 13 wire = 2 ohms,

1000 feet No. 16 wire = 4 ohms, etc.,

1000 feet No. 7 wire = \ ohm,

1000 feet No. 4 wire = \ ohm,

1000 feet No. 1 wire = J ohm, etc.

To change microhms per centimeter-cube to ohms per mil-foot
multiply by 6.014. To change ohms per mil-foot to microhms
per centimeter cube multiply by 0.166. (Statement taken from
Catalogue J, Driver-Harris Wire Company.) f

IV. PHYSICAL DATA.

(1) Resistivity of Mercury.

The following data was furnished the author by the Bureau of
Standards. (In his own work the author has used the value,
volume resistivity of mercury at 20 C. = 95.782.)

The values for the resistivity of mercury are those computed
from the temperature formulae of F. E. Smith of the National
Physical Laboratory of England (Phil. Trans. 204, p. 112; 1904),
C. E. Guillaume of the International Bureau (Comptes Rendus,
115, p. 414; 1892), and Kreichgauer and Jaeger of the Reichsan-
stalt (Wied. Ann., 47, 527; 1892). In the following table volume
resistivity is given in microhms per centimeter cube and mass
resistivity is given in ohms per meter-gram.

* The constants under this heading are reproduced with the permission
of the Standard Underground Cable Company, of Pittsburgh, Pa., from their
"XVII Hand-Book, Standard Underground Cable Company, Copyright, 1906."

t Since the material given in Appendix III was prepared, the Bureau of
Standards has issued circular No. 31, entitled " Copper Wire Tables." This
circular should be consulted for the most authoritative information upon wire
sizes, standards, and temperature coefficients.

PHYSICAL DATA

377

Volume resistivity

Mass resistivity

0C.

20 C.

100 C.

0C.

20 C.

100 C.

Smith

94.073
94.073

94.073

95.783
95.782

95.782

103.410
103.379

103.56

12.7898
12.7898

12.7898

12.9751
12.9749

12.9748

13.8076
13.8034

13.828

Guillaume
Kreichgauer and
Jaeger

The C. values are computed from the quantities given in the
definition of the international ohm, 14.4521 grams mass and
106.300 centimeters length; and, in the case of volume resistivity
at C., the density is assumed to be such as to make the cross-
section 1 mm. 2 Smith's temperature formula was obtained from
observations between C. and 24 C., Guillaume's between C.
and 61 C., and Kreichgauer and Jaeger's between 14 C. and
28 C. Accordingly the values given for 100 C. are based on
extrapolation.

The temperature formula for mass resistivity is of course not
the same as for volume resistivity. Thus, letting d represent mass
resistivity, p volume resistivity, and d density,

^ = EL . \$L.
do po do

The temperature formula of resistance, as measured in a glass
tube, is different from either of the temperature formulas .for
resistivity. Thus, letting 7 denote the resistance as measured in
a glass tube, and y g the linear coefficient of expansion of the glass,

7t = Pt . 1

7o po 1 + y g t

(2) Resistivities at 20 C.; Densities and Melting Points of the
Solid Elements.

Resistivity or the specific resistance is given in microhms. (To
change to ohms multiply by 10" 6 .) The resistivity is the ohmic
resistance between opposite faces of a centimeter cube of the sub-
stance. Resistivity is quite dependent upon the purity of the
material, which is not generally recorded. It is not useful, there-
fore, to record values beyond three, or at the most four, figures.
Where values given by different observers differ a mean value
is given here. The table is arranged in the order of decreasing
resistivity.

378

APPENDIX

Element

Resistivity
in mi-
crohms at
20 C.

Density,
grams per
cubic cen-
timeter

Melting temperature,
degrees C.

Bismuth

119*

9.80

269

Mercury

95. 782 f

13.5462

-38.80

Silicon

59.5

2.3

1200 (?)

Antimony

41 3

6 62

629 20 5 F P

Thorium

40 9

11 3

1690

Arsenic

38

5 73

volatilizes

Strontium . . .

25

2 54

900

Tellurium

21

6 25

450

20 96

11 37

327

Steel (1% C.)

20

7.8(?)

Thallium

19

11.9

301

Tantalum

14.7

16.6

2910(?)

Rubidium

12.3

1.53

38.5

Iron (0 1% C.)

12 1

7 86

Tin

11 4

7 29

232

Tungsten (wire) ...

6-12

18 8

3002

10 78

11 4

1549 22 F. P.

Calcium

10 5

1 55

780

Platinum

10 2

21 5

1755 05 F. P.

Cobalt

9.71

8 6

1489 82 F. P.

Nickel

9.52

8.9

1452 3 2. OF. P.

Osmium

9 5

22 5

2200

Lithium

9 0711

534

186

Indium

9

7 12

155

7 57

8 64

320 20 3 F. P.

Potassium .

7 11U

862

62 5

Zinc

6 1

7 1

418 20.3F.P.

Rhodium

6 04

12 44

1907

Iridium

5 34

22 41

2290

Sodium

4 87H

971

97

Magnesium

4.57K

1.723H

633

Molybdenum

4

8 6

very high

Aluminum

3

2 65

657

Gold

2 44

19 32

1062 40 8 F. P

Copper .

1 721

8 89

1082 60 8F. P.

Silver (99.9%)

1 65

10 5

960 00 7 F. P.

Barium

3 75

850

Beryllium

1 93

1430

Boron

2.5(?)

above 2000.

Caesium

1.87

26.4

Graphite, carbon

2 3

vaporizes at

Lanthanum

6 12

810

Manganese

7 39

Neodymium

6 96

840

Sulphur (amorphous)*.

insulator

1 92

444 6 (boils).

Titanium

3 54

2500

5.5

1620

Zirconium

4 15

1300

* Changes in a magnetic field.

t See Appendix, IV, 1.

J Estimated. Value at 15 C.

40.1.

Estimated. Value at 0C. = 17.6.
|| Estimated. Value at C. = 8.4.
IT Author's value.

PHYSICAL DATA

379

The density of a substance may depend upon its previous treat-
ment and its physical state; hence values are generally not given
closer than three figures. The densities given are the grams per
cubic centimeter of the substance at room temperature and at
atmospheric pressure. When authorities differ a mean value is
given.

The melting point is given in degrees centigrade at which the
substance melts. In the case of several substances the melting
points are very sharp and have been determined with great care.
They serve as fixed points of temperature which are used for
reproducing the temperature scale. In these cases the symbol,
F.P., follows the recorded temperature; the numerical figure, as
db 0.8 states that the recorded temperature of melting is known
within that number of degrees centigrade.

(3) Data on a Few Alloys.

Alloy

Composition

Maker

Resis-
tivity in
mi-
crohms
at20C.

Temperature
coefficient
over small
range

Density

Driver- Harris

109 6

00016

8 02

Nichrome

Nickel steel

Wire Co.

96.6
87 1

0.00044
low

8.15

8 14

Constantan
German silver, 30%

60Cu+40Ni
30 Ni+Cu+Zn

49

48

0.00001
00023

8.88

Therlo
Manganin
German silver, 18% . .
Yankee silver
Platinoid

Cu+Mn+Al
84 Cu+4 Ni+12 Mn
18 Ni+Cu+Zn

62Cu+i5Ni+22Zn

;;

46.7
44.5
36
33
32 5

0.0000056
0.00002
0.0003
0.00028
00025

8.15
8.5
8.5
8.6
9

Ferronickel

28.2

0.002

8.2

Brass

70 Cu+30 Zn

6 to 9

0.001

8. 4 to 8. 7

(4) Standard Solutions for Calibrating Purposes. (See 1121.)
The table gives the resistivity p t at six temperatures t of NaCl t

and KC1 solutions.

The numbers -in the columns are resistivities. They express the

resistance in ohms of the solution (at the temperature in degrees C.

heading the column) between opposite faces of a centimeter-cube

of the solution. The reciprocals of the resistivities expressed in

ohms are conductivities expressed in mho, cubic centimeter, units.

[Note that the resistivity of a saturated solution is roughly one

million times the resistivity of a pure metal.]

n = normal solution.

380

APPENDIX

Thus, 1 n = normal KC1 = 74.59 gms. of the salt dissolved in
1 liter, at 18 C., of pure water.

NaCl, Sat. = saturated solution of NaCl at temperature head-
ing a column.

Solution

oc.

8C.

12 C.

16 C.

20 C.

24 C.

NaCl Sat

7 435

5 924

5 342

4 847

4 425

4 062

KC1, In...

15 ..288

12.572

11.509

10.592

9.797

9.104

KC1, O.ln
KC1, 0.02n

139.86
657.9

112.61
526.3

102.14

478.5

93.283
436.7

85.690
400.0

79.113
369.0

KC1, 0.01 n

1282.0

1031.0

934.6

852.5

782.47

721.50

(5) Resistivities of Insulators.

These vary so widely with the temperature, the purity and
character of the material, the state of the surface,* and the con-
ditions of the test, that the values given below are only roughly
approximate and merely serve to indicate the order of magnitude
of the quantities. Expressed in megohms resistance between
opposite faces of a cubic centimeter of the material the resistivities
of a few materials at ordinary temperatures are:

Paraffin wax = 3 X 10 12 ,

Mica = 9 X 10 9 ,

Ebonite = 2 X 10 9 ,

Porcelain, 50 C., = 2 X 10 9 ,

Rubber (used as insulation on wire) = 4.5 X 10 8 ,
f Fused Silica = 2 X 10 8 ,

t Glass (soda-lime) = 5 X 10 5 .

Consult par. 815.

National Physical Laboratory, England.

INDEX.

(Numbers refer to pages.)

A.

i values of, 363.

1000 -a

Accuracy, checked by using dif-
ferent methods, 6.
Ageing of thermometers, "304.
Alloys, data on, 379.
"Alternating Currents," Bedell and

Crehore, 205.

Alternating current, resistance de-
termined with, 199.
Alternating-current resistance, appa-
ratus to measure, 200.
error in measuring, considered, 206.
remarks upon, 199.
test of method of measuring, 207.
Aperiodic motion, 348.
Approximation formulae, 372.
Armagnat, H., 347.
Arrangements of rheostat coils, 81.

five plans described for, 81.
Assumptions, when using deflection

instruments, 20.
Ayrton shunt, 160.

errors in using, considered, 164.

full theory of, 160.

galvanometer constant obtained

with, 166.
insulation measurement using an,

167.
numerical illustrations in using an,

165.
table relating to, 161.

B.

Babcock, H. D., 327.
Balance, systematic method of ob-
taining, 97.
Batteries, curves for, 217.

Batteries, Continued.
internal resistance of, 214.
tested by condenser method, 215.
Battery, resistance of, by Kelvin's

method, 235.
resistance of, by Mance's method,

218.
resistance of, by Siemen's method,

236.
resistance of, by voltmeter and

ammeter methods, 220.
Battery resistance, alternating-cur-
rent methods of measuring,
226.

bridge method of measuring, elec-
trodynamometer detector, 230.
bridge method of measuring, tele-
phone detector, 226.
diminished deflection method, 233.
galvanometer deflection methods

of measuring, 233.
test of A. C. method of measur-
ing, 228.

Bedell and Crehore, 347.
Bell Telephone Company, 288.
Bell Telephone Company method,

248.

Bell Telephone Company test, 288.
Bimetallic conductors, conductivity

of, 368.
Bridge, Bureau's form for comparing

standards, 328, 329.
Bridge wire, calibration of, 70.
Bureau of Standards, 4, 148, 299, 301,

326.

Burgess, C. F., 29.
Burgess, method of, 29.
Bus-bar, measurement of current in,

108.
resistance of, 106.

381

382

INDEX

C.

Cable, insulation resistance per mile,

169.
Cables, faults on heavy underground,

284.
formula for calculating insulation

resistance of, 185.
insulation resistance of, 185.
Calibration of bridge wire, 70.
application of, 73.
coils used for, 71.
curve for, 73.
sample measurement, 75.
theory of method of, 72.
Callender and Griffiths, 298.
Capacities, comparison of, 285.
Capacity and resistance, theorem on

relation between, 186.
Capacity of conductors in cables, 285.
Cardew, Major, 156.
Cardew's electrometer method, 156.
Carey-Foster bridge, mechanical de-
sign of, 65.
standardization of bridge wire of,

68.
Carey-Foster method, connections

for, 61.
for comparing resistances which

differ considerably, 66.
methods for determining bridge

wire resistance in, 63.
shunt for bridge wire in, 65.
theory of, 62.

three bridge wires used in, 65.
unique feature of, 61.
uses of, 65.

Celluloid, specific resistance of, 179.
Celluloid condenser, resistance of,

176.
C.G.S. System, conversion of units

in, 371.
Closed circuit, resistance measured

without opening, 103.
resistance of section of, 102.
Columbia dry cell, resistance tested,
229

Combinations of resistance coils, 80.

formulae for, 80.

Committee on dry cell test, 218.
Condenser, method of connecting a

variable, 182.

resistance of celluloid, 176.
standard, 3.

Condenser method of testing bat-
teries, 215.
Condensers, theory of leakage of,

170.

Conductance, defined, 132.
Conductivity, calculated from resist-
ance data, 148.
of bimetallic conductors, 368.
commercial measurement of, 140.
equipment for determining, 145.
determined with variable ratios,

. 150.
relation to temperature coefficient,

148.

standards of, 132.

Conductivity and resistance, rela-
tions between, 367.
Conductor considered as a conveyor

of energy, 133.
Conductors, general and specific

properties of, 136.
money value of, 370, 371.
Conjugate conductors, 51.
Connection, methods of ascertaining,

and fault location, 292.
Constant, arbitrary galvanometer,

168.
Contact resistances, expression for

errors due to, 79.
in arms of Wheatstone bridge, 78.
Conversions to different systems of

units, 371.

"Cooling curves," footnote, 345.
Copper wire, table for, 374.

weight of, per 1000 feet, 374.
Correction factor, errors by neglect-
ing, 119.
in formula of Kelvin double bridge,

118.

Corrections, methods of applying, in
loop test, 278, 280.

INDEX

383

Crosses, method of locating induc-
tive, 288.

Crosses or grounds, loop methods for
locating, 258.

Curves, of galvanometer motion, 348.
of insulation resistance, 195.

D.

Damping of galvanometer system,
348.

D'Arson, a unit, 356.

Data exhibited by curve, 5.

the, 83, 85.

combinations of four coils to give,
84.

Deflection indicator for measuring
temperature, 318.

Deflection instruments, low accu-
racy of, 16.

Densities of solid elements, 377.

Density of copper, 134.

Dial bridges for temperature meas-
urements, 314.

Differential circuits, application of, to

thermometry, 46.
proof of a useful property of, 43.
properties of, 41.

Differential methods, 41.

Differential galvanometer, for tem-
perature measurement, 312.
used with shunts, 48.

Diminished deflection method, 233.

Dry cells, report on methods of
testing, 217.

E.

e, functions of, 365.

Electric wiring system, insulation of,
210.

Electrical measurement, subjects con-
sidered under, 1.

Electrical Review, reference to, 79.

Electrical World and Engineer, ref-
erence to, 30.

Electrodynamometer, for battery re-
sistance, 230.
the Rowland, 200.
used in substitution method, 231.
Electrolytes, cell for containing, 245.
not measurable by direct current,

238.

resistance of, 238.
resistance of, by method of Kohl-

rausch, 240.
resistivities of, 244.
special bridge for measuring, 242.
Electrostatic induction, relation to

other quantities, 188.
Energy, money value of electrical, 6.
English-metric conversions, 365.
English Post Office bridge, 89.
Errors, absolute, 8.
accidental, 6.

calculation of, applied to deflec-
tion instruments, 14, 15.
calculation of, extended to several

variables, 10.
gross, 5.
mean, 8.
per cent, 9.
relative, 8.
systematic, 6, 7.

tions, 97.

F.

Factory testing set, 198.
Fault, distance to, in loop test, 260.
faulty wire of known length, two
good wires of unknown length,
267.
located with faulty wire and good

wire of unknown length, 277.
Fault finder, a lineman's, 294.
Fault-locating apparatus, the Fisher

set, 293.

Fault location, lead wires used in, 281.
practice and accuracy in, 290.
problems in, 253.

relation of principles to practice
in, 253.

384

INDEX

Fault location, Continued.

two faulty wires and one good
wire of unknown length, 276.
Faults, definition of, 251.
list of, 252.

location of, as opens, 284.
methods of locating, 251.
upon low-tension power cables, 283.
Fiber, specific resistance of, 183.
Figure of merit, defined, 354.
of galvanometers, 350.
unit of, 356.

Fisher, H. W., 267, 276, 293.
Fisher's loop test, modification of,

270.

Fisher's method, loop test when
length of cable is known, 269.
special case, 276.
Five-coil combinations, 86.
Formulae for conductivity, 137, 138,

139.
Four-coil arrangement of resistances,

Northrup's method, 82.
Four-coil arrangement used with dial

switches, 84.

Franklin Institute, Jour, of, foot-
note reference, 358.
Fundamental coefficient, defined, 299.
Fundamental interval, defined, 299.

G.

Galvanometer, arbitrary constant of,

168.
constant of, obtained with Ayrton

shunt, 166.
current reduction thru, by Ayrton

shunt, 162.
description of a high sensibility,

361.

Einthoven string, 357, 358, 359.
flat-coil pointer type, described,

340.

indicator in null methods, 40.
moving magnet and D'Arsonval

type of, 339.

portable pointer, used with ohm-
meter, 58.

Galvanometer, Continued.
portable type, for temperature

measurement, 311.
proportionality for flat-coil type,

345.
resistance of, measured by second

property of bridge, 69.
sensibility of pointer type, 340.
Galvanometer constants, table of, 360.
Galvanometer shunts, 157.
theory of ordinary, 157.

of, 357.

equation of motion of, 346.
Galvanometers, comparison of, 349.
diverse qualities of, 350.
drawing of flat-coil type, 341.
flat-coil type of, 340.
sensitive, for insulation testing, 346.
Gas, expansion of, 297.
Graphite, resistivity of, 4.
Ground, located upon a single line,

253.

on single line, sample test, 257.
testing from each end of line for,

254.

testing from one end of line for, 255.
Grounds, location of, on high-tension

cables, 281.
resistance of, 248.

Grounds or crosses, loop methods for
locating, 258.

H.

Heraeus platinum, 302.
Herseus wire, purity of, 307.
Hering, Dr. Carl, 29.
Bering's conversion tables, 7.
Bering's liquid potentiometer, 247.
High resistance, electrometer method

for measuring, 175.
leakage method I for measuring,

171.
leakage method II for measuring,

175.
leakage method III for measuring,

180.
measured by leakage methods, 170.

INDEX

385

High resistance, measured by method

of mixtures, 180.
High resistances, capacity used in

measuring, 155.
deflection methods for measuring,

153.

galvanometer for measuring, 157.
measured with Wheatstone bridge,

153.
metallic resistances excluded from,

152.

specified and described, 152.
two general classes of, 152.
without appreciable capacity, 157.
High-tension cables, location of

grounds on, 281.
testing outfit for, 283.
Hoopes bridge, 140.

operations required in using, 143.
precautions in using, 144.
standards for, 142.
theory of, 141.

Humidity, effect of, on resistance
standards, 326.

I.

Inductive crosses, location of, 288.
Inertia, moment of, of galvanometer

system, 352.
Insulation measurements, factory

testing set for, 198.
with galvanometer and Ayrton

shunt, 167.
Insulation resistance, measured by

deflection methods, 191.
of a long cable, 191.
operations required in measuring,

by deflection, 191.
per mile of cable, 169.
Insulation resistance of a cable, for-
mula for calculating, 185.
Insulators, resistivities of, 380.
Instruments, distinction between in-
dicator and deflection, 338.
proposed treatment of, 324.

K.

Kelvin double bridge, a network of
nine conductors, 115.

Kelvin double bridge, Continued.
assembled from resistance boxes,

126.

correction factor in formula for, 118.
diagrams of, 116.
formula for, 118.
formula for sensibility of, 121.
methods of applying principle of,

123.

Otto Wolff's ratio coils for, 123.
ratio coils variable, 123.
standard variable, 125.
theory of, 117.

Kelvin's method, for measuring gal-
vanometer resistance, 69.
Kelvin- Varley slides, 75.

equivalent to a long slide-wire, 77.
Kempe's Handbook of Electrical

Testing, 53.

Kohlrausch, Dr. F., 30, 372.
Kohlrausch's method for resistivity
of electrolytes, 240.

L.

Landolt, etc., 246.

LeChatelier, 306.

310.

used in fault location, 281.
Leakage methods, 170.

condition for highest precision, 173.
Leakage of condensers, theory of, 170.
Leeds, Morris E., 312.
Leeds and Northrup Co., 58, 101, 119,
126, 145, 146, 198, 200, 265,
283, 340, 359.

Lineman's fault finder, 294.
Live wires, methods of measuring

resistance of, 210, 212.
Loop methods, for locating grounds

or crosses, 258.
H. W. Fisher's method, 267.
modified to meet special condi-
tions, 267.

the Murray loop, 258.
Loop test, defined, 258.

Fisher's method with slide-wire
bridge, 269.

386

INDEX

Loop test, Continued.

from both ends of faulty wire, 271.
illustrative example, 274.
modifications of Fisher's method,

269.

position of galvanometer in, 259.
testing from one end when return
wire is of unknown resistance,
273.

testing with return wire of un-
known length, 271, 273.
testing from one end, method II, 274.
Loop tests, correction for conductors

of different sizes in, 280.
methods of applying corrections

in, 278, 280.
Lord Kelvin, 115.
Low resistance, distinguished from

medium, 100.
measured with ammeter and milli-

voltmeter, 101.

Low-resistance standards, set of pre-
cision, 101.

Low resistances, compared by Carey-
Foster bridge, 114.
compared by modified slide-wire

bridge, 114.

compared by potentiometer, 115.
Low-tension power cables, location
of faults upon, 283.

M.

Magnesium, conductivity of, 139.
resistivity of, 127.

Mains, resistance of underground, 110.

Mance's method, 218.

Manganin, temperature coefficient
of, 101.

Manganin resistance, 5.

Marine cable testing, 292.

Marvin, Prof. C. F., 299.

Matthiessen's standards of conduc-
tivity, 134.
relation between, 134.

Maxwell's rule, 96.

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