r
REESE LIBRARY
UNIVERSITY OF CALIFORNIA
A HANDBOOK
FOR THE
ELECTRICAL LABORATORY
AND
TESTING ROOM.
BY
J. A. FLEMIiMG, M.A., D.So., F.R.S.
M
PROFESSOR OF ELECTRICAL ENGINEERING IN UNIVERSITY COLLEGE, LONDON ;
MEMBER OF THE INSTITUTION OF ELECTRICAL ENGINEERS ;
FELLOW OF THE PHYSICAL SOCIETY OF LONDON, &c., &c.
VOLUME I.
UNIVERSITY
CALI
LONDON :
THE ELECTRICIAN" PRINTING AND PUBLISHING COMPANY,
LIMITED,
SALISBURY COURT, FLBLT STREET,
[All Rights Reserved.]
'
WORKS BY DR. J. A. FLEMING
ALL FULLY ILLUSTRATED.
A Treatise on The Alternate Current Transformer in Theory
and Practice.
Vol. I. THE INDUCTION OF ELECTRIC CURRENTS. 612 pp.
3rd Edition. 12s. 6d.
Vol. II. THE UTILISATION OF INDUCED CURRENTS. 600 pp.
12s. 6d.
Electric Lamps and Electric Lighting.
A Course of Lectures delivered at the Royal Institution of
Great Britain. 93 Original Illustrations. 2nd Edition.
Extended and revised. 6s.
Magnets and Electric Currents.
An Elementary Treatise for the use of Electrical Artisans and
Science Teachers. 136 Illustrations. 408 pp. 7s. 6d.
Electrical Laboratory Notes and Forms.
A series of 40 Elementary and Advanced Laboratory Sheets for
the use of Demonstrators and Students in Electrical Labora-
tories. Each Sheet contains full practical instructions (illus-
trated when necessary) for carrying out some one particular
measurement in electrical testing, and a ruled-up form for
entering observations. The Laboratory Notes are useful to
all engaged in any description of Electrical Testing. Price 4d.
each, 3s. 6d. per dozen ; complete set, 10s. 6d. ; in portofolio,
12s. ; bound in cloth, 12s. 6d.
A Cheaper Set, half the above prices, is issued for the use of
Students in Polytechnics and Science Classes.
The Centenary of the Electric Current, 1799-1899.
A Lecture delivered before the British Association at Dover,
September, 1899. Price Is.
PREFACE.
r I ^HE only excuse that can be offered for adding
another book to the already full catalogue of
Electrical literature, especially under the heading
of Electrical Measurements, is that, in spite of the
numerous excellent works on this subject, there seemed
room for one dealing more particularly with the require-
ments of electrical engineers as distinguished from electrical
physicists. Several valuable handbooks exist dealing with
the subject of Electrical Testing from the point of view of
the telegraphist or physicist, but these generally contain
either too much or two little for the purposes of those who
have to deal with the class of electrical measurements
which it is necessary to make in electrical stations or
factories.
For this latter purpose, what is required is not a multi-
plication of methods gathered together without regard to
their applicability or accuracy, but a selection of approved
and well-tried methods.
In many text-books on Electrical Measurements there
is an absence of critical discussion on the intrinsic utility
of the various methods of measurement given. A process
which looks well on paper does not always work out well
in practice, and the practical engineer, therefore, requires
to have placed before him a series of selected methods of
measurement rather than a collection made as inclusive as
possible. The present treatise has therefore been divided
into a series of chapters, each of which deals with one
particular class of measurements. No attempt, however,
has been made to include a description of all the methods
under that particular heading, far less of all the implements
or instruments, but certain processes which experience has
95814
IV. PREFACE.
shown to give good results are described as fully as pos-
sible, and a detailed description given of certain typical
forms of widely used instruments.
In the case of electrical instruments there is a process
of evolution and a survival of the fittest. Many ingenious
or otherwise interesting instruments for some particular
reason drop out of existence, whilst other forms survive,
and it is to these surviving forms that attention has been
most directed.
In the First Volume, in addition to a chapter on the
Equipment of electrical laboratories, the subject of the
measurement of Electrical Resistance, Electric Current,
Electromotive Force and Electric Power is dealt with in
the remaining chapters.
It is intended that the Second Volume shall contain
chapters devoted to the measurement of Capacity and
Inductance, Electric Quantity and Energy, including Bat-
tery and Meter testing, the Magnetic testing of iron,
Photometric and Electric lamp testing, and the testing of
Dynamos, Motors and Transformers.
Each chapter is as far as possible complete in itself, and
where tables or numerical data are given they are placed
at the end of the chapter to which they belong, and not, as
usual, at the end of the book.
As the object has been to place in the hands of the
reader a practical handbook rather than a theoretical
treatise, such brief mathematical discussions as are intro-
duced have generally been placed in smaller type so that the
non-mathematical reader may leave them out of considera-
tion ; and as the desire has been to produce a handbook
useful in the test rooms of electrical factories and stations,
descriptions of instruments more usually found in a physical
laboratory than a testing room have been omitted.
J. A. F-
University College, London,
August, 1901.
TABLE OF CONTENTS.
CHAPTER I.
PAGE.
EQUIPMENT OF AN ELECTRICAL TESTING BOOM ]
1. The Equipment of an Electrical Testing Room or Laboratory ; The
Dynamo Room ; The Electrical Laboratory ; The Accumulator
Room. 2. The Fundamental Standards of Length, Mass and
Time. 3. The Principal Electrical Units and Standards. 4.
The Practical Standard of Electrical Resistance ; Mercury Stan-
dards; Resistance Alloys ; Standard Resistance Coils. 5. Current
Carrying Standard Resistances. 6. The Recovery of the Standard
or Unit Electric Current ; The Board of Trade Specification ;
Ampere Balances. 7. The Regulation of Current ; Rheostats,
8. The Practical Standard of Electromotive Force ; the Clark
Cell ; Standard Cells. 9. The Literature of the Mercury Standard
Cell. 10. Mechanical Standards of Electromotive Force. 11.
The Instrumental Outfit of an Electrical Laboratory. 12. Current
Measuring Instruments. 13. Voltage Measuring Instruments.
13a. Resistance Measuring Instruments ; Wheatstone's Bridge.
14. Electric Quantity Measuring Instruments. 15. Instru-
ments for the Measurement of Electric Power ; Wattmeters.
16. General Hints on the Outfit of a Testing Laboratory ; the
Board of Trade Electrical Laboratory.
CHAPTER II.
THE MEASUREMENT OF ELECTRICAL RESISTANCE ... 191
1. The Comparison of Electrical Resistance. 2. Networks of Con-
ductors ; Calculation of Resistance of Networks of Conductors.
3. The Slide Wire Form of Wheatstone's Bridge. 4. The Plug
Pattern of Resistance Bridge. 5. Portable Forms of Wheatstone's
Bridge ; The Trotter Bridge. 6. Theory of the Wheatstone
Bridge. 7. The Matthiessen and Hockin Bridge. 8. Calibration
of a Slide Wire. 9. The Determination of the Temperature
Coefficient of a Coil. 10. The Mean Temperature Coefficient of a
Metallic Alloy ; Variation of Resistance of Metals with Tempera-
ture. 11. The Determination of the Specific Resistance of a
Metal or Alloy ; Volume Resistivity ; Mass Resistivity. 12. The
Determination of the Volume and Mass Resistivity of Metals and
vi. TABLE OF CONTENTS.
CHAPTER II. (Continued).
Alloys ; Matthiessen's Standard for the Resistivity of Copper.
13. The Determination of Low Resistance by Fall of Potential.
14. The Measurement of Low Resistance by the Matthiessen
and Hockin Bridge. '15. The Kelvin Double Bridge. 16.
Modifications of the Kelvin Double Bridge for Low Resistance
Measurement. 17. Modifications of the Ordinary Wheatstone
Bridge for Low Resistance Measurement. 18. Measurement of
High Resistances by Direct Galvanometer Deflection. 19.
Measurement of Insulation Resistance; Price's' Guard Wire.
20. Measurement of Dielectric Resistance by Time of Fall to
Half Charge. 21. Cardew's Differential Method for Measuring
High Resistance. 22. Practical Measurement of Electric Light
Wiring Insulation; The Ohmmeter. 23. Regulations for House
Wiring Insulation. 24. Measurement of the Resistivity of
Liquids. 25. The Absolute Measurement of Electrical Resistance.
26. Resistance of Conductors to Alternating Currents.
Table I. Atomic Weights and Densities of Metals. Table II.
Electrical Mass-Resistivity of Metals. Tables III., IV. and V.
Electrical Volume Resistivity of Pure Metals. Table VI. Elec-
trical Conductivity of Metals. Table VII. Volume Resistivity of
Alloys. Table VIII. Volume Resistivity of Liquids. Table IX.
Volume Resistivity of Badly Conducting Liquids. Table X. Volume
Resistivity of Solutions of Copper and Zinc Sulphate. Table XI.
Volume Resistivity of Dielectrics. Table XII. Resistance of
Various Sizes of Platinoid Wire. Table XIII. Resistance of Various
Sizes of Manganin Wire. Table XIV. Resistance of Various Sizes
of Copper Wire. Table XV. The Value of the Ohm. Table XVI.
The Resistance of Copper Conductors to Alternating Currents.
Table XVII. The Resistivity of Various Materials.
CHAPTEE III.
THE MEASUEEMENT OF ELECTRIC CURRENT 339
1. Classification of Electric Currents. 2. The Measurement of
Current by the Electrolysis of a Solution of Copper Sulphate ; The
Standardisation of an Ammeter. 3. The Measurement of Current
by the Electrolysis of Silver Nitrate. 4. Standard Current-
Measuring Instruments ; Magnetic Field of a Circular Conductor.
5. Absolute Galvanometers ; Helmholtz Standard Tangent Galva-
nometer. 6. The Electro-Dynamometer. 7. Current Balances.
8. Laboratory Ampere-Meters. 9. Calibration of Laboratory
Ammeters. 10. Measurement of Current by the Potentiometer.
11. Current Carrying Capacity of Wires. 12. The Calibration of
a Galvanometer by the Potentiometer ; The Measurement of Small
Currents ; Shunt Boxes. 13. Alternating- Current Measurement.
TABLE OF CONTENTS. vii.
CHAPTER III. (Continued.}.
14. Wave-Form Measurement ; Oscillographs. 15. The Use
of Transformers in Alternating-Current Measurement. 16.
Measurement of the Frequency of an Alternating Current ;
Frequency Tellers. 17. Measurement of the Phase Difference
of a Periodic Current ; Phase Meters. Table I. Fuse- Wire Currents
(Sir W. H. Preece). .Table II. Electro-Chemical Equivalents.
CHAPTER IV.
THE MEASUREMENT OF ELECTROMOTIVE FORCE 421
1. Electromotive-Force Measurement. 2. The Practical Recovery
of a Standard Potential Difference. 3. The Potentiometer
Measurement of Electromotive Force. - 4. The Measurement of
Small Potential Differences ; A Combined Potentiometer and
Wheatstone's Bridge ; The Elliott Potentiometer ; The Fleming
Potentiometer. 5. Calibration of a Low-Tension Voltmeter ;
Error Curve of a Voltmeter. 6. The Calibration of a High-
Tension Voltmeter ; An Inductionless Safety Resistance. 7. Self-
Recording Voltmeters. 8. Extra High-Pressure Voltmeters.
9. Laboratory and Switchboard Voltmeters ; Qualifications for a
Good Switchboard Voltmeter. Table I. Electromotive Force of
the Clark Cell at Various Temperatures.
CHAPTER V.
THE MEASUREMENT OF ELECTRIC POWER 469
1. Electric Power, Mean Power and Power Factor. 2. Measurement
of Power in the Case of Unvarying, Continuous or Direct Currents.
3. Measurement of Continuous-Current Power by the Wattmeter.
4. Measurement of Alternating- Current Power. 5. Measure-
ment of Power taken up in the Case of High-Tension Alternating-
Current Circuits. 6. Power Measurements in theCaseof Circuitsof
Small Power Factor. 7: Power Measurement by Direct Measure-
ment of Power Factor. 8- The Three- Voltmeter Method of
Measuring Alternating-Current Power ; Limitations of the Method.
9- The Three Ammeter Method. 10. Dynamometer Methods
of Measuring Power. 11. Power Measurement in the Case of
Polyphase Circuits. 12. Practical Forms of Wattmeters ; Siemens
Wattmeter ; Fleming Wattmeter ; Kelvin Wattmeter ; Kelvin
Engine-Room Wattmeter ; Kelvin Three-Phase Wattmeter ; Elec-
trostatic Voltmeters. 13. Wattmeter Testing ; Construction of
a Coil of Maximum Inductance and Known Power Factor ; The
Measurement of Small-Power Factors.
ERRATA.
Page 40. First line of footnote, for Platinum read Platinoid.
144. Line 9, for 13 read 13A.
tt 455. Line 3 from bottom of page, for small read simple.
FOR THE
ELECTRICAL TESTING-ROOM AND LABORATORY
CHAPTER I.
THE EQUIPMENT OF AN ELECTRICAL
TESTING ROOM.
1. The Equipment of an Electrical Testing Room or
Laboratory. In the following pages the class of electrical
measurements we shall chiefly consider are those required in
the engineering applications of electricity and magnetism as
far as regards that range of work included in the so-called
heavy electrical engineering. We shall omit all references to
measurements and tests particularly limited to Telegraphic
and Telephonic work, as on this part of the subject several
excellent text-books already exist.
In the establishment of an electrical testing laboratory
the electrician will not often be called upon to design
the structure or enjoy the advantages of a building erected
especially to meet his own views. Usually he will have
to adapt or utilise for the purpose some existing rooms
in a factory, electric supply station, college, or technical
institution. If, however, the opportunity presents itself of
being able to begin by designing the laboratory buildings to
be occupied, a great advantage is gained at the outset. If,
2 ELECTRICAL LABORATORY EQUIPMENT.
moreover, the space available can be arranged in the most
convenient and suitable way, and if initial outlay is not an
obstacle to the possession of the most desirable arrangements,
the following conditions may be realised. We shall assume
that, in the testing room or electrical laboratory being
arranged, at least one or more large and convenient rooms
are available for the purposes of a general testing labora-
tory, and that, in addition, a dynamo room and also an
accumulator room are provided. If the laboratory is in
a technical teaching institution, an apparatus room, at least
one, and preferably several, private rooms, as well as a
lecture and preparation room, will also be required. It is a
great convenience to have, if possible, all these rooms located
on one level. Time and labour are economised in the day's
work, and it is easier to take heavy apparatus backwards
and forwards.
At one end of each electrical laboratory a partition should
be run up separating off a space at least 5ft. wide and 30ft.
long to form a photometric gallery. Then with regard to the
special arrangement and equipment of each apartment, these
should be as follows:
Dynamo Room. Even although current is obtainable from
public electric supply circuits or from factory lighting
dynamos, it will generally be necessary to provide special
means for generating the testing currents. Many tests are
impossible unless the electric pressure is exceedingly steady,
and ordinary public electric supply or that from a gas engine
and dynamo is generally quite useless for the purposes of
incandescent lamp tests, transformer tests, and numerous
other purposes. Hence provision has to be made in the first
place for continuous current supply. This should be taken
from secondary batteries which are regularly charged by a
dynamo set apart for the purpose. It is better, if possible,
to charge by a steam engine than a gas engine, as the charging
current is then more uniform and the cell plates are less
rapidly deteriorated. If continuous current is supplied from
ELECTRICAL LABORATORY EQUIPMENT. 3
public electric supply circuits at 100 or 110 volts it- may
be used to run a motor-generator or "booster" to take
power from the mains at 100 or 110 volts and reduce it to
35 or 40 volts. This machine consists of an electromotor and a
dynamo coupled together and bolted on to the same bedplate.
The motor takes current at 100 or 110 volts and drives the
dynamo. The dynamo can generate a current equal to the
maximum required for charging the cells at a pressure
of 35 or 40 volts. This voltage, added in series with
the circuit voltage of 100, will give the necessary 135 or
140 volts pressure for charging a local battery of 53 or 54
cells. Proper controlling resistances must be inserted in
series with the motor armature circuit of the booster, and in
series with the motor and dynamo fields. In addition to
means for providing continuous current at 100 volts, it is
necessary to be able to obtain a supply at pressures of 10 or
15 volts or less, and at about 200 volts or more. This is best
obtained by having two similar dynamo machines bolted on
one bedplate, so that the machines can be coupled with their
shafts in one line. One of these machines is a motor, and
takes current at 100 or 110 volts from the secondary battery,
resistances being provided in the armature circuit and fields
for regulating the speed; the other coupled machine is a
dynamo, and should be provided with three separate armatures,
which can be inserted at pleasure, one giving, say, 10 volts at
the standard or proper motor speed, one giving, say, 100
volts, and the other 200 or 250 volts. The fields of each
machine are best separately excited at 100 volts. A com-
bined motor-generator, consisting of these two coupled
machines, each of one or two kilowatts output and running
at 1,800 or 2,000 revolutions per minute, is a very convenient
appliance.
In the next place, provision must be made for generating
alternating currents. This is best done by means of an
alternator coupled directly to a continuous current motor. A
very convenient arrangement, designed by the Author for use
B2
4 'ELECTRICAL LABORATORY EQUIPMENT.
in the electrical laboratory at University College, London,
consists of a pair of alternators of 5-kilowatt capacity, each
coupled to a continuous current motor, so as to be driven by
it, and provision made by a coupling to join the shafts of
both sets in one line. The four machines are bolted down to
one bedplate, and a flanged pulley on the inner end of each
shaft has the flange pierced with holes so that the pulleys
can be coupled in such positions that the alternating currents
from the two alternators are in any desired relative phase.
Eesistances are provided in the field and armature circuit of
all machines, so that the speeds and electromotive forces are
under complete control.
This compound machine provides alternating current of
single or two-phase kind, and of any required electromotive
force up to 200 volts. Machines so coupled should be well
bedded down. It is worth while to expend the necessary
sum on good foundations to secure perfect steadiness of
running and freedom from vibration, as the commutators
are thus more easily kept in order. One or both ends of the
double alternator shaft can be provided with a curve tracer,
to be described later on, by means of which the curves of
alternating currents can be taken.
Well insulated cables from the dynamo terminals should
be brought along covered chases in the floor, from the
dynamo room to the electrical laboratories to double- pole
switches and terminals suitably placed. Whilst laying
these leads it is a good plan to run a number of pairs of
spare cables and wires of different sizes for voltmeter wires,
telephone or bell wires, extra circuits, and other purposes,
so that the use of temporary cables lying about on the
floor may be avoided. Positive and negative cables should
be distinguished by being coloured red and black as usual.
In the selection of dynamo plant for purely experimental
purposes much must depend on the resources and purpose of the
laboratory. As far, however, as regards the generation of
current for most purposes in the electrical laboratory, nothing
ELECTRICAL LABORATORY EQUIPMENT. 5
is so convenient as the coupled motors and continuous or
alternating current generators ; the motors being worked off
a secondary battery. This arrangement leaves nothing to be
desired in steadiness of pressure and ease of working. The
speed is more easily regulated than in the case of a dynamo
driven off counter-shafting with coned pulley speed regulator.
For the dynamo room at University College a combined
motor-alternator plant, as above described, was built in
1893, by Messrs. Johnson and Phillips, to the Author's
specification and to Mr. Kapp's designs, of which a general
description is as follows :
"The machine consists of four separate machines bolted
on to the same bedplate, viz., two Kapp alternators and two
continuous-current motors (see Figs. 1 and 2). Each alter-
nator is coupled permanently to its own motor, the com-
mutators of the continuous-current machines being on the
outside end of the shaft. The shafts of each pair of machines
are truly lined, and the inside ends each carry a flange
pulley. These pulleys can be coupled together through the
flanges by bolts, so as to drive the whole as one machine,
or they can be separated for use as two machines. By
coupling them together with the armatures in the proper
relative position, two-phase currents can be got out of the
united machine. Each of the continuous-current motors is a
5-H.P. motor, designed to work at 100 volts. The armature
is ring- wound, and there are 216 turns of wire on it,
connected to a 72-part commutator. The magnets of the
motors are of cast steel, 6f in. in diameter. Each armature
can carry 35 or 40 amperes comfortably. The alternator
armatures contain an iron core, and are wound over with
eight coils, each having 16 turns of wire. The field magnets
have eight poles, and corresponding poles are opposite to one
another. The alternators, when driven at a speed of 1,250
revolutions, give an electromotive force of 100 volts.
"The four machines are fixed on a cast-iron bedplate 9ft.
long and 2ft. wide, which is carried on slide rails in the
usual manner. The ends of all the armature and field
magnet circuits are brought to terminals fixed in a box
on the front of the machine. In the field-magnet circuit
of each machine is an appropriate resistance, and in the
ELECTRICAL LABORATORY EQUIPMENT.
armature circuits of the motors there are also resistances for
starting the motors. To the shafts of both motors is fixed a
hydraulic speed indicator. A small centrifugal pump is
ELECTRICAL LABORATORY EQUIPMENT.
8 ELECTRICAL LABORATORY EQUIPMENT.
driven by the shaft, and this pump forces coloured water
from a small reservoir placed over the pump through a pipe
into which are connected two vertical glass tube pressure
gauges, one of which is placed on the wall of the dynamo
room, and the other is placed on the wall of the electrical
laboratory 30ft. away. When the motor alternator is running,
the centrifugal pump forces the water up these tubes, until
the hydrostatic pressure of the column of liquid supported
in the tube balances the pressure due to the pump. The
height of the column of liquid, therefore, can be made to
measure the speed of the machine after these gauges have
been carefully calibrated. The special advantage of this
hydraulic speed indicator is that it is so exceedingly
responsive to changes in speed. A change in speed of less
than one per cent, can be certainly detected and measured,
whilst the accuracy of the indication is independent of the
density of the liquid used. The speed of the motor can be
regulated from the laboratory by the use of a carbon rheostat
inserted in the field or armature circuit and can thus be
kept exceedingly constant."
The above described motor-alternator plant has many uses.
The alternators can be run in parallel either coupled or free.
They can be coupled and joined in series, so as to give a
current at 200 volts pressure. They can be set to give a two-
phase current. Efficiency tests can be made with the direct
current motors, driven as coupled machines, or with the
alternators. Alternating current curve tracing can be
carried out in many different experiments. For experimental
work with polyphase currents, a very convenient appliance
is a small three-phase alternator coupled direct to and driven
by a continuous current motor ; the fields of both being
separately excited at 100 volts.
Electrical Laboratory. In the design of the electrical
laboratory the important matter is to provide sufficiently
steady tables or supports for galvanometers and instruments.
It is not a good plan to build up, as is sometimes done, brick
tables in the middle of the laboratory, because these cannot
afterwards be moved if space is required for special work. It
ELECTRICAL LABORATORY EQUIPMENT. 9
is best to provide round the room, at a standard height of say
3ft. Gin. from the floor, strong stone or slate slabs, let into the
main walls of the building. If the main walls are strongly
built, and have good foundations, very steady supports can
in this way be obtained. Circumstances, however, must
decide what is best to be done. In any case, several firm
slabs must be provided, either by building up brick pillars,
covered with a slate surface, on independent foundations,
thus forming solid tables, or by building up stone supports
to the level of, but not touching, the floor, on which can
rest the legs of special steady wooden tables for carrying
the galvanometers, ampere balances, and other instruments.
All that is necessary is to secure steadiness for certain
particular pieces of apparatus. In some instances special
precautions may have to be taken to eliminate the effects of
vibration due to adjacent machinery or traffic. In these
cases the galvanometers may be placed on slabs of slate
which are suspended at the four corners by stout india-
rubber bands from brackets let into the wall, and heavier
instruments, such as ampere balances, may be placed on
slabs of Yorkshire stone carried on three or four blocks
of india-rubber.
One of the greatest difficulties which generally presents itself in arranging
an electro-technical laboratory is the contrivance of suitable means to prevent
the mirror instruments being disturbed by vibrations of the building due' to
machinery or traffic in the neighbourhood. The usual method of securing
steadiness is to build up brick pillars on very solid foundations formed in the
ground, as supports for the legs of ordinary stout deal tables, and to keep the
laboratory floor from contact with these pillars. This plan, however, is not
always entirely a success, and then sometimes a remedy may be found by
placing the galvanometer or mirror instruments, as above suggested, on a slab
of slate or flagstone of considerable weight, resting the slab on four india-
rubber blocks. Or it may be possible to suspend from the ceiling, by india-
rubber door springes, a heavy wooden slab or board on which the instrument is
placed, and so take up the vibrations. A combination of the independent
brick pillar with capstone resting on india-rubber blocks is the best method
in difficult cases. One device, said to be very effective, is to support the
galvanometer on a wooden base placed on a thick pad of hair felt laid in a
tray, the corners of the base board and tray being connected by stretched
india-rubber bands. See Electrical Review, 1898, Vol. 42, p. 592.
10 ELECTRICAL LABORATORY EQUIPMENT.
In the next place, it is convenient to arrange a standard
height and size of working table. A convenient size is 5ft.
long, 2ft. Gin. wide, and 3ft. Sin. in height. These tables can be
arranged together as required. Around the room, however,
should be fixed benches or tables with strong top surfaces,
having cupboards and drawers underneath, and on which may
be arranged certain sets of apparatus never to be moved. It is
essential that such standard sets of apparatus as the Bridge for
resistances measurements, the Potentiometer for electromotive
force measurements, and the Ballistic Galvanometer, should
never be moved, but should be kept always connected up
and be available at a moment's notice for use. Apparatus
stored in glass cases, and therefore not ready when required,
is a fruitful source of waste of time and energy, and the
plan of so keeping it should be avoided. Dust and light
may be kept off the arranged apparatus by simply throwing
over the articles a black velveteen cloth, or, better still,
keeping every important piece of apparatus in a wooden
or cardboard box, which is shut up when the apparatus
is not in use. The laboratory should be provided, if possible,
with double windows, and these windows be darkened
when required by blinds made of black American oilcloth or
some material impervious to light. The laboratory can
then be kept in the proper state of illumination necessary to
see well the spots of light on galvanometer scales. As far as
possible an equable temperature should be maintained in
the rooms all the year round. A sink with hot and cold
water, and a fume cupboard must be provided, and a table,
having a top covered with sheet lead, with a narrow fillet or
edge round it, and drainage tube, is useful for experiments
with primary batteries or secondary cells, and other things
likely to be messy. It is a good plan in preparing the room to
form covered floor chases around and across the room in which
wires and cables can be laid. The permanent leads and cables
are placed in casing fixed to the floor of these chases. The
cover boards of the chase can be made to take up in sections
ELECTRICAL LABORATORY EQUIPMENT. 11
so as to lay temporary cables, and thus avoid the danger and
nuisance of loose electric cables lying about all over the
floor. Eound the room should run several separate insulated
circuits, having terminals, fuses, and switches at each place
where current is likely to be required. One of these should
be a circuit from the battery for supplying current to incan-
descent lamps to be used for galvanometer scale lamps, and
for a special table lamp if required.
The incandescent lamps best adapted for galvanometer purposes are the
Edison form with single horse-shoe shaped carbon filament. The lamp bulb
should be covered with a cylindrical asbestos hood having a slit in it which
permits the light from one leg of the filament loop to pass out. The galvano-
meter is then arranged so that the mirror, with or without the assistance of a
lens, throws an image of this straight incandescent carbon on to a divided
ground glass or semi-transparent celluloid scale suitably placed. In this
manner an exceedingly sharp, bright line, being the image of a part of the
filament is thrown on the divided scale. This image can be seen in daylight
or in a slightly darkened room. If the scale is placed at the right focal
distance from the mirror, and if the scale is divided into millimetres, a reading
to one quarter of a millimetre can be taken, provided the galvanometer
mirror is a good one.
This circuit should be provided with numerous wall plugs
(preferably of the concentric pattern) by which a lamp with
a socket and flexible cord can be plugged in where required.
Another circuit should run from the main secondary battery
and provide, where required, at several places larger currents
at 100 volts pressure. A third circuit should give continuous
current at various pressures from the continuous motor gene-
rator in the dynamo room, and a fourth circuit should bring
alternating currents from the alternators. In laying out these
circuits, blank terminals with double-pole porcelain cut-outs
and double-pole switches should be provided in as many
places as possible. Comfort and convenience in subsequent
work will greatly depend on the care with which all these
little details are thought out by the electrician in arranging
his laboratory. In order to avoid disturbing magnetic needle
galvanometers by strong stray magnetic fields, it is desirable
to run all these laboratory supply circuits with concentric
cable.
12 ELECTRICAL LABORATORY EQUIPMENT.
Accumulator Room. This room may be at any con-
venient and necessary distance from the laboratory working
rooms. It should, if possible, have walls built with glazed
brick, and a ceiling of glazed tiles. In any case, all exposed
wood and metal work and all cables should be thickly painted
with anti-sulphuric paint or enamel. The cells should be
placed on low brick table supports covered with slate slabs,
or on the usual painted wooden supports. In any case, they
should be well insulated. Cables joined' to various points
on the battery should be brought out through th walls
of the battery room, to a switchboard outside, by leading
them through porcelain tubes plugged with slag-wool, so
that they are spray-tight. Changes in the electromotive
force of the working circuit can then be made as required
without entering the battery room. If possible, a separate
battery should be provided for incandescent lamp tests
or for any special purposes when great uniformity of
pressure is required. The choice and size of cell must be
left to the user of the laboratory to determine. One or
more large accumulator cells are useful. These can be
charged from the low voltage side of the motor-generator
set, and are very useful in yielding the large currents required
for testing ammeters.
An additional essential is a series of small secondary cells,
for giving high electromotive forces. Of these the most
convenient are the cells known as Lithanode cells.
Lithanode is not compressed peroxide of lead, as is sometimes stated,
for, however strongly lead peroxide may be compressed, the resulting
mass will disintegrate when immersed in a liquid electrolyte. It is
produced from litharge, made into a pasty mass with a solution of sulphate of
ammonia, which causes the material to "set," so that it will no longer
disintegrate when placed in a fluid. The " forming," according to the
original idea, was performed in a bath of sulphate of magnesia. In ordinary
practice the elements are made up of a number of small slabs of lithanode,
whose outer edges are V-shaped. These slabs or pellets are arranged in a
casting mould of any suitable dimensions, and are placed at such a distance
apart and from the edges of the casting frame as to allow of sufficient space
for the requisite quantity of metal to run in and impart adequate mechanical
strength to the completed element. After the pellets have been arranged
ELECTRICAL LABORATORY EQUIPMENT. 13
in this manner, an alloy of lead and antimony is run into the interstices, and
1;hus a complete plate is formed. Before being cast up, the positive pellets
are converted into peroxide of lead in a forming bath ; those for the negative
plate are simply dried and cast up direct, the lithanode in the latter case
being reduced to a condition of spongy lead by the ordinary electrolytic
method.
These cells are contained in small glass tubes or cylinders,
about lin. in diameter and 4in. high. A series of 50 of these
cells, contained in a portable box or case, can be charged
through an incandescent lamp off a 200-volt circuit. Two or
more sets of 50 cells each of these small testing cells are most
useful for insulation tests and voltmeter testing. Finally,
some sets of single or double cells, having a capacity of about
40 or 50 ampere-hours, are requisite for the potentiometer
testing. In a well-organised laboratory there should be
regular days when all these cells are recharged by being
suitably arranged in series with resistances or lamps, so that
the cells are charged with their proper charging current taken
from the dynamo circuit. The particular type and size of
cells are matters which must be determined by the work to
be done. If many tests are likely to be made on complete
batteries, it is an advantage to have the accumulator room as
near as possible to the electrical laboratory. In any case, it
must have well fitting double doors, to prevent the egress of
acid vapours. Assuming a certain area available on the
ground floor to be arranged as an electrical laboratory, the
space might be conveniently divided up as shown in Fig. 3.
The battery room should be separated completely from the
engine and dynamo room and from the private room, but
cables should be carried spray- tight through the walls, as
above suggested, to the regulator switchboard and to the
various laboratories.
In each electrical laboratory should be a photometric
gallery, forming a completely closed and darkened space of
about 30ft. long, 5ft. wide, and 10ft. high. The cables
bringing current from the dynamo room to each laboratory
should be laid along a chase in the floor of the passage, and
14
ELECTRICAL LABORATORY EQUIPMENT.
distributed to each room as required. Every room except
the dynamo and battery room should have windows, provided
with black opaque cloth blinds, which can be drawn down so
as to darken the room more or less as required. Dimensions
are not added in the sketch plan below, because various
circumstances must determine the space required, but an
arrangement of rooms as here suggested forms a convenient
one for a small testing or teaching electrical laboratory.
tofel DIRECTOR'S
pljj PRIVATE
ROOM
(C
V A
' V >, s
^/ PASSAGE A m O
V
'<?*"
'<" !\
STORES
LABORATORY
1 I
WORKSHOP 1
1 HEAVY
PHOTOMETER
ROOM
J
FIG. 3.
As an example of the arrangements of an electrical
laboratory, which, though not large, is well equipped,
a| brief description may here be given of the Fender
Electrical Engineering Laboratories in University College,
London, the internal arrangements for which were designed
by the Author, and embody some thought and experience in
this work* :
" The portion of the buildings allotted for the purpose of an
electrical engineering laboratory consists of six rooms, in all
* The architect of these buildings was Prof. Roger Smith, F.R.I.B.A.,
Professor of Architecture in University College, London. A full description
of these laboratories, given by the architect and the professors who
collaborated with him in their internal design and fittings, is given in the
Journal of the Royal Institute of British Architects, Vol. L, 3rd series,
p. 294, from which, by kind permission of the Council of the Institute, this
description of the electrical laboratories, written by the Author, is taken.
ELECTRICAL LABORATORY EQUIPMENT. 15
of which the interior arrangements have been very carefully
designed. The four principal rooms open into one another.
These are the dynamo room, the lecture theatre, the
apparatus room, and the electrical laboratory. The general
arrangement of the building permitted the dynamo room floor
to be placed on solid ground, and thus secured the possibility
of making both floor and machine foundations of great
steadiness. This dynamo room is 31ft. long and 22ft. wide,
built in white glazed brick. The plant placed in the
dynamo room consists in the first place of a 9-H.P. nominal
Otto-Crossley gas engine, capable of working up to 19
I.H.P. This engine is fitted with all the most recent
improvements. It is bedded on a slab of Yorkshire stone
resting on the concrete foundation floor, 24in. in thickness,
which is carried over the whole room. In this concrete floor
all the pipe trenches are formed, and these last are lined with
brick and covered with the usual cast-iron chequer plates.
The engine is provided with a self-starting arrangement
designed by Messrs. Crossley Bros. This contrivance consists
simply of a massive cast-iron chamber, into which a charge
of gas and air is pumped by an auxiliary hand-pump. If
the engine is stopped, so that the crank is on the middle ot
the top stroke, it suffices to fire the compressed charge at a
touch-hole to start the engine even under full load. This
arrangement is as simple as it is effective, and not the
slightest difficulty has ever been experienced in starting
the engine with it. The engine is provided with two very
massive flywheels, to secure steady running, and the crank
shaft carries outside the left-hand wheel a Mather and Platt
clutch pulley 60in. in diameter, and on the right-hand side a
36in. pulley for driving on to a counter-shaft. From the
Mather and Platt clutch pulley is driven by a belt a
Crompton continuous current six-unit dynamo, which is
employed exclusively for charging the secondary battery.
This clutch pulley permits the charging dynamo to be
thrown into and out of action whilst the engine is running.
The engine is provided with a double service of cylinder
cooling water : one service being brought from two wrought-
iron tanks placed on an elevated platform in one corner of
the engine-room, and the other service comes direct from the
water supply mains of the building, and is taken through
a water meter. The water circulating through the cylinder
jacket from the continuous supply is carried away by
16 ELECTRICAL LABORATORY EQUIPMENT.
a funnel into the main drain. The temperature of the
in-coming and out-going water can be taken with thermometers,
and the quantity of water which circulates is registered by
the meter. Hence the number of units of heat removed
from the cylinder becomes known. The gas for the engine is
taken direct from the street mains, through a separate gas
meter. The indicating gear fixed to the engine operates
a suitable high-speed indicator, designed to give a good
indicator diagram on gas engines. It will be seen that
arrangements have been provided for making a technical
study of the gas engine itself as a prime motor. Against
one wall of the dynamo room is fixed a series of cast-
iron brackets, which carry a 2in. steel counter-shaft. This
counter-shaft is driven by a belt from the right-hand drum of
the engine, at a speed of 280 revolutions per minute. This
counter-shaft carries a fast and loose driving pulley with belt-
shifting gear. The shaft is cut in the centre and provided
with a clutch-gear and two driving pulleys, one on each
side of the clutch. The counter-shaft is supported upon
ball-bearings, which are carried on cast-iron brackets,
built into the 14-in. wall set in cement which carries
them.
"Keturning, then, to the construction of the dynamo-room
floor, it has already been mentioned that this consists of a
concrete floor 24in. in thickness. This concrete is finished
2in. from the wall all round the room, and slag wool packed
into the interspace. On the concrete are laid, 18in. apart r
teak beams Gin. deep by 4in. wide. These beams are held
down by 24-inch holding-down bolts, which pass right
through the concrete, and are terminated in anchor plates at
the bottom. The space between the beams is filled in
with granolithic cement^ The cement is cupped out between
the beams, and given a slight cant towards a main drain
running down the room formed in the cement. By this
means oil or water spilt on the floor is easily got rid of and
the floor kept dry. The floor has proved itself to be so-
satisfactory that no sensible vibration is propagated up the
building when the engines and dynamos are at work; and
delicate electrical instruments can be used in the room when
the engine is in operation. The silencing chamber of the gas
engine is placed in a pit in one corner of the room, and is air-
jacketed to keep the temperature of the room down. The
engine discharges into an exhaust pipe carried up a brick
ELECTRICAL LABORATORY EQUIPMENT. 17
chase in one corner of the room, and then through the
roof.
"Turning next to the dynamo plant, this consists, in the
first place, of a Crompton continuous-current dynamo, giving
an output of 45 amperes at 140 volts. This dynamo is
driven through an intermediate Kummer transmission dyna-
mometer, which measures the mechanical power given to it
from the Mather and Platt pulley of the dynamo. It can
also be driven by a Bumsted and Chandler steam engine in
the adjoining room. This engine can be belted when required
to the main countershaft. The duty of this dynamo is to
provide the charging current of the secondary battery. The
electromotive force of this machine is regulated by a variable
resistance placed in the circuit of its field magnets, whilst an
automatic cut-out is placed in the main circuit to prevent the
charge of the cells from coming back into the dynamo. In
addition to this dynamo, the room contains the motor-
alternator plant by Messrs. Johnson and Phillips, already
described. This machine consists of four independent
dynamos, bolted down on to one common cast-iron bedplate
10ft. in length. Each half of the machine comprises a direct-
current motor, which is directly coupled to a Kapp
alternator, each dynamo being of 5 H.P., or capable of an
output of 3,500 watts. Each coupled motor-alternator has a
pulley with a flange on it, and the machines are so set on the
bedplate that the pulley flanges are in close contiguity
with each other, but do not quite touch. The flanges can, if
need be, be coupled by two bolts, so as to unite the two
halves of the shaft into one, and make all four dynamos
drive together as one machine. With this compound motor-
alternator it is possible to carry out a large range of
instructional work. Thus, either motor can be driven by the
current from the secondary batteries, and will drive its own
coupled alternator. Hence, by properly exciting the fields of
the motor and alternator, an alternating current is furnished
by the alternator of any required frequency and electro-
motive force within certain limits. The two halves of the
plant can be driven together or separately, and the
alternating currents delivered by the alternators may be put
in any relative difference of phase by properly uniting the
pulley flanges with the coupling bolts. As an illustration of
the work which may be done with this plant in teaching,
besides employing it for the generation of either continuous
18 ELECTRICAL LABORATORY EQUIPMENT.
or alternating currents, we may point out that the following
experimental work can be carried out :
" 1. Either plant may be run separately by a belt from
pulleys on the counter-shaft, and will produce from the
alternator an alternating current of 100 volts or 150 volts,
according as the fields are arranged, the current being 35
amperes, and from the continuous - current machines a
continuous current of 35 amperes and 100 volts or less.
" 2. By coupling the shafts rigidly together they may be
run as one plant, and either the currents or potentials of the
two similar machines added together, thus giving continuous
or alternating currents of 35 amperes at 200 volts, or 70
amperes at 100 volts.
" 3. Either of the continuous-current machines can be run
as a motor by current from the secondary battery, which is
charged by the Crompton dynamo. By regulating resistances
the speed may be regulated within wide limits. In this way
alternating currents of various frequencies can be drawn
off from the alternators either separately or running as one
machine.
" 4. The two separate plants may be coupled together
by the bolts through the respective pulley flanges, so that
the alternating currents given by the two alternators are
in any relative phase. They may be coupled together so as
to give the effect of a two-phase generator, with the
alternating currents 90deg. different in phase.
u 5. Efficiency tests can be made on the combination either
of continuous and alternating current machines or of two
similar machines.
" 6. The alternators can be run in parallel, each being
driven by its own separate motor, and the conditions of
parallel working thus explored.
" In addition to these dynamos there is also a small J-H.P.
continuous -current Crompton dynamo and a pair of small
coupled two-kilowatt dynamos, which serve for Hopkinson
tests or as a motor-generator for experimental purposes. On
a spare set of slide rails any dynamo can be bolted down for
test, and driven from the counter-shaft or by a continuous-
current motor. The walls of the dynamo room are occupied
with the switches and resistances for operating these
dynamos and motors. There is, in the first place, a
resistance frame which acts as a standard power absorber.
This consists of 80 wires of a high resistance alloy, each 25ft.
ELECTRICAL LABORATORY EQUIPMENT. 19
long, stretched up and down one side of the room over
porcelain insulators. The wires can be joined in parallel as
required by a set of special switches. When so arranged,
their resistance is capable of dissipating a power of 8,000
watts, or about 11 H.P. This is used for taking up the
power of dynamo machines under test. Other resistances are
provided for starting the continuous current motors, for
varying the fields of the alternators and continuous current
machines. A bank of 30 100- c.p. incandescence lamps is
.also fixed to the wall, and serves as an adjustable load for any
dynamo to work on. The dynamo room is well lit by a
skylight roof, and is warmed by hot- water pipes, and provided
with gas, water, and electric incandescent lighting. A small
vice-bench under the window enables all small repairs to be
done on the spot.
" The dynamo room opens into the lecture theatre, which is
32ft. wide and 35ft. long. On a platform is placed a lecture
table 20ft. in length. To the back of this platform are
brought the electric mains from the dynamo room. These
are laid in covered chases on the floor, and all this cable
work has been carried out with the highest quality of
india-rubber covered cable laid in white wood casing, and no
joints are made in any position under the floors. The cables
from the dynamo room conducting the current from the
various machines all terminate in lock-up cupboards at each
end of the lecture table, and thence proceed to a main
switchboard at the back of the lecture table. The battery
charging current from the Crompton dynamo is brought
through an ammeter and voltmeter to a main battery switch-
board, and thence it is distributed to the secondary battery in
the room beneath. From this switchboard a main runs all
round the laboratories, distributing at various points as
required continuous current at a pressure of 100 volts. The
currents from the two alternators are brought to the lecture
table, one to one end and the other to the other.
Experiments with two-phase currents can thus be shown.
The arrangements for charging and discharging the secondary
battery are conveniently to hand, and the instruments show
at a glance what current is going into the battery and what
is coming out of it. In front of the lecture table is a raised
gallery of seats capable of seating 60 students. At the back
of this gallery, in a space 8ft. wide under the windows, is a
long work-bench fitted with vices, at which instrument
c2
20 ELECTRICAL LABORATORY EQUIPMENT.
making and other simple metal and wood-work is carried
out. The lecture room is well lighted by pendent incan-
descent electric lamps, and the switchboard for controlling
the supply of the lighting current, which comes from the St.
Pancras Electric Lighting Station, is placed at the back of
the lecture table.
" At the end of the lecture table is a specially designed
vertical electric lantern, for projection work. This is fitted with
a Brockie arc lamp having inclined carbons. The arrangement
has been so worked out that not only lantern slides but any
apparatus, whether horizontal or vertical, capable of projection
can be immediately shown on a 10-ft. screen by simply
switching on the arc lamp. The lecture-room can be darkened
in a few seconds by pulling up dark blinds over the three win-
dows which light the room. These blinds are pulled up by cords,
which are brought over the ceiling to the back of the lecture
table. Every arrangement has been made for quickly and
readily enabling any experiment to be shown which requires
the optical lantern to exhibit it. At the sides of the room
and at the back of the lecture table are suitable screens for
carrying diagrams and plans.
" The electrical laboratory opens out of the lecture room.
This is a room 50ft. long and 32ft. wide. In order to secure
quietness and to keep out the dust, the room has been built
with double windows, the outer ones being ordinary sashes.
and the inner ones French windows. Black blinds are
provided, so as to darken each window when required. All
round the room a series of stout stone slabs are let into the
wall at a height of 4ft. above the floor, between the windows.
These stone slabs are intended as steady tables to carry
various measuring instruments. It is found by experience
that it is better to arrange the steady tables in this way than
to build them up as brick pedestals through the floor of the
room, because advantage is then taken of the greater
steadiness of the footings of the main walls, and the central
portion of the room is kept clear. Across and around the
floor of the laboratory chases are left, covered in by floor
boards, in which electrical mains are carried, and these
terminate in lock-up switch and fuse boxes in various parts
of the room. At one end of the laboratory is a long photo-
metric gallery, 30ft. long, 10ft. high, and 6ft. wide. In this
gallery is placed the photometer and various apparatus
required in testing arc and incandescent lamps. One end of
ELECTRICAL LABORATORY EQUIPMENT. 21
this gallery is formed into a small dark room for photo-
graphic purposes. Around the room are placed a series of
strong tables having drawers and cupboards, and each of
these tables is provided with electric currents from the
mains, and with a special circuit for working the incan-
descent lamps required by the galvanometers. In the centre
of this room numerous other tables are arranged for special
work. On the stone steady slabs are placed all the standard
electrical instruments, and the general principle has been
adopted of having each particular piece of apparatus
required for each special electrical measurement set up and
arranged so that it is never disturbed, and is always ready at
a moment's notice for use and experiments. One side of
the room is devoted to the current- weighing instruments and
standard voltmeters. The laboratory is provided with a very
fine set of Lord Kelvin's standard electrical balances and
electrostatic voltmeters. These balances are checked by
weighing the copper deposit produced in a voltmeter in
circuit with them, and for this purpose an Oertling chemical
balance has been specially built, and which is a remarkably
fine instrument. On other tables are set up the apparatus
for the measurement of resistances, insulation tests, magnetic
induction, electrical capacity and potential, and as these
permanent pieces of apparatus are never disturbed, a great
economy of time is effected in setting up and taking down
apparatus. In addition to the above, the experimental
apparatus is provided for complete tests of alternating
current transformers and other alternating current appliances.
Beneath the lecture-room is a large accumulator room built
in white glazed brick. On stone shelves round the room
are placed fifty-four cells of a D.P. battery. This battery
has a storage capacity of 250 ampere-hours, and will discharge
at the rate of 50 amperes. The current from the battery
is laid on to all the working benches of the laboratory.
"The general plan of the laboratory, of having all the
rooms opening one into another, is an immense convenience,
and saves much time. The arrangement of apparatus in
permanent groups for special measurement effects also a
great economy in time, as apparatus once set up is not
unnecessarily disturbed. The care with which the heating
and ventilation have been considered, as well as the universal
adoption of the electric light, has made these laboratories
exceedingly comfortable to work in. The rooms are all
22 ELECTRICAL LABORATORY EQUIPMENT.
excellently lighted. Although the lahoratory stands in a
main street, no difficulty has been found to arise from
vibration. The stone steady shelves let into the main walls
provide all that is necessary in the way of support for the
instruments which must be kept steady.
"Besides the above rooms, a diagram and model room r
apparatus room, and professor's private room are included.
The apparatus room opens into the lecture room close to the
lecture table. The apparatus room is well provided with
dust-tight apparatus cases and cupboards for the laboratory
apparatus. Access is obtained to the accumulator room
when required by a cellar-flap door opening out of the
lecture room, and through this opening any cells can
be hoisted up or let down which are required for exam-
ination."
2. The Fundamental Standards of Length, Mass, and
Time. The outfit of an electrical laboratory or testing room
must include, in the first place, means for making comparisons
with the fundamental standards of Mass, Length, and Time.
These comparisons involve the possession of standard
weights, a good balance, standard lengths, scales and callipers^
and an adjusted chronometer. The degree of refinement
necessary in these fundamental measurements will depend
upon the nature of the work to be done in the electrical
laboratory. In a standardising laboratory the actual working
instruments viz., the scales, weights, and watches used for
observations should be checked by comparison with certain
more carefully preserved and seldom used principal standards.
These last should be brought into careful comparison with
the legal standards kept at the Standards Office of the
Board of Trade in Great Britain or with the principal legal
standards in other countries.
The Unit or Standard of Length to which all other measure-
ments of length in scientific work are now referred in Europe
is the Metre International, or Standard Metre. It is a bar of
platinum-iridium deposited with the International Committee
of Weights and Measures, and is carefully preserved at
ELECTRICAL LABORATORY EQUIPMENT. 23
Sevres, near Paris. The length between two marks on it,
taken at 0C., is defined to be the standard of length, and is
called the Metre.
The metre is equal to 39*37011 British standard inches or
to 1-09361426 British standard yards.
Comparisons of actual metre scales or yard measures are,
or can be, made at the Standards Office of the Board of
Trade with a certified copy of the standard yard or metre.
Every electrical laboratory in which accurate work is being
carried out should possess certain metre scales for working
use, and a standard comparison scale which has been thus
compared and certified at the Standards Office of the Board
of Trade.
Similarly the Standard or Unit of Mass in scientific work
is the Kilogramme International, preserved at the same place
as the standard metre. The kilogramme is equal to 2'20462
British standard pounds.
The Unit of Time in scientific operations is the mean solar
second as defined by the mean solar clock at Greenwich
Observatory.
The time of one complete revolution of the earth on its
polar axis is called a sidereal day, and is the ultimate unit or
standard of reference in measuring duration. It is equal to
86164*09 mean solar seconds. The mean solar day is the
average time interval between two successive transits of the
sun across a meridian, and it is divided into 86,400 mean
solar seconds.
A good chronometer should be provided, and should be
adjusted to show Greenwich mean time or mean solar time,
and, from time to time, should be rated by comparison with
the mean solar clock at Greenwich.
It seems hardly necessary to say that the standard chronometer, unless
a non-magnetic one, should be kept carefully at a distance from all dynamos
and strong magnets or currents.
The electrical laboratory should also be provided with a
good standard metre scale, divided into centimetres and
24 ELECTRICAL LABORATORY EQUIPMENT.
millimetres ; a box of standard gramme weights, multiples,
and submultiples ; and the above-mentioned standard
chronometer, showing Greenwich mean time.
Comparisons with the principal standards of length, mass,
and time are made by means of working scales, various
working balances, and stop-watches or pocket chronometers.
The laboratory must, in the first place, be provided with a
number of suitable measuring instruments for determining-
lengths. A number of metre scales, divided into centimetres
and millimetres, engraved on steel, brass, or boxwood, are
essential. Outside and inside callipers, measuring by a
vernier to one-ten-thousandth of an inch or one-four-hundredth
of a millimetre, are required. A spherometer for measuring
the thickness of thin metal plates is useful.
For measuring the diameters of exceedingly fine wires a
microscope micrometer may occasionally be required. In its
best form this consists of an ordinary achromatic microscope
with a calliper eye-piece. It is provided with a slide con-
sisting of a glass slip on which has been engraved with a
diamond a scale in hundredths and thousandths of an inch.
The eye-piece of the microscope has two needle points
projecting inwards and moved by external screws, so that
these points can be made to approach or recede from each
other in one plane. These needles are fixed in the focus
of the eye lens of the eye-piece. To measure the diameter
of a fine wire or, say, the filament of an incandescent lamp,
the wire is placed in the focus of the microscope and the
needle points screwed in or out until they appear to touch
the two edges of the image of the object to be callipered.
The eye-piece must, of course, be turned round until the
needles are exactly at right angles to the image of the wire.
This being done, the wire is removed from the microscope
stage and the divided glass scale placed on it. The image of
the scale will then be formed in the plane of the needle
points. The observer can read off on the scale the length of
the interval between the needle points, which is therefore
ELECTRICAL LABORATORY EQUIPMENT. 25
the diameter of the wire or filament. The arrangement
forms an optical calliper, and is a very convenient one
to employ in determining the diameter of a very fine
wire.
For measuring short lengths or large diameters, a calliper
of the following kind is found to be useful.* A steel tube
has two flat surfaces planed on it at right angles to each
other. The tube has a scale of centimetres and millimetres
engraved on it. Two brass blocks slide on this tube, and
can be clamped. One of them has a slow motion screw, and
carries a vernier. These blocks carry straight steel trans-
verse bars, which act as calliper jaws and remain parallel
when placed any distance apart. The object to be callipered
is placed between the jaws, and contact is judged as usual
by the "feel." One or two of the ordinary inside and outside
steel vernier callipers should also be provided, and the best
forms have a loose head screw which prevents undue pressure
being put upon the object measured.
The laboratory must be provided with a standard balance
and with other rougher balances for ordinary weighing. The
chief standard balance should be one of the type called a
short-beam chemical balance, which is adjusted to carry at
least 200 grammes and turn to a tenth of a milligramme.
Another balance, to carry 500 grammes and turn to a milli-
gramme, may be used for less accurate weighings.
These balances should stand on stone shelves let into the
wall of the laboratory, and be enclosed in glass cases. In
each case should stand a beaker containing some lumps of
well-baked pumice stone saturated with strong sulphuric
acid. The use of this is to dry the air in the balance case
and keep all steel parts bright. The standard balance case
should be kept locked when not in use. Young students or
assistants should not be allowed to use a very good balance
without proper instruction as to its employment. On the
side of the case should be fastened a notice with four rules
* Made by the Cambridge Scientific Instrument Company.
26 ELECTRICAL LABORATORY EQUIPMENT.
distinctly printed thereon for the guidance of the inex-
perienced :
1. Never put any object directly on the balance pans, but
always weigh it in a tared porcelain crucible, watch glass, or
on a disc of glazed writing paper.
2. Never add weights to or remove from the pans unless
the balance is clutched or off its knife edges.
3. Never leave the balance case open when making the
final adjustment of the rider.
4. Never omit to return the weights to their proper places
in the weight box as they are taken off the pan, or to
remove the balance from its knife edges when the weighing
is finished.
From time to time a careful adjustment of the balance
should be made by an experienced person.
The balance should be provided with a special short suspen-
sion scale pan called a specific gravity pan, and a glass stoppered
bottle should be kept by the case containing well-boiled
distilled water for use in taking specific gravities.
The object of which the specific gravity is required should
be suspended from the hook at the bottom of the short pan
and so hung by a fine hair taken from a horse's tail that it
hangs freely in the distilled water. The temperature of the
balance case should be taken at the same time. In
using the balance to determine the mean diameter of a wire
which is one of the operations the electrician may
occasionally have to perform the known length of wire
may be folded up into a suitable compact coil so that
it can be suspended in the water in a small beaker. Air
is then entangled in the meshes. This should be removed
by boiling the wire in the water and letting the wire cool
in the water and not removing it until the weight of the
mass hanging freely in the water has been taken.
In many operations in the electrical laboratory, such as in
meter testing, time has to be determined very accurately.
For this purpose a good stop-watch or working chronometer
ELECTRICAL LABORATORY EQUIPMENT. 27
(preferably non-magnetic) is required. It is often possible
to purchase a second-hand ship's chronometer by a first-class
maker at a reduced price. If the chronometer is in good
order it may be sent to Kew Observatory or to Greenwich
to be rated and its true time and temperature rate errors
determined. The laboratory will then be provided with
a good timekeeper by which other watches may be
checked.
It is useless to make very careful observations of meter
errors or electrolytical experiments with a common watch
having a possible large rate error. Under the head of time
standards, reference may be made to the speed indicators and
speed counters which are in frequent use in the dynamo
room. A most useful form of speed counter is one supplied
by Messrs. O. Berend & Co., consisting of a revolution counter
of the usual kind combined with a stop-watch counting
seconds. The stop-watch is thrown into action by the act
of pressing the contact point against the end of the shaft,
the speed of which is required. The time and number of
revolutions in that time are thus recorded in the same
period. There are many forms of mechanical speed indica-
tors or tachometers which record directly on a dial the
revolutions per minute. None of these, however, are accurate
instruments or can be depended upon to give the actual
speed within 5 per cent. In careful dynamo and motor trials-
the actual revolutions per minute must always be taken by
one observer.
A very accurate speed indicator which can be practically
applied to dynamo machines is one depending on the centri-
fugal pressure of a revolving mass of liquid. A small, flat
cylindrical box has in it a small four-vane paddle-wheel r
the shaft coming out through a stuffing box or gland. The
paddle shaft is attached to the axis or shaft, the speed of
which is to be measured. The box is carried on an indepen-
dent support. Two pipes lead to this box, one entering near
the centre and one leaving near the circumference. The
28 ELECTRICAL LABORATORY EQUIPMENT.
pipe to the centre communicates with a small reservoir of
coloured water. The pipe from the circumference leads to a
vertical glass stand-pipe which may be fixed at any distance
from the dynamo. When the paddle revolves it acts as a
centrifugal pump, and pumps water from the reservoir up the
stand-pipe. Equilibrium is established when the hydrostatic
pressure of the column of liquid in the stand-pipe just
balances the centrifugal pressure at the circumference of the
revolving mass of liquid in the paddle-box. The apparatus
can be calibrated once for all, and the true speeds, corre-
sponding to various heights of liquid in the stand-pipe,
marked on a wooden scale-board behind the pipe. An
arrangement of this kind attached to an alternator is very
useful in enabling the operator to set the machine to give a
certain frequency and to keep it at this frequency during
the test.
In cases where the above hydrostatic tachometer cannot
be fixed on account of the power required to drive it,
recourse must be had to a simple worm-wheel gearing by
which the speed of the shaft is made to turn a wheel at
one-tenth, one-hundredth, or less of its own speed. This
slow-revolving wheel can be made to close the circuit of a
single-stroke electric bell once every revolution, and thus
strike a blow at every ten or hundred revolutions of the
shaft.
By counting the bell strokes per minute or the time in
seconds extending over ten bell strokes the speed of the
shaft is ascertained.
3. The Principal Electrical Units and Standards.
Next in importance in the equipment of an electrical testing
room to the standards and instruments for making the
fundamental measurements of length, mass, and time come
the principal standards of electrical resistance, electromotive
force, and the means for recovering the standard or unit
electric current.
ELECTRICAL LABORATORY EQUIPMENT. 20
These principal electrical units have been given legal
definition in Great Britain, and identical units have been
adopted in other countries. They are accordingly now
called the International units of resistance, electromotive
force and current, and are defined as follows :
The, electrical resistance offered to an unvarying electric
current by a column of pure mercury at the melting point
of ice, 106'3 centimetres long and weighing 14' 4 521
grammes, and of constant cross-section, is defined as the
unit of resistance, and is called one ohm.
The ohm so defined is intended to represent 10 9 absolute
electromagnetic units (C.G.S.) of resistance.
The unit electric current is defined by an operation of
electrolysis performed with a solution of a silver salt, as
follows :
The electric current of unvarying strength ivhich, when
passed through a neutral solution of nitrate of silver
containing 15 parts ~by weight of the salt to 85 of u -cater -,
using a silver anode and a platinum cathode, deposits silver
at the rate of G'001118 of a gramme per second, is defined
as the unit of electric current and is called one ampere*
The ampere so defined is intended to represent or repro-
duce 10- 1 of an absolute electromagnetic (C.G.S.) unit of
current.
From the unit of resistance and current is defined the unit
of electromotive force :
The unvarying electromotive force which creates in a
circuit having a resistance equal to one ohm an unvarying
current of one ampere is defined as the -unit of electro-
motive force, and is called one volt.
* See remarks on page 58 with reference to more recent determinations of
the Electro-chemical Equivalent of Silver.
30 ELECTRICAL LABORATORY EQUIPMENT.
The electromotive force so defined is intended to represent
or reproduce 10 8 absolute electromagnetic units (C.G.S.) of
electromotive force.
The above units are defined and recovered in the laboratory
by the use of certain practical standards of resistance, electro-
motive force and appliances or processes, for electric current
measurement. -
A principal necessity in an electrical laboratory is, then,
the possession of satisfactory means for recovering or repro-
ducing the International ohm, the volt, and ampere.
Carefully constructed apparatus made for this purpose is
in use at the British Board of Trade Electrical Laboratory,
in accordance with the following regulations :
/. Standard of Electrical Resistance.
The standard of electrical resistance denominated one ohm
shall be and is the resistance between the copper terminals of
the instrument marked " Board of Trade Ohm Standard,
verified 1894," to the passage of an unvarying electrical
current when the coil of insulated wire forming part of the
aforesaid instrument and connected to the aforesaid terminals
is in all parts at a temperature of 15'4C.
The ohm so reproduced is generally called the Board of Trade Standard
ohm, to distinguish it from the theoretical or true ohm, which is defined as 10 9
centimetres per second in C.G.S. measure. The density of pure mercury at
0C. is 13'5956. Hence a volume of mercury having the form of a right
circular cylinder 106'3cms. in length and a mass of 14*4521 grammes, has a
<;ross- sectional area of one square millimetre or 0*01 sq. cm. The actual
principal standard ohm of the Board of Trade has been constructed to repre-
sent as nearly as possible the International ohm. This last may be otherwise
defined as the true electrical resistance at 0C. of a column of mercury
106'3cms. long and one square millimetre in section. Present knowledge
seems to show that the actual Board of Trade ohm standard is 0'02 per cent,
larger than the true ohm.
II. Standard of Electrical Current.
The standard of electrical current denominated one ampere
shall be and is the current which is passing in and through
the coils of wire forming part of the instrument marked
" Board of Trade Ampere Standard, verified 1894," when on
reversing the current in the fixed coils the change in the
ELECTRICAL LABORATORY EQUIPMENT. 31
forces acting upon the suspended coil in its sighted position
is exactly balanced by the force exerted by gravity in West-
minster upon the iridio -platinum weight marked A and
forming part of the said instrument.
///. Standard of Electrical Pressure.
The standard of electrical pressure denominated one volt
shall be and is one-hundredth part of the pressure which when
applied between the terminals forming part of the instrument
marked "Board of Trade Volt Standard, verified 1894,"
causes that rotation of the suspended portion of the instru-
ment which is exactly measured by the coincidence of the
sighting wire with the image of the fiducial mark A before
and after application of the pressure and with that of the
fiducial mark B during the application of the pressure, these
images being produced by the suspended mirror and observed
by means of the eyepiece.
In the use of the above standards the limits of accuracy
attainable are as follows :
For the ohm, within one-hundredth part of 1 per cent.
For the ampere, within one-tenth part of 1 per cent.
For the volt, within one-tenth part of 1 per cent.
4. The Practical Standard of Electrical Resistance.
The practical standard or unit of electrical resistance is
officially denned as above-stated in terms of a certain length
and mass of pure mercury. Great labour has been expended,
both in England and in other countries, on the determination
of the absolute specific resistance or the resistivity of pure
mercury.* The following are some of the values which have
* See " The Specific Resistance of Mercury," Lord Rayleigh and Mrs.
Sidgwick, Phil. Trans. Roy. Soc., 1883, Part I., p. 173. Also R. T. Glaze-
brook, Phil. Mag., October, 1885. Also R. T. Glazebrook and T. C. Fitz-
patrick, " On the Specific Resistance of Mercury," Phil. Trans. Roy. Soc.,
June, 1883; or Pros. R>y. S>c., Vol XLIV., No. 270; or The Electrician,
Vol. XXL, p. 533, 1888 ; Kohlrausch, Abhandt der K. Biyer Akad der Wiss,
Vol. XVI., Abth III., 1887 ; Mtscart, Nerville and Benoit, Jour nil de Phy-
sique, 188^ ; Sorecker, Wiedemann Ann%len, Vol. XXV., 1835 ; L. Loreaz,
Wie lemann Annalen, Vol. XXV., 1885; Rowland, Proc. British Association,
1887. Also Hutchinson and Wilkes, " John H opkin's University Circular,"
May, 1889. Also " Recent Determinations of the Absolute Resistance of
Mercury," R. T. Glazebrook, The Electrician, Vol. XXV., pp. 543, 588, 1890.
Also see Prof. J. V. Jones, " On the Determination of the Specific Resistance
of Mercury in Absolute Measure," Phil. Trjtns. Roy. Soc., 1891, A, p. 2.
32 ELECTRICAL LABORATORY EQUIPMENT.
been obtained for the resistivity of pure mercury at 0C. in
C.G.S. units per centimetre cube :
Observer. Date. Resistivity.
Lord Rayleigh and Mrs. Sidgwick 1883 ...... 94,133
Mascart, Nerville and Benoit 1884 94,096
Strecker 1885 94,057
L. Lorenz '..., 1885 94,108
Eowland 1887 94,072
Kohlrausch 1887 94,054
Glazebrook and Fitzpatrick 1888 94,074
Hutchinson and Wilkes '... 1890 94,064
J.V.Jones _, .. 1890 94,067
The present accepted value of the specific electrical resistance or resistivity
of pure mercury at 0C. is 94,070 C.G.S. units. Hence, a column of mercury
one metre in length and everywhere of 1 sq. millimetre in cross section has at
the temperature of melting ice a resistance of 0'94070 ohms, as far as the
mean of the best determinations will allow us to pronounce.
The following are the values obtained by the above observers
for the length in centimetres of a column of mercury
one square millimetre in section and having a resistance
of one ohm at 0C. :
Observer Length of column
in centimetres.
Lord Rayleigh and Mrs. Sidgwick 106'23
Mascart, Nerville and Benoit 106-33
Strecker 106'32
L.Lorenz 106'26
Rowland , ... 106'32
Kohlrausch 106'32
Glazebrook and Fitzpatrick 106'29
Hutchinson and Wilkes 106'34
J. V. Jones 106-31
The value now accepted for the length of the column of mercury one square
millimetre in section, which has at 0C a resistance of one International ohm, is
106-3 cms.
Continental physicists have devoted considerable time and
knowledge to the construction of primary and secondary
mercury resistances, consisting of mercury specially purified
and preserved in glass tubes of known dimensions, and
intended to practically realise the Board of Trade or Inter-
national definition of the practical unit of resistance.
For the most part, English investigators have given their
attention to the re-determination in absolute measure of
ELECTRICAL LABORATORY EQUIPMENT, 33
the electrical resistance of certain wire standards, notably that
called the mean British Association unit, and hence from the
known resistivity of mercury proceeded to construct the
most closely approximate realisation of the ohm in wire
resistances.*
In the majority of instances the standards of resistance
used in an electrical laboratory are preserved in the form of
a uniform metallic wire drawn from an alloy of permanent
composition, and having a small change of resistance with
temperature.
a End of mercury tube, s Platinum wire electrode, g Platinum wire,
galvanometer wires.
FIG. 4. Glass Spherical Terminal Vessel of the Berlin Reichsanstalt Standard
Mercury Ohm.
Owing to its fragility and non-portability, a standard of
resistance consisting of mercury in a glass tube is not
likely to be constructed or used in any but a national standard-
ising laboratory. The construction of an original mercury-
in-glass resistance by which to reproduce the standard or
international ohm from its definition is a matter requiring
the highest skill and knowledge. Broadly speaking, it
consists in preparing and filling a glass tube of known
dimensions with pure mercury, the weight of which at 0C. is
* For additional information on the determination of resistance in absolute
measure see Chap. II., RESISTANCE MEASUREMENT ; also Tables at the end of
the same chapter.
34 ELECTRICAL LABORATORY EQUIPMENT.
accurately determined.* This tube has its ends included in
large spherical vessels of mercury to which electrical connection
is made by means of platinum wires (see Fig. 4). In calculat-
ing the resistance of the column of mercury from the
dimensions of the tube and the resistivity of the mercury, a
correction has to be made in accordance with known
principles by which the effective length of the tube is taken
as greater than the actual length by 0'82 of the diameter of
the tube. For the full details of the construction of an
original mercury-in-glass standard of electrical resistance the
reader must be referred to the detailed accounts which have
been given of the production of the mercury standard set up
in the Physikalisch-Technische Keichsanstalt, in Berlin, and
the similar work carried out in Parisf by Benoit (see Fig. 5).
Mercury-in-glass standards are, however, used only as
original reference standards. The labour involved in their
construction and the necessity for great precautions in their
employment to reduce the whole mass of glass and mercury to
a known temperature before making a measurement with
them renders them unfit for ordinary laboratory use. For
all ordinary standards, multiples and submultiples of the ohm,
a wire resistance standard is much more convenient and is
usually employed. The two principal alloys which have been
found sufficiently permanent and of sufficiently small tem-
perature coefficient to use in the construction of such a wire
standard are a platinum-silver alloy and a ternary alloy of
copper-manganese and nickel called Manganin. There are
therefore, preserved in the various national electrical labora-
tories numerous copies of the ohm in the form of wire
standards, which are intended to have, as nearly as possible,
a resistance equal to the true ohm.
* For instructions for the purification of the mercury, see the Keichsanstalt
directions, as set forth by Dr. Jaeger, The Electrician, Vol. XXX.. p. 395.
f See The Electrician, Vol. XXXVII., p. 569, " On the Standard Mercury
Ohm of the Physikalisch-Technische Eeichsanstalt," by Dr. Jaeger, translated
from the Zeitschrift fur Instrumentenkunde, Vol. XVI., pp. 134-146, May,
1896. Also see Benoit, Comptes Rendus, Vol. XCIX, p.. 864, 1884.
ELECTRICAL LABORATORY EQUIPMENT.
35
D2
36 ELECTRICAL LABORATORY EQUIPMENT.
The original British Association wire resistance standards
are in the custody of the Secretary of the British Associa-
tion Committee on Electrical Standards ; the Board of Trade
standards are kept at the Government Electrical Laboratory,
Whitehall, London ; and carefully constructed standards
of electrical resistance of the same character are preserved
at the Physikalisch-Technische Eeichsanstalt, in Berlin,
and at the Bureau International des Poids et Mesures, near
Paris.
FIG. 6. Secondary Standard Mercury Ohm.
Secondary standards or copies of the ohm, consisting of
mercury contained in tubes of Jena glass with platinum
electrodes sealed through the glass, have also been con-
structed at the Physikalisch-Technische Eeichsanstalt, in
Berlin (see Fig. 6) and by Benoit, in Paris. These secondary
mercury standards consist of u or W shaped tubes of glass
ELECTRICAL LABORATORY EQUIPMENT. 37
most carefully filled in vacuo with mercury and then fixed in
a suitable case.
A comparison in 1892 and 1894 of all the mercury and
manganin copies of the ohm, made at the Eeichsanstalt in
Berlin, showed that these standards had remained constant in
resistance for two years to within one or two parts in one
hundred thousand.
A series of very elaborate experiments were made in the
year 1892 on the variation of resistance with temperature
of mercury-in-glass tubes between and 28C., and it was
found by Drs. Kreichgauer and Jaeger* that the resistance
at tPC. (K,) of mercury in Jena glass tubes can be expressed
between 0C. and 28C. as follows :
K, = K (1 + 0-000875 * + 0-00000125 1 2 ),
where E is the apparent resistance at 0C.
The true resistance of mercury (r t ) at tC. is related to its
resistance (r ) at 0C. by the relation
r t = r (1 + 0*0008827 Z + 0'00000126 * 2 )
for a range of temperature between 0C. and 28C. These
values are not very different from those found by Benoit*
Guilleaume, and others in 1890.t
In spite, therefore, of the advantages gained by the use of
a, pure, unchangeable and fluid metal, such as mercury, as
against the supposed possible non-permanency of structure
of a solid metallic alloy, we have to take into account the
difficulties raised by the larger temperature coefficient of the
pure metal.
Experience is as yet wanting to show how far the various
alloys, now used for the resistance wires of standard
* See Wied. Ann., No. 1, 1893 ; also The Electrician, Vol. XXX. p. 567.
f Researches carried out in 1889-1890 by M. C. E. Guillaume, at the
Bureau International dea Poids et Mesures (see The Electrician, Vol. XXIX.,
p. 553), gave by two determinations the true temperature variation of mercury
between 0C. and 61C. as follows :
(a) n = TO (1 + 0-00088745 1 + O'OOOOOIOISI 2 )
(6) r t = ro ( 1 + 0-00088879 1 + 0*0000010022 1 2 )
38 ELECTRICAL LABORATORY EQUIPMENT.
coils, will remain absolutely unaltered over long periods
of time. It is certainly to a considerable degree dependent
on the manner in which the standards are made, and how
far they are allowed to undergo changes of temperature
in use.
In the employment of a wire of a metallic alloy as a
standard of electrical resistance there is always an element
of uncertainty as to the extent to which time may affect the
electrical qualities of the alloy. Experiments made by the
author in 1878 and 1879 on the original British Association
standard coils (fourteen in number) made of various alloys
showed that this fear was not altogether groundless, some
coils in the course of 14 or 15 years having certainly
changed in electrical resistance. Attention has, therefore,
been devoted to this question especially in connection with
the use of manganin and platinum-silver. In 1894 a
number of resistance coils of manganin (42 coils) and of
constantan (three coils) were tested at Berlin which had
been in use about three years. Of these
25 coils showed a variation of from O'OO to 0*01 per cent.
13 0-01 to 0-02
5 0-02 to 0-05
2 0-05 to 0-25
when re-compared with primary standards.
Confidence in the absolute permanency of electrical resist-
ance in the case of wire standards can hardly be said to have
been established beyond doubt. The balance of evidence
seems to show that for coils carefully made of well aged
manganin or platinum-silver it will not be serious.
One argument which has been used to support the conten-
tion that an ultimate standard should take the form of
mercury in glass is the assumed unalterable character of the
materials thus used. There is a possibility, however, that
the platinum electrodes may in time slightly dissolve and
thus contaminate the mercury.
The alloys which have been found practically satisfactory
ELECTRICAL LABORATORY EQUIPMENT. 39
as materials to employ in the construction of wire-resistance
standards are
1. Platinum Silver. An alloy consisting of two parts of
silver and one of platinum. This alloy was originally recom-
mended by the Electrical Standards Committee of the
British Association. It has a resistivity of 25 to 30 microhms
per centimetre-cube and a temperature coefficient of nearly
0-0003, or nearly 0*03 per cent, per degree centigrade.
2. Manganin. This alloy is composed of 84 parts of
copper, 12 of manganese and 4 of nickel. Its electrical
properties and suitability for employment as an electrical
resistance material were made known by experiments con-
ducted in the Physikalisch-Technische Keichsanstalt in Berlin.
Its specific resistance is about 42 microhms per centimetre-
cube. Between 0C. and 10C. its temperature coefficient is
0*000025. At some temperature generally lying between
15C. and 30C. it has a nearly zero temperature coefficient,
and beyond about 30C. a negative temperature coefficient.
It has not nearly so great a thermo-electric power with
copper as German silver or platinoid. It must, however,
be aged for use as a resistance material by first heating it
to a temperature of 140C. for five or ten hours in an air
bath to prevent subsequent changes in resistance. It is
somewhat easily oxidised, and when used exposed to air must
be either gilt or varnished. It must not be soldered with
solder containing zinc.*
In the manufacture of commercial resistance coils not
intended as standards the following alloys are useful :
3. German Silver. This is an alloy of copper (50 to 66
parts), nickel (13 to 18 parts) and zinc (19 to 31 parts), and
is of somewhat variable composition in different specimens.
It is not suitable for the construction of other than commercial
* See Dr. St. Lindeck, The Electrician, Vol. XXX., p. 119, " On Alloys for
Resistance Coils." " On the Permanency of Manganin Resistances," see Prof.
W. E. Ayrton, The Electrician, Vol. XL., p. 39, also p. 227 ; also W. Watson,
Proc. Phys. Soe., Lend., Vol. XVI., p. 25 ; also Drs. Jaeger and St. Lindeck,
Science Abstracts, Vol. I., p. 336.
40 ELECTRICAL LABORATORY EQUIPMENT.
resistances, on account of its rather large temperature coeffi-
cient (0-0004). It has a resistivity varying from 20 to 30
microhms per centimetre-cube.
4. Platinoid. An alloy resembling German silver in com-
position, but containing in addition about 2 per cent, of
tungsten. It has a smaller temperature coefficient (0*0003)
than German silver, and preserves a better surface in air.
In some specimens, however, time and temperature produce
a certain brittleness, and it seems to be attacked when
exposed in moist air containing carbonic acid."* It has in
some specimens as high a resistivity as manganin, viz., 40 to
45 microhms per centimetre-cube, but in other samples the
resistivity is as low as 30 microhms per centimetre-cube.
In addition to the above well-known alloys of definite
composition, a number of patented and commercial alloys,
the composition of which is not made public, are in use for
the construction of resistances in which a small temperature
coefficient is not of the greatest importance. These alloys
are employed in the manufacture of regulating resistances,
but are not used for resistance standards. Such alloys are
5. Rheostene. A nickel-steel alloy, having a resistivity of
about 77 microhms per centimetre-cube and a temperature
coefficient of 0-00119.f
6. Kruppin. An alloy having a resistivity of 83 microhms
per centimetre-cube and a temperature coefficient of 0'0013.J
7. Hadfield's Resista. An alloy having a resistivity of 76
microhms per centimetre-cube and a temperature coefficient
of 0-0011.
8. Eureka. An alloy having much the same electrical
qualities as platinoid, but not so liable to brittleness. Its
* See Mr. Hollo Appleyard, " On the Failure of German Silver and Platinum
Wires," The Electrician, Vol. XL., p. 227, 1897 ; also ibid. Electrical Review,
Vol. XLIL, p. 536 ; Science Abstracts, Vol. I., p. 412 ; Proc. Phys. Soc., Lond.,
Vol. XVI., p. 17.
t See Van Aubel, The Electrician, Vol. XL., p. 315 ; or Science Abstracts,
Vol. I., p. 19.
t See The Electrician, Vol. XXXII., p. 351 ; also Electrotechnische Zeitschrift,
December 15, 1893 ; also see Van Aubel, The Electrician, Vol. XXXI1L, p. 122.
ELECTRICAL LABORATORY EQUIPMENT. 41
chief mechanical fault is its considerable extensibility and
non-elastic yielding under tension.
9. Bruntoris Beacon Alloy. An alloy having a resistivity
of 60 to 80 microhms per centimetre-cube and a temperature
coefficient of 0'0007.
A large number of alloys have been found which have high
resistivity and small temperature coefficient, but in many
cases they have also poor mechanical qualities and are brittle,
or ill suited for being drawn into fine wire.*
As made at present, a standard of electrical resistance
consists of a carefully-drawn and well-annealed wire of
manganin or platinum-silver. If made of manganin it has to
be aged, as above described. This wire is then spun over
with two or three layers of white silk, and is wound on a
bobbin and preserved in a case in such manner that its
temperature can be controlled.
The actual resistance wire has to be attached at both ends
to terminal blocks or rods of copper, and has to be enclosed
for security in a metal case of some form or immersed in an
insulating oil.
Many English electricians are still somewhat sceptical
as to the permanency of manganin. t It has been stated that
all alloys containing zinc are liable to erratic changes of
resistance. Zinc solder or soft solder should never be em-
ployed in the construction of standard coils. Silver solder,
containing 75 per cent, of silver, should be used in soldering
manganin, and shellac varnish, and not paraffin wax, should
be used as an insulator.
* For further information see " Alloys for Resistance Standards," E. G.
Willyoung, Journal of Franklin Institute, or The Electrician, Vol. XXIX.,
p. 277 ; " Experiments on Nickel Steel Alloys," C. E. Guillaume, The
Electrician, Vol. XL., p. 348; "The Composition of Various Alloys for
Resistance Coils," Drs. Feussner and St. Lindeck, The Electrician, VoLXXVL,
p. 493. Also The Electrician, Vol. XXX., p. 119.
t In all these more or less complicated alloys there may be variations of
electrical and mechanical qualities caused by irregularities in manufacture.
It is not unusual to find samples of German silver and platinoid, and perhaps
manganin, which seem quite inferior to the general run of specimens of these
particular materials.
42
ELECTRICAL LABORATORY EQUIPMENT.
The authorities of the Berlin Eeichsanstalt have devoted
great attention to the consideration of the best form to give
to a wire standard of electrical resistance, and the following
is a description of the form adopted at present (1900). A
section of the standard is shown in Fig. 7.
FIG. 7. Berlin Keichsanstalt Wire Standard of Electrical Resistance or Standard Ohm.*
The resistance wire is a carefully insulated wire wound on
a brass cylinder, the wire being doubled on itself to annul
inductance as much as possible. The wire is laid on in a
single layer. The ends of the wire are silver soldered to
square nuts, which are in turn soft soldered to heavy copper
terminal rods. The final adjustment of resistance is made by
shortening a much finer parallel wire. Thus the 0*1 ohm
standard consists of two wires in parallel : one the principal
ELECTRICAL LABORATORY EQUIPMENT. 43-
wire, and another wire one-tenth of the section and ten times
as long as the first. Hence a change in length of one metre
of the fine wire is equivalent to only one millimetre change
in length of the principal wire. The coil so wound and
adjusted is hung in a bath of paraffin oil and contact is made
with the copper leads of the coil by means of the mercury
cups. When in use the oil is kept well stirred by a stirrer
driven by a small electromotor. In preparing the coil the
silk-covered resistance wires are wound on the brass core
and made to adhere to it by melted shellac. The coil
is then heated for ten hours to 140C. This baking not
only gives the coil the necessary insulation from layer to
layer (which is of the order of a million megohms), but
ages the manganin and prevents subsequent secular change
in resistance.
In the use of a coil of the above kind as a standard ot
resistance it is desirable, if extreme accuracy of comparison
is required, that the power wasted in the resistance coil shaE
not exceed one watt. The oil in which the coil is immersed
must be kept in thorough circulation, preferably by means of
a stirrer driven by a small electromotor, when a measurement
of resistance is being made. For further and fuller information
on the details of the construction and mode of use of the Keich-
sanstalt standard wire coils, the reader is referred to a paper
by Drs. K. Feussner and St. Lindeck in the Zeitschrift fur
Instrumentenkunde, November and December, 1895.*
In addition to the principal standards of resistance in a
laboratory, which must always be carefully used, it is neces-
sary to possess certain working standards for general use. A
convenient form for these secondary reference standards ha&
been designed by the author.!
This laboratory standard resistance coil is made as follows:
The brass case or shell which contains the coil is in the form
* See The Electrician, Vol. XXXVI., p. 509, 1896 ; also Drs. Jaeger and
K. Kahle, Wied. Ann., No. 3, 1898 ; The Electrician, Vol. XL., p. 847 ; Science
Abstracts, Vol. I., p. 412.
f See Phil. Mag., January, 1889.
44
ELECTRICAL LABORATORY EQUIPMENT.
of a ring (see Fig. 8). This ring consists of a pair of square-
sectioned circular troughs provided with flanges which can
be screwed together so as to form a square-sectioned, hollow,
circular ring.
ELECTRICAL LABORATORY EQUIPMENT. 45
From this ring proceed upwards two brass tubes about five
or six inches in length. Down these brass tubes pass the
copper electrodes or rods, and these rods are insulated from
the tubes at the top and bottom by ebonite insulators. The
insulator at the bottom of the tube, where it enters the ring,
is a simple collar, that at the top has the form of a funnel
corrugated on its outer surface. The use of this funnel will
be referred to presently. The actual resistance-coil is a
length of platinum-silver wire three-fold silk-covered. The
silk- covered wire is first baked above 100C. to dry it com-
pletely, and then immersed in melted ozokerit, or better, in
shellac varnish made up with absolute alcohol.
The so insulated wire is cut about the proper length and
laid double or folded once upon itself, and then rolled up on
a wooden mandril so as to form a circular coil of diameter
suitable to drop into the hollow of the brass ring. The wire
being wound double, its coefficient of self-induction is
rendered very small, This coil of wire is then wrapped over
with white silk and again dipped in melted ozokerit. The
ends of the wire are next soldered into nicks in the ends of
the copper rods, they having been previously pushed a little
way through the brass tubes for the purpose, and afterwards
drawn back into proper positions. The coil is then packed
into the circular groove, and, after adjusting the resistance to
the proper value, the bottom half of the ring is placed over it.
A thin washer of indiarubber is inserted between the flanges,
and the whole screwed tightly together. The resistance-coil
is thus enclosed in a thin ring of metal, and can be placed
wholly below the surface of water or ice. In order to test
the tightness of the joints, a little test-pipe is provided on the
upper surface of the ring. By placing the ring coil below
water and blowing into the test-pipe, the good fitting of the
joints can be assured. The aperture of this test-pipe is after-
wards closed by solder or a screw (see Fig. 8).
Apart from the insulation of the coil itself, it will be appa-
rent that the insulation is limited by the amount of insulation
resistance secured at the ebonite insulators at the top end of
the brass tubes. Any leakage from the copper rod over
these insulators to the brass tube destroys to that extent the
insulation of the coil. The object of making these external
insulators funnel-shaped is to prevent surface-creeping due
to condensation of moisture on them, by placing paraffin oil
or insulating liquid in the funnel-shaped cavity. When
46 ELECTRICAL LABORATORY EQUIPMENT.
this is done, even if dew should collect on the outer
surface of the funnels, the inner surface is kept dry by
the paraffin oil placed in them, the action being the same
as that in the well-known Johnson and Phillips fluid
insulator.
The ring coils when in use are placed in rather shallow
zinc troughs, which can be filled with water, and are closed
with a wooden lid. When so placed the whole of the
actual coil or resistance part is down beneath the liquid at
one level, where the temperature can be accurately ascer-
tained. The insulators and point of emergence of the
electrodes are away up above the level of the water, and well
protected from any action which might permit of leakage
over them. The large metallic mass of the ring assists in
bringing the resistance-coil quickly back to the tempera-
ture of the surrounding water, and the coil therefore
"tests quickly." In all other respects these standards of
resistance are as compact and portable, and not more
-expensive to construct, than the old form of B.A. standard,
whilst obviating the difficulties which present themselves
in the use of the old form in very accurate comparisons of
resistance.
It is quite possible to have two or more coils of wire inside
the same ring, each coil having its separate pair of electrodes.
A useful coil of this form can be made up containing 1, 10,
and 100 ohms, so that comparisons can be quickly made at
the same temperature with these three multiples of the same
unit of resistance.
In an ordinary electrical laboratory the electrician will not
often be called upon to make and adjust the principal stan-
dards of resistance himself. This is an operation requiring
great care and patience and some skill. Suffice it to say that
one of the best means of making the final adjustment of
resistance coils to an exact value is to wind on the coil two
insulated wires of the same material in parallel. One of
these is the principal resistance wire, and the other is a
much longer wire of smaller section, and is the adjusting
wire. The principal wire is, in the first instance, cut to a
length which shall be greater than the resistance required.
The following table may serve as a rough guide in making
ELECTRICAL LABORATORY EQUIPMENT. 47
resistance coils of platinum silver, but a margin should
always be allowed in cutting off wire :
To make a resis- Take platinum-silver wire of
tance coil of Length. Gauge in S.W.G.
1 ohm 9ft. No. 22 = 0-036in. dia.
10 ohms 42-5ft. No. 24 = 0-025in. dia.
100 ohms 133ft. No. 30 = 0-01 4in. dia.
1,000 ohms 675ft. No. 34 = 0-010in. dia.
The principal wire being roughly adjusted to a resistance
a little greater than the resistance desired, it is joined in
parallel with a wire of one-tenth its diameter and ten times
the length. The final adjustment is then made by lengthen-
ing or shortening this finer wire until the two wires in
parallel have exactly the required resistance. The resistance
wires are wound doubled or non-inductively on themselves
on a metallic core. The greatest care must be taken in
insulating the different turns of wire from each other and
from the . core. The wire should be double -covered with
white silk and never be touched with the moist hand.
When the coil is prepared as above described it must be
placed for use in a vessel of water or paraffin which is kept
well stirred and the temperature of which can be taken with
a correct thermometer. In all very accurate measurements
it is better to work with the coils in melting ice. The true
temperature of the wire is then known with a considerable
degree of exactness if the coil is allowed to remain for a
sufficient time in the melting ice to arrive exactly at 0C.
The source of error to be avoided is a difference in tempera-
ture between different parts of the resistance wire and
between the wire and the external bath. In making a
resistance measurement sufficient time must always be
allowed to elapse between two measurements to permit the
coil to reach its original and desired temperature. The only
method of making such a measurement with certainty as to
the temperature of the wire is to make the resistance
measurement after keeping the coils for 12 hours immersed
in melting ice.
48 ELECTRICAL LABORATORY EQUIPMENT.
In consequence of the slight uncertainty which still exists
as to the true value of the various practical standards of re-
sistance, it has been proposed by Prof. J. Viriamu Jones that
the ultimate standard of resistance shall not be embodied in
the form of a wire, but shall be recovered when required by an
absolute determination (see The Electrician, Vol. XXV., p. 552;
also Proc. British Assoc., Leeds, 1890, " Suggestions Towards
the Determination of the Ohm,"). With this object he has
perfected the Lorenz apparatus for the absolute determination
of resistance. His proposal is that such an apparatus shall be
set up in national standardising laboratories, and that when
it is necessary to evaluate a secondary standard of resistance
this shall be done by an absolute determination of the same.
In the Lorenz apparatus the essential portion consists of a
metallic disc revolving in the interior of a carefully arranged
spiral coil of wire. If an electric current is sent through the
coil, and if the disc is set in revolution, the disc becomes the
seat of an electromotive force. This electromotive force may
be balanced against the fall of potential down a certain
resistance in circuit with the coil. When once the dimen-
sions of the apparatus have been determined, the actual
observations necessary to obtain the absolute value of the
resistance of the inserted conductor are reduced to the deter-
mination of the speed of revolution of the disc, and the
absolute value of the resistance is given as the product of a
calculated coefficient of mutual induction and an observed
number of revolutions per second. Since the things actually
observed are merely a speed and the absence of a current in
a circuit, extreme accuracy of measurement can be obtained.
These necessary measurements can be carried out with a
very high degree of precision, and with a well-made Lorenz
apparatus it is possible to determine the value of a resistance
of the order of an ohm with an accuracy of one part in 10,000.*
* For a full description of the Lorenz apparatus the reader is referred to a
lecture given by Prof. J. V. Jones at the Royal Institution, May 24, 1895,
see The Electrician, Vol. XXXV., pp. 231 and 253 ; also the Proceedings of
the Royal Institution, Vol. XIV., p. 601. Also to an account of " A Deter-
ELECTRICAL LABORATORY EQUIPMENT. 49
5. Current-Carrying Standard Resistances. In addi-
tion to resistance coils, which are intended to be used merely
with very small currents passing through them, the electrical
laboratory must be provided with a graduated series of
resistances capable of carrying or passing large currents and
for use in measurements in which the fall in potential down
a conductor of known resistance is made to yield a know-
ledge of the current passing through a conductor in series
with the resistance.
These resistances are called Current Resistances, or some-
times Mho Standards. Eesistances of the above kind are
now made by instrument makers in the form of thick
FIG. 9. Standard O't Ohm Resistance to carry 10 amperes.
manganin wires in well- ventilated brass cases (see Fig. 9),
and in the form of manganin strip soldered to end blocks
(see Figs. 10 and 11), or in the shape of tubes of manganin
with end terminals (see Fig. 12). The great aim in the con-
struction of these resistances for large currents is to afford
urination of the Ohm made in Testing .the Lorenz Apparatus of the McGill
University, Montreal," Profs. Ayrton and Jones, see The Electrician, Vol. XL.,
p. 150, 1897. These experiments seemed to show that the Board of Trade
standard ohm is between two and three parts in 10,000 larger than the true
ohm. In other words, it is 0'02 per cent, greater than 10 9 centimetres per
second. (See Prof. Ayrton on " Our Knowledge of the Value of a Resistance,"
The Electrician, Vol. XL., pp. 133 and 149.) See also Chapter II., RESISTANCE
MEASUREMENT.
50
ELECTRICAL LABORATORY EQUIPMENT.
sufficient surface to carry off the heat generated by the
current, either by air convection or by radiation.
With the object of obtaining great current-carrying
capacity, some makers, such as Mr. Crompton, make these
FIG. 10. Bare Metal Strip Resistance for Currents up to 1,500 amperes.
FIG. 11. Metal Strip O'l Ohm Resistance for Currents up to 15 amperes.
standards in the form of tubes of manganin through which
water can be passed, and by this means they construct
standards of resistances capable of carrying without sensible
ELECTRICAL LABORATORY EQUIPMENT.
51
heating very large currents. In Fig. 12 is shown a tubular
resistance made to carry 1,500 amperes. The resistance is
O'OOl of an ohm. Hence the fall in potential down it at full
FIG. 12. Crompton Water-Tube Low-Resistance Standard.
52 ELECTRICAL LABORATORY EQUIPMENT.
load is 1-5 volts. The water used for cooling is circulated
through the pipe by a rubber hose, and the current density
in the metal rises to 13,000 to 20,000 amperes per square
inch without risk. The potential measuring connections are
attached to terminals on clamps which are fixed at such
distances as to define exactly the resistance required.
These current-carrying resistances are always provided with
two pairs of terminals, one pair called the current terminals,
by which the current is led in and out, and another pair
called the potential terminals, between which the resistance
has its stated value.
A most essential possession in an electrical laboratory or
testing room is a set of low resistances of the following
capacity :
1. One-ohm resistance, carrying one ampere.
2. One-tenth of an ohm resistance, carrying 10 amperes.
3. One-hundredth of an ohm resistance, carrying 100
amperes.
4. One-thousandth of an ohm resistance, carrying 1,000
amperes.
These resistances should be of manganin strip or wire,
the surface being gilt to prevent oxidation and the surface
of such sufficient area that the resistances do not become
heated beyond 60C. when kept in circuit for some time.
In using them the electrician may either take their value
for granted from the reputation of the maker, or, if possible,
and far better, get them checked by some authority. In
default he may proceed ab initio, and construct for himself
low-resistance standards by means of the resistance standards
prepared for use in Wheatstone bridge measurements.
The method which may be adopted of creating a standard
of low resistance, which shall have approximately a defined
value, is as follows : Let 1, 2, 3, &c. (Fig. 13), be mercury
cups, connected, as shown, by resistance coils r v r 2 , &c, Let
there be an even number of mercury cups on each side, and
therefore an odd number of resistance coils, Arranged in
ELECTRICAL LABORATORY EQUIPMENT. 53
this way, the coils r v r 2 , &c., are in series. If r be the resis-
tance of each coil such as r lt and there be n coils, the total
resistance in series will be n r. Let two copper combs, A and
B, made of very thick high-conductivity copper rod, be pro-
vided with claws, which enable them to connect together the
mercury cups on each side when dipped into them. Suppose
the cups 1, 3, 5, &c., connected on one side, and the cups
2, 4, 6, &c., on the other, then the coils r 1} r 2 , &c., will now be
in parallel between A and B, and the joint resistance between
A and B will be . The mercury cups must be made of
copper amalgamated in the interior, and the ends of the comb
FIG. 13.
terminals be pressed down very strongly on the bottom of
these cups when the resistances are thrown into parallel.
If E be the joint resistance of the n coils in series, then ^
fi
will be the joint resistance in parallel. If, however, the
resistance of each coil is different, then, if &i,& 2 , &c., be
the conductivities of each coil in mhos that is to say,
the reciprocal of its resistance measured in ohms the
total conductivity K, when arranged in parallel, will be
= K, or the total parallel mho conductivity is
54 ELECTRICAL LABORATORY EQUIPMENT.
the sum of the separate mho conductivities of each coil.
Suppose that a current is passed through such resistances in
parallel, it distributes itself between the coils, and, if we
know the conductivity of each coil, and can measure the
difference of potentials between A and B, we have at once
the means of calculating the current.
Moreover, we can discover whether the initial resistance
of the combined resistance has appreciably changed by the
heat due to the passage of the current, for, by raising the forks
out from the mercury cups, the n resistances, which were a
moment ago in parallel, are now in series, and the actual
change in resistance of the n in series is n 2 times the actual
change in resistance of the n in parallel. We get, therefore,
a resistance of considerable, or, at least, not very small magni-
tude to determine, and by performing the operation of
throwing the coils into series and measuring their resistance
on a bridge we can determine within a small amount any
change in resistance due to heat generated in any time in the
conductors. Hence, generally speaking, the method consists
in providing an arrangement by which resistances can be
arranged in parallel and traversed by the current to be
measured, and then thrown into series to determine what
change, if any, the conductor has experienced in resistance,
and calculating from this change, when measured in series,
the change when arranged in parallel.
Accordingly, the procedure is as follows : Suppose it is
desired to construct a resistance of one-tenth of an ohm and
capable of carrying ten amperes. The first step is to
measure on the Wheatstone bridge, as subsequently ex-
plained, the resistance of a series of wires, and to make them
exactly equal. For this purpose select platinoid wire No. 18
S.W.G. and measure the resistance of any length of this wire
on the bridge. Then calculate the length of the wire, which
will have a resistance of slightly more than one ohm.
Prepare in this way ten similar wires. Each platinoid wire
is then silver soldered to a square nut of well tinned copper,
ELECTRICAL LABORATORY EQUIPMENT. 55
which is drilled with a central hole. The resistance of each
wire is then made exactly the same by rubbing down with
glass-paper all the wires until they are exactly equal in
resistance to each other and to the highest in resistance of
the ten. This process needs much care and patience. The
ten wires having been made absolutely equal in resistance
at the same temperature, the true resistance of each one is
determined. The ten wires are then joined in parallel by
passing a screw through the holes in the ten terminal nuts,
and by heating these tinned blocks to the melting point of
tin, they are compressed and soldered together into one mass.
We have then a resistance of one-tenth of an ohm con-
structed of ten one-ohm wires in parallel. A potential wire
or terminal is then soldered to the terminal blocks as near
as possible to the place of contact of the resistance wires and
the terminal blocks.
A more careful comparison must then be made between
this one-tenth ohm standard and a one-ohm standard coil by
means of a low resistance bridge or potentiometer, as sub-
sequently described, and the nearest value determined for the
resistance at a known temperature of the one-tenth ohm
standard. A much more tedious process of the same nature
would result in the construction of a one-hundredth of an
ohm standard. When once original standards of low resis-
tance have been standardised or measured by means of the
Lorenz apparatus, it is comparatively an easy matter to copy
or reproduce them.*
The minimum outfit of carefully standardised resistances
which any electrical laboratory should possess is as follows :
1. A 100-ohm standard.
2. A ten-ohm standard.
3. A one-ohm standard.
the above to be coils suitable for comparison on a
* For determinations of the value of low resistances by the Lorenz apparatus
see Prof. J. Viriamu Jones " On Standards of Low Resistance," The Electrician,
Vol. XXXI., p. 620.
56 ELECTRICAL LABORATORY EQUIPMENT.
Wheatstone Bridge, but not necessarily adapted for carrying
large currents. In addition should be provided :
4. A one-ohm standard, capable of carrying one ampere.
5. A one-tenth of an ohm standard, for carrying up to ten
amperes.
6. A one-hundredth of an ohm standard, capable of carrying
up to 100 amperes.
7. A one-thousandth of an ohm standard, capable of carry-
ing up to 1,000 amperes.
The last four coils or strips must be suitable for measurement
of current by the fall of potential method, and have potential
terminals attached to them.
In addition to resistances of the above kind, for much
work, especially on insulators, it is necessary that the
laboratory should possess certain high resistance standards
A standard wire resistance megohm is, however, a somewhat
expensive article. Many cheap substitutes have been pro-
posed in the form of carbon or other admixtures of semi-
conductors. For really careful work nothing, however, is
satisfactory except a high resistance wire standard, preferably
of manganin in the form of ten coils each having a resistance
of 100,000 ohms. In the case of these high resistance
standards the insulation of the separate coils and of their
terminals becomes a very important matter. The coil
terminals must be carried on tall corrugated ebonite pillars,
and these must be placed a considerable distance apart on an
ebonite base. A standard megohm box of this kind must be
carefully protected from light and dust. Exposure to light
destroys the surface insulation of ebonite.* The coils
themselves must be insulated with well-baked solid shellac,
and be suspended or carried on glass rods, also varnished.
or covered with well-baked shellac.
* The action of light and air oxidises the sulphur in the ebonite and
produces a conducting layer, probably of sulphuric acid. This can be
removed by washing with a dilute solution of soda, then thoroughly drying
the surface and rubbing with a clean rag moistened with perfectly dry
paraffin oil.
ELECTRICAL LABORATORY EQUIPMENT. 57
6. The Recovery of the Standard or Unit Electric
Current. We proceed, in the next place, to consider the
means and instruments necessary to recover the standard
electric current, and to compare currents with the autho-
rised unit of electric current, called the ampere. The
practical and legal definition of the ampere or unit of
current is based upon the power of the current to cause
electrolytic decomposition in a standard electrolyte, such as
a neutral solution of the nitrate of silver when electrolysed
with a silver anode and a platinum cathode. The British
Board of Trade have issued a specification for the electrolytic
measurement of unvarying electric currents, and the arrange-
ment of apparatus and process is as follows :
BRITISH BOARD OF TRADE SPECIFICATION FOR MEASURING ELECTRIC
CURRENT.
In the following specification the term silver voltameter means the
arrangement of apparatus by means of -which an electric current is passed
through a solution of nitrate of silver in water. The silver voltameter
measures the total electrical quantity which has passed during the time of
the experiment, and by noting this time the time average of the current, or
if the current has been kept constant, the current itself can be deduced.
In employing the silver voltameter to measure currents of about one
ampere the following arrangements should be adopted. The cathode on
which the silver is to be deposited should take the form of a platinum bowl
not less than 10cm. in diameter, and from 4cm. to 5cm. in depth.
The anode should be a plate of pure silver some 30 sq. cm. in area and 2mm.
or 3mm. in thickness.
This is supported horizontally in the liquid near the top of the solution by
a platinum wire passed through holes in the plate at opposite corners. To
prevent the disintegrated silver which is formed on the anode from falling
on to the cathode, the anode should be wrapped round with pure filter paper,
secured at the back with sealing wax.
The liquid should consist of a neutral solution of pure silver nitrate,
containing about 15 parts by weight of the nitrate to 85 parts of water.
The resistance of the voltameter changes somewhat as the current passes.
To prevent these changes having too great an effect on the current, some
resistance besides that of the voltameter should be inserted in the circuit.
The total metallic resistance of the circuit should not be less than 10 ohms.
Method of Making a Measurement.
The platinum bowl is washed with nitric acid and distilled water, dried by
heat, and then left to cool in a desiccator. When thoroughly dry it is weighed
carefully.
58 ELECTRICAL LABORATORY EQUIPMENT.
It is nearly filled with the solution, and connected to the rest of the circuit
by being placed on a clean copper support to which a binding screw is attached.
This copper support must be insulated.
The anode is then immersed in the solution so as to be well covered by it and
supported hi that position ; the connections to the rest of the circuit are made.
Contact is made at the key, noting the time of contact. The current is
allowed to pass for not less than half-an-hour, and the time at which contact
is broken is observed. Care must be taken that the clock used is keeping
correct time during this interval.
The solution is now removed from the bowl, and the deposit is washed with
distilled water and left to soak for at least six hours. It is then rinsed
successively with distilled water and absolute alcohol and dried in a hot-air
bath at a temperature of about 160C. After cooling in a desiccator it is
weighed again. The gain in weight gives the silver deposited.
To find the current in amperes, this weight, expressed in grammes, must be
divided by the number of seconds during which the current has been passed,
and by O'OOlllS.
There seems reason to believe that the above officially-
adopted value of the electrochemical equivalent of silver is
about one part in a thousand too small, if the ampere so denned
is to represent one-tenth of the absolute C.G.S. unit of current.
A careful discussion of the different values obtained for the
mechanical equivalent of heat (=J= Joule's equivalent) has
shown that the best results obtained by the heating of water
electrically are in excess of the best results obtained by
mechanical friction methods by about one part in 400. Thus
at 191 by the Paris nitrogen thermometer the values of J
are as follows per degree Fahr. :
By Mechanical Methods.
Joule 774 foot-pounds.
Rowland .. .. 776*1
By Electrical Methods.
Griffiths 7791 foot-pounds.
Schuster & Gannon 778'5
More recent determinations of the electro-chemical equiva-
lent of silver gives the value 0*0011192 grammes per ampere-
second (see Electrical Review, September 30, 1898) and the
adoption of this constant instead of 0*001118 removes nearly
all difference between the value of J when determined
mechanically and electrically.
The result of the measurement carried out as above specified
will be the time-average of the current if during the interval
the current has varied.
ELECTRICAL LABORATORY EQUIPMENT. 59
Iii determining by this method the constant of an instru-
ment the current shall be kept as nearly constant as possible,
and the readings of the instrument observed at frequent
intervals of time. These observations give a curve from
which the reading corresponding to the mean current (time-
average of the current) can be found. The current, as
calculated by the voltameter, corresponds to this reading.
The every-day practical measurement of current is best
performed by some instrument which gives not merely the
time-average, but the precise value at any instant. Such in-
struments are called amperemeters or ammeters. Of the many
principles employed in the construction of amperemeters
none is so well adapted to the construction of a standard
instrument as the utilisation of the fact that forces of
attraction and repulsion exist between conductors carrying
electric currents. These instruments, which are variously
called electro-dynamometers, current balances or ampere
balances, may all be said to be modifications of the electro-
dynamometer, which was first described by Weber in his
" Electro-dynamische Maasbestimmungen " (Leipsic, 1846).
The principle on which these instruments act was made known,
however, twenty-five years previously. On September 25, 1820,
Ampere announced to the Academy of Sciences in France
that he had discovered the existence of forces of attraction
and repulsion between conductors of non-magnetic material
traversed by electric currents. The experiments of Ampere
and the subsequent elaborate researches of Weber (W. Weber,
" Electro-dynamische Maasbestimmungen," Thl. I., s. 10,
1846, Auszug in Pogg. Annal., Bd. LXXIIL, s. 193) estab-
lished the fact that, if there be a fixed and a movable
conductor in the neighbourhood of each other, traversed by
the same electric current, there will in general be a
mechanical stress brought into existence, which will tend
to displace the movable conductor and to bring it into a
position relatively to the fixed conductor in which the
mechanical stress between them is zero. The mutual force
60 ELECTRICAL LABORATORY EQUIPMENT.
or stress between these mutually influencing portions of the
same circuit is, in any given position, proportional to the
square of the strength of the current traversing the two
portions of the circuit. In the ampere balances invented by
Lord Kelvin this stress is measured by comparing it with or
balancing it against the weight of certain standard masses ;
in other words, the electro-dynamic stress between electric
circuits is compared with the gravitation stress on a given
mass.
The great difficulty which has hitherto presented itself to
all who have attempted to design instruments on the electro-
dynamometer principle for any but very small currents has
been that of getting the current into and out of the movable
conductor. The device on which most experimentalists have
fallen back is that adopted by Ampere himself, viz., to use
mercury cups as a means of constructing a flexible and
conducting joint. The use of mercury is open to many
objections. The surface gradually becomes oxidised, the
cups must be filled and emptied each time the instrument
has to be transported, and the joint with impure mercury is
by no means exceedingly flexible. The great novelty in the
ampere balances of Lord Kelvin was the invention of a joint
or electric coupling which is excessively flexible, and at the
same time capable of being constructed so as to carry with
safety any current desired. This was accomplished by the
introduction of a device which may be called a metallic
ligament. The general principle of its construction, and the
mode of rendering a circuit freely movable, yet accessible
to a large current, may be described as follows : Let A A
(Fig. 14) be a pair of semi-cylindrical fixed trunnions, which
are carried on some form of supporting frame and held with
the flat sides downwards. Let B B be two similar trunnions,
which project out from the sides of two strips, connecting
together a pair of rings C C. The pair of rings and the
connecting strips constitute the circuit which is to be
rendered movable. A current entering by the trunnion
ELECTRICAL LABORATORY EQUIPMENT. 61
-f B flows round the two halves of the circuit, as shown by
the arrows, and emerges at the trunnion B. In Fig. 14
the current is shown, for simplicity, dividing round the
two rings. The circuit should in reality be shown so
that the current goes round both rings in series in figure
of eight fashion. This is the case in all but the kilo- and
hecto-ampere balances, in which the current divides round
the ring, as shown in Fig. 14. To the upper surface of the
upper trunnion are soldered a very large number of exceed-
ingly fine copper wires (No. 60 B.W.G.), which are laid close
together. These wires are also soldered to the under surface
of the lower trunnion. The movable circuit C C thus hangs
from the upper trunnion by two ligaments, which appear like
thin strips, but which are really composed of an immense
number of very fine wires. In Fig. 14 these ligaments are
intentionally drawn much longer in proportion to the rest of
the figure than they really are in the instrument, the object
being to render the mode of suspension clear. This method
of suspension enables the conductor C C to vibrate freely
like a balance by a motion which is partly a bending of the
flexible ligaments, and partly a sort of rolling and unrolling
of the lower trunnion on the ligament attached to it. By
this ingenious method not only can a heavy copper con-
ducting circuit of the shape shown be suspended as freely as
the beam of a good balance, but at the same time a very
large current density can be permitted in the flexible liga-
ment, since its great radiating surface, and the freedom with
62
ELECTRICAL LABORATORY EQUIPMENT.
which heat is taken out of it by conduction into the mass of
the trunnions, allows a proportionately very large current
to be transmitted. If, then, the trunnions A and B are the
electrodes, the method above described affords the means of
passing a very large current into the circuit C C, which yet
at the same time retains within certain narrow limits great
freedom of movement. Let such a suspended conductor be
arranged so as to have a circular conducting circuit of
annular form, briefly called an ampere ring, placed above and
below each of the movable rings of the balanced arm. Let
the connections be made as shown diagrammatically in
Fig. 15, in which it will be seen that the current entering by
the 4- electrode flows in series through all four fixed
FIG. 15.
ampere rings F, and through the two movable ampere
rings M. An examination of the direction of current flow in
each ring will then show that, in consequence of Ampere's
law (parallel currents in same direction attract, in opposite
direction repel), forces of attraction and repulsion will be
brought into play between each fixed ring and the movable
rings, which tend to lift one ring M and depress the other,
and tilt over the balance arm to which they are attached.
The amperian forces thus exert a couple on the movable
part. To bring back the movable part to its initial position,
which we may suppose to be half-way between each fixed
ring, an equal and opposite mechanical couple must be
applied. We shall in what follows call the movable part
ELECTRICAL LABORATORY EQUIPMENT. 63
of the conducting circuit the balance coils, and the other
portion of the circuit the fixed coils. The operation of
weighing an electric current consists, therefore, in bringing
first of all the balance coils into a definite sighted position
between the fixed coils, then passing the current, and
bringing back the balance coils into the sighted position
against the displacing electro-dynamic forces by applying to
the balanced part a couple produced by a standard weight.
The restoring couple is applied as follows : Attached to the
balanced part or movable portion is a stiff metal bar,
turned up at the bottom edge so as to form a sort of long
shelf. This shelf or tray extends the whole length of the
movable beam, and moves or tilts with it when the balanced
part is displaced (see Fig. 16). At one end of the balanced part
is a small V-shaped tray, in which a weight is placed. A
standard weight is then placed at the opposite end of the shelf.
This weight is of such form as to slide along the shelf
easily. When placed at the zero position on the shelf it
exactly balances the counterpoise in the V-trough, and the
balanced part should be in equilibrium when no current is
passing. If it is not so, then a small adjustment can be
made by means of a metal flag on the beam similar to that
on a gravimetric balance, so as to alter slightly the position
of the centre of gravity of the balanced part. If the sliding
weight on the shelf is moved along towards the middle the
equilibrium is disturbed and a couple brought to bear upon
the balanced part, which is proportional to the displacement
of the sliding weight from its zero position. If a current is
passed through the circuit, and the sliding weight displaced,
so as to restore the balance to its sighted position, the current
strength is proportional to the square root of the distance by
which the sliding weight has to be shifted in order to restore
equilibrium. The shifting of this weight is performed by a
very ingenious piece of mechanism, which will be understood
from the enlarged view (Fig. 17). On the base board of the
instrument, and just underneath the shelf on which the
64
ELECTRICAL LABORATORY EQUIPMENT.
ELECTRICAL LABORATORY EQUIPMENT.
65
weight slides, is placed a little metal block, which carries a
stout vertical wire extending a little above the shelf carried
on the balanced beam. From the top of this wire is carried
a pendent wire, which hangs down through a notch in the
weight which slides on the shelf. This block, carrying the
pendant, is pulled along the railway by a silk cord. When
pulled it drags with it the weight on the shelf ; but when
the string is released the pendant returns to its vertical
position and disengages itself automatically from the weight,
leaving the balance free to tilt according to the direction of
the forces acting upon it. By this means the weight can be
shifted along until a balance is obtained, whilst at the same
time the whole balance is covered with a glass case to protect
it from currents of air.
FIG. 17. Shifting- Weight Apparatus of Kelvin Ampere Balance.
With each current balance four sliding weights and four
corresponding counterpoises are provided ; the weights being
in the ratio of 1 : 4: 16 : 64. Thus if with the ampere balance
the lightest weight on the sliding tray in a certain position
corresponds to a current of half an ampere through the
instrument, the next weight at the same place corresponds
to one ampere, and with the third weight on it the current
is two amperes. The upper edge of the shelf on which
the weights slide is graduated into equal divisions, and
66 ELECTRICAL LABORATORY EQUIPMENT.
the weight is provided with a sharp tongue of metal, in
order that its position on the shelf may be readily and
accurately determined. For the purpose of avoiding con-
tinual reference to square root tables, another fixed scale
is placed behind the shelf, called the inspectional scale. On
the upper edge of the shelf, along which the graduations are
made, a small notch is cut at those divisions whose numerical
denominations are exact squares ; thus, corresponding to
divisions 1, 4, 9, 16, 25, 36, &c., on the scale engraved on the
shelf are cut little notches in its upper edge. The inspec-
tional scale is fixed close behind this, and yet not touching,
and at those points on it exactly behind the notches are
engraved numbers which are twice the square roots of the
corresponding numbers on the shelf; thus, corresponding to
1, 4, 9, 16, 25, &c., on the shelf, the numbers 2, 4, 6, 8, &c.,
are engraved on the inspectional scale. Since the current
passing through the balance when equilibrium is obtained
with a given weight is proportional to the square root of the
couple due to this weight upon the balance, it follows that
the current strength when equilibrium is obtained is pro-
portional to the product of the square root of weight used,
and the square root of the distance of this weight from
its zero position ; but the inspectional scale is so graduated
as to show at a glance the square root of the distance of the
weight from its zero position, and hence the numbers on the
inspectional scale indicate half-amperes, amperes, or double
amperes, according to the weight used.
In using these and all other gravity instruments it should be remembered
that the acceleration of gravity, and therefore also the weight of a given mass,
varies with latitude and with the height above the earth's surface. If M is
the mass of a body and g is the acceleration of gravity, then its weight
W=Ma, and
^=980-6056-2-5028 Cos 2\ - O'OOOOOSA,
where \ latitude and A = height above sea level in centimetres.
If, then, an ampere-balance is set to read correctly at Glasgow, it will need a
correction to be applied if used in other places. The weight of each weight,
and therefore the corresponding current, will vary proportionately with
gravity.
ELECTRICAL LABORATORY EQUIPMENT. 67
The following table shows for eaeh type of instrument the
value per division of the inspectional scale corresponding to
each of the four pairs of weights :
I. II. III. IV.
Centi-amperes Deci-amperes Amperes per Amperes per
per division. per division. division. division.
1st pair of weights 0'25 0'25 0'25 T5
2nd 0-50 0-5 0'5 3'0
3rd 1-0 I'O 1-0 6-0
4th 2-0 2-0 2-0 12-0
The fixed inspectional scale shows approximately enough
for many purposes the strength of the current ; the notches
in the top of the aluminium sliding scale or shelf show the
precise position of the weight corresponding to each of the
numbered divisions on the inspectional scale, and practically
annuls error of parallax due to position of the eye. When
the pointer on the weight is not exactly below one of the
notches corresponding to integral divisions of the inspectional
scale, the proportion of the space on each side to the space
between two divisions may be estimated inspectionally with
accuracy enough for all practical purposes. Thus, we may
readily read off 34'2 or 34' 7 by estimation, with little chance
of being wrong by 1/0 in the decimal place. But when the
utmost accuracy is required, the reading on the fine scale of
equal divisions must be taken, and the strength of the
current estimated by aid of a table of square roots supplied
with each instrument.
These general principles being understood, we proceed to
describe the details of the several types of instruments
adapted for various ranges of useful measurement. The
range of each instrument is from 1 to 100 or 1 to 25 times,
the smallest current for which its sensibility suffices. The
ranges of the different types of instrument regularly made
are :
The Centi-ampere balance from 1 to 100 centi-amperes.
Deci-ampere 1 to 100 deci-amperes.
Ampere
Deca- ampere
' Hecto-ampere
, , Kilo-ampere
1 to 100 amperes.
1 to 100
6 to 600
100 to 2,500
F2
68
ELECTRICAL LABORATORY EQUIPMENT.
Fig. 16 shows the general appearance of the centi-arnpere,
deci-ampere and ampere balances, and Fig. 18 that of the
standard kilo-ampere balance. In these instruments the
outer diameters of the fixed coils are slightly greater, and the
inner diameters slightly less than those of the movable rings
attached to the balance arms. The position of the movable
rings when in equilibrium and equi-distant from the fixed
ones above and below it, is a position of minimum force, and
the sighted position, for the sake of stability, is above it, at
one end of the beam and below it at the other, in each case
being nearer to the repelling than to the attracting ring by
such an amount as to give about T 2 a per cent, more than the
FIG. 18. Kelvin Kilo-ampere Balance.
minimum force. In order to adapt these balances for alter-
nating currents, a special mode of arranging the conducting
circuit has to be adopted. In the balances intended for
alternate currents (which may be used also for direct
currents) of from five amperes to 250 amperes, the main
current through each circle, whether consisting of one turn
or of more than one turn, is carried by a wire rope, of which
each component strand is insulated by silk covering or
otherwise from its neighbour, in order to prevent the
inductive action from altering the distribution of the currents
across the transverse section of the conductor ; whilst to-
ELECTRICAL LABORATORY EQUIPMENT.
69
70 'ELECTRICAL LABORATORY EQUIPMENT.
avoid induced currents in these parts the coil frames and base-
board are constructed of slate. The hecto-ampere (see Fig. 19)
and kilo-ampere balances are slightly different in arrangement
from the foregoing. In the last instrument the whole
current to be measured is passed through a single fixed ring
and then divides through the two halves of a movable ring,
which are urged, one up and the other down, by the resulting
attractive and repulsive forces.
For the British Board of Trade Electrical Laboratory Lord
Kelvin designed a special form of ampere balance for
recovering or defining a current of one ampere, of which
the following is the official description :
CONSTRUCTION AND USE OF THE PRINCIPAL INSTRUMENT FOR
DETERMINING THE STANDARD OF ELECTRICAL CURRENT.
The complete instrument is shown in perspective in Fig. 20,*
and the details and connections in Figs. 21 and 22. It is
constructed as follows :
Balance and Supports. A sensitive balance, suitable for
the accurate determination of weights up to five kilogrammes
with a beam 16in. in length between the knife edges from
which the scale pans are hung, is fixed on an upper hori-
zontal platform of marble, supported on four marble columns
at a height of 2ft. 3in. above a similar platform fixed on a
suitable stone pier, bedded solidly in a mass of concrete, and
kept clear from contact with the wooden floor of the
laboratory.
Marble Cylinder. On the lower platform is placed on
three supports, details of which are given below, a cylinder
of white statuary marble, partly hollow (see Fig. 20).
The cylinder is thoroughly impregnated with paraffin wax.
A block of ebonite e (Fig. 21) is fixed on one side of the
cylinder, and serves as a terminal board.
Fixed Coils. Two circular grooves are cut completely round
the cylinder, in which are wound coils of No. 18 standard
* This illustration and many others used in this book are taken from The
Electrician by permission of the Proprietors.
ELECTRICAL LABORATORY EQUIPMENT.
71
wire gauge (012cm. diameter), insulated with two coverings
of white silk. The wire was passed through a bath of shellac
FIG. 20. The Board of Trade Standard Ampere Balance, showing the Weight
raised from the Scale Pan by the Lifting Gear.
and alcohol as it was wound on the marble, and each layer
was well coated with the same material when in its place.
Each coil has 16 turns per layer and 16 layers of wire.
72
ELECTRICAL LABORATORY EQUIPMENT.
The coils are both wound in the same direction, and the
outer ends are strained tight and secured to terminals 1 1
(Fig. 21).
The inner ends are passed through the marble and secured
to bolts in connection with terminals i i (Fig. 21).
Sighting Holes. Between the grooves on the marble
cylinder, at points equi-distant from each other, are bored
FIG. 21. Elevation and Part Section of Marble Cylinder of Board of Trade Standard
Ampere Balance.
through the marble three sighting holes, one of which is
shown at h (Fig. 21). These holes are closed on the inside
by glass, the exact centres being indicated by the intersection
of two straight lines engraved in the glass, and also by the
angle of a quadrant of tinfoil affixed to the glass.
ELECTRICAL LABORATORY EQUIPMENT. 73
Suspended Coil, Suspending Wires, &c. A circular coil,
shown in sectional elevation at c (Fig. 21), and of the
dimensions given, is suspended from one end of the beam of
the balance by means of three gilded phosphor bronze wires
0'086cm. diameter, w w w (Fig. 21). These wires pass
through an aperture in the upper marble platform.
The wire in this coil is the same as in the fixed coils, and
is similarly insulated and varnished. There are 18 turns of
wire in each layer and 18 layers. Each complete layer was
allowed 24 hours to dry alter being coated with shellac
varnish before the next layer was put on.
The coil is covered with a taping of silk ribbon, closely
laid on to overlap, and varnished with shellac in alcohol, four
coats, each being allowed to thoroughly dry before applying
the next one.
The ends of the coil are brought out near each other on
the upper surface at I (Fig. 21). A considerable length of
wire is left for each end, and is formed into a spiral, and then
projected horizontally to the centre of the coil, where the
stiff wires terminate, and flexible connections are made by
three silk-covered silver wires, No. 40 S.W.G., from each to
the posts p (Fig. 21), which are connected to terminals nn.
Three ebonite blocks I (Fig. 21) are fitted over the coil, as
shown, and secured by a lashing of silk thread, the suspend-
ing wires being attached to brass eyelets screwed into the
ebonite.
At d d d (Fig. 21) are shown ivory cranks for effecting the
vertical adjustment of the suspended coil.
The attachment of the suspending wires to the balance is
effected by ivory rings, which are hooked on to a three-legged
fitting, this being hooked to the stirrup, hung on the knife
edge of the beam (see Fig. 21).
The scale pan is also hung from this stirrup, as shown in
Fig. 21.
On the upper part of each ebonite piece &, facing the
sighting hole h, is fixed a mirror M, the centre being fixed by
74 ELECTRICAL LABORATORY EQUIPMENT.
the intersection of cross lines and by the angle of a quadrant
of tinfoil.
Adjustments. The proper adjustment of position of the
suspended coil is indicated by the coincidence of the angles
of the tinfoil quadrants on the mirrors in, and the glass back
of holes A, when the eye is so held that no reflected image
can be observed.
Eccentric Movement for Horizontal Adjustment. A means
of fine horizontal adjustment is provided in the supports of
the marble cylinder, which are three short slate cylinders,
k k k (Fig. 21), having projections from their upper and
lower surfaces, the upper projection being eccentric and
fitting in a hole in the bottom of the marble cylinder, and
the lower projection being concentric and fitting in a radial
groove in the marble slab.
The Weight. The iridio-platinum weight shown in Fig. 20'
can be lowered into the scale pan, and released from the
outside of the case by a system of levers.
The weight is accurately 33*55 grammes.
Enclosure. The marble cylinder is enclosed by means of
three sheets of plate glass, which slide in grooves cut in the
marble platforms, and when in position are in contact with
the sides of the three marble columns adjacent to the
cylinder, these sides being coated with baize, the plan of
this, enclosure being an equilateral triangle with the axis
of the marble cylinder at its centre. The planes of the
three glass sheets are respectively parallel with those of
the glass at the back of the sighting hole viewed through
them.
The balance is enclosed within a case of mahogany and
glass (see Fig. 20), and arrangements are made as indicated
for manipulating the rider weights of the balance and the
ampere weight from the outside of this case.
The whole enclosure is fairly dust-tight, and sufficiently
air-tight to prevent any disturbance of the weighing opera-
tions by currents of air.
ELECTRICAL LABORATORY EQUIPMENT.
75-
Connections. The connections to the reversing switch Z
(Fig. 22) are brought outside the enclosure by means of rods
passing through the marble column adjacent to the ebonite
block. Fig. 22 shows these connections, and the direction of
the current through the various parts of the apparatus, the
lower arrows over the fixed coils showing the alteration of
direction caused by operating the switch.
Fixed Coil
FIG. 22.
Auxiliary Current Balance.
In the construction of the standard ampere balance, the
chief object aimed at has been the securing of the greatest
possible constancy and precision of determination.
On account of the slow period of vibration of the beam r
however, the use of an auxiliary instrument has been found
advantageous.
This is a special form of Lord Kelvin's current balance
instrument arranged to balance with a current of one ampere
passing through the coils when a certain weight is applied to
one end of the beam, equilibrium being also maintained
when, with no current passing, this same weight is applied
to the other end of the beam.
76 ELECTRICAL LABOR AT ORT EQUIPMENT.
Use of the Instrument. The standard balance, auxiliary
'balance, and the instruments to be standardised are con-
nected in circuit with a sufficient number of accumulators
and an adjustable resistance, part of which is capable of
continuous variation. The whole circuit is arranged so that
a current of approximately one ampere will pass on comple-
tion of the circuit.
This current is allowed to pass continuously for at least
one hour, being directed through the coils of the standard, so
as to increase the force of gravity on the suspended coil, and
the counterweight in the right hand pan being adjusted from
time to time.
At the end of this preliminary period the current is
stopped for a short time to take a reading of the zero of the
auxiliary balance, and apply a correction by means of the
rider weight, if necessary. The current is then again put on,
3,nd as rapidly as possible regulated by means of the adjust-
able resistance to exactly the value of one ampere, as
indicated by the auxiliary balance.
The counterweight in the right hand pan standard balance
is also exactly adjusted.
The switch Z (Fig. 22) is then operated to reverse the
-current in the fixed coils, and at the same time the weight is
lowered into the left-hand scale pan.
The balance should then still be maintained when the
current, after adjustment, if requisite, is exactly one ampere
by the auxiliary balance.
The above-described laboratory forms of Kelvin ampere
balances are made in two types. They are constructed in
one form with a sliding weight and scale so as to enable
any constant current to have its ampere value determined, or
they are constructed with fixed weights so adjusted that on
gradually varying the current the balance tips over at certain
fixed standard currents, say, one ampere or ten amperes, &c.
In this last mode of use of the balances there is no sliding
weight and tray but the balances have to be employed in
ELECTRICAL LABORATORY EQUIPMENT. 7*
connection with a carbon rheostat or some means for con-
tinuously varying the current strength with extreme precision.
In the case of a primary standard laboratory balance it is-
better to have it arranged in the second manner so that by
its means the observer may weigh out, as it were, an ampere
or ten amperes rather than determine the true value of a,
non-integral current.
In this last manner the standard ampere balance (see
Fig. 23) of the Board of Trade is used, and it is desirable,
where extreme accuracy is required, that the laboratory
should be provided with a one-ampere fixed standard balance
of the above-mentioned description.
FIG. 23. Standard One-ampere Kelvin Balance as made for the Board ofr
Trade Electrical Laboratory.
Deferring, for the present, details of the standardisation of
these ampere balances, we may say that the electrical
laboratory should be provided, at the very least, with two-
standard Kelvin ampere balances, the most useful being the
deci-ampere balance weighing from one-tenth to ten amperes-,
and a deca-ampere balance weighing from one to a hundred
amperes.
These balances should be carefully set up on level stone
shelves of such height that an observer seated on a stool can.
comfortably read the scale and manipulate the rider.
78 ELECTRICAL LABORATORY EQUIPMENT.
After setting up the deci-ampere balance it should be most
carefully standardised by a silver voltameter, using the
process described in the Board of Trade specification. After-
wards the balance should not be moved or touched except to
regulate the position of the equilibrium flag before each
weighing. A comparison should then be made between the
. standard Clark or Weston cell and the balance as follows :
Pass through the ampere balance and a tenth of an ohm
standard coil a current of about six or seven amperes and
regulate this current to perfect steadiness. Then measure
with the potentiometer the potential difference between the
terminals of the standard resistance and calculate from this
the value of the current. The current as read by the
. ampere balance and the current as determined by the stan-
dard cell and resistance should agree within one-tenth of 1
jper cent., or to one part in a thousand.
If any refined or careful measurements are to be made the
director of the laboratory should spare no pains to make sure
that he is in possession of the means of recovering or pro-
ducing the ohm, the volt and the ampere in his own
laboratory, and that these should be in exact agreement as
far as possible with the Board of Trade standards and with
each other.
It is desirable that the special appliances which form the
primary electrical standards of the laboratory the standard
ohm, the standard Cadmium or Weston cell or the standard
Clark cell and the standard deci-ampere balance shall not
be used for every-day work, but kept for special verification
purposes.
The laboratory being in the above-described manner pro-
vided with means for making the three fundamental com-
parisons of length, mass and time by means of a standard
metre, standard gramme or kilogramme weights and chrono-
meter must also be provided in the best possible manner
with the appliances for making the three principal electrical
measurements of resistance, electromotive force and current
ELECTRICAL LABORATORY EQUIPMENT. 79
by comparison with the standard ohm, standard cell or
voltage and standard current. Before describing the stan-
dards of electromotive force it is necessary to mention certain
current regulating devices which are essential requisites.
7. The Regulation of Current. One of the most
frequently required operations in the electrical laboratory is
that of the regulation of a current by means of resistances.
Each working bench or table should be provided with
terminals between which a constant potential difference of
100 volts is maintained. From these terminals, however,
have to be taken currents of the desired strength. This is
best done by providing the laboratory with an outfit of
regulating resistances which, when placed in series with
any apparatus and across the main terminals, can permit
only the desired current to flow.
After many trials and experiments the author devised the
following form of working resistance, which is exceedingly
useful in a laboratory :* Each .element of the resistance is
called a cage (see Fig. 24), and is made in the following
manner. A brass rod about 3ft. long carries on it two
porcelain head-pieces or discs having porcelain pin projec-
tions on their upper surfaces. One of these is fixed to the
rod and the other is movable, but is pushed outwards by
a strong spiral spring. To a terminal wire attached to the
fixed head-piece is soldered one end of a fine wire of
platinoid, reostene or any high-resistance wire. This wire
is generally about No. 32 gauge. The movable head-piece
is pressed in a little way, and the resistance wire is then
laid backwards and forwards over the pin projections on the
head-pieces so as to form a zigzag conductor; the end of
the resistance wire being then finally connected to another
terminal wire passing through the fixed head-piece. When
the cage is so made the movable head-piece is released and
the spiral spring forces it out, and thus keeps the resistance
* See The Electrician, Vol. XXXVI., p. 476.
80 )
FIG. 24. Inductionless Ventilated
Kesistance Ccages (Fleming).
ELECTRICAL LABORATORY EQUIPMENT. 81
wire always tight, even although it expands on heating. By a
proper selection of the resistance wire a perfectly ventilated
and practically non-inductive resistance may be made in this
manner, having a resistance of 100 ohms or more which, will
carry safely, without undue heating, a current of one ampere.
A series of these cages can then be fixed in a wood frame
placed on castors, with all the several resistances connected
in parallel between two omnibus wires ; each resistance
being provided with its own switch. It will then be seen
that the whole resistance frame can be put across the 100-
volt terminals, joined in series with a switch and with any
apparatus to be traversed by the current, and that the current
FIG. 25. Paul's Carbon Plate Rheostat.
which passes through the circuit can then be regulated by
the number of cages which are switched on in parallel.
When currents of less than one ampere are required these
can be obtained by joining cages in series. In this case
each cage can be coupled with a switch in parallel with
it, so that when the switch is on, the cage resistance is cut
out of circuit.
In addition to a set of the above cages it is necessary to
possess several carbon rheostats. One of the most convenient
forms of this regulating resistance consists of plates of
hard battery carbon or graphite roughened on the surface
and about Sin. square (see Fig. 25). A series of about 30 to
82 ELECTRICAL LABORATORY EQUIPMENT.
50 of these plates are placed in an iron frame and prevented
from touching the guide rods by porcelain or fibre insulators.
The carbon plates can be more or less squeezed by a strong
screw. Metal plates with screw terminals can be slipped in
between any carbon plates, and, by means of the pressure
applied, a very gradual variation can be made in the inter-
posed carbon resistance. It is essential that the carbon
plates shall be hard but not smooth, and the best plates are
those cut out of gas-oven graphite.
FIG. 26. Kelvin Wire Rheostat.
The above resistances are a great convenience in the
laboratory. They can be used to carry large currents up to
50 or 100 amperes, but they have not a very great range ot
resistance variation.
For the gradual variation of resistance Lord Kelvin's form
of wire rheostat, in which a platinoid wire is wound off a
metal cylinder on to a marble or porcelain cylinder, will be
found convenient (see Fig. 26). In this appliance the
resistance wire is kept tight by means of a clock spring
in the interior of the metal cylinder, which always acts so
as to keep a little tension on the resistance wire.
For many purposes a form of rheostat devised by Mr.
Shelford Bid well is useful. This consists of a slate or
ELECTRICAL LABORATORY EQUIPMENT. 83
porcelain cylinder on which a platinoid wire is wound in a
helical groove, one end of the resistance wire being insulated
and the other fixed to a metal plate which forms the carrier
for the cylinder. The cylinder is centred on a long screwed
shaft, the screw on which is cut to the same pitch as the
helical groove on the cylinder. This screw rod works in
tapped bearings. A fixed spring contact presses against the
platinoid wire, and the other end of the platinoid wire is in
metallic contact with one screw bearing. As the cylinder is
turned round a greater or less length of platinoid wire is
interposed between this spring terminal and the fixed terminal.
This form of rheostat is substantial and works well if the
wire and contact are kept clean. The contact spring should
be tipped with platinoid. It is a good plan to keep these
rheostats in boxes with glass lids, the winch handle alone
protruding, so that dust does not fall on the resistance wire
or contacts. If it does, the resistance is apt to vary in a
capricious manner as the handle is turned.
For some cases incandescent lamps can be used for regu-
lating resistances. It is useful to have some boards on
which are mounted half-a-dozen key sockets, wired up in
parallel between two brass terminal screws. If incandescent
lamps are placed in these sockets the resistance between the
terminals can be decreased by steps by switching on lamps.
If the light given out by the lamps is objectionable it can be
shielded off by dropping over each lamp an asbestos card-
board hood or cylinder like a canister, the top of which is
pierced with small holes for ventilation. Incandescent lamps
as resistances, owing to the light and heat given out by them,
are not nearly so convenient as the resistance cages above
described.
For the regulation of currents for dynamos and motors
many forms of rheostat have been introduced. One con-
venient form, as designed by the Author for use in the
electrical laboratory at University College, London, consists in
suspending from porcelain insulators placed against the wall
o2
84
ELECTRICAL LABORATORY EQUIPMENT.
of the dynamo room long wires of nickel steel or eureka.
These wires are kept tight when expanded by heat by means
of a spiral bell spring attached to the extremity of the wire.
The wires are electrically connected in parallel as required by
means of a parallelising switch (see Fig. 27). The length of
each wire is adjusted so that the current through it, when the
difference of potential of its extremities is 100 volts, does not
FIG. 27. University College Dynamo Rheostats.
exceed that value which will make it too hot to touch with the
hand. The total resistance between the terminals is then
reduced, step by step by adding resistance wires in parallel.
It is much better thus to reduce resistance by equal steps by
adding equal resistances in parallel than to increase it by
adding equal resistances in series. In the former case the
current increases by equal increments per step, and in the
latter it decreases in harmonic ratio per step of resistance.
ELECTRICAL LABORATORY EQUIPMENT.
85
In cases where large currents have to be regulated or
varied continuously liquid resistances may be sometimes
advantageously employed. One useful form is Lyon's
Liquid Eesistance (see Fig. 28). This consists of two zinc
FIG. 28. Lyon Liquid Rheostat.
cones fitting each other, which are immersed in a strong
solution of zinc sulphate, and by means of a screw or lever
the distance of these metal cones can be varied from perfect
metallic contact to a position in which a considerable length
86 ELECTRICAL LABORATORY EQUIPMENT.
of electrolyte is interposed between them. The resistance
can thus be gradually varied. If continuous currents are
employed with it, the direction of the current through the
resistance should be changed every few minutes by a current
reverser. and the current density or amperes per square foot
of zinc cone surface should not exceed the limit at which
zinc begins to be deposited in irregular crystals or trees on
the cathode cone.
The subject of power absorbing resistances will be con-
sidered in the chapters dealing with dynamo and transformer
testing.*
8. The Practical Standard of Electromotive Force.
The practical unit of electromotive force is equal to the
terminal difference of potential produced when a current of
one ampere flows through a resistance of one ohm. The
most satisfactory method of recovering a known difference of
potential say, of one volt is to pass a current of one
ampere, measured by a standard ampere balance, through a
suitable resistance of one ohm. There are, however, many
cases in which this is not a convenient method of recovering
a known difference of potential. Hence attention has been
directed to the construction of a standard of electromotive
force which shall produce directly a known difference of
potential between two terminals. Experience shows that,
although the ultimate standard of electromotive force must
be recovered by the passage of a known current through a
* The following references to papers or information on liquid resistances
and power absorbing resistances may be found useful : " Lyon's Liquid
Resistances," The Electrician, Vol. XXVI., p. 759. " Water Rheostats," G. T.
Hanchett, The Electrician, Vol. XXXVII., p. 833. " Water Rheostats," The
Electrician, Vol. XL., p. 696, contains useful facts and figures ; see also
Science Abstracts, Vol. I., p. 356. " Water Resistance for Alternator Testing,"
The Electrician, Vol. XLI., p. 279. "Motor Starting Resistances," Pochin,
The Electrician, Vol. XXXIX., p. 38. "Commercial Forms of Electricial
Resistances," L. B. Atkinson, The Electrician, Vol. XL., p. 863. " Current
p.
Commercial Resistances," D. K. Morris, The Electrician, Vol. XXXIII., pp.
605, 627, 667.
ELECTRICAL LABORATORY EQUIPMENT. 87
known resistance, yet the adoption of a voltaic or electro-
chemical standard of electromotive force, by the use of a
standard voltaic cell, has considerable practical convenience.
Great attention, therefore, has been given of late years to
the minute details of the construction of certain voltaic cell
standards of electromotive force. Experience has shown
that a very convenient standard of electromotive force is
obtained by the use of some modification of the mercury-zinc
cell, which was first proposed by Mr. Latimer Clark as a
standard of electromotive force, and made in 1873.* The
elements of this cell are mercury, mercurous sulphate, zinc
sulphate and zinc. Since the above date other forms of
voltaic cells have been proposed as standards of electromotive
force. The various species and modifications of standard
mercury cell in use at present are as follows :
(".) THE ORIGINAL FORM OF CLARK CELL.
(ii.) THE MUIRHKAD FORM OF CLARK CELL.
(in.} THE RAYLEIGH H FORM OF CLARK CELL.
(iv.) THE CARHART FORM OF CLARK CELL.
(v.) THE BOARD OF TRADE FORM OF CLARK CELL.
(vi.) THE REICHSANSTALT FORM OF CLARK CELL.
(vii.) THE CALLENDAR FORM OF CLARK CELL.
(viii.) THE WESTON CADMIUM CELL.
(ix.) THE REICHSANSTALT H FORM OF CADMIUM CELL.
(x.) THE HELMHOLTZ CALOMEL CELL.
These cells are not employed as current generators, but
merely as standards of electromotive force by using them as
subsequently to be described. A few words of description
may be given of each of these cells.
(i.) The Original Clark Cell. The original form of Clark
cell, suggested by Mr. Latimer Clark in 1873 as a standard
of electromotive force, consisted of a glass cup or beaker in
the bottom of which is placed some pure mercury. Into this
mercury a platinum wire dips, which is sheathed throughout
its length with glass or gutta perch a except at the extreme
* See Telegraphic Journal, Vol. I., p 9.
88
ELECTRICAL LABORATORY EQUIPMENT.
end where it dips into the mercury. Above the mercury
rests a paste formed of mercurous sulphate mixed with zinc
sulphate. Above the paste there is a saturated solution of
zinc sulphate, and in this latter is dipped a rod of pure zinc.
The zinc has a platinum wire soldered to it, and the two
wires connecting the zinc and mercury are brought up to
insulated terminals (see Fig. 29).
(ii.) The Muirhead- Clark Cell. In the above original
form the Clark cell is not very portable and cannot be
turned upside down without producing a change in its
Marine Glue
Glass Tube
Platinum Wire
Glass Cell
Zinc Sulphate Paste
Mercury
FIG. 29. Original form of Clark Cell.
electromotive force by bringing the mercury in contact
with the zinc and thus contaminating the mercury. An
improved form of cell was therefore devised by Dr. Muirhead,
in which this difficulty is overcome.
In the Muirhead cell there is no large free mass of
fluid mercury. The end of the platinum wire is coiled into
a spiral, and this platinum is well amalgamated, and when
dipped in mercury it retains a globule of mercury within
the spiral by capillary attraction, and this is so adherent
that it is not easily detached. The spiral of amalgamated
ELECTRICAL LABORATORY EQUIPMENT.
89
platinum is buried in the mercurous paste (see Fig. 29) ;
above this is placed the saturated solution of zinc sulphate,
and in this latter a zinc rod.
A Muirhead cell, if properly sealed, can be sent by parcels
post, or otherwise carried about without injury to its
electromotive force.
(Hi.) The Rayleigh H form of Clark Cell. Lord Eayleigh
investigated in 1885 with great care the causes of the
differences in electromotive force between Clark cells set up
Marine Glue
Zinc Sulphate
Mercurous Sulphate
Glass Tube
Platinum Wire
Platinum Spiral
FIG. 30. Muirhead form of Clark Cell.
by various persons using apparently the same quality of
materials and equal care.
He came to the conclusion that the greatest source of
error was due to variations in the density of the zinc
sulphate solution. The electromotive force of the cell
depends upon the concentration of the zinc sulphate solution.
If the solution is not a saturated solution the electro-
motive force of the cell is too high. In some cases the
zinc sulphate solution may be super-saturated, especialty
90 ELECTRICAL LABORATORY EQUIPMENT.
when the cells have been heated during or after charging.
Lord Kayleigh summarises the sources of variation of
E.M.F. in Clark cells as follows : The E.M.F. may be
too high (1) because the mercurous paste is acid ; (2) because
the paste is not saturated with zinc sulphate. The first
fault tends to cure itself, and is rarely found after cells are a
month old. The second is the usual cause of variation. If
the E.M.F. is too low it may be (1) because the cell has
become dry, in which case the drop in voltage will be pro-
gressive; (2) the solution is super-saturated with zinc
sulphate ; or (3) the mercury is impure. It follows that to
secure the correct or normal E.M.F. the mercury used should
FIG. 31. Lord Rayleigh's H form of Clark Cell.
B Amalgam of Zinc. C Pure Mercury. D Mercurous Sulphate. E Saturated Solution
of Zinc Sulphate. F Corks.
be free from other metals. It must, therefore, be distilled at
a low temperature in vacuo. Next, the zinc sulphate solu-
tion must be at all temperatures saturated, and hence solid
crystals of zinc sulphate must be present in the cell.
Thirdly, the cell must be hermetically sealed with marine
glue to prevent evaporation ; and, fourthly, the cell must not
be heated during manufacture. The zinc sulphate must be
rendered neutral by adding a little carbonate of zinc.
Lord Eayleigh devised a convenient form of cell called the
H form of cell. This cell consists of a pair of test-tube-
shaped glass vessels connected by a horizontal tube or channel
(see Fig. 31). In one side tube is placed some pure mercury,
ELECTRICAL LABORATORY EQUIPMENT. 91
and in the other an amalgam of mercury and zinc. Platinum
wires sealed through the glass make contact with the metals..
Over the pure mercury is put a paste made of mercurous
sulphate and zinc sulphate. The cell is filled up to above
the level of the horizontal tube with a saturated solution of
zinc sulphate, and the open ends are closed with corks sealed
over with marine glue. This H form of cell is very con-
venient for many experimental purposes.
s^Rgatisi '
Zinc Sulphate
Asbestos Wad llulummmummim ^
Mercurous Sulphate
Platinum Wire -A^afiBfiiF
Mercury
FIG. 32. Carhart Clark Cell.
Lord Eayleigh found the electromotive force of the K
form of cell to be 1-434 volts at 15C.* and the temperature
coefficient to be O08 per cent, per degree, or the E.M.F. in
volts at tfC.=E|, to be given by the formula
E,=1434 {1-0-00077 (<-15)}.
A more exact expression for the temperature correction
is obtained if the simple coefficient '0007 7 is replaced by
the quantity 0'00078 + 0'000017 ($15). If the electro-
chemical equivalent of silver is taken as 0'001119 instead of
0-001118, then the E.M.F. of the Clark cell becomes 14327
volts at 15C. and not 14342.
* The electromotive force of the H form of Clark cell, as determined by
K. Kahle and W. Wien, ie 1-4488 volts at 0C., or 1*4322 volts at 15C. The
Board of Trade value is 1-434 volts at 15C.
92 ELECTRICAL LABORATORY EQUIPMENT.
(iv.) The Carhart-Clark Cell. In this cell the zinc is
made in the form of a plunger or piston (see Fig. 32), and
the shank or piston rod is covered with glass. In between
the bottom of the zinc and the mercurous paste is interposed
a wad of asbestos and the cell is sealed.
(>.) The Board of Trade form of Clark Cell. The British
Board of Trade Electrical Department have issued a specifi-
cation for the preparation of standard Clark cells, which is a
little elaborate and enters into great detail as to their mode
of manufacture. The following is the Board of Trade specifi-
cation for the preparation of a Clark cell :
ON THE PREPARATION OF THE CLARK CELL.
Definition of the Cell.
The cell consists of zinc or an amalgam of zinc with mercury and of
mercury in a neutral saturated solution of zinc sulphate and mercurous
sulphate in water, prepared with mercurous sulphate in excess.
Preparation of the Materials.
1. The Mercury. To secure purity it should be first treated with acid in
the usual manner, and subsequently distilled in vacuo.
2. The Zinc. Take a portion of a rod of pure redistilled zinc, solder to one
end a piece of copper wire, clean the whole with glass paper or a steel
burnisher, carefully removing any loose pieces of the zinc. Just before
making up the cell dip the zinc into dilute sulphuric acid, wash with distilled
water, and dry with a clean cloth or filter paper.
3. The Mercurous Sulphate. Take mercurous sulphate, purchased as pure,
mix with it a small quantity of pure mercury, and wash the whole thoroughly
with cold distilled water by agitation in a bottle ; drain off the water, and
repeat the process at least twice. After the last washing drain off as much of
the water as possible.
4. The Zinc Sulphate Solution. Prepare a neutral saturated solution of
pure (" pure re-crystallised ") zinc sulphate by mixing in a flask distilled water
with nearly twice its weight of crystals of pure zinc sulphate, and adding
zinc oxide in the proportion of about 2 per cent, by weight of the zinc
sulphate crystals to neutralise any free acid. The crystals should be dissolved
with the aid of gentle heat, but the temperature to which the solution is
raised should not exceed 30C. Mercurous sulphate treated as described in 3
should be added in the proportion of about 12 per cent, by weight of the zinc
sulphate crystals to neutralise any free zinc oxide remaining, and the solution
filtered, while still warm, into a stock bottle. Crystals should form as it
cools.
5. The Mercurous Sulphate and Zinc Sulphate Paste. Mix the washed
mercurous sulphate with the zinc sulphate solution, adding sufficient crystals
ELECTRICAL LABORATORY EQUIPMENT.
93
of zinc sulphate from the stock bottle to insure saturation, and a small
quantity of pure mercury. Shake these up well together to form a paste of
the consistence of cream. Heat the paste, but not above a temperature of
30C. Keep the paste for an hour at this temperature, agitating it from time
to time, then allow it to cool ; continue to shake it occasionally while it is
cooling. Crystals of zinc sulphate should then be distinctly visible, and
should be distributed throughout the mass ; if this is not the case add more
crystals from the stock bottle, and repeat the whole process.
This method insures the formation of a saturated solution of zinc and
mercurous sulphates in water.
To set up the Cell.
The cell may conveniently be set up in a small test-tube of about 2cm
diameter and 4cm. or 5cm. deep (sec Fig. 33). Place the mercury in the bottom
Mercury
FIG. 33. Board of Trade form of Clark Cell.
of this tube, filling it to a depth of, say, O'Scm. Cut a cork about 0'5cm. thick
to fit the tube ; at one side of the cork bore a hole through which the zinc rod
can pass tightly ; at the other side bore another hole for the glass tube which
covers the platinum wire ; at the edge of the cork cut a nick through which
the air can pass when the cork is pushed into the tube. Wash the cork
thoroughly with warm water, and leave it to soak in water for some hour&
before use. Pass the zinc rod about 1cm. through the cork.
Contact is made with the mercury by means of a platinum wire about
No. 22 gauge. This is protected from contact with the other materials of the
cell by being sealed into a glass tube. The ends of the wire project from the
ends of the tube ; one end forms the terminal, the other end and a portion of
the glass tube dip into the mercury.
.94 ELECTRICAL LABORATORY EQUIPMENT.
Clean the glass tube and platinum wire carefully, then heat the exposed end
of the platinum red hot and insert it in the mercury in the test-tube, taking
care that the whole of the exposed platinum is covered.
Shake up the paste and introduce it without contact with the upper part
of the walls of the test-tube, filling the tube above the mercury to a depth of
^rather more than 1cm.
Then insert the cork and zinc rod, passing the glass tube through the hole
.prepared for it. Push the cork gently down until its lower surface is nearly
in contact with the liquid. The air will thus be nearly all expelled, and the
-cell should be left in this condition for at least 24 hours before sealing, which
should be done as follows :
Melt some marine glue until it is fluid enough to pour by its own weight,
and pour it into the test-tube above the cork, using sufficient to cover com-
pletely the zinc and soldering. The glass tube containing the platinum wire
should project some way above the top of the marine glue.
The cell may be sealed in a more permanent manner by coating the marine
.glue, when it is set, with a solution of sodium silicate, and leaving it to
harden.
The cell thus set up may be mounted in any desirable manner. It is con-
venient to arrange the mounting so that the cell may be immersed in a water
bath up to the level of, say, the upper surface of the cork. Its temperature
can then be determined more accurately than is possible when the cell is
in air.
In using the cell sudden variations of temperature should as far as possible
be avoided.
The form of the vessel containing the cell may be varied. In the H form
the zinc is replaced by an amalgam of 10 parts by weight of zinc to 90 of
onercury. The other materials should be prepared as already described.
Contact is made with the amalgam in one leg of the cell, and with the
mercury in the other, by means of platinum wires sealed through the glass.
The cell resulting from operations carried out in accord-
ance with the above specification has been criticised
considerably, and it has been stated that in consequence of
diffusion-lag there is always some delay in the change of
saturation of the zinc sulphate solution when the temperature
changes. Hence it is said that it is not possible to obtain
the true electromotive force of the cell to a greater accuracy
than O'l per cent, by applying the ordinary temperature
correction.*
(vi.) The Reichsanstalt form of Clark Cell. A specification
for the preparation of a modification of the H form of Clark
* See Prof. Ayrton and Mr. Cooper, Proc. Roy. Soc., Lond., Dec., 1895. '
Also Mr. Cooper " On the Permanency of the Board of Trade Clark Cell,"
The Electrician, Vol. XL., p. 748.
ELECTRICAL LABORATORY EQUIPMENT.
95
cell has been issued in Germany on the basis of the experience
gained at the Physikalisch-Technische Reichsanstalt in Berlin.
The following are the details of these instructions as given by
Dr. K. Kahle* :
Definition and Properties of the Cell.
The cell contains mercury as the positive electrode, amalgamated zinc as the
negative electrode, and as electrolyte a concentrated solution o zinc sulphate
and mercurous sulphate. Its E.M.F. is 1-4328 Internationa 1 volts at 15C.
and between 10C. and 25C. decreases by O'OOllS volt with i n increase of
temperature of Ideg.
Construction of the Cell.
The vessel used for the cell consists, as shown in Fig. 34, of two vertical
branches closed at the bottom, and joined at the top into a neck closed by a
FIG. 34. Eeichsanstalt form of Clark Cell.
ground-glass stopper. The diameter of the branches should be at least 2cm.
and their length 3cm. The neck of the vessel should be 1'Scm. wide, and at
least 2cm. long. Platinum wires about 0'4mm. thick are fused into the
bottom of both branches.
The vessel is filled in a manner depending upon whether the cell is to be
used at the place of construction or is to be transported.
* See The Electrician, Vol. XXXI., p. 265-6.
96 ELECTRICAL LABORATORY EQUIPMENT.
In the former case pure mercury is poured into one branch, and into the other
amalgam of about 90 parts mercury and 10 parts zinc, which is fluid when
hot and solidifies on cooling. The platinum wires must be completely covered
by the mercury and the amalgam respectively. Upon the mercury is poured
a layer of paste 1cm. deep, made by rubbing together mercurous sulphate,
mercury, zinc sulphate crystals, and concentrated solution of zinc sulphate.
This paste and the amalgam are then both covered with a layer 1cm. deep of
zinc sulphate crystals, and finally the whole vessel is filled with concentrated
zinc sulphate solution until the stopper on being introduced just touches the
surface. Care should, however, be taken that the vessel contains a small air-
bubble, since that prevents it bursting in the case of a great rise of tempera-
ture. At the final closing of the vessel the glass stopper is brushed over at its
upper edge with shellac dissolved in alcohol and then firmly inserted.
If the cell is to be portable, a circular electrolytically-amalgamated piece
of platinum foil, about 1cm. long and O'lmm. thick, takes the place of the
mercury, and is firmly attached to the platinum wire introduced through the
bottom. Zinc amalgam forms, as before, the negative electrode, and is
covered with a layer of zinc sulphate crystals 1cm. deep. The rest of the
vessel is filled up to the stopper with mercurous sulphate paste. The final
closing is affected as already described.
Preparation of the Materials to be Used in the Cell.
Mercury. All mercury to be used in the cell should be purified by the
ordinary processes, and distilled in vacuo.
Zinc. The commercial pure zinc may be employed. To prepare te
amalgam, add one part zinc to nine parts mercury, and keep both in a
porcelain dish at lOOdeg., stirring gently until the zinc is completely dissolved
in the mercury.
Sulphate. Before use, test the commercial zinc sulphate for acid with litmus
and for iron with potassium sulpho-cyanide. If it is sufficiently pure it may
be at once re-crystallised in the way detailed below. If it contains appreciable
traces of free acid, equal parts of the zinc sulphate and distilled water are
boiled with zinc filings in a suitably formed porcelain dish until no further gas-
is given off at the zinc, and the solution shows after cooling a white, or, in the
presence of ferric hydrate, a brownish precipitate of zinc hydrate. If the
solution is free from iron it may be filtered off after standing for two days.
Otherwise it is again heated to 60C. or 80C.,and electrolysed for six hours by a
current not exceeding 0'2 amperes introduced by two pieces of platinum foil
of about 50 sq. cm. surface suspended in the liquid. The liquid having cooled
over night, litmus is again employed to test whether any acid has been formed
during electrolysis. In that case the boiling with zinc filings must be repeated,
and the solution again electrolysed by weak currents. During this whole
treatment care has to be taken that the concentration of the solution remains
approximately constant. It is, therefore, well to cover the vessel containing
the solution with a glass plate, so that but little water vapour can escape. As
soon as the solution is sufficiently free from acid and iron it is filtered off. To
each litre of the filtrate about 50gr. of mercurous sulphate, free from acid, are
ELECTRICAL LABORATORY EQUIPMENT. 97
added and well stirred. The mercury salt will in general assume a yellow
colour after long standing. If the solution has stood for a day, and a portion
of it, on being shaken up with more mercurous sulphate, does not turn per-
ceptibly yellow, the solution may be filtered off and concentrated in a flat
porcelain dish over a water bath. Here we must take care that the crystals
do not form at too high a temperature, as otherwise they easily lose a portion
of their water of crystallisation. To secure this the flame under the water-
bath is extinguished, and the dish left in position covered with a glass plate.
If after further cooling no crystals are separated, further concentration is
necessary. If the heating was too protracted, and the crystals were formed
under unfavourable conditions, a little water must be added and the whole
warmed until everything is redissolved. The concentrated solution is-
poured off, and either further evaporated or kept for future use. The last
traces of the solution are removed from the crystals by letting the dish stand
for some time in a slanting position. It is not advisable to sharply dry the
crystals, as they thereby lose water of crystallisation. For the same reason
they must be kept in a closed vessel.
Sulphate of Mercury. The mercurous sulphate used must not be coloured
yellow by a basic salt. If that should be the case, stir up one part of the salt
with two parts distilled water, and add, constantly stirring, so much of a
solution of one part mercuric sulphate to 1,000 parts of water as is necessary
to make the colour disappear. Then pour off the liquid and wash the paste
several times with distilled water, but without thereby causing another yellow
colouration. If the sulphate is white to begin with, and only shows a faint
yellow colouration after considerable time on shaking up with distilled water ; .
it may be used at once. If this colouration is not shown on shaking up with
water, the salt must be washed out several times with distilled water until the
first traces of yellow colouration appear. If the salt had to be wetted for
cleaning, the water should be driven off as much as possible by mechanical
means. If dried by heat the yellow colouration will reappear. In order not
to have to keep the wet salt only so much salt should be treated by the above
process as is necessary for the purpose in hand.
To prepare the paste, two parts of the sulphate should be added to one part
of mercury. If the sulphate was dry, it should be stirred up with a paste
made of zinc sulphate crystals and concentrated zinc sulphate solution until
the whole forms a stiff mass everywhere permeated by zinc sulphate crystals
and small globules of mercury. But if the sulphate was wet, only zinc
sulphate crystals should be added, taking care, however, that they are in
excess, and are not dissolved even after prolonged standing. Here, also, the
mercury must permeate the paste in small globules. It is well to crush the
zinc sulphate crystals a little before using, so that the paste may be more
easily manipulated later on.
Details of Construction.
For the preparation of cells containing mercury as the positive electrode
the following details should be attended to : Before introducing the hot zinc
amalgam place the glass vessel, well cleaned and carefully dried, in a hot
water bath. Then pass a suitable thin-walled glass tube through the neck.
08 ELECTRICAL LABORATORY EQUIPMENT.
of the vessel on to the bottom of the branch \vhich is to contain the amalgam.
The tube ought to be as wide as is consistent with the dimensions of the
vessel. It is intended to protect the rest of the vessel from contamination.
The amalgam is introduced by means of a glass tube about 10cm. long drawn
out into a point, the other end being provided with an indiarubber tube about
3cm. long closed by a short glass rod. The point of the tube is inserted below
the surface of the liquid amalgam heated in a dish, and a portion of the
amalgam is sucked into the tube by compressing and releasing the india-
rubber. The point is then quickly freed from external impurities derived from
the surface of the amalgam, introduced into the cell through the wide tube,
and emptied by pressure on the indiarubber. The point ought to be so fine
that the amalgam does not issue except on pressing the rubber. The process
is continued until the branch contains the required quantity of amalgam.
The vessel is then taken out of the water-bath. After cooling the amalgam
should adhere firmly to the bottom of the vessel and exhibit a bright metallic
surface.
To introduce the mercury and the paste a suitable funnel with a long tube
is used. The paste should not touch the upper walls of the vessel, but may
be pushed in with a glass rod if too stiff to flow.
Before pouring in the zinc sulphate solution the paste and the zinc amalgam
should be covered with zinc sulphate crystals, as these prevent a creeping up
of the paste after wetting with the solution. In filling, the zinc sulphate
crystals and the paste should not contain large air-bubbles. These may be
removed by knocking.
If the cell is to contain amalgamated platinum foil as the positive electrode,
the amalgamation may be performed as follows : The cell vessel is first filled
with aqua regia and heated in a sand-bath until a rapid development of gas
takes place at the platinum. Then rinse with water, pour mercury into the
branch intended to contain the zinc amalgam, and fill the entire vessel with a
concentrated solution of mercurous nitrate containing a little nitric acid.
Then connect the mercury with the positive and the platinum foil with the
negative pole of a battery, and send a current of about 0'5 ampere through
the solution until the platinum foil is covered over with firmly-attached
mercury globules. The whole process lasts about five minutes. Finally the
vessel is thoroughly rinsed with distilled water until not a trace of the
nitrate remains.
The zinc amalgam is introduced with the precautions mentioned. After
cooling, it is covered with zinc sulphate crystals, to which concentrated zinc
sulphate is added after filling until the whole forms a paste. The vessel should
stand for two days, so that the crystals are closed up and form a layer
impervious to the paste. Then the whole vessel is filled up with the latter.
The following points should be specially borne in mind in the construction :
1. The mercury intended to serve as positive electrode must be kept rigidly
free from contamination by more positive metals. Special care should be
taken that no portion of the zinc amalgam comes into contact with the
mercury.
2. The cell should always be so arranged that at all temperatures the whole
electrically active surface of the electrodes is in contact with zinc sulphate
ELECTRICAL LABORATORY EQUIPMENT. 99
solution concentrated for the temperature in question. Hence during the
process of filling, crystals should be added in such quantity as to ensure their
presence in excess even at the highest temperatures which the cell may attain.
3. The zinc sulphate used must not contain free acid. For one thing, the
E.M.F. of the cell is affected by it, and, on the other hand, the circuit of the
cell may be broken by hydrogen developed at the zinc. For the gas produced
cannot escape through the zinc sulphate crystals, but collects underneath
them, and finally pushes them up, thereby interrupting the connection
between the zinc and the zinc sulphate.
For easy and safe handling the cell is included in a metal case, which may
be closed and placed in a petroleum bath. Its lid is provided with two bind-
ing screws, each of which is joined to one of the electrodes ; the bottom is
perforated, so that the cell is surrounded by the petroleum. To determine
the temperature of the cell, a thermometer must be enclosed in the case whose
scale can be read from outside. The best plan is to fuse a thermometer into
the glass stopper, as shown in the figure, so that the bulb penetrates as far as
possible into the cell and the scale projects through the lid.
The great objection which has been raised to the form of
Clark cell constructed in accordance with the Board of Trade
specification, in which the zinc rod is surrounded throughout
the whole or part of its length by clear solution of zinc
sulphate, is that there is a source of possible error or
uncertainty in its use due to the fact that changes of tem-
perature and consequent changes in the state of saturation of
the zinc sulphate are not propagated immediately through
the cell. If the temperature of the cell is raised, more zinc
sulphate must be dissolved to keep the solution saturated at
that temperature, and this saturated solution is not diffused
immediately to all parts of the tube. The existence of this
diffusion -lag has been proved, by the experiments of Lord
Rayleigh, Prof. Carhart, Prof. Ayrton, Mr. Cooper and others,
undoubtedly to be a source of error.
The remedy proposed by Lord Eayleigh for this diffusion
lag was the H form of cell.
The remedy suggested by Prof. Carhart was to use a cell
containing a solution saturated at 0C.
(mi.) The Callendar- Clark Cell. Prof. Callendar and Mr.
Barnes have proposed a remedy for diffusion lag as follows :
The cell is made up in a rather thin and long test-tube, and
has two glass-covered platinum wires or electrodes ; the ends
100
ELECTRICAL LABORATORY EQUIPMENT.
of the platinum wires protruding from the sealed ends of the
glass tubes (see Fig. 35). In the bottom of the tube is placed
a small button of a 10 per cent, amalgam of zinc and mercury,
and in this is immersed one electrode. Over this a layer of
moist crystals of zinc sulphate ; on the top of the zinc sulphate
a layer of mercurous sulphate paste, in which the end of the
second amalgamated platinum wire is buried. The cell is
sealed with marine glue in the usual manner. The cell is
thus an inverted narrow pattern of the Board of Trade cell.
Mercury
External
Cups
FIG 35. Callendar form of Clark Cell.
The inventors state that diffusion lag is absent, and that
changes of E.M.F. follow immediately all changes of
temperature between 0C. and 40 C.
The large temperature variation of the Clark cell led
inventors to search for a modification with a less temperature
coefficient. This was found, in 1891, by Mr. Weston in the
arrangement known as the cadmium cell. In this cell the
elements are mercury, mercurous sulphate, cadmium sulphate
and cadmium. The combination has a temperature variation
ELECTRICAL LABORATORY EQUIPMENT.
101
very much less than that of the corresponding zinc combina-
tion. The cadmium sulphate being much more equally
soluble at all ordinary temperatures than the zinc sulphate,
diffusion-lag does not occur. The only difficulty is that the
E.M.F. varies with the proportions of the metals in the
cadmium-mercury amalgam used. Hence it is best to
employ the H form of cell, in which the cadmium is kept
out of contact with the mercurous sulphate. Mr. Weston
makes the cell as follows :
(viii.) The Weston Cadmium Cell. The considerable varia-
tion in the solubility of zinc sulphate in water at different
FIG. 36. Weston Cadmium Standard Cell.
temperatures led Mr. E. Weston, in 1891, to suggest the use
of cadmium sulphate instead of zinc sulphate (U.S. Patent
No. 22,482 of 1891). The cadmium salt has nearly the same
solubility at all temperatures. The cadmium cell is made up
in the Kayleigh H-form, as shown in Fig. 36. In one side-
vessel is placed a little pure mercury, entirely covered with
a layer of mercurous sulphate. In the bottom of the other
102
ELECTEICAL LABORATORY EQUIPMENT.
limb is placed an amalgam of cadmium, and the tube is filled
up with a saturated solution of cadmium sulphate. The cell
is then sealed. Platinum wires sealed through the glass at
the bottom of the side tubes enable connection to be made
between the mercury and the cadmium amalgam and the cell
terminals.
Mr. Weston states in his patent specification that the
electromotive force of this cell is 1*019 volts, and its tem-
perature coefficient is O'Ol per cent, per degree centigrade.
Cadmium Amalgam Mercury
FIG. 37. Keichsanstalt form of Cadmium Standard Cell.
A valuable feature, therefore, of the cadmium cell is its
small temperature coefficient; this may be made by using
proper proportions of cadmium and mercury to be as low as
0*004 per cent, per degree centigrade instead of 08 as in
the case of the Clark cell.
Special attention has been paid to the details of the
construction of this cell at the Physikalisch-Technische
Keichsanstalt in Berlin, and the following are the instruc-
tions for its manufacture as laid down by Prof. W. Jaeger:
(ix.) The Beiclisanstalt Cadmium Cell. This cell is made
up in the Kayleigh H-form (see Fig. 37). The two legs of
ELECTRICAL LABORATORY EQUIPMENT. 103
the side vessels are provided with platinum wires sealed
through the glass at the lower ends. The negative element
consists of a cadmium amalgam one part of cadmium to six
parts of mercury. Over this is placed a layer of pulverised
crystals of cadmium sulphate to ensure saturation. The
positive element is formed of pure mercury, over which is
placed a paste formed by the trituration of mercurous
sulphate with metallic mercury and a concentrated solution
of cadmium sulphate in which are crystals of the salt. This
paste must not be too thin, but must form a stiff pulp. The
remainder of the cell is filled up with a saturated solution of
cadmium sulphate. The tubes are then closed by a layer of
melted paraffin poured on, then a thin washer of cork, and,
lastly, the cell is closed with melted sealing wax.
A more portable cell may be made like the Muirhead-
Clark cell with an amalgamated platinum spiral instead of
liquid mercury. The electromotive force E 4 of the cadmium
cell in the H-form at C. is given by the formula,
E,=E 20 [3-8 X 10~ 5 (t- 20) - 0-065 X 10" 5 (t - 20) 2 ],
where E 20 =the electromotive force at 20C. in volts and is
1*019 volts. The above applies to cells in which the
amalgam contains from 7 to 14 per cent, of cadmium.
In making the cell the following precautions must be
employed :
Amalgamation of the Platinum Wire. After the platinum wires are sealed
through the glass place a little aqua regia in the cell legs until bubbles of gas
arise from the platinum. Then throw this out and replace it by a solution of
mercurous nitrate, and, using another piece of platinum as an anode, deposit
mercury upon the platinum electrolytically. The platinum may also be
amalgamated by making it white hot in a Bunsen flame, and plunging it
whilst hot in the mercury.
Preparation of the Cadmium Amalgam. Dissolve one part of pure cadmium
in six parts of pure mercury, and whilst warm and fluid place it in one limb
of the H cell and warm it to ensure perfect contact with the platinum.
Cadmium Sulphate Solution. Digest a saturated solution of cadmium
sulphate with cadmium hydroxide to remove free acid, but be careful not to
raise the temperature above 70C. Then digest it still further with mercurous
sulphate until no more precipitation occurs. The cadmium sulphate solution,
must be saturated and have free crystals of the salt in it.
104 ELECTRICAL LABORATORY EQUIPMENT.
Mercurous Sulphate. This must be free from acid, and made neutral by
triturating with finely divided mercury. In making the paste so much cadmium
sulphate must be added that a saturated solution of that salt is formed and is
present in the cell.
The cell has the electromotive force above stated if the amalgam of cadmium
has from 6 to 13 parts of mercury to 1 of cadmium.
The German investigators seem to have a great preference for the H form
of cell, but it is clear that a narrow tubular cell of the Board of Trade form
not only more quickly comes to the temperature of the water bath hi which
it is placed, but is more certain to be wholly at one temperature.
(#.) The Helmholtz Calomel Cell. It was proposed by
Yon Helmholtz to employ a cell, the elements of which are
mercury, mercurous chloride or calomel, zinc chloride and
.zinc, as a standard of electromotive force (see " Sitzber. der
Akad. der Wiss," Berlin, 1882, p. 26).
This cell can be adjusted to have an electromotive force of
exactly one volt by the use of a solution of zinc chloride
of a certain density, viz., T380 at 15C. Its temperature
coefficient of electromotive force is small, being only 1 part
in 10,000 per degree centigrade, whereas that of the Clark
sulphate cell is 8 parts in 10,000 per degree centigrade. Its
electromotive force varies, however, with the state of satura-
tion of the solution of zinc chloride, and as evaporation
from the cell tends to increase the density of the zinc chloride
solution it is not so definite and permanent as a standard as
the zinc sulphate or cadmium sulphate form of cell, unless
hermetically and permanently sealed. According to Mr. W.
Hibbert (The Electrician, Vol. XXXVII, p. 320), the cell
rapidly recovers its normal electromotive force if short-
circuited.
The Standard Daniell Cell. In addition to the above-
described mercury-zinc or mercury-cadmium standard cells,
the Daniell cell or copper, copper-sulphate, zinc sulphate,
.zinc cell has been used as a standard of electromotive force.
Although not a rival in uniformity of electromotive force to
the Clark or cadmium cell, it has the advantage that its
temperature coefficient within the range of ordinary labora-
tory temperatures is practically zero. Its electromotive
ELECTRICAL LABORATORY EQUIPMENT.
105
force is, however, a function of the density of the solutions
used.
The Author described, in 1885,* a convenient form of stan-
dard Daniell cell as follows : A glass u-tube is prepared
FIG. 38. Fleming Standard Daniell Cell.
having side bulb reservoirs and taps as shown in Tig. 38.
The whole apparatus can be made out of glass by a skilful
* See Phil. Mag., August, 1885.
106 ELECTRICAL LABORATORY EQUIPMENT.
glass-blower. It is then fixed up against a board. In this
U-tube a Daniell cell is formed by inserting rods of amalga-
mated zinc and of freshly electrotyped copper in the two
limbs, which are respectively filled up with solutions of zinc
sulphate and copper sulphate.
The solutions required are made by dissolving the purest re-crystallised
sulphate of copper and sulphate of zinc in distilled water.
For the zinc solution, take 55'5 parts by weight of crystals of zinc sulphate
(ZnS0 4 , 7 OH 2 ), and dissolve in 44'5 parts by weight of distilled water ; and
the resulting solution should have a specific gravity of 1*200 at about 20C
For the sulphate of copper solution, take 16*5 parts by weight of pure crystals
of copper sulphate (CuS0 4 , 5 OH 2 ), and dissolve in 83*5 parts by weight of
water ; and the resulting solution should have a specific gravity of I'lOO at
20C. If not exact, adjust to these densities precisely.
These solutions should be kept in stock bottles and the reservoirs of the cell
filled up when required.
The operation of filling is as follows : Open the tap A
and fill the whole U-tube with the denser zinc sulphate
solution ; then insert the zinc rod, and fit it tightly by the
rubber cork P. On opening the tap C the level of the liquid
will begin to fall in the right hand limb, but be retained in
the closed one. As the level commences to sink in the
right hand limb, by opening the tap B copper sulphate
solution can be allowed to flow in gently to replace it ; and
this operation can be so conducted that the level of demar-
cation of the two liquids remains quite sharp, and gradually
sinks to the level of the tap C. When this is the case, all
taps are closed and the copper rod inserted in the right hand
limb.
It is impossible to stop diffusion from gradually mixing
the liquids at the surface of contact; but whenever the
surface of contact ceases to be sharply defined, the mixed
liquid at the level of the tap C can be drawn off, and fresh
solutions supplied from the reservoirs above.
A freshly electrotyped copper rod is always to be used.
The copper surface must have a clean salmon colour free
from brown spots of oxide.
* See Phil. Mag., August, 1885.
ELECTRICAL LABORATORY EQUIPMENT. 107
The cell freshly prepared has then an electromotive force
on open circuit of TO 72 volts.
The use of this Daniell cell enables an approximate
recovery to be made of the unit of electromotive force, but it
is neither so convenient nor permanent as the improved forms
of Clark or cadmium cell.
Every electrical laboratory or testing room should be
provided with a number of specimens of the above-described
standard cells, either Muirhead-Clark cells, Weston cadmium
cells, or the Eeichsanstalt pattern of cadmium cells will be
found to be most trustworthy. These should be numbered
or lettered and careful comparison made at observed tem-
peratures of their relative electromotive forces from time to
time, and the values entered under date in the laboratory
book. Occasionally comparisons of these with the other volt
standards should be made by methods to be described, and
with the results of electromotive force determinations by the
ampere balance as presently to be discussed. With care and
vigilance the laboratory need never be uncertain in its
recovery of the standard of electromotive force by more than
one part, or at most five parts, in 10,000.
The standard cells should have thermometers placed in
the brass cases containing them or, better still, be immersed
in water when using them, and in taking careful observa-
tions sufficient time should always be allowed to elapse
before taking the voltage readings to enable the cell to take
the same temperature as that indicated by the thermometer,
assuming them to be under circumstances in which the final
temperature of both cell and thermometer will ultimately be
the same.
9. The Literature of the Mercury Standard Cell.
As it is impossible to transcribe in these pages the detailed
results of all the very numerous researches which have been
made during the last fifteen years on the standard Clark,
Weston and Helmholtz mercury cells, we shall give here
references to some of the principal investigations, and leave
108 ELECTRICAL LABORATORY EQUIPMENT.
the reader desirous of more information to consult the
original papers :
(a) Investigations on the Absolute Electromotive Force of
Standard Cells.
LATKIER CLARK. " On a Voltaic Standard of Electromotive
Force." Telegraphic Journal, Vol. I., p. 9 ; or Proc. Roy.
Soc., Lond., 1872.
LORD BAYLEIGH and MRS. SIDGWICK. " On the Absolute Electro-
motive Force of Clark Cells." Phil. Trans. Roy. Soc.,
Lond., 1884, Part II., p. 411.
LORD RAYLEIGH. ' On the Clark Cell as a Standard of Electro-
motive Force." Phil. Trans. Roy. Soc., Lond., 1885, Part
II., p. 781.
R. T. GLAZEBROOK and S. SKINNER. " On the Clark Cell as a
Standard of Electromotive Force." Phil. Trans. Roy. Soc.,
Lond., 1892, Vol. CLXXXIIL, pp. 567-628.
The authors conclude that the E.M.F. is 1/434 volts at 15C., confirming the
value given by Lord Rayleigh.
C. LIMB. " On the Determination of the Electromotive Force of
the Clark Cell in Absolute Measure." Journal cle Physique,
1896 ; also The Electrician, Vol. XXXVII., p. 138.
The E.M.F. of the cell was balanced against an E.M.F. produced by the
rotation of a magnet inside a coil of wire. The value obtained for the E.M.F.
of the cell is 1'4535 volts at 0C.
H. S. CARHART and K. E. GUTHE. Physical Revietv, Nov., 1899,
p. 288 ; also Science Abstracts, March, 1900, No. 646.
The E.M.F. of the Kahle form of H-cell was determined by balancing it
against a fall of potential down a resistance due to known current. Result
found was 1*4333 volts at 15C.
(b) Modifications of the Clark Cell.
H. S. CARHART. " An Improved Standard Clark Cell with Low
Temperature Coefficient." Phil. Mag., 1890 ; The Electri-
cian, Vol. XXIV., p. 271.
The author constructed a cell with low temperature coefficient
E t = E 15 [1 - 0-000387(< - 15) + 0'0000005( - 15) 2 ],
where E* = electromotive force in volts at tC. The above paper was criticised
by Lord Rayleigh (The Electrician, 1890, Vol. XXIV., p. 285) who, suggests
that the low coefficient found by Carhart was due to the zinc sulphate not
being saturated. He gives a diagram of his H form of cell.
ELECTRICAL LABORATORY EQUIPMENT. 100
H. S. CAEHART. " A Portable Clark Cell." Electrical World,.
1895 ; or The Electrician, Vol. XXXV., p. 844.
He describes the cell shown in Fig. 32. He uses a solution of sulphate of
zinc saturated at 0C.
E. WESTON. "The Cadmium Standard Cell." Electrical
Engineer (New York), 1893 ; also The Electrician, Vol. XXX.,.
p. 741.
He describes fully his mercury-cadmium sulphate cell.
H. L. CALLENDAR and H. T. BARNES. " On a Simple Modifica-
tion of the Board of Trade Standard Clark Cell." Proc.
British Assoc., 1897, Toronto ; also The Electrician^
Vol. XXXIX., p. 638 ; also Vol. XL., p. 165.
In this pattern of cell, called the " inverted " cell, the zinc amalgam lies at
the bottom of the test-tube, and an amalgamated platinum \vire forms the
other element.
For correspondence on this form of cell see The Electrician,
Vol. XXXIX. (K. Kahle), p. 869 (H. L. Callendar), p. 869.
W. JAEGER. " The Keichsanstalt Type of Cadmium Standard
Cell." Electrotechnische Zeitschrift, October 21, 1897 ; also
The Electrician, Vol. XL., p. 9.
This is an important paper, and describes in great detail the construction'
of a standard H form of cadmium cell.
W. HIBBERT. " On the Helmholtz or Calomel Cell." The Elec-
trician, Vol. XXXVII., p. 320 ; also ibid., Vol. XXXVIII.,
p. 177 ; also ibid., Vol. XLL, p. 317.
In this cell zinc chloride and mercurous chloride replace the sulphate salts.
of the Clark cell. It can be made to have an E.M.F. of exactly one volt, and
a negligible temperature coefficient.
(c) Specifications for preparing Clark and Western Cells.
" The British Board of Trade Specification for Clark Cells."
The Electrician, Vol. XXVII., p. 99; also Ibid., Vol.
XXXIIL, p. 518.
K. KAHLE. " Instructions for Preparing Clark Standard Cells :
the Reichsanstalt Specification." Zeitschrift fur Instru-
mentenkunde, 1893 ; also The Electrician, Vol. XXXI., p. 265.
\V. JAEGER. " The Reichsanstalt Specification for Preparing
Cadmium Cells." Electrotechnische Zeitschrift, October 21,
1897 ; also The Electrician, Vol. XL., p. 9.
110 ELECTRICAL LABORATORY EQUIPMENT.
(d) On Temperature Variations of Standard Cells.
W. E. AYRTON and W. B. COOPER. " The Variation of E.M.F.
of Clark Cells with Temperature." Proc. Eoy. Soc., Lond.,
1897, Vol. L1X. ; also The Electrician, Vol. XXXVIII.,
p. 303.
An exhaustive examination of the effect of temperature on the Board of
Trade Clark cell. The authors give numerous curves.
W. HIBBERT. "The Temperature Coefficient of the Calomel
Cell." The Electrician, Vol. XXXVI1L, p. 177.
F. S. SPIERS, F. TWYMAN and W. L. WATERS. " Variations in
the Electromotive Force of the H form of Clark Cells with
Temperature." Proc. Phys. Soc. Lond., Vol. XVI., p. 38;
also Phil. Mag., 1898, Vol. XLV., p. 285.
A. DEARLOVE. " Note on the Temperature Coefficient of the
Cadmium Standard Cell." The Electrician, Vol. XXXI.,
p. 645.
A very full and detailed account of experiments on the Weston cell. The
.author advocates a cell of Muirhead type made with cadmium salts and
cadmium.
A. CAMPBELL. " A Self-acting Temperature Compensation for
Standard Cells." Proc. Phys. Soc., Lond., Vol. XVI., p. 34 ;
also The Electrician, Vol. XXXV., p. 601.
W. JAEGER and K. KAHLE. "A Comparison of the Clark and
Weston Cells as regards Temperature Coefficient." See
Wied. Ann., No. 8, 1898; also The Electrician, Vol. XLL,
p. 642.
The authors have examined 68 cells (27 Clark cells and 41 Weston cells)
constructed since 1891. They have been tested at intervals of about a year
and the maximum difference observed between the Clark cells was 0'14
millivolt and between the Weston cells 0*18 millivolt, which last in two years
decreased to 0'08 millivolt. The cadmium cells should only be used between
20C. and 70C. The E.M.F.'s are-
Clark cells (H form)=l-4328 international volts at 15C.
Weston cell =1-0186 volts at 20C.
The ratio of
Clark at 0C. to Weston at 20 3 C. = T42277
Clark at 15C. to Weston at 20C. = 1 '40663.
The temperature correcting factors are
for Clark cell = 1 - 0'00119 (t- 15) - O'OOOOO? (t - 15) 3
for Weston cell = 1 - 0'000038 (* - 20) - 0'00000065 (t - 20) 2 ,
.and these factors, by multiplication with the value of the E.M.F. at 15C. or
20C, respectively, give the value of the E.M.F. of each cell at t
ELECTRICAL LABORATORY EQUIPMENT. Ill
K. KAHLE. " On the Clark Cell." The Electrician, Vol. XXIX.,
p. 516 ; also Proc. Brit. Assoc., 1892, Edinburgh.
This paper contains a valuable table giving the temperature coefficient of
different types of H-form Clark cell. The mean value of the temperature
coefficient (a) of the H form of cell according to the author is given by
a =0-000783 + 0-000017(4 - 15)
and the E.M.F. at t = E.M.F. at 15 X [1 + a(t - 15)].
The above author strongly advocates the use of the H form of cell. He
says he has set up about 60 H-form cells and has found no difficulty, when
using pure materials, in keeping the differences of E.M.F. of the various cells
to less than one ten-thousandth of a volt. He gives the following table
showing the temperature coefficient (a) for various forms of Clark cell :
Form of Cell.
Temperature Coefficient.
H-cell set up in Lord
Rayleigh's manner
H-cell, the paste covering both
electrodes
The Reicheanstalt form of H-cell,
paste covering both electrodes
+ 0-C00812 + 0-000013 (t - 15)
-f 0-000774 + 0-000020 (t - 15)
+ 0-000791 + 0-000017 (t - 15)
The electromotive force of the H form of cell appears to be about 4 parts in
10,000 less than that of the Board of Trade or original form when taken
at 15"C.
(e) Various Investigations.
J. SWINBURNE. " On the Causes of Variation of Clark Cells."
The Electrician, Vol. XXVII., p. 500; also Brit. Assoc.
Eeport, 1891, Cardiff.
S. SKINNER. "The Clark Cell when Producing a Current."
Proc. Phys. Soc., Lond., Vol. XIII., p. 218 ; The Electrician,
Vol. XXXIII., p. 644.
W. E. COOPER. " The Permanency of Board of Trade Clark
Cells." The Electrician, Vol. XL., p. 748 ; or Science
Abstracts, Vol. I., p. 492.
The author has tested a number of Clark cells set up according to the
Board of Trade specification, and finds, after 3 years, the mean differences or
mean errors in E.M.F. amount to 1 part in 700 or even 1 in 500. Time
introduces a progressive variation in E.M.F., the E.M.F. steadily falling.
IV. JAEGER. " On Cadmium Cells." Ann. Phys. Chem., 1898,
65, 1, p. 106 ; or Science Abstracts, Vol. I., p. 493.
112 ELECTRICAL LABORATORY EQUIPMENT.
T. WULF. "The Clark Cell on Closed Circuits." Science
Abstracts, Vol. L, p. 340.
. After repeatedly short-circuiting cells through 50 ohms the E.M.F. was not
permanently affected.
W. C. FISHER, " The Recovery of Clark Cells after Sending a
Current." The Electrician, Vol. XXXVI., p. 647.
The author finds repeated short-circuiting produces no permanent injury
to the cell.
W. JAEGER. " On Change in the Zinc Sulphate in Clark Cells."
Ann. Phys. Chem., 1897, 63, 1, pp. 354-365.
KOHNSTAMM and COHEN. " The Weston Standard Cell." The
Electrician, Vol. XLL, p. 381.
J. HENDERSON. " On Cadmium Standard Cells." Phil. Mag.,
Vol. 48, July, 1899, p. 152.
For various correspondence on the subject of the Clark cell
see The Electrician, Vols. XXXIX. and XL., for 1897 and 1898.
10. Mechanical Standards of Electromotive Force.
Voltmeters. In addition to the standard cells or electro-
chemical standards of electromotive force, an electrical
laboratory must be provided with mechanical standards
for the measurement of potential difference or electromotive
force. These instruments are called voltmeters, and are
each constructed to be suitable for a certain range of
voltage or potential difference applied to their terminals.
These appliances are roughly distinguished into low and
high voltage voltmeters, according as they are designed
to read over ranges of from 500 volts downwards or from
500 volts upwards. Some of these types of instruments
are adapted only for ordinary or not very accurate
measurements. These are called working voltmeters. Others,
for very careful work, are called standard voltmeters. If
the instrument shows by a scale deflection or pointer
indication directly the value in volts of the potential differ-
ence of its terminals it is called a direct-reading voltmeter.
For the British Board of Trade electrical laboratory a
mechanical standard of electromotive force was designed
by Lord Kelvin, which, as a standard of voltage, is considered
ELECTRICAL LABORATORY EQUIPMENT. 113
to be more permanent than an electro-chemical standard
consisting of a battery of standard cells. This mechanical
standard consists of an idiostatic electrostatic voltmeter,
in which the difference of potential between a series of
fixed metallic surfaces and a series of metallic plates
suspended by a torsion wire, is made to exert a mechanical
torque twisting the suspending wire, carrying one set of
plates through a certain angle against the torsional rigidity
of the wire. The description of this principal Board of Trade
100-volt standard is as follows :
CONSTRUCTION AND USE OF THE BOARD OF TRADE ONE HUNDRED VOLTS
STANDARD OF ELECTROMOTIVE FORCE OR VOLTAGE.
The instrument is shown in plan and sectional elevation on the accompanying
diagrams (see Figs. 39 and 40). It consists of :
Suspended Vanes. (a) An arrangement of 10 parallel paddle-shaped vanes,,
in form similar to the moving portion of Lord Kelvin's Quadrant Electrometer,
fitted on an axis passing through the centre of gravity of each vane and
separated by distance pieces to a distance of nine millimetres apart.
Concave Mirror. (6) On the same axis is fixed the aluminium frame of a con-
cave mirror 19 millimetres in diameter and about 61 millimetres focal length,,
which is held in the frame by means of three light phosphor bronze springs.
Suspending Wire. (c) This arrangement is suspended by means of a wire
0'05 millimetre in diameter and 18 centimetres in length, formed of an alloy
of 10 parts of indium to 90 parts of platinum, attached to the end of the
axis above the mirror so that the axis hangs in a vertical line.
Horizontal Adjustment of Position of Vanes. (d) The upper extremity of
the suspending wire is fixed to the centre of a circular brass plate having
teeth cut in the circumference, into which a tangent screw is geared so as to
enable the end of the wire to be rotated in the horizontal plane for the hori-
zontal adjustment of the vanes.
Vertical Adjustment of Vanes. (e) The vertical adjustment of the position,
of the vanes is accomplished by the raising or lowering of the platform on
which the circular brass plate mentioned above is pivoted by means of three
screws for raising and three for lowering. These screws regulate the distance
of the platform above a similar platform fixed by means of three supports to
the framework of the instrument.
Quadrants. (/) The vanes are suspended so as to slightly enter at the
zero position of the instrument into the spaces between two sets of 11 thin
polished brass plates shaped as quadrants of a circle, which are fixed horizon-
tally one above another to a vertical support. These two sets of plates are
in metallic connection, and are carefully insulated from the framework of the
instrument.
Vibration Checking Arrangement. (g) In order to reduce the vibration of
the suspended system, and the time which must elapse before an accurate
114
ELECTRICAL LABORATORY EQUIPMENT
CM
CO
ELECTRICAL LABORATORY EQUIPMENT.
115
N
m
116 ELECTRICAL LABORATORY EQUIPMENT.
observation can be taken, a thin horizontal brass disc is suspended in refined
mineral oil contained within a glass vessel, by means of a wire attached to
the lower portion of the axis of suspension of the vanes.
Outer Case. (h) The suspended system and quadrants, with their supports,
are enclosed in a brass case having in front of the mirror a rectangular
window of parallel- worked glass. A hole is cut in this case for the insertion
of a key fitting the squared arbor of the tangent screw (d).
Terminals. (z) The terminals, by means of which connection is obtained
with the vanes and quadrants, are fixed on a thick piece of polished ebonite
projecting beyond the brass cover h. One terminal is in connection with the
metal framework, the other is entirely insulated ; and a tongue of brass or
switch connected by means of a brass rod with the two sets of quadrants
can be turned so as to make contact either with the insulated or with the
uninsulated terminal.
Framework and Supports. (&) The arrangement described above, forming
the electrical portion of the instrument, is mounted near the apex of a frame-
work of brass in the form of a circular arc which rests by means of three feet
on a horizontal slab of polished marble supported on a large block of Portland
stone on a concrete foundation. A screw thread is cut on the feet for
accurate levelling of the framework, to which two spirit levels are attached.
Eyepiece and Cross Wire. (I) On a support attached to the centre of the
curved portion of the framework is fixed the observing portion, consisting of
a magnifying eyepiece in front and in the focus of which is stretched a vertical
copper wire 0'06mm. in diameter.
Fiducial Marks. (m) At each end of the arc is erected a vertical support,
to which is fixed a tablet of brass with the surface facing towards the mirror
platinised. On each of these faces is engraved a vertical line. These lines
form the fiducial marks ; that on the left of the observer giving the zero
position, and that on the right the correct position for 100 volts pressure.
The distances from the mirror (b) of these tablets and of the sighting wire (I)
is adjusted so that the image of the line on the tablet, when the mirror is at
the proper angle, coincides with the sighting wire.
USK OF THE INSTRUMENT.
Adjustments. The instrument must be in accurate adjustment as regards
level and position of the suspended system. The vertical adjustment of the
latter is obtained by trial. The vanes should be at equal distances from the
quadrants above and below, this position giving minimum sensibility. The
horizontal adjustment of the suspended system is obtained when the image of
the zero fiducial mark produced by the mirror (6) exactly coincides witli the
sighting wire (I), the switch (t) being turned so as to connect the quadrants
with the metal framework of the instrument. (The levelling of the framework
and vertical adjustment of the suspended portion of the instrument were
carefully attended to when the instrument was first set up, and these adjust-
ments have since that time remained constant. The horizontal adjustment of
the suspended system requires occasional attention from time to time. )
Headings. Arrangements should be made for obtaining a pressure which
can be continuously varied from about 98 to 102 volts. This pressure is
ELECTRICAL LABORATORY EQUIPMENT.
117
applied to the 100-volt standard, and to the instruments to be compared with
it, and is adjusted until the image of the fiducial mark indicating 100 volts
pressure exactly coincides with the sighting wire (I) by observation through
the eyepiece. This coincidence is maintained, by adjustment of the pressure,
if necessary, until the expiration of five minutes from the time of first
applying the pressure, when, if there is no visible vibration of the mirror, the
pressure is exactly 100 volts.
A perspective view of this absolute 100-volt standard is
shown in Fig. 41.
Instruments of the same design can be made for any
range of electromotive force, and a set of six standard
FIG. 41. Board of Trade Standard Kelvin Voltmeter.
voltmeters of the above described form, covering a range
from 20 to 3,200 volts, has been made for the British Board
of Trade Electrical Standardising Laboratory. With these
instruments an accuracy of standardisation can be attained
within 1 part in 3,000.
The possession of an absolute 100-volt standard of the
above kind is a great convenience when much standardising
of commercial voltmeters has to be carried out.
For general purposes, and as a secondary standard, a
convenient form of voltmeter is Lord Kelvin's Multicellular
118 ELECTRICAL LABORATORY EQUIPMENT.
Electrostatic Voltmeter (see Fig. 42). In this instrument
there are a series of connected fixed and movable metal
plates as in the standard voltmeter, but the movements of
the movable system are indicated by the displacement of a
needle over a scale. The scale of the instrument is divided
so as to read directly in volts. If the plates forming the
fixed portion of the instrument and the movable plates are
not made of the same metal there will be a small difference
or discrepancy amounting to a fraction of a volt between the
FIG. 42. Lord Kelvin's Multicellular Electrostatic Voltmeter.
readings of the instrument taken with continuous potentials,
when the fixed plates are positive and the movable negative,
and when they are reversed in sign of potential. This is due
to the contact difference of potential of the metals. In this
case any statement of the instrumental reading must be
accompanied by a statement as to the nature of the relative
sign of electrification of the movable plates.
11. The Instrumental Outfit of an Electrical Labor-
atory. The majority of the measurements made in the
ELECTRICAL LA BORA TOR T EQ UIPMENT. 119
electrical laboratory resolve themselves ultimately into one or
more of the following five measurements :
(i.) The measurement of the value or strength of an
electric current, or else proving the absence of a current, in
some circuit.
(ii.) The measurement of a potential difference or of an
electromotive force, or else proving the absence of a potential
difference.
(iii.) The measurement of a resistance or its reciprocal
conductance.
(iv.) The measurement of the time integral of a current
or of an electric quantity.
(v.) The measurement of the rate of expenditure or dissi-
pation of electric energy in a circuit, or of electric power
taken up in it.
To describe all the instruments in detail which have beer*
invented for the above measurements would be to transfer
these pages the contents of a library of trade catalogues ana
circulars. We shall limit ourselves here to mentioning the
general results of experience as to the most trustworthy and
convenient appliances for performing the above electrical
measurements which should be provided in a well-equipped
electrical laboratory or testing room.
12. Current - Measuring Instruments. The most fre-
quently recurring and fundamental of all electrical measuring
processes is the operation of determining the presence, or
proving the absence, of an electric current in a circuit. If
present, its strength or magnitude generally has to be deter-
mined in terms of the standard or unit current called the
ampere. An instrument which merely shows the presence or
absence of a current in a circuit is called a detector or
galvanoscope. If it gives, in addition, a means of comparing
the relative value of two currents, it is called a galvanometer.
If it shows by its indications the ampere-value of the current
it is called an amperemeter or ammeter.
120 ELECTRICAL LABORATORY EQUIPMENT.
By far the most numerous class of instruments in use as
galvanoscopes, galvanometers and ammeters depend for their
operation on the fact that a magnetic flux exists round a
'Conductor, conveying, as we say, an electric current. This
flux can be detected and measured by the mechanical force or
torque acting either upon a magnet placed near the conductor,
or upon a small mass of iron ; or upon another movable
conductor traversed by the same current. Another class of
instruments depends upon the heating effect produced by a
current in a conductor and the measurement of the linear
expansion of the conductor due to this heating.
We may, then, classify the current measuring or detecting
instruments required in the laboratory as follows, depending
upon the principle employed in their construction :
I. Galvanoscopes or Detectors.
(a) Simple linesman's or laboratory detector, or magnetic needle
suspended in a coil of wire.
(6) Pole-testing paper or solution.
II. Galvanometers or Current Measurers.
(a) Movable needle galvanometers with coil fixed and suspended
magnetic needle, either simple or astatic, e.g., Kelvin mirror galvanometer,
or ordinary needle or mirror instruments of high or low resistance such
as Wiedemann's galvanometer.
(6) Movable coil galvanometers, in which a coil traversed by the
current to be measured is suspended between the poles of a strong fixed
magnet, e.g., Kelvin recorder pattern galvanometer or d'Areonval gal-
vanometer, as modified by Holden, Ayrton and Mather, and Crompton.
(c) Tangent galvanometers, in which the suspended magnetic needle
has a magnetic length very small compared with the diameter of a
large fixed coil or coils, e.g., the Post Office pattern, or ordinary single-
coil tangent galvanometer ; the Helmholtz, or two-coil tangent galvano-
meter ; the three-coil tangent galvanometer.
III. Amperemeters
(a) Electrodynamic instruments, in which the forces acting between
conductors conveying currents are utilised as an ammeter principle, e.g.,
Kelvin ampere balances, Siemens dynamometer, Weber's electrodynamo-
meter, as modified by Siemens ; Pellat's absolute electrodynamo-
meter, &c.
(6) Electromagnetic instruments, in which the mechanical force
between a magnet and a conductor conveying a current, or between a
ELECTRIC A L LA BORA TOR Y EQ UIPMENT. 121
mass of soft iron and a conductor conveying a current is utilised as an
ammeter principle. 'These are variously designed as follows :
(i.) Movable coil instruments, e.g. : Kelvin recorder pattern of ammeter,
d' Arson val and Weston ammeters, and similar instruments.
(ii.) Movable soft iron instruments, e.g.: Ayrton and Perry, Nalder,
Evershed, Dobrowolsky, Thomson, and most ordinary trade
ammeters.
(c) Electrothermal instruments, in which the heating property of the
current is utilised, e.g. : Hartmanu and Braun ammeters, Cardew, Holden
and other hot-wire instruments.
(d) Electrochemical instruments, in which the time-average of a
current is measured by an operation of electrolysis. This method of
current measurement is the ultimate process of determination, and
defines the current quantity in terms of the unit current by the operation
on which the official definition of unit current is based. Instruments for
electrochemical measurement of current quantity are called voltameters,
The chief electrolytic processes are those in which a solution of a silver salt,
or of a copper salt, or etae dilute sulphuric acid, are employed as electrolytes.
(e) Electro-optic insi ruments, by which a current can be measured by
measuring the optical n-tation produced in the plane of polarised light
by its magnetic field acting on a standard substance of which the Verdet
constant is known. If a tube with glass ends, and fitted with bisulphide
of carbon, is placed in the interior of a solenoid, a current passing through
the helix exerts a magneto-rotary effect on a ray of plane polarised light
passing along the tube in the direction of the axis of the helix. Such an
arrangement may be calibrated as an amperemeter, but it is only suitable
for a^very limited class of work.
(/) Electrostatic instruments. A current can be measured most
accurately by the measurement of the electrostatic fall in potential down
a conductor conveying the current. If a current is passed through
a known resistance, and if an electrostatic voltmeter or electrometer
is applied to measure the fall of potential down it, we have at once
a measure given of the strength of the current.
This last method in its various modifications is by far
the most practical and useful method of current measure-
ment.
The resistance through which the current to be measured
flows is not necessarily placed in the immediate neighbour-
hood of the potential-measuring apparatus. This last may
be either an electrostatic voltmeter, as described in the next
.section, or else an electromagnetic voltmeter effecting the
same purpose.
Further details will be given in the sections devoted to
current measurement.
122
ELECTRICAL LABORATORY EQUIPMENT.
In addition to simple detectors, now and then required, by
far the most convenient form of galvanometer for all ordinary
work in the testing room and electrical laboratory are the
movable coil galvanometers. These consist of a fixed permanent
magnet having suspended between its poles a small light coil
of insulated wire. The current to be detected or measured
FIG. 43. Holden-Pitkin Movable Coil Galvanometer.
passes through the coil, entering and leaving, through the
suspending wires which may be arranged either bifilarly,
as in the Crompton pattern of galvanometer, or attached to
the top and bottom of the coil, as in the Holden-Pitkin
pattern. The movable coil galvanometer has two great
advantages in use : Firstly, it is not much affected by the
ELECTRICAL LABORATORY EQUIPMENT.
123
passage of currents in neighbouring wires or stray magnetic
fields, and hence may be used in places where an ordinary
. 44. Coil and Core of Holden-Pitkin Galvanometer.
Fio. 45. Ayrton-Mather Movable Coil Galvanometer.
124
ELECTRICAL LABORATORY EQUIPMENT.
movable needle galvanometer would be useless; secondly,
the L coil can be very quickly brought to rest by short-
circuiting the terminals. Hence the galvanometer is or may
be made very dead-beat or damped. In the form designed
FIG. 46. Crompton Movable Coil Galvanometer.
by Holden and made by Pitkin (see Figs. 43 and 44), or
that designed by Ayrton and Mather and made by Paul
(see Fig. 45), or that designed and made by Crompton
(see Figs. 46, 47, and 48), the movable coil galvanometer is
ELECTRICAL LABORATORY EQUIPMENT.
125
by far the most practical and useful form of galvanometer
for an electrical testing laboratory. It was originally designed
FIG. 47.
by Lord Kelvin for cable signalling, although now often
called the d'Arsonval form of galvanometer.
FIG. 48.
The varieties of electromagnetic galvanometer which have
been designed are innumerable. In all of them the current
126 ELECTRICAL LABORATORY EQUIPMENT.
in a conductor is measured by the measurement of the
mechanical action of the associated magnetic field either on
(a) Another magnet,
(&) A mass of soft iron,
(c) Another movable conductor carrying the same
current.
The magnetic force may produce, in either (a), (5) or (c), a
rotation or torque, or a forcive or bodily displacement. In
the first case a uniform field is required, in the second a
non-uniform field. Hence we may classify the fields as :
(A) Uniform for rotational deflection,
(B) Non-uniform for translational displacement.
Then the principal currents or current to be measured may
be in the fixed or the movable part of the instrument.
Hence we have a further classification into :
(a) Fixed coil galvanometers.
OS) Movable coil galvanometers.
Lastly, some arrangement, or control, is necessary to bring
back the displaced portion, whether magnet, soft iron or coil,
to its original zero position when the current is stopped.
This may be achieved by the aid of another magnetic field, or
the elasticity of a spring or torsion of a wire, or by the
weight or inertia of the moved mass. Hence we classify
according to the control into :
I. Magnetic control,
II. Elastic control,
III. Gravity control,
IV. Inertia control.
We can, therefore, symbolise any given type of galvano-
meter by an expression of four symbols denoting the classes
in which it is placed. Thus the ordinary mirror Kelvin
galvanometer is represented by the symbol (aAaL). The
d'Arsonval or recorder type of galvanometer by the symbol
ELECTRICAL LABORATORY EQUIPMENT. 127
(a A fill.). The above method of classification of galvano-
meters is that due to Prof. G. F. FitzGerald.*
In appraising a galvanometer, or evaluating its applica-
bility for any purpose, we have to take into account five
qualities which, when numerically expressed, may be called
the five specific constants of the galvanometer. These quali-
ties are :
(i.) The periodic time of the movable system, or time
of one complete small oscillation when the
movable part is disturbed and then left to
itself.
(ii.) The logarithmic decrement corresponding to different,
or some known, amplitudes of swing, i.e., the
logarithm (Napierian) of the ratio of the amplitude
of one excursion on one side to the next one on
the other side of the zero point*
(iii.) The sensitiveness, both ballistic and deflectional.
(iv.) The internal resistance, or coil resistance,
(v.) The zero-keeping quality, or degree of precision,
with which the movable part returns exactly to
the original zero position when disturbed and left
to itself again.
If the needle or coil of a galvanometer is disturbed, it
comes to rest after one or more vibrations. The time of one
complete vibration, or interval between passing the zero
point in the same direction, is called the periodic time. These
swings of the needle or coil are resisted by the air or other
causes of friction, and the amplitude of the excursions
gradually diminishes. If the amplitude of each swing is
measured, it will generally be found that successive ampli-
tudes decrease nearly in a. geometric progression. Hence, in
this case, the logarithm of one excursion bears a nearly
constant ratio to the logarithm of the next one. This ratio
is called the logarithmic decrement of the galvanometer. The
logarithms taken are generally Napierian. The logarithmic
* See The Electrician, Vol. XXXVIIL, p. 715.
128 ELECTRIC A L LABOR A TOR Y EQ UIPMEN2.
decrement usually varies with the amplitude of the swing,
owing to the fact that the retardation experienced by the
coil or needle depends to some extent on the velocity with
which it leaves its zero position.
If a small constant current, say a micro-ampere, is passed
through the galvanometer coil, it will cause a certain steady
deflection of the movable needle or coil. These deflections
are nearly always read by means of a mirror and scale. A
concave mirror attached to the galvanometer needle, or coil, as
the case may be, has a ray of light thrown upon it and a sharp
image of an illuminated wire or incandescent lamp filament is
by it thrown upon a scale. The scale is generally placed one
metre or 1,000 millimetres from the mirror.
The sensitiveness or deflectional constant of a galvanometer
may be denned as the scale deflection in millimetres pro-
duced by a current of one micro-ampere passing through
the galvanometer coil, the scale being at one metre distance
from the mirror. It may also be stated in terms of the
potential difference in micro-volts, which must be applied
to the terminals of the galvanometer to produce this same
unit deflection, or as the deflection in millimetres, at metre
distance of scale, per micro-volt on the terminals. The sensi-
tiveness of a galvanometer must always be controlled by the
possession of good zero-keeping quality. By this is meant
that when the current is stopped the galvanometer needle
or coil returns again to a fixed and constant zero position.
It is easy to give a galvanometer a spurious sensitiveness,
but if the zero position of the movable portion is not constant,
the value of the galvanometer for quantitative purposes is
very small.
A galvanometer with a very large logarithmic decrement
is called a dead-beat galvanometer. One with a very small
logarithmic decrement is called a ballistic galvanometer. The
ballistic constant of a galvanometer is defined as the reciprocal
of the " throw " or excursion of the needle or coil when one
micro-coulomb of electric quantity is discharged through it.
ELECTRICAL LABORATORY EQUIPMENT. 129 1
The electrical laboratory should be provided with a collec-
tion of movable coil dead-beat, and movable coil ballistic
galvanometers of various resistances, some large, 500 or 1,000
ohms or more, and some of low resistances, such as 0*5, 5
or 10 ohms. It is desirable also to have at least one very
sensitive Kelvin mirror astatic movable needle galvanometer
of 6,000 to 10,000 ohms resistance.
Generally speaking, tangent galvanometers and needle
instruments are more suitable for a physical laboratory
than for an electro-technical laboratory, the disturbances
caused by the presence of large electric currents rendering
it most difficult to use the movable needle deflectional
instruments. As regards ammeters, for ordinary working
purposes the most convenient are those which, like the
Weston ammeters, are movable-coil instruments. These
instruments are very dead-beat, and have equal or nearly
equal scale divisions per ampere or per milliampere. These
instruments are, however, only available for continuous
currents.
For use with alternating currents, some form of hot-wire
ammeter, such as that of Hartmann and Braun, is very^
useful. Its indications are entirely independent of the
frequency of the alternations, and the instruments are also
very dead-beat.
For many purposes the Siemens dynamometer is an
invaluable laboratory instrument (see Fig. 49). It consists
of a fixed coil or coils, and a suspended coil which embraces
the fixed coil, and the normal position of which is with
its plane or axis at right angles to the plane or axis of
the fixed coil. The movable coil is hung by a few fibres
of floss silk, and its position is controlled by a spiral spring,
the lower end of which is attached to the movable coil and
the upper end to a torsion-head. The current is led into and
out of the movable coil by means of mercury cups. The
wires forming the fixed and movable coils should always
be brought to separate terminals. The instrument can then
130
ELECTRICAL LABORATORY EQUIPMENT.
be used for several purposes. If the coils are joined in
series, and a current, either alternating or continuous, sent
through them, forces are brought into existence which
cause the movable coil to be acted upon by a couple or
torque, and to be twisted round. If, then, a contrary twist
is given to the torsion-head and the movable coil brought
back to its zero position, the angular twist required to
effect this is proportional to the square of the strength
of the current. The dynamometer can thus be calibrated
FIG. 49. Siemens Electrodynamometer.
to measure current strength. If the current is unvarying,
the square root of the torsion or scale reading gives, when
multiplied by a constant, the current strength. If the
current is alternating and periodic it gives the square
root of the mean of the squares of the equi-distant
instantaneous values during the period or the root-mean-
square (RM.S.) value of the current, provided that the
periodic time of the current is small compared with the
periodic time of a free oscillation of the movable coil. If
ELECTRICAL LABORATORY EQUIPMENT. 131
different currents are sent through the two coils the
instrumental readings can be made to give the mean
value of the product of their maximum values multiplied
by their power-factor or cosine of the angle of phase
difference, if the currents are simply periodic.
13. Yoltage Measuring Instruments Any of the
above galvanometers or amperemeters, if wound with
wire of sufficiently high resistance, becomes an instrument
which may be used for the determination of the steady
potential difference between two points. For the current
through any current-measuring instrument is proportional
to the steady potential difference between its terminals,
and inversely as the resistance of the instrument. Hence,
if the resistance of the instrument is so high (say, 1,000
to 20,000 ohms) that the current it takes off, when placed
as a shunt circuit between two points on any other circuit,
open or closed, does not disturb sensibly the potential
difference between those points, the indications of the
instrument are proportional to the original potential differ-
ence between those points.
For many laboratory purposes electromagnetic voltmeters^
as they are called, of the above type will be found convenient.
There are, however, many measurements in which it is
desirable that no current shall be taken off between the
points, the potential difference (P.D.) of which is required.
Also it is often necessary to use the same instrument for
continuous and for alternating currents. In these cases the
best voltage-measuring instruments to employ are the electro-
static voltmeters. These, are now made to measure voltages
varying from 1 volt up to 40,000 volts or more. Their
general principle is as follows :
Let there be two sets of plates or metallic surfaces, one
fixed and the other suspended, so as to be capable of moving
in between the fixed surfaces. Let the normal position of the
movable plate be just outside the fixed one. The two sets
132
ELECTRICAL LABORATORY EQUIPMENT.
of plates are insulated from each other, and thus form a con-
denser or Leyden jar having a certain capacity. If we
produce a certain potential difference between these plates,
this P.D. brings into existence forces of attraction between the
plates proportional to the square of the difference of potential,
FIG. 50. Kelvin Multicellular Electrostatic Voltmeter.
and therefore independent of its sign. This force draws
the movable plates in between the fixed ones, so as to
increase the capacity of the condenser formed by the two
plates or sets of plates. If this force is resisted, either by
the torsion of a suspending wire or by gravity, we have
ELECTRICAL LABORATORY EQUIPMENT.
133
an'arrangement called an electrostatic voltmeter, which can be
calibrated to show difference of potential, either the steady
value or the root-mean-square value, according as the pressure
is uniform or periodic.
Voltmeters of this form have been designed by Lord
Kelvin, Prof. Ayrton, and others. Of these the most
FIG. 51. Kelvin Electrostatic Voltmeter.
convenienOo-rm f or the electrical engineering laboratory are
thThorizontal and vertical pattern of multicellular electro-
static voltmeters, as designed by Lord Kelvin for measuring
electrical potential difference from 50 to 150 or 250 volts (see
Fig. 50) ; high-pressure electrostatic voltmeters, as designed
by Lord Kelvin (see Fig. 51) and by Prof. Ayrton for high
134 ELECTRICAL LABORATORY EQUIPMENT.
pressures from 1,000 to 2,500 volts; and the low-pressure
electrostatic voltmeters of Prof. Ayrton, for pressures from
2 to 50 volts, are also exceedingly useful instruments.
These electrostatic voltmeters are also available as current-
measuring instruments. If a current is sent through a
resistance, and the fall of potential down the resistance is-
measured by a correct electrostatic voltmeter, the current
through the resistance becomes known. This method of
current-measuring is convenient in measuring small alter-
nating currents, such as the magnetising current of a
transformer.
Electrothermal voltmeters, such as those of Cardew r
Holden, and Hartmann and Braun, are at times required
when dealing with alternating currents. They are, however,
less generally useful than the electrostatic instruments
because they take up much more power to operate them.
As regards the method of standardising all the above
instruments, and obtaining measurements of current and
potential difference by means of the potentiometer method,
the details of these processes will be discussed in a later
section of this treatise.
The instrument called the potentiometer is of the greatest
utility in the electrical laboratory, and a good potentiometer
is one of the fundamental requisites of an electrical testing
room. In its simplest form it consists of a uniform wire
stretched over a scale divided into 2,000 parts. This wire
has its extremities connected to a couple of secondary cells
(see Fig. 52), and an interpolated resistance inserted in the
circuit. By varying this resistance it is possible to adjust
the current in the wire so that the fall of potential down
a length of the wire equal to 2,000 scale divisions is just
2 volts. This is achieved by placing a Clark cell and a
sensitive galvanometer .as a shunt on the wire, and making
contact at two scale divisions 011 the wire the interval
between which corresponds numerically to the electromotive
force value of the Clark cell. Thus, suppose the cell has an
ELECTRICAL LABORATORY EQUIPMENT. 135
electromotive force of 1434 volts at 15C., then two sliding
contacts on the galvanometer and standard cell circuit are
set to make contact at the zero and at the 1,434th scale
division. When this is done the resistance in series with the
two-cell secondary battery is altered until the galvanometer
indicates no current. In order that it shall be possible to do
this, the positive pole of the Clark cell must be connected
with that end of the potentiometer wire to which is joined the
positive pole of the secondary cells, called the working
battery. When this adjustment is made, the potentiometer
is said to be set. If, then, it is desired to measure any other
potential difference, say that due to the passage of a current
FIG. 52.
through a low resistance, wires called potential wires are
brought from the ends of this resistance, and in one of these
circuits a galvanometer is inserted. One potential wire viz.,
that attached to the highest potential point is joined to that
end of the slide wire in connection with the positive pole of
the working battery. The other potential wire is attached to
a slider making a variable contact on the slide wire. The
slider is then moved until the galvanometer indicates no
current. This can be always done if the fall in potential
down the resistance is less than that down the slide wire. The
reading on the slide wire, as shown by the position of
the slider, gives at once the potential difference in volts
between the potential wires.
136 ELECTRICAL LABORATORY EQUIPMENT.
ELECTRICAL LABORATORY EQUIPMENT.
137
The practical potentiometer takes one of two forms. It
may be, as described, a simple slide wire potentiometer, or
the slide wire may be in part or in whole replaced by coils
of wire arranged in series, as in the potentiometers of
Crompton, Fleming, Nalder, Wulf, and others.
The electrical laboratory should be provided with one
or two potentiometers.* One should be a simple slide wire
instrument for rough work, the other a standard instrument
for exact work, made entirely with carefully adjusted coils of
wire.
If-
Secondary Battery,
do SO 80 70 60 60 40 (
3 30 20 10 a 4 *
a 10 17 i
B SCALE
( I 100 volts.
Galvanometer
1 ->
R High Resistance.
I () MWWVW
AdjuKtahU
FIG. 53A. Crompton Potentiometer Connections.
The Crompton potentiometer is shown in Fig. 53, and the
connections in Fig. 53A. The external appearance of the
Nalder potentiometer is shown in Fig. 54. In the former
(the Crompton) instrument the slide wire consists of 14 coils
placed inside the case of the instrument, and a slide wire
equal in resistance to one of these coils stretched over a scale
outside the box. In series with these coils is a circular
rheostat for adjusting the potentiometer current. There is
a double pole six-way switch, which enables any one of six
* The arrangement now called the potentiometer was first described by
Poggendorff, Poggendor/'s Annalen, Vol. LIV., page 161, 1841. The method of
making the potentiometer direct reading, so as to give the potential difference
without calculation, is due to the Author, and was first described in Industries,
July and August, 1886.
138 ELECTRICAL LABORATORY EQUIPMENT.
test circuits to be placed in series with a galvanometer and
in shunt with any portion of the slide wire. The galvano-
meter circuit has one end attached to a sliding contact
which moves over the slide wire. The other end can be
attached to the junction between any one of the 14 coils in
series with it. When the potentiometer is " set," the current
through the slide wire is such as to make the fall in potential
down the whole wire 1*5 volts. The scale is divided into
FIG. 54. Nalder's Potentiometer.
1,000 parts, and each slide wire unit represents one-ten-
thousandth of a volt.
In the Nalder instrument the whole of the slide wire
consists of coils placed within the box containing the instru-
ment, and contact is made with the junction between these
coils by means of a circular revolving arm.
In Fig. 55 is shown a diagram of the connections of
the instrument as depicted in Fig. 54. Eeferring to the
second figure, it may be seen that a secondary battery
is joined on to the terminals F, and sends a current
ELECTRICAL LABORATORY EQUIPMENT.
139*
140 ELECTRICAL LABORATORY EQUIPMENT.
through the resistances connected with the dials C and D,
and then through adjusting resistances K and H. The
dial D has 100 equal coil resistances in it, the whole
set being equal to the resistance of one coil in C. The
dial K contains 19 equal small wire resistances, and the
resistance H is a carbon resistance for fine adjustment.
A standard cell is joined up to A A, and a galvanometer
to the terminals marked galv. If the cell has a voltage
14412 volts, the arm of dial C is set to 144 and that
of D to 12. The resistances H and K are then adjusted
so that the galvanometer shows no current, and the
potentiometer is then " set." The voltage to be measured
is connected to the terminals B B if below 1*6 volts, and if
above that to the terminals marked volts, in Fig. 55, which
are bridged by a wire of high resistance. A fraction of
this potential difference, either J, T ^, TOO, or 3^, is then
measured, according as the switch M is on the contact
marked 3, 10, 100, or 300,
In practice it is found that potentiometers in which
the contact with the galvanometer circuit is made either
by rubbing or pin contacts, or by a slide contact moving over
a wire, give trouble owing to imperfect contacts due to
the deposition of dust on the contact surfaces and on
the wire, and time is wasted in getting the necessary
adjustments made. These defects led the Author to design
a form of potentiometer in which there is no slide wire
and no rubbing or pin contacts, but in which the whole
of the potentiometer wire or resistance is represented by
coils of wire contained in a case. The galvanometer circuit
containing the electromotive force to be measured is brought
to two terminals, which are in connection with two bars
or rings of brass, by means of plugs fitting into holes
bored out partly in these bars or rings and partly in
adjacent metal blocks. It is possible to insert any required
portion of the whole potentiometer wire resistance, within
limits, in between the galvanometer terminals, whilst at the
ELECTRICAL LABORATORY EQUIPMENT. 141
same time resistance is~ added or subtracted from a main
current circuit, on which the galvanometer circuit is a shunt,
in such fashion that a constant current flows through the
main potentiometer circuit. This compensating resistance is
added or removed by plugs, as in the case of a plug pattern
Wheatstone bridge. Fuller details of the use of the instru-
ment will be given in a later section of this work.
Generally speaking, the most convenient ammeters for
laboratory use are those which depend upon the measure-
ment of the fall of potential down a low resistance. The
ammeter then consists of two parts :
(L) A suitable resistance, which carries practically the
whole of the current, and which may even be
removed a considerable distance from the re-
mainder of the instrument.
(ii.) A potential measuring part, which consists of some
form of movable coil galvanometer of high
resistance, or for special tests may be a potentio-
meter.
The galvanometer will generally take the form of a
permanent and well-aged magnet for producing a field
in which is suspended a light high resistance coil, with
pointer attached, moving on jewelled centres, and also-
a steel spiral controlling spring to keep the coil in a
normal position, and against which the electromagnetic
force acts (see Fig. 56). These instruments have the
advantage that the scale divisions are usually very nearly
equidistant. There is no blank part or non-readable portion
of the scale, and they are also very dead-beat. In Fig. 56 is
shown part of the mechanism of a Siemens and Halske volt-
meter constructed on the above principle. Part of the
magnet is removed to show the coil. The coil consists of an
insulated wire wound on a copper frame to damp the move-
ments. The coil has attached to it an index needle, and its
displacement is resisted by a steel spiral spring. The
142
ELECTRICAL LABORATORY EQUIPMENT.
resistance traversed by the current to be measured may be
contained in the case of the instrument, or it may be entirely
FIG. 56.
separate and used B outside. In Figs. 57 and 58 are shown the
-details and mode of use of an Arnoux-Chauvin dead-beat
FIG. 57.
ammeter and shunt constructed on the above principles,
consisting of a high resistance movable-coil galvanometer
ELECTRICAL LABORATORY EQUIPMENT. 143
with equi-divisional scale used as an ammeter by measuring
the fall in potential down a low resistance shunt of known
value.
Instruments of the above-described type are much
employed in the laboratory as ammeters and voltmeters
for the measurements of continuous currents and potential
differences. A series of very convenient and portable
FIG 58
instruments of the above kind have been devised by Mr.
Weston. These are remarkable for the almost exact
equality of distance of the scale divisions. They are made
for various ranges of work, such as ammeters to measure
from to 15 amperes, O'O to 100 amperes, milliamperemeters
and voltmeters.
144
ELECTRICAL LABORATORY EQUIPMENT.
The three most convenient "Weston instruments for general
laboratory work are the ammeter, reading from zero to 15
amperes ; the milliammeter, reading from zero to 1*5
amperes by hundredths of an ampere ; and the voltmeter,
which reads from zero to 150 volts on one pair of terminals
and from zero to 15 volts on another pair.
Instruments of a similar kind are made by many other
manufacturers.
13. Resistance-Measuring Instruments. The com-
parison of conductors in regard to the quality called their
electrical resistance is generally conducted by means of
FIG. 59. Wheatstone's Bridge, arrangement of Circuits.
instruments technically termed bridges or Wheatstone's
bridges, provided the resistances to be compared are neither
of them very large or very small in magnitude. In its
simplest form the arrangement called a Wheatstone bridge
consists of six conductors joining four points. In one of
these circuits is placed a source of electromotive force such
as a battery, and in one other circuit, called the conjugate
circuit, is placed a galvanoscope for detecting the presence or
absence of a current.
The circuit arrangement is depicted in Fig. 59. When the
resistance of the circuits is so adjusted that closing the battery
circuit (B) does not produce any permanent current in the
conjugate galvanometer circuit (G), the " bridge " is said to be
ELECTRICAL LABORATORY EQUIPMENT. 145
balanced. To effect the balancing, two of the resistances
(P and Q) are adjusted to a certain ratio, and these are called
the ratio arms of the bridge. Of the other pair of resistances
or arms of the bridge, one is a standard of resistance (S) and
the other (E) is the resistance to be compared. The balance
is obtained either by altering the ratio arms or by altering the
value of the resistance of the standard or measuring arm.
The bridge may be employed in one of two ways :
(i.) To obtain the ratio of two resistances,
(ii.) To obtain the difference of two resistances.
The first method is the one generally employed in ordinary
work, and may be called the Wheatstone method. The
second is that used in very exact work, and is due to Prof.
G. Carey Foster.
The ordinary bridge, as a laboratory instrument, takes one
of two forms :
(i.) The Slide Wire Bridge, in which the ratio arms can
be continuously varied, and the standard of
resistance generally remains unchanged,
(ii.) The fixed coil pattern, or Plug Bridge, in which the
ratio arms can only be given certain decimal
ratios, but the standard or comparison resistance
can be varied within wide limits by adding fixed
resistances in series.
The complete theory of the bridge will be considered in
Chapter II. under the head of KESISTANCE MEASUREMENT ;
but meanwhile we may state the simple principles of the
bridge as follows :
First, let it be assumed that the bridge is balanced. Then
it is clear that, starting from point a, the voltage or fall in
potential down P and E is the same, because the points b and
d are, by supposition, at equal potentials, as they must be if
no current flows through the galvanometer. Similarly the
potential fall down Q and S is equal. Call these potential falls
Vp, V Q , V B , V s . Then also, since no current flows through
the b d circuit or galvanometer circuit, we must have equality
146 ELECTRICAL LABORATORY EQUIPMENT.
in the currents in P and Q and in those in E and S. Call
these currents C P , C Q , CR, C s , and the resistances of the arms
P, Q, E, S. Then we have
also C P =:C Q and C R =C S .
But, by Ohm's law, . P =P,-- Q =Q, R =E,-^ S =S.
Hence J=? or E=rS^.
Q S Q
If the bridge is not balanced that is, if the current
through the galvanometer circuit is not zero, but has a value
C, then it will be subsequently shown that the galvano-
meter current can be calculated from the expression
where E is the electromotive force of the battery and
. E+S)+r(P+E Q + S)
i
E being the resistance of the battery circuit, and r that of
the galvanometer circuit.*
The practical forms of bridge required in the electrical
laboratory are as follows :
I. A standard slide wire bridge, for the careful comparison
of standard coils with other nearly equal resistance coils.
II. A simple form of plug bridge, for approximate measure-
ments of resistance.
III. A well-constructed form of dial plug bridge, for
accurate work.
IV. A differential bridge, for exact comparisons between
standard coils.
V. A low-resistance bridge, for very small resistances.
* For the method of dealing with problems of networks of conductors see
2, Chap. IT., where the reader is referred to a Paper by the Author in the
Phil. Mag., August, 1885 ; also Proc. Phys. Soc. London, Vol. VIL, 1885.
ELECTRICAL LABORATORY EQUIPMENT.
147
The simplest form of (I.) or slide wire bridge consists of a
stout mahogany board, on which is strained a gilt manganiii
or platinum-silver wire, the wire being uniformly stretched
between heavy terminal pieces of copper. The ends of this
wire are united by a parallel bar of copper in which are two
gaps, one to be closed by the standard resistance (S) and the
other by the resistance (E) to be measured. These resistances
are inserted either by means of good terminal screws or by
the use of mercury cups. In the practical construction of a
slide wire bridge one of the difficulties consists in keeping
FIG. 60. Simple Slide Wire Resistance Bridge.
the slide wire tight and yet in allowing it to expand or
contract. The arrangement of the simple slide wire bridge
is shown in Fig. 60. The slide wire is attached to thick end
blocks of copper drawn back by springs which keep the
wire just tight enough without overstraining it. By cali-
brating the wire, as explained in the next section, the
resistance of these copper terminal blocks can be deter-
mined in terms of the resistance of a centimetre of length of
the wire. Over the slide wire moves a slider (c) having a knife-
edge contact and key, and parallel with the slide wire is a
divided scale equal in length to the slide wire. The battery,
L2
148
ELECTRICAL LABORATORY EQUIPMENT.
consisting of two or three dry cells, is connected to the end&
of the slide wire through a contact key, and the galvanometer
is connected to a terminal between the standard resistance
and resistance to be measured and the knife contact of the
slides. The galvanometer used with the bridge is preferably
one of the movable coil dead-beat type. The battery may
consist of three dry cells. The operation of measurement
consists in finding the point at which the slider must make
contact with the wire so that no current passes through the
galvanometer. The ratio arms of the bridge are then the
sections into which the slider divides the slide wire, and
the value of the resistance (R) being tested is equal to>
FIG. 61. Double-gap Slide Wire Bridge.
the comparison resistance (S) multiplied by the ratio (P : Q');
of the slide wire sections. Increased sensitiveness is given,
to this bridge by making double gaps in the copper bar and
adding two more coils or resistances to the ends of the slide
wire. These coils are then extensions of the slide wire, and the
slide wire becomes only a portion of the ratio arm resistance.
Thus, let the resistances of these added coils (see Fig. 58)
be A and B, and let x and y be the lengths of the sections,
into which the slide wire is divided by the contact piece (c)
when the balance is obtained. Then, if R is the resistance
being measured and S is the standard resistance, we have
ELECTRICAL LABORATORY EQUIPMENT. U9
A displacement of the slide of one millimetre along the slide
wire corresponds then to a much less difference between E
and S than would be the case if the coils A and B were not
present. This extension enables us to compare together very
accurately two coils by measuring the difference between the
resistances of the two coils by a method due to Prof. Gr.
Carey Foster, and also to calibrate the wire or determine the
resistance of the slide wire per unit of length.
Let the bridge be first balanced with coils A and B (as
.shown in Fig. 61).
Then let the position of the coils A and B be interchanged
.and a fresh balancing position be found at a distance x r
divisions of the slide wire from the left hand end.
Let p be the resistance of the length of x divisions of the
.slide wire, and let W be the resistance of the whole slide
wire a b.
Let p' be the resistance of the length of the x' divisions of
the slide wire.
Then corresponding to the two cases we have resistance
-equations
R:S=B+/>':A+W P'.
A+p B + W-p
Hence lT - -.= . ^ T - M
B+p' A+W p
or
B+W p~A+W-p'
"Therefore it follows that
A-B-W+2p_B-A W+2p'
A + B+W B+A+W
or A-B=p' p.
In other words, the difference of the two resistances A and B
is equal to the resistance of that length of the slide wire
included between the x' and x divisions at which the balance
is found on the slide wire in the two experiments.
150 ELECTRICAL LABORATORY EQUIPMENT.
If, then, the wire is of uniform resistance per unit of length,
and if this resistance per centimetre is known, the difference
between the resistances A and B is known.
The slide wire can be calibrated or tested for uniformity
as follows :
In place of the resistances K and S substitute another
slide wire and another contact slider piece, so that the ratio
arms of the bridge can be varied at pleasure. Then by moving
the second slider the balancing position on the slide wire a b
can be brought to any required position for any two given
coils A and B. For A and B select two coils of wire having
a very small difference in resistance, and proceed as above
described to find the length x'x of the bridge wire which
has a resistance equal to A B. Then move the second slider
a little, so as to change the ratio of K : S, and find again in
another place on the slide wire a b the length x'x equal in
resistance to A B. If this length x' x is not equal to the
same number of slide wire divisions in all parts of the wire>
the wire is non-uniform in resistance. It is possible, by
moving the second slider, to regularly inspect and measure
the resistance per centimetre of the slide wire; but the
process of applying the necessary correction for non-uni-
formity of slide wire is so troublesome in practice that it is
better to reject the slide wire if non-uniform and obtain
another and better wire.
If, then, we obtain a slide wire the resistance of which
per centimetre is uniform and is known, we can at once
determine the difference in resistance between any resis-
tance coil and a standard resistance not differing from it
in resistance by a greater amount than the resistance of the
whole slide wire.
The Author designed in 1880 a special form of slide wire
bridge for making such difference measurements very quickly,
and this has been found especially convenient in comparing
together standard coils and others intended for standards.*
* This bridge is still employed at the Cavendish Laboratory, Cambridge, in
the comparison of standard coils.
ELECTRICAL LABORATORY EQUIPMENT. 151
Following is a description of this form of standard comparison
bridge :
Description of the Resistance Balance. A circular disc of
mahogany 18in. in diameter and about lin. thick (/, Figs. 62
and 6:3) stands upon three short feet, L. Upon this, and con-
centric with it, is screwed down a disc of ebonite 14in. in
diameter and fin. thick (e). This ebonite disc has a semi-
circular groove turned in its circumference. The circular
wooden base extends on one side into a narrow rectangle,/,
4in. wide and of the same thickness as the disc. To this are
connected two other rectangular pieces Ji, i, which are joined
together by slotted brass bars y, (Fig. 62) underneath, in
such a manner as to permit the two intervals to be made
wider or narrower at pleasure. This promontory is of wood,
of the same material and thickness as the disc/, and is sup-
ported and levelled by three levelling-screws, n, n', n".
Through the centre of the ebonite disc passes a brass centre-
pin 1) D' (Fig. 62), on which is centred a brass arm, H H',
capable of revolving just clear of the disc. Beneath the
arm, and soldered to it, is a short brass spring x } which
depends vertically downwards. This spring carries at its
extremity a small prism of platimmi-iridiuin with one edge
vertical and turned inwards. In the groove turned in the
disc e is stretched a platinum-iridium wire about /oin.
in diameter. The wire extends round about f f of the
circumference, and is about 39in. long ; and the groove is of
such a size that the wire lies with exactly half its thickness
embedded in it. This wire is represented by the thick black
line A C A' in Fig. 62. The ends of this wire are soldered to
copper strips k, k. On the wood rectangles /, h, i is fastened
an arrangement of longitudinal copper strips k, k, which
connect together eight transverse square copper bars in the
manner shown in Fig. 62. On the ends of these transverse
bars are fixed vertical copper pins j^in. i n diameter and fin.
high. On these pins are slipped short lengths of india-
rubber tube, which extend beyond the pins so that they form
152 ELECTRICAL LABORATORY EQUIPMENT.
j
1
o
to
a
ELECTRICAL LABORATORY EQUIPMENT.
153
small cups about lin. deep, p' (see Fig. 62). The top of the
copper pin is well amalgamated with mercury, and forms the
bottom of the cup. These cups are filled about a quarter full
of mercury. On the longitudinal strips of copper are fixed
three binding screws B, B', G ; and a fourth (G') simply goes
through the wood, and is connected by a wire t underneath
the baseboard with the centre-pin D, and is therefore in
metallic connection with the spring x. The battery is connected
with the terminals B, B', and the galvanometer with the
terminals G, G'. To the arm H H' is adapted a trigger, T,
of such shape that when the button iv, which is of ebonite,
FIG. 63.
is pressed down, the spring x, carrying the platinum-indium
knife-edge, is bent inwards until it touches the wire strained
round the circumference of e. The arm caries a vernier, N,,
which travels round sunk in a shallow groove in the face
of the ebonite disc ; and the ebonite is graduated on the
face on the margin of the groove. The graduations are cut
into the ebonite, and then rubbed over with powered chalk
mixed with gum and water. This gives a graduation very
legible and pleasant to look at. The length of the wire is
just one thousand divisions ; and the vernier enables these
to be divided into tenths. The zero of graduation is so
lf>4 ELECTRICAL LABORATORY EQUIPMENT.
placed that, when the pointer of the vernier reads zero, the
knife-edge on the spring x is exactly opposite the extremity
of the platinuiii-iridium wire.
It is thus clear that the revolving arm carrying its knife-
edge can be moved round so that, on pressing the trigger
button w, the knife-edge makes contact at any point of this-
wire, and thus connects this point with the terminal G'.
This part of the arrangement answers to the sliding block
and piston-contact piece of the ordinary divided-metre bridge.
Method of using the Balance. Let now two resistance
coils of about equal resistance be provided, and let the coil
terminals of one coil be placed in the mercury cups p and r,
and those of the other be placed in q r and &'. And let two-
more coils be taken of not very unequal resistance which it is
desired to compare with each other ; let the terminals of one
be placed in the mercury cups a and c } and those of the other
in b f and d'. It will then be seen that, if a battery be
connected with B B' and a galvanometer with G G', that we
have the usual Wheatstone bridge arrangements (see Fig. 64
for a diagram of the connections). Two quart Leclanche cells-
are best suited for ordinary use. If a more powerful battery
is used, there is danger of heating the platinum-indium wire,,
and so expanding it that it may slip down out of its groove.
The coils in the intervals between the cups p and r and q r
and s f form two branches; and the coil in the interval
between a and c, together with the resistance of the platinum-
iridium wire round to the place where the spring x touches-
it, forms the third branch, whilst the coil in the interval V d' f
together with the remainder of the wire, forms the fourth.
The " bridge " wire consists of the arm H H' and the wire
under the baseboard, together with the galvanometer inserted
between G and G'. By moving round the arm H H' and
pressing the button u\ we can find a position where there is
no current through the galvanometer. The copper strips
kk are made of copper so thick that their resistance is
practically nothing. Having established a balance between
ELECT RICA L L A DORA TOR Y EQ U1PMENT.
155
the conductors and read the vernier, the next operation is to*
lift up the legs of the coil which were inserted in the cups a
and c and drop them into the cups b and d. Likewise a
similar change is effected on the other side; the terminals
of the coil inserted in I' and d r are changed to a' and c'.
An examination of the connections as shown in Fig. 64 will
show that the result of the operation is as if the coils had
changed places whilst preserving their former connection,
Now let the arm be moved round and a fresh position of
equilibrium found by pressing the trigger and reading the
vernier. A little consideration will show that the difference
COIL
FIG. 64.
of these readings gives the difference between the resistances
of the coils in terms of a length of the bridge wire ; for the
amount by which one coil exceeds the other in resistance is-
equal to the resistance of that part of the bridge wire included
between the two readings.* In order to render this method
of determining the difference of the two coils practicable, the
platinum-iridium wire must be exceedingly uniform in
* This method of obtaining the difference of two resistances in terms of a
length of the calibrated bridge wire was suggested by Prof. G. C. Foster, F.R.S.,
in a Paper read before the Society of Telegraph Engineers, May 8, 1872.
In this Paper is given an account of the method of calibrating a wire. It is
obvious, without any further proof, that if the coil placed in a and c exceeds-
in resistance that placed in 6 and d, then on exchanging them, since the united
resistance of coils and bridge wire remains the same, that the contact knife-
edge must be moved back along the bridge wire by a length exactly equal in
resistance to the excess of one coil over the other.
156 ELECTRICAL LABORATORY EQUIPMENT.
resistance, or else a table of calibration will have to be
made. Great pains were taken to procure a length of wire
as uniform in size and resistance as possible ; and considerable
care was taken, in laying the wire in its groove, not to strain
it in any way. It lies evenly in its groove, just sufficient
tension being put upon it to keep it in its place. The whole
resistance of the wire from end to end is not far from
oV of an ohm at about 15C.
The wire was carefully calibrated by measuring the difference
in the resistance of two pieces of thick brass wire of such lengths
that the difference of their resistances was about equal to
that of thirty divisions of the bridge wire : and this difference
was measured at about a hundred different equidistant
positions all along the bridge wire, and found to be so nearly
the same that no table of calibration was deemed requisite.
To protect the bridge wire from injuries, as well as to preserve
it from being heated by radiation from surrounding bodies, a
wooden ring vv is fastened down on the baseboard. The
ring is IJin. wide and fin. deep, and its internal
diameter is lin. greater than that of the ebonite disc. The
wire, therefore, lies hidden away on the side of a square-
sectioned circular tube ; and, furthermore, a shield of
cardboard faced with tinfoil lies upon the face of the disc e,
extending just beyond the ring. An aperture is cut in this
shield to permit the passage of the trigger, as well as to allow
the vernier to be read. By this means the wire is not only
out of sight, but out of reach of all radiation as well as
mechanical injury.
Arrangements for determining the Temperature Variation
Coefficients of Coils. To determine the temperature variation
coefficient of any given coil we proceed as follows : Three
other coils are provided, two of them nearly equal in resistance,
which we will call 1 and 2. A third coil, 3, must be taken,
whose resistance is nearly equal to that of 4, the coil whose
variation coefficient is desired (see Fig. 62). The terminals of
3 are inserted in the mercury cups a and c, those of 4 in V and
ELECTRICAL LABORATORY EQUIPMENT. 157
d', those of 1 in p and r, and those of 2 in q r and s'. Now the
operation to be conducted is to keep the coils 1, 2, and 3 at a
fixed temperature, and to keep 4 successively at two known
temperatures differing by about 15C., and to obtain the differ-
ence of the resistances of 3 and 4 at these two temperatures.
The difference of these differences, divided by the difference of
the temperatures, is the mean coefficient of variation of resist-
ance between these temperatures. The chief difficulty to be
contended with is that of keeping the temperature of the coils
constant during the operation, and of ascertaining what that
temperature is ; for, as Prof. Chrystal has remarked in his
report (Brit. Assoc. Report, 1876), it is not easy to tell whether
the temperature of the water in which the coil rests is identi-
cally the same as that of the wire, since the latter is embedded
in a mass of slowly conducting paraffin. To reduce as far as
possible the difficulty of keeping the coils at a constant tem-
perature, they are placed in water vessels made of zinc (see
Fig. 65). These water boxes are composed of two cylindrical
vessels an outer case 9iu. high and 8in. in diameter, and an
inner one of lesser size ; the two are connected at the top, so
that they form a sort of jar with hollow sides and double
bottom. This interspace forms an air-jacket. Around the
inside vessel near the top is a row of small holes ; and two
tubes communicate at the bottom one with the inner vessel
and the other with the annular interspace. The top is closed
by a wooden lid with apertures for thermometer and stirrer.
Water can be made to flow from the supply pipes into the
inner vessel : it rises up and overflows through the holes, and
drains away down the interspace and out by the other pipe.
The bodies of the four coils are placed in four water boxes
of this description; and water from the town mains being
sent in a continuous stream through all four water boxes, the
coils are rapidly brought to and maintained at a known
temperature. Any desired temperature can be given to one
coil by leading warm water from a cistern into its vessel. The
annular air-tilled space renders the rate of cooling very slow.
158
ELECTRICAL LABORATORY EQUIPMENT.
Hence the coils, once at the desired temperature, can easily
be kept there. Fig. 63 gives a sketch of the arrangement, two
of the water boxes being removed to show the connections.
The advantage of the somewhat complicated arrangement of
copper bars will now be seen. We can, without withdrawing
the coils 3 and 4 from their water boxes, and without in any
way disturbing the other arrangements, reverse the position of
ihe coils 3 and 4 on the bridge, by simply lifting up the legs
FIG. 65.
half an inch and changing the mercury cups into which they
clip. Thus the legs of coil 3 are changed from cups a and c
to I and d, and those of coil 4 from V and d r to a' and c'.
This exchange does not occupy more than a few seconds ; and
hence we can obtain the two readings necessary to give the
difference of the resistance of the coils 3 and 4 when they are
.at different temperatures in a very short time. During this
short time the temperatures of the two coils will not change
perceptibly, protected as they are by an air-jacket.
ELECTRICAL LABORATORY EQUIPMENT. 159
In the ordinary form of straight bridge there is considerable
trouble in exchanging the coils, because the water vessels
have to be moved and the mercury cups readjusted ; and
all this time the coils are cooling, so that the two
readings are never made under the same circumstances as
regards temperature. Beginning, then, with all four coils at
the same temperature, we take the difference between 3 and 4.
To get them all at the same temperature, water from the town
mains is allowed to circulate through the system for half an
hour. At the end of this time the difference of 3 and 4 is
taken ; and several readings are taken at small intervals of
time to see if the temperatures are constant. This being
done, the temperature of coil 4 is raised by the introduction
of warm water until it is about loC. above that of coil 3. It
is best to raise the temperature about 20C. above the other at
first, and keep it there for 20 minutes, and then let it fall
very slowly. In this way coil and water cool together, and
an equilibrium of temperature is established between them.
The diffeience between 3 and 4 is again taken; and from
these two readings we have, as seen above, the mean
variation coefficient between the two temperatures. Another
method, which would probably be a more accurate one for
obtaining the mean coefficient of variation between 0C. and
15C., would be to wait until the temperature of the water in
the town mains was about 15C., and then to keep three of
the coils at that temperature, and to cool the fourth by means
of ice to zero. If then all four were kept at 15C. and the
observations repeated, we should have the means of finding
the variation coefficient of the fourth coil between 0C. and
15C. Prof. Chrystal in his report threw out the suggestion that
resistance coils should have a thermoelectric couple attached
to them, one junction being buried in the heart of the paraffin
surrounding the wire, and the other outside. This has been
tried in some coils recently made, and proves a satisfactory
method of ascertaining the equilibrium of temperature
between the wire and the water.
160 ELECTRICAL LABORATORY EQUIPMEXT.
Another source of error in the ordinary methods arises
from uncertain or variable resistances at the mercury cups.
It is important that the copper legs of the coil terminals
should press very firmly against the tops of the copper pins-
on which the india-rubber tube cups are fixed. To ensure
this, the plan adopted is to fasten on the coil legs an ebonite
clamp. Along the edge of the wooden promontory j h i
(Fig. 62) are put brass pins, m ; and by means of steel spiral
springs fixed to these and attached to the clamps the coil
legs are pressed down very firmly (see Fig. 63). The ends of
the pins which carry the india-rubber cups and the ends of
the coil legs being well amalgamated, we get, when they are
thus firmly pressed in contact, a very good joint, and one
whose resistance is small and constant. If the clamps are
not used, then one leg may get lifted up a little, and thus a
short length of mercury interposed, which leads to an error in
a reading.
Example of a Determination of the Variation Coefficient of
a Coil. In the bridge constructed on the above plan for the
Cavendish Laboratory, Cambridge, the whole resistance of the
platinum-iridium wire is very nearly O0512 of an ohm, or
not far from V of an ohm, at about 15C. As the whole
length can be divided by the vernier into 10,000 parts, this
gives as the value of y^ of a division ^W^rro of an ohm.
The unit in the following example is y 1 ^ of a division. To
secure the greatest accuracy of measurements a sensitive low-
resistance galvanometer must be used. The image of a
wire strained across a slit is reflected on a scale in the usual
way, and read at a distance by means of a telescope. The
galvanometer should give an indication, when used with pre-
cautions, due to a difference of one-tenth of a division when
comparing two ohm coils. But as the temperature can hardly
be measured with certainty to within less than ^ of a degree,
this alone renders such refinement of reading nugatory, in the
absence of better methods of ascertaining with certainty the
real temperature of the wire.
ELECTRICAL LABORATORY EQUIPMENT.
161
An example may be here given of the use of this bridge in
comparing two resistance coils. Call them F and K. Let K
be the coil whose variation coefficient is required.
I. Difference of Resistance of Coils F and K at 11C.
Bridge Readings.
Difference.
Exp i
5000
4955
4954
4955
45
46
45
5000
j 5000
The first column gives the number of experiment, the
second the reading with the coils F and K in one position on
the bridge, the third when F and K are reversed or have
exchanged places on the balance; and the fourth gives the
difference of their resistance at 11C. in units of the bridge
wire.
II. Difference of Resistance of Coils F and K at 28'2C.
Bridge Readings.
Difference.
Exn. i. .
5439
5442
5440
4492
4497
4490
947
945
950
Exp ii
As before, the fourth column gives the difference of F and
K at 2S-2C. Taking the mean difference at 28'2C. to be
947 units, and that at 11C. to be 45 units, we have
947 -45
--^ umts
as the mean variation coefficients between 11C. and 28C.
in units of bridge wire. Since the coils F and K are approxi-
mately ohm coils, this gives as the variation coefficient of the
coil K -0262 per cent. This coil was of platinum-silver wire.
These three determinations occupied about an hour and a half,
during which time many more readings were taken, all closely
agreeing with the above. The actual measurement of the
differences requires but a few moments to effect, the principal
162 ELECTRICAL LABORATORY EQUIPMENT.
expenditure of time being that required to bring the coils
to the same temperature as the water.
In practical laboratory or testing room measurements of
resistance the slide wire form of bridge is not much used.
It is more convenient to employ one of the forms of plug
bridge. In this arrangement the resistances, which form
three arms of the bridge, consist of coils of insulated wire
wound on bobbins and contained in a box. These resistance
coils are connected in series as required. There are two
principal modes of effecting this junction. The top surface of
the box generally consists of a slab of ebonite, on which are
fixed brass blocks. In the series pattern or Post Office pattern
FIG. 66. Arrangement of Resistance Coils, Blocks and Plugs in a Series
Pattern Bridge.
of bridge the brass blocks are arranged in rows and the coils
connected between them, as shown in Fig. 66. Each block
is bored out in such a manner that a brass plug fitting into a
conical hole drilled partly in one block and partly in the
adjacent one metallically connects the blocks and short-
circuits the coil joined in between them. The plug is care-
fully ground in, so that the interconnection offers only a
negligible resistance. Hence, in the case of such an arrange-
ment of coils interconnected by blocks, the insertion or
withdrawal of plugs cuts out or adds resistance into the circuit
in which these coils are connected.
In the series form of plug bridge the ratio arms generally
consist of five coils having resistances respectively of 1, 10,
100, 1,000, and 10,000 ohms. The third or measuring arm
ELECTRICAL LABORATORY EQUIPMENT.
163
-consists of a series of sixteen coils having resistances of 1, 2,
2, 5, 10, 20, 20, 50, 100, 200, 200, 500, 1,000, 2,000, 2,000,
5,000 ohms. The box is usually provided with two contact
keys and terminals for the galvanometer, battery, arid resistance
to be measured. The chief objections to the series pattern of
plug bridge are that the withdrawal of any plug from a hole
tends to loosen all the rest and so creates bad contacts. Hence
it is necessary to be continually going over the plugs and
tightening them up. Moreover, plugs withdrawn are not in
1
FIG. 67. Arrangement of Coils in Dial Pattern Wheatstone Bridge.
tise, and are therefore in danger of being oxidised or spoilt by
l>eing laid about on the table or held in a damp hand.
These objections are avoided in the form commonly called the
dial pattern of bridge. In this form the measuring arm of the
bridge consists of a series of decimal coils viz., nine 1-ohni
coils, nine 10-ohm coils, nine 100-ohm coils, &c. These coils are
connected between ten blocks fixed on the upper surface of
the box. These blocks are arranged round a central block (see
Tig. 67). Ten conical holes are bored out in between the
164 ELECTRICAL LABORATORY EQUIPMENT.
central block and the outside blocks, and only a single plug is
employed. As the plug is moved from hole to hole it puts in
series between the first outside block and the central block any
resistance from zero to 9 ohms, zero to 90 ohms, and so on,
A set of three, four, or five of these coils and dials are arranged
in and on the box, and serve to set in series units, tens,
hundreds, &c., of ohms, the different dials being intercon-
nected, the central block of one dial being connected to the
FIG. 68. Standard Bar pattern Wheatstone Bridge.
first outside block of the next. Manufacturers often arrange
the blocks in a rectangular form, as in Fig. 68. In Fig. 69 is
shown a diagrammatic scheme of the arrangement of coils in
a standard Wheatstone bridge of the above kind.
In an electrical laboratory one table should be devoted to
a dial or bar pattern resistance bridge. The bridge should
be contained in a wooden box, which can be closed when
the apparatus is not in use to keep light and dust from
EL ECTRICA L LA BORA TOR Y EQ UIPMENT.
165
the ebonite slab. The battery should consist of three or four
dry cells of the Leclanche type. The galvanometer should
be a movable coil galvanometer, having a resistance of 500 to
1,000 ohms. Thick flexible copper cable connectors should
be brought from the terminals of that arm of the bridge in
which the resistance to be measured is placed to two
mercury cups fixed on a wooden stand. In these cups can
be inserted the extremities of any coil or wire the resistance
of which is required, and this can be determined in a few
moments of time. Fuller details of the processes of measure-
ments and necessary precautions are given in Chapter II. of
this volume dealing with the measurement of resistance.
FIG. 69. Arrangement of Resistance Coils, Plugs and Block in Bar
Pattern Bridge.
The laboratory equipment must include some form of slide
wire bridge suitable for rough measurements, and also a
standard slide wire bridge for the comparison of coils by the
arey Foster method.
A compact form of bridge for this latter purpose is that
devised by F. H. Nalder, as shown in Figs. 70 and 71.* The
ratio arms of the bridge consist of two coils, generally 1 ohm,
10 ohms, 100 ohms, or 1,000 ohms, wound on one bobbin.
* See The Electrician, Vol. XXXI, p. 241, or Proc. Phys. Soc. Lond., June 1893.
166
ELECTRICAL LABORATORY EQUIPMENT.
The bridge consists of massive bars of copper mounted on an
ebonite slab. In these bars are formed mercury cups, into
which the copper terminals of the coils are dipped. The-
ratio arm coils are connected in between the cups A A lr
B B x (see Fig. 71). The coils to be compared are connected
to the cups I Ij, J J r In the space between the bars is-
a circular disc of ebonite which carries certain copper con-
necting bars. When these bars are placed in one position
they connect the coil placed in cups A A 1 in series with the-
coil placed in cups I I x and that placed in cups B B x with
FIG. 70. Nalder Differential Resistance Balance..
that placed in cups J J^. When however the copper inter-
connectors are lifted up and replaced in a different position
they exchange the places of the coils in I I x and J J r The
slide wire of the bridge is a very short platinoid wire, G,
and the instrument is provided with a n umber of these
slide wires of suitable resistance per centimetre for various
comparisons.
Bridges are also constructed for quick measurement, where
great accuracy is not required, in which radial arms moving,
round dials and making contact with studs are made to/
ELECTRICAL LABORATORY EQUIPMENT.
167
throw the necessary resistance coils into the measuring arm
of the bridge. A bridge of this kind is useful in rapidly
taking the preliminary reading of the resistance of a coil to
be subsequently more carefully measured in a standard
bridge. It then answers the same purpose as the " finder "
on an astronomical telescope.
The special forms of low-resistance bridge will be dealt
with in the section on resistance measurement.
FIG. 71. Connections of Xalder Kesistance Balance.
Owing to the action of light and dust in deteriorating the
surface insulation of ebonite, the ordinary form of plug
Wheatstone bridge with lacquered brass blocks and ebonite
slab is not a good one to employ in the workshop. The
Author has therefore designed a form of workshop resistance
balance in which there is no exposed ebonite or metal parts.
168
ELECTRICAL LABORATORY EQUIPMENT.
The box is made of oak, and the lid or upper surface presents
only a set of rows of holes (see Fig 72). Underneath the lid
and attached to it are a series of ebonite rings, on which are
arranged a row of brass blocks and a brass disc. Eesistance
coils of equal value viz., units, tens, or hundreds of ohms
are joined in between the blocks as in the dial arrangement,
and plugs shaped like a bradawl, placed in one of the
holes bored out partly in the blocks and partly in the central
disc, serve to throw in any required resistance between the
first block and the disc. The resistances forming the ratio
arms are in the same manner arranged to be used in series
with one plug only for each ratio arm. The ratio arm coils
are therefore O'l, 0'9, 9, 90, and 900 ohms, and these, when
joined in series, give 1, 10, 100, and 1,000 ohms as required.
-20-
FIG. 72. General View of the Fleming Workshop Bridge.
The resistance bobbins on which the coils are wound are
formed in the following manner :
Two hollow half-cylinders of thin sheet copper (Fig. 73) are
constructed, each having a lug, and two of these half-cylinders
are put together with a thin separating piece of ebonite and
bound together with a thin silk tape. This constitutes the
bobbin. The resistance wires of manganin are then cut the
proper length, and the two ends of the wire are soldered to
the two lugs of the copper half-cylinders (Fig. 74), the
ELECTRICAL LABORATORY EQUIPMENT.
169
remainder of the wire being wound non-inductively on the
bobbin and tied in position by a thin silk tape. The wire is
therefore so arranged that it quickly gets rid of any heat, and
no paraffin wax is used to overlay the wire or coils.
The measuring arm of the bridge consists of three sets of
coils units, tens, and hundreds each set consisting of nine
coils interposed between 10 brass blocks, which are arranged
in a cii demand carried in a sort of ebonite tray fixed on the
EBONITE SEPARATOR
COPPER -
HALF BOBBIN
^.COPPER
HALF BOBBIN
FIG. 73. Construction of the Resistance Bobbins.
FIG. 74. Method of Winding.
underneath side of the teak lid of the box. These blocks are
interconnected as required with a central brass ring by means
of a travelling plug. A diagram of the bridge is given in
Fig. 75, and a section of the dials in Tig. 76. The plugs
resemble bradawls, except in their lower extremities, and
have a substantial handle ; they are kept when not required
in a sort of umbrella stand attached to the box, seen in the
170
ELECTRICAL LABORATORY EQUIPMENT.
general view of the instrument, Fig. 72. These plugs are
inserted into interconnecting holes between the brass blocks,
1
&l
Q
,3
to
5
l
ELECTRICAL LABORATORY EQUIPMENT.
171
and the common ring through small holes bored into the lid
of the box. Hence the outer surface of the box exhibits only
sets of small holes arranged in circles and which ars marked
respectively units, tens, hundreds.
In order to prevent dust getting into the holes between the
brass blocks, there is a contrivance in the form of a self-
closing shutter. On the underneath side of the lid are a
series of circular discs of thin ebonite, which are perforated
by holes corresponding with the holes for the plugs in the lid
of the box. These circular shields move round a central
pivot, and by means of a spring are kept so turned that the
holes in the shield do not normally coincide with the holes in
the box lid. Hence all these box lid holes are closed as it
were by a small shutter, but when once opened and a plug
inserted in the hole the plug prevents the shutter from closing.
The circular shutters can be turned round by means of a
BRASS BLOCK
BRASS BLOCK
EBONITE RING
FIG. 76. Section of Dial.
common bar and finger pin protruding through the lid, so
that, in order to insert the first plug when commencing his
test, the user presses back the pin and thereby opens all the
shutters. But the moment all the plugs are withdrawn from
their hole, the shutter under the lid springs back and closes
all the holes belonging to that dial.
The ratio arm of the bridge is formed of a series of coils
which are arranged dial fashion, and which are therefore not
1, 10, 100, 1000 ohms as usual, but 1, 9, 90, 900. Two plugs
are therefore provided for the ratio arm dials, and the ratio
arm dial is furthermore marked in such a manner that the
user has no difficulty in discovering the number by which he
must multiply and the number by which he must divide the
ratio arrn resistance to get the resistance of the circuit
measured. The shutter closing the holes of the ratio dial is
172 ELECTRICAL LABORATORY EQUIPMENT.
independent of the others, and is not provided with a finger
pin for opening. The spring which keeps the shutter of this
dial normally closed is not very strong, and the shutter is
easily pushed back by the point of the first plug as it is
inserted.
The whole of the connections are made under the lid to
three pairs of terminals, marked on the outside as in Fig. 72,
and in addition two keys are fixed under the lid, which are
manipulated by two little ivory buttons, like electric bell
pushes, protruding through the lid. There is therefore abso-
lutely no exposed ebonite to deteriorate in insulation, and no
lacquered brass, with the exception of the aforesaid six ter-
minals, the handles by which the bridge is carried about, and
the plugs. The terminals are constructed with a peculiar
kind of lip, which renders it easy to grip in them either a
single large wire like a No. 10 wire or a single small wire
like a No. 40.
One other point is worthy of notice. In the ordinary pat-
terns of plug bridges the frequent use of the plugs wears
them down into a shoulder, so that they no longer fit tightly
into the plug holes. In this workshop form of bridge the
plug has a semi-circular groove turned in it at such a height
in the plug that when in place the top of the block is just
on a level with the middle of the groove. This device is an
effective cure for " shouldering " in the plugs.
In the selection of a Wheatstone bridge for very accurate
work in resistance measurement it is well to have in view
the objections which can be raised against the ordinary form
of plug and coil bridge. These objections may be summarised
as follows : The bridge, as supplied by most makers, consists
of a wooden box, with an ebonite slab forming the top, on
which are fixed the brass blocks with conical brass plug
connectors. The resistance coils are in the box, and are
connected between the plug blocks. If platinum-silver wire,
or any material not having a zero temperature coefficient,
is used for the manufacture of the coils, then there is very
considerable difficulty in ascertaining the true temperature
of the coils when the resistance measurement is actually
being made. A thermometer placed with its bulb in the box
ELECTRICAL LABORATORY EQUIPMENT. 173
merely gives us the temperature of the air in the box ; that
of the coils, perhaps embedded in paraffin or shellac, may
be very different, and moreover, the temperature of each
coil which has current passing through it may not be the
same.
In the next place, very great labour is involved in checking
the relative value of the coils, and, owing to dirt or slight
want of fitting of the conical plugs, the value of the resistance
added or removed by withdrawing or inserting a certain plug
may not be at all times precisely identical. In the series coil
or Post Office pattern of plug bridge the putting in of one
plug slightly displaces all the brass blocks, and the expansion
of the ebonite top -prevents perfect fitting of the coned
plugs.
The dial pattern of bridge is therefore preferable to the
series coil pattern, because each of the plug blocks is-
independent. Furthermore, the coils, as usually made r
cannot be annealed after being wound, and hence are liable
to secular changes in resistance due to strain.*
Finally, the last adjustment of balance cannot always be
made with integer coils, and the last decimal place in the
resistance measurement has to be estimated from the
galvanometer deflection (as described in the section on
resistance measurement).
To meet the above objections a form of standard bridge has
been designed by Messrs. Callendar and Griffiths, of which a
description is given in Chapter II. f
14. Electric Quantity-Measuring Instruments.
Ballistic Galvanometers. The passage of a certain electric-
discharge or quantity of electricity through a circuit,
* For a good summary of all that can be said against the ordinary form of
plug resistance bridge the reader is referred to a series of articles on
"The Electrical Measurement of Temperature," by Mr. G. M. Clark, in.
The Electrician, Vol. XXXVIII., p. 274, 1897.
f See also Tlie Electrician, Vol. XXXVIII., p. 747, 1897.
174 ELECTRICAL LABORATORY EQUIPMENT.
reckoned as the time-integral of a varying electric current
having finite limits, is measured practically either by a
ballistic galvanometer, if the whole discharge is over in
a second or less, or, if the discharge endures for a very
considerable time, it is measured by some form of ampere-
hour meter. For a certain class of magnetic work the
ballistic galvanometer is a necessary appliance. The most
practical and useful form of this instrument is a movable
coil fixed magnet galvanometer. The movable coil may be
either a narrow, shuttle-shaped coil, as in the instruments
designed by Ayrton and Mather, or a circular, ring-shaped
coil, as in the ballistic galvanometer of Cronipton.
Deferring at present a detailed discussion of the principles
of the ballistic galvanometer, we may here merely state that
the elementary theory of this instrument is as follows : If
through the coil of the galvanometer an electric discharge or
very brief current is permitted to take place, the magnetic
field due to the discharge causes an impulsive torque or
couple to act upon the movable portion of the instrument,
whether the latter is the magnet or the coil. // the discharge
is all concluded before the movable portion has been sensibly
displaced from its zero position, then the following conditions
hold good :
Let I denote the moment of inertia of the movable portion of
the galvanometer.
Let pO denote the control or torque brought into existence
to restore that part to its original position when displaced
through an angle 6.
Let o> be the angular velocity of the moving portion at
any time t after the displacement begins.
If, in the first place, we neglect the retarding effect of
friction, we may say that the equation of motion of the
moving system at the time t is expressed by the equation
which is the analytical statement of the fact that the rate
ELECTRICAL LABORATORY EQUIPMENT. 175
at which the angular momentum of the moving system is being
destroyed at any instant is proportional to the angular dis-
placement of the movable portion.
Since o> = ,
at
we have lff+ M =
at*
as the equation of motion of the coil when we neglect
frictional retardation of all kinds.
From the above equation it is easily shown that the
duration (T) of one complete oscillation of the movable
system is given by the equation
-2* /?.
V M
Suppose the coil at rest in the field of the controlling
magnet, and let a discharge be made through the. coil, which
is all completed before the impulse sensibly overcomes the
inertia of the coil and gives it an angular displacement or
" throw." If B is the induction density or field strength due
to the fixed magnet at the place where the coil is situated,
and if i is the coil current at any time t after the beginning
of the discharge, then, assuming the coil has not sensibly
moved from its zero position, and neglecting as small the
reaction of the coil current on the fixed magnetic field, we
may say that the coil is experiencing a torque or couple
represented by CBt, where C is some constant depending on
the form of the coil.
Hence, as above, if o> is the angular momentum of the coil
at that instant,
4 =
dt
or Ida =
where I is the moment of inertia of the coil. The product
idt is numerically equal to the small quantity of electricity
176 ELECTRICAL LABORATORY EQUIPMENT.
dq which has passed through the coil in the element of time dt-
Hence
Suppose time reckoned from the instant when the discharge
begins, and that the discharge is complete before the coil has
experienced any appreciable change in position. The result of
the passage of the whole quantity Q of the discharge through
the coil will be to apply to it an impulsive torque which will
cause it to leave its zero position with a definite velocity 12,
Under the above conditions we can integrate the last equation,
and omitting the constant of integration, write
(1)
The angular energy with which the coil leaves its zero position
is equal to JI12 2 .
If the impulsive torque gives the coil a twist through an
angle 0, and if /m is the torque due to the suspension, whether
bifilar or unifilar, per unit angle, then ju.9 is the restoring
or opposing torque due to the suspension brought into
existence by the displacement through an angle 0. Hence
the potential energy of the coil system at the end of its swing
is equal to J/x$ 2 , or to half the product of the torque /mO and an-
gular displacement 0. Accordingly, we must have an equation
between the kinetic energy imparted to the coil and its
potential energy when at the position of final displacement, or
iK 2 =M>- ........ (2)
Combining together equations (1) and (2), we arrive at_the
equation
or, Q = G0.
The above equation shows that, under the limitation assumed,
the angular excursion of the coil is proportional to the whole
quantity of electricity which has passed through the galvano-
meter.
ELECTRICAL LABORATORY EQUIPMENT. 177
If to the coil is attached a mirror in the usual manner, and
the lamp and scale is placed at a distance of say one or two
metres so that the angular deflection of the coil does not exceed
5 deg. or 10 deg., the corresponding excursion or displacement
of the spot of light upon the scale will be proportional to the
total quantity of electricity which has passed through the coil.
The ballistic constant (G) of the galvanometer is the number
by which the scale deflection in millimetres or centimetres
must be multiplied in order to obtain the total quantity of
electricity in microcoulombs which produced that observed
deflection.
In the chapter on the Measurement of " Electric Quantity "
instructions will be given for the proper standardisation of
the galvanometer. In the meantime, a few of the qualities
which should be possessed by a ballistic galvanometer may
be discussed.
The movable magnetic needle ballistic galvanometer is a
most troublesome instrument to use, owing to the needle dis-
turbances created by outside currents and magnetic fields.
The most practical form of ballistic galvanometer for the
electrical testing room or laboratory is a movable coil galvano-
meter with fixed magnet. This galvanometer must have its
coil wound on a non-conducting frame, and may be either a
narrow coil i.e., a coil of long or shuttle-shaped form, as in
the Ayrton-Mather galvanometer shown in Fig. 45, page 123
or a circular bifilar suspended coil, as in the Crompton-
d'Arsonval galvanometer shown in Tig. 46, page 124. In
either case, if the galvanometer is to be used for ballistic pur-
poses, as little "damping" must be present as possible. Hence
the coil must not be wound on a closed metallic frame, and
preferably not surrounding a soft iron core. On the other
hand, when used simply as a deflectional instrument it is
desirable to secure as much damping of the coil as possible.
In this last case winding the coil on a metallic frame is an
advantage, because the eddy currents set up in the frame by
its movement in a strong field retard the movement and bring
178 ELECTRICAL LABORATORY EQUIPMENT.
the coil to rest without unnecessary vibrations when the
current through it is stopped.
When, however, the galvanometer is to be used for ballistic
purposes, then it should be as little damped as possible. The
free period of vibration of the coil in this case, when
disturbed, should not be less than five seconds, and for many
purposes preferably 15 seconds at least. It is quite useless to
employ for many experiments a ballistic galvanometer having
a smaller free period of vibration, since then the fundamental
requirement for ballistic work is not fulfilled. The galvano-
meter should, however, have a damping arrangement by which
a small, properly-timed current may be sent through the galvano-
meter coil to bring it to rest when its excursion has been made,
and thus save unnecessary loss of time in experiments. This
may be achieved by the use of a shunt circuit (consisting of
a small dry cell), a very high resistance (consisting of a slip
of vulcanised fibre rubbed over with plumbago), and a contact
key, all joined in across the galvanometer terminals. By
making suitably timed taps on the key the galvanometer coil
can have small currents sent through it which will bring it
at once to rest. In the case of low resistance ballistic
galvanometers, merely short-circuiting the terminals of the
galvanometer by closing a key in that circuit is sufficient to
destroy at once the vibration of the coil and bring it to rest.
Each ballistic galvanometer used in the laboratory should
be set up on a very steady stone shelf or pillar, and the usual
lamp and scale adapted to it. In this connection it may be
pointed out that by far the most convenient scales to use for
galvanometer purposes are the semi-transparent celluloid
scales. These are divided into millimetres, and should be
set up on a firm stand at a distance of one metre or
1,000 millimetres from the mirror. The source of light
should be an incandescent lamp with a simple horseshoe
filament. Over this may be placed an asbestos hood with a
slit in it, so that only the image of one side of the filament
is thrown upon the scale. The galvanometer should be
ELECTRICAL LABORA TOR Y EQ UIPMENT. 179
provided with a concave mirror of one metre focus. It is
then easy to so place the incandescent lamp that the sharp
image of one leg of the filament is thrown upon the semi-
transparent scale. The scale must have a lateral movement,
so that it can be moved parallel to itself and perpendicular
to the direction of the ray of light reflected from the mirror
when the galvanometer coil is in its zero, or undeflected,
position. The scale deflection of the sharp line of light upon
the screen, measured in millimetres and divided by 1,000,
gives very approximately the tangent of twice the angle of
deflection of the galvanometer coil ; and this may be taken to
be proportional to the coil deflection when that angle does
not exceed 10 deg.
The testing room should be provided with at least two
ballistic galvanometers, one having a resistance of about
20 ohms and the other a resistance of 500 to 1,000 ohms or
more. This latter galvanometer should have a time of free
vibration of its movable coil of at least 12 to 15 seconds.
The correction to be applied to the excursion of the coil
to allow for air friction or other retarding forces which tend
to diminish the deflection, as well as other precautions in the
use of the ballistic galvanometer, will be given in a later
chapter.
In connection with the standardisation of this instrument
it is useful to possess an apparatus called a graded condenser
as well as a standard half-microfarad condenser. These last
instruments are virtually Leyden jars, consisting of insulating
sheets of mica or of paraffined paper coated on both sides
with tinfoil, but so as to leave a margin of uncoated surface.
A collection of these elements is assembled together, so that
all the tinfoil coatings on one set of sides are in metallic
connection and all the corresponding opposite side coatings
also in connection.
The construction of a standard condenser is a matter
requiring some experience, and it need only here be said that
it is not worth while to purchase one from any except a
N2
180 ELECTRIC A L LABOR A TOR Y EQ UIPMENT.
manufacturer of repute. A standard half -microfarad con-
denser is, however, a necessary article. Two or three other
condensers should be also obtained, having a capacity of
about one microfarad each. Also a graded condenser,
divided into microfarads and fractions of microfarads such as
01, 0-2, 0-2, 0-5, 1-0, 2-0, 2-0, and o'O, is a very useful appliance.
All these condensers should have been tested with 1,000 volts
on their terminals by the maker, so that no risk may be
incurred in using them on 100-volt circuits. The proper
charge and discharge keys for use with the condensers can
be procured as required.
In connection with the measurement of electric quantity,
in those cases in which the duration of the discharge is
considerable (as in secondary battery tests) it is exceedingly
desirable to have at hand an ampere-hour meter which will
automatically record the total quantity which has passed
through it in coulombs or microcoulombs, and at the same
time show the variations of current. Of these instruments
the most useful is the graphical recording ampere-hour
meter. In this instrument a drum covered with paper is
rotated by a clock train at a uniform rate, say once in 24
hours. A pen moving over the surface of the drum is
displaced by some mechanism which acts as an ampere meter.
In the Holden ampere-hour meter this current-measuring
part is constructed by utilising the expansion produced in a
series of fine wires placed in parallel. A lever arrangement
enables the " sag " of these wires, when heated, to displace
the pen over the drum by an amount depending on the
current through the wires. If, then, the pen is variably
displaced as the drum revolves, we have a curve described 011
the paper which shows, by the value of its ordinates at each
moment, the ampere value of the current. If the displace-
ment of the pen is exactly proportional to the current, and if
the speed of the drum is uniform, then the area of the curve
described by the pen is proportional to the whole quantity in
ampere-hours which has passed through the instrument. In
ELECTRICAL LABORATORY EQUIPMENT. 181
^secondary cell testing the possession of a correct graphic
recording ampere-hour meter of the above kind saves much
itime and many tedious observations.
Bemarks on the subject of ampere-hour meters generally
for use in the commercial supply of electric current will be
reserved for the section dealing with meter testing.
15. Instruments for the Measurement of Electric
Power. Wattmeters. In many pieces of testing work,
particularly in certain alternating-current measurements, it
is necessary to be able to measure at one operation the
power, or mean power, given to an electrical circuit, which
may be called the power circuit. This measurement is made
by means of a wattmeter.
In its most general form a wattmeter consists of two coils
of wire, one of which is fixed and is called the current coil
.and the other of which is movable and is called the pressure
coil. The circuit in which the power to be taken up is to be
measured is joined up with the wattmeter, so that the current
passing through the circuit is that passing through the
current coil. The pressure coil is then joined up so (i.) that
one terminal is connected to the entrance end of the current
coil and the other to the exit end of the power circuit, or
(ii.) so that the pressure coil is connected to the ends of the
power circuit.
It will be seen that, if the pressure coil is joined up in the
first manner, the voltage on the pressure coil is that due to
the fall in volts down the current coil as well as that in the
power circuit. If, on the other hand, it is joined up in the
second way, then the current in the current coil is not
simply that in the power circuit, but takes account also of
the current in the pressure coil.
In dealing with the particular measurements in which the
wattmeter is employed we shall point out how it should be
used. Meanwhile, it may here be stated that if the pressure
coil is held in a position either with its plane parallel to that
182 ELECTRICAL LABORATORY EQUIPMENT.
of the current coil or embracing it, and with its plane at right
angles to it, then, when connected up with the power circuit
there will be found to be a mechanical force or torque
between the coils. The restraining force required to hold the
coils in any definite relative position in which the electro-
dynamic force between them is not zero is proportional to the
mean product of the values of the currents passing through
the coils. If one current is the current through the power
circuit, and the other current is proportional to the potential
difference between the ends of the power circuit, then their
mean product is proportional to the mean power taken up in
the power circuit. The controlling condition, however, is
that the free time of vibration of the movable coil of the
wattmeter must be large compared with the periodic time of
the currents, if these are periodic.
The wattmeters used in the testing laboratory generally
take one or two forms. In the Siemens form the movable
coil embraces the fixed coil (see Fig. 77). The movable coil
is suspended by a few fibres of floss silk, and has attached to
it one end of a spiral steel torsion spring. The other end of
this spring is fixed to a torsion head, with an indicating arm
moving over a circular divided scale. The movable coil
carries a pointer, by which it can be brought into a recognised
and fixed position. The arm attached to the torsion head
can be moved independently of the head, and clamped when
desired by a clamping screw. The current enters and leaves
the movable pressure circuit by means of mercury cups, into
which dip the amalgamated ends of the movable coil. The
instrument is provided with four terminals, two of which
are the extremities of the fixed coil and two are the terminals
of the movable coil.
The other form of wattmeter is that of Lord Kelvin r
which is similar in general construction to an ampere balance.
The circuit formed by the coils of the suspended or balance
arm is, however, brought to a separate pair of terminals.
The circuit formed by the fixed coils is separate from that of
ELECTRICAL LABORATORY EQUIPMENT. 183
FIG. 77.- Siemens Wattmeter.
184 ELECTRICAL LABORATORY EQUIPMENT.
the movable ones. One of these forms the pressure circuit
and the other the current circuit of the wattmeter.
Another form of wattmeter is that in which the pressure
coil is suspended by a bifilar wire suspension. In this case
the current enters and leaves the movable coil by the
suspension wires. This form is well adapted for a deflectional
instrument in which the deflections of the movable coil are
read by a mirror and scale.
In the selection of a wattmeter for use in the testing
laboratory, especially if it is to be used with alternating
currents, it is necessary to be guided by the following
facts :
For use with alternating currents there must be no metal
work near the fixed or movable coils. Instrument makers
are far too fond of lacquered brass. They put brass covers
and shields round wattmeters, and carry the coils on brass
pillars and supports. The result is that eddy currents are set
up in these metal portions, which react upon the currents in
the movable coil and destroy the correctness of the indications
of the instrument. An alternating-current wattmeter should,
as far as possible, be constructed of hard, well-seasoned
wood and ebonite, with the exception of wire circuits and
terminals.
A useful form of the instrument is made by providing with
separate terminals to its two circuits the ordinary and cheap
form of Siemens electro-dynamometer.
If the wattmeter is being used with continuous currents,
then it is necessary to so place it that the magnetic axis of the
movable coil is in the direction of the earth's horizontal
magnetic field at the place where it is used. If this is not
done, the terrestrial force will exercise a deflecting action on
that coil. Hence the wattmeter should be used on a rotating
turn-table, which enables it to be rotated in azimuth without
disturbing the level of the instrument.
In dealing with the special uses of the instrument the
various precautions attending its use will be pointed out.
ELECTRICAL LABORATORY EQUIPMENT, 185
16. General Hints on the Outfit of a Testing Labora-
tory. In concluding this chapter a few general hints may
be given as to the equipment of an electrical testing
laboratory.
In most cases where this has to be done by the inexperi-
enced, the general desire seems to be to provide a number of
glass door apparatus cases, and to stock the shelves as far as
possible with the beautiful creations in ebonite and lacquered
brass of the electrical instrument maker. Hence it is that
in so many colleges and technical institutions we find a large
collection of expensive apparatus, very little of which is of
real use in research or commercial work.
The guiding principle in equipping an electrical testing
room should be to buy at first as little as possible, unless and
until the purpose of the laboratory is very clearly defined.
The instruments that are bought as standard instruments
should be very carefully selected, and, as far as possible,
made to careful specifications. An odd lot of galvanometers
bridges, resistance coils, keys, c., should not be bought.
The main purpose of the laboratory having been defined,
whether for teaching, research, commercial testing, or stan-
dardising, the first provision should be in the conveniences
for generating and distributing the currents. Bound the
laboratory should run several ciicuits, with means for bringing
the potential difference at any place to the standard volt-
meters and potentiometer. The principal resistance bridge,
the principal potentiometer, the ballistic galvanometers, the
ampere balances, standard voltmeters, and low resistance
bridge should each be set up complete on its own table,
with everything required for that measurement screwed
down to the table. There should be no moving about of
galvanometers and keys from one place to the other. The
.small local currents required should be obtained from dry cells
of Leclanche type, or from small 2-cell secondary batteries.
The set of apparatus on each table, when not in use, may
be kept free from dust by having a black cloth thrown over
186 ELECTRICAL LABORATORY EQUIPMENT.
it. It stands there, however, ready for use, and the resistance
of a bit of wire or coil or the checking of a voltmeter can be
carried out at a moment's notice without loss of time.
In many laboratories there is an enormous waste of time in
collecting together out of cases, setting up, and connecting
apparatus for the simplest measurement. There is also a
great amount of capital sunk in apparatus pretty to look at
but perfectly useless for real work.
Ample provision should be made, by wire resistances and
carbon resistances, for regulating currents. Galvanometers
should, as far as possible, be movable coil galvanometers, so
that they are not disturbed by the presence of currents in
neighbouring wires. These may be kept covered over when
not in use with cardboard boxes or hoods.
No attempt has been made in the sections of the present
chapter to indicate all the apparatus necessary, as that must
depend on the purpose of the laboratory. In the following
chapters instructions will be given for carrying out the chief
electric and magnetic measurements.
As an illustration of the equipment required in an elec-
trical standardising laboratory, we may conclude this chapter
by a brief description of the arrangements in the British Board
of Trade Electrical Laboratory at No. 8, Kichmond- terrace,
Whitehall, London.* This laboratory was established in
consequence of a deputation, comprising most of the pro-
minent members of the electrical profession, to the Board of
Trade in 1889, for the purpose of urging the necessity of the
establishment of such an institution. A scheme was sub-
mitted by this deputation for the establishment and working
of a standardising laboratory, and this scheme has been kept
in view as far as was consistent with the amount of money
procurable from the Treasury :
The first suggestion for the establishment of a Government electrical
standardising laboratory was given in a Paper read by the Author in
November, 1885, to the Institution of Electrical Engineers (then called the
* See The Electrician, October 5 and 12, 1894, Vol. XXXIII., pp. 665, 693.
ELECTRICAL LABORATORY EQUIPMENT. 187
Society of Telegraph Engineers and Electricians). This Paper was entitled
"On the Necessity for a Standardising Laboratory for Electrical Test
Instruments." The discussion on the Paper led to the formation of a
committee to further this object, and four years later the suggestions of the
Author were realised.
The laboratory exists for three purposes : First, to obtain and preserve
standards for the measurement of electrical quantities ; second, for giving
the standard measurements of those quantities ; and third, to enable the
Electrical Adviser of the Board of Trade to make such tests of instruments
and material as may be necessary in the performance of his duties. No
scientific work outside these purposes can be undertaken.
Six rooms are in occupation in the basement of No. 8, Richmond-terrace,
Whitehall, London. One of these is occupied by the gas engine and dynamos,
used solely for charging accumulators ; another by the accumulators, from
which all the power used in making electrical measurements is obtained.
These two rooms are outside the main building. The rooms within the main
building are, first, the room containing the standards for current and pressure
and the necessary adjuncts ; second, the room containing the transforming
machinery, where the power derived from the accumulators is transformed as
required ; third, the room occupied by the standards of resistance and the
Clark cells used as sub-standards, this room being used exclusively for
measurements connected with resistance and the comparison of electromotive
forces ; and, fourth, the verification room, where commercial instruments
sent for the purpose are verified. Beyond the verification room is fitted a
small chemical laboratory.
The general arrangement of the laboratory is shown in the plai in Fig. 78,
and consists of the various rooms already enumerated. The accumulators in
use consist of a battery of four large 61-plate Crompton-Howell cells, which
are generally used two in parallel for the direct production of large currents,
and 108 11-L E.P.S. cells. The large cells can supply currents of any
amount up to 2,000 amperes for a short time, and are charged in series at
the rate of 200 amperes. The E.P.S. cells are used for running the trans-
forming machinery and for supplying continuous pressure up to 200 volts.
The discharge rate is never allowed to exceed 22 amperes even for short
periods. Current from the large cells is brought into the room containing
the standards of current by mains consisting of flat copper strips, the lead and
return being sandwiched together to avoid magnetic disturbance. A break is
provided just outside this room for the insertion of regulating resistances,
which for the most part consist of carbon rods with suitable terminals. The
use of carbon in this connection has this great advantage in addition to that
of handiness, that as the resistance diminishes with increase of temperature,
the fall of current which would otherwise take place from the slight polari-
sation of the cells and the warming of the metallic circuit can be completely
obviated by choosing suitable lengths and cross sections of carbon. Great
steadiness of even the largest currents for ample time has thus been obtained.
Fine adjustments of current are secured by the use of rheostats formed of
carbon plates under variable pressure inserted either in the main circuit or as
a shunt to the measuring instruments.
188
ELECTRIC A L LA BORA TOR Y EQ UIPMENT.
ELECTRICAL LABORATORY EQUIPMENT. 189
A large electric balance (A, Fig. 78), made under Lord Kelvin's supervision,
is fixed immediately at the point of entry of the above- mentipned large
mains. This instrument can read up to 10,000 amperes. Round two sides
of the current and pressure standards room is fixed a concentric main of
the same pattern as those used by the London Electric Supply Corporation
for trunk mains from Deptford. The outer conductor is cut across at
intervals, and large terminals clamped on at each side of these breaks, to
which the current-measuring instruments are attached, while copper bars are
provided for short-circuiting every instrument. The inner conductor is only
exposed at the two ends, where it can be similarly connected to the outer
conductor either through an instrument or by means of a short-circuiting
strap. A complete anti-induction circuit is thus provided for current. A
shelf of enamelled slate is carried on corbels let into the external wall of
the building underneath the concentric main, as a support for the current-
measuring instruments. The ampere standard B is placed upon a stone
pedestal near the centre of the room, and the auxiliary ampere balance O
upon a similar adjacent support. The volt standard D, which really
measures 100 volts, or one hekto-volt, occupies a third stone pedestal in the
centre of the room. Another instrument of the same pattern is placed at E.
On the shelves round the wall of the room are five sub-standard Kelvin
balances of the following ranges : 1 to 5 amperes (F, Fig. 78), 5 to 30 (G), 30
to 120 (H), 100 to 600 (K), and 500 to 2,500 (L). The first two of these
have aluminium beams. A composite watt-balance is placed at M. One of
the remaining walls R is occupied by various pressure-measuring instruments
for low pressures, and the fourth wall partly by pressure-measuring
instruments for high pressures Q and partly by a switchboard P for
regulating the transforming machinery. A highly insulated platform is
provided for standing on when manipulating the high - pressure instru-
ments. On this board are a pair of Cardew voltmeters, supplemented by
twelve resistance tubes. Each of these is practically a complete Cardew
voltmeter, but without hand movement and dial. Each contains the usual
wires and pulleys, under exactly the same " live " condition as in a working
voltmeter. By means of these resistances, which can, of course, be
independently checked and mutually compared, differences of potential up to
2,150 volts can be measured. A "chain" of voltmeters that is to say, a
set of instruments, the range of each one overlapping two others, as with the
sub-standard ampere balances are placed in this room.
The chief work which has been done in this room is the comparison of the
three standards of current, electromotive force, and resistance. The standard
ampere, as obtained by many repeated determinations by the silver volta-
meter, was passed through the ampere standard, the auxiliary balance, and
through a resistance of 100 ohms, and gave a difference of potential of
ICO volts, which was observed on the volt standard. This 100-ohm resistance
is made of manganin, and is maintained at a constant temperature by oil
circulated by a small electric motor, and by the circulation of water in an
outer jacket. This 100-ohm resistance was compared with the ohm standard,
the value of which was accepted from the British Association determinations.
The volt was thus deduced from the correlation of the ampere and the ohm.
190 ELECTRICAL LABORATORY EQUIPMENT.
The scale of the volt standard is long enough to include the pressures due to
69, 70, and 71 Clark cells, and by direct comparison the value of the cell was
thus determined. The work of carrying out this triple comparison occupied
many months.
A current of about 0*8 ampere is kept continually passing through the
ampere standard to keep it warm and dry. The period of a complete swing
of the standard of current is about half a minute, and hence the need for an
auxiliary balance, to act as the " finder " of a telescope.
The machinery for "gen era ting the required currents consists of a continuous-
current motor and an alternator with shafts in line and both keyed to a
common pulley, while a continuous-current high-pressure dynamo can be run
from this pulley by means of belting. By varying the exciting currents of
these different machines a very delicate adjustment of the transformed
current or pressure is obtained. There are, in addition, various alternating-
current transformers for giving a range of current up to 500 amperes and of
pressure up to 10,000 volts.
The room containing the standard of resistance and Clark cells is a small
room arranged to be kept at a uniform temperature of 16C. In this room
is a Carey Foster bridge, and a Kelvin reflecting galvanometer with a
transparent scale.
The verification room is fitted with a concentric main running around
three sides, elate shelves for the support of instruments ; and a large fireclay
oven 2ft. Sin. wide, 2ft. 6in. deep, and 3ft. high, with plate glass front
perforated with holes for leads, is heated by gas, for testing instruments at
various temperatures. It has been run to a very high temperature, but it is
not proposed to use it for more than 30 C. This room is fitted up with
secondary standards for the measurement of current and pressure up to the
limits of instruments in common use. In this room calibration and tests of
meters have been carried out. This work has nothing to do with the
calibration and sealing of actual house meters, which is carried out by the
London County Council, but relates to the approval of the patterns. In this
room the deci-ampere, deka-ampere, and hekto-ampere Kelvin balances are
fixed.
In the verification of instruments in this laboratory definite
methods are employed for defining the inaccuracy. For
instance, if an instrument reading to 100 volts is sent for
verification at certain points, say 90, 95, and 100, the readings
of those instruments when pressures of those amounts are
applied are given, and not the true values of the scale indica-
tions 90, 95, and 100 on the instrument. It is obvious that
where a large number of instruments have to be checked,
this method results in economy of time and power.
CHAPTER II.
THE MEASUREMENT OF ELECTRICAL RESISTANCE.
1. The Comparison of Electrical Resistances. The
electrical resistance of a conductor may be defined as that
physical quality of it in virtue of which energy is dissipated
in it when an electric current flows along it. This amounts
to saying that a fall of electrical potential accompanies the
flow of a steady unvarying current along a conductor. The
ratio between the numerical values of the fall or drop in
potential (P.D.) down a conductor and the current (C) in it
is a measure of the electrical resistance of that conductor, if
the current is an unvarying or continuous current.
The energy dissipated in the conductor, measured by the
product of the values of the potential fall and the current,
takes the form of heat, and raises the temperature of the
conductor. This temperature change affects the physical
state of the conductor and alters the ratio of potential fall
to current, and hence changes the numerical value of the
resistance. If, however, the heat is so rapidly removed that
change in temperature is not allowed to occur in the
conductor, or if a correction is made equivalent to making
allowance for this change in temperature, then it has been
found that the ratio between the fall in electric potential
down the conductor and the electric current in it remains
the same for the same conductor whether the current is large
or small. This interdependence, or rather exact pro-
portionality of potential fall to current strength, in the case
of conductors traversed by steady currents is called Ohm's
Law.
192 MEASUREMENT OF ELECTRICAL RESISTANCE.
Ohm's law is not a mere truism : it is the expression of a physical fact, and 1
our confidence in the general truth of the statement is an induction from the
results of experiment in particular instances. Ohm's law states the exact pro-
portionality of the current when unvarying to the unvarying electromotive
force producing it. This is not a necessary truth. The electromotive force
E required to produce a current C in a conductor might, for instance, have-
been a function of the current C of the form
Only odd powers of C could have occurred in the expression, because, as the
current reverses its direction when the electromotive force is reversed, the
right hand side of the expansion representing E in terms of C must change
sign with C.
Suppose we consider as important only the first two terms, and write the
expression for E in the form
E = RC(1-K) 2 ).
It has been experimentally shown by Chrystal and Saunders (see British
Association Report, Glasgow, 1876) that in the case of copper A is a quantity
less than 10~ 12 , assuming all proper corrections for temperature made. It
has been also shown by FitzGerald and Trouton* that in the case of a solution-
of sulphate of copper h in the above formula is less than 3 x 10~ 6 , the
maximum current used being 10 amperes per square centimetre. Similar
verifications have been made by Beetzt for zinc sulphate solution, by
F. KohlrauschJ for dilute sulphuric acid employing electromotive forces-
between O'l and 1 volt, and by E. Cohn for solutions of sulphuric acid and
sulphate of copper, using alternating currents of low (100 M and high
(25,000 a.) frequency.
Hence there is a certain mass of experimental proof that the electromotive
force is proportional simply to the first power of the current when it reaches
a steady value.
Although no d priori reasoning would suffice to establish this law as a
general truth, yet, as remarked by "W. N. Shaw (B. A. Report on " Electrolysis,"
1890), Ohm's law evidently belongs to that class of physical law which, though
in the first instance discovered empirically, expresses in numeral relations
necessary consequences of the nature of the physical quantities involved.
J. Hopkinson has suggested (Phil. Trans. R.S., 1877, p. 614) that the law
asserts the superposition of the effects of electromotive force in bodies in
which conduction is not complicated by any residual effects, and may there-
fore be regarded as a special instance of the general law of superposition.
Although, therefore, demonstrated experimentally only in the case of a few
metallic and electrolytic conductors, no facts have been found which are
inconsistent with a conviction of its universal truth as regards metals. It is T
* B. A. Report, 1888, p. 341 ; 1886, p. 312 ; 1887, p. 345,
t Pogg. Ann., 125, 1865, p. 126 ; 117, 1867, p. 15.
J Pogg. Ann., 138, 1869, pp. 280, 370.
Wied. Ann., 21, 1884, p. 646.
MEASUREMENT OF ELECTRICAL RESISTANCE. 193
however, not true in the case of every conductor. According to Braun,* it is
not true for psilomelane, iron pyrites, and copper pyrites. Quincket states
that some liquids of high resistance, such as ether, carbon bisulphide, turpen-
tine oil, and benzene are disobedient for electromotive forces of 30,000 volts
and upwards. He also refers to a similar departure from Ohm's law in the
case of thin layers of gutta-percha, sulphur, paraffin, and shellac for small
electromotive forces.
In the case of liquids, when a departure from Ohm's law shows itself
evidence of chemical decomposition also appears. Actual or initial chemical
decomposition may, in all cases, be at the root of the deviations from exact
obedience to Ohm's law so far found. It has been asserted that the conduc-
tivity of a plumbago line or pencil mark drawn on ground glass does not
follow Ohm's law, and it is well known that the conduction current through
gases is not proportional to the total electromotive force acting.!
Assuming the Volt (equal to 10 8 absolute C.G-.S. electro-
magnetic units) as the practical unit of potential difference,
and the Ampere (equal to lO' 1 absolute C.G.S. electromagnetic
units) the practical unit of current, the practical unit of
resistance is the Ohm (equal to 10 9 absolute C.G.S. units).
For the denomination of very large or very small resistances
the terms Megohm or Microhm are used, denoting respectively
one million ohms and one-millionth part of an ohm. A
resistance measured or appropriately reckoned in megohms
is called a high resistance; one conveniently expressed in
microhms is called a low resistance. An extra high resistance
can be measured in mega-megohms or billions of ohms.
Hence methods of resistance measurement are correspond-
ingly described as methods for the measurement of ordinary
or moderate, of low, and of high resistances.
We shall, in the following pages, deal separately with
the methods for the measurement of electrical resistance in
the three cases: (i) when the resulting value is most
conveniently expressed in ohms ; (ii) when the result is best
expressed in microhms ; and (iii) when the result is most
suitably expressed in megohms.
Each range of resistance measurement has its own most
appropriate methods. Processes in which the numerical
* Pogg. Ann., 153, 1874, p. 556.
t Wicd. Ann., 28, 1886, p. 542.
Maxwell, " Electricity and Magnetism," 2nd ed Vol. ., p. 463, 370.
194 MEASUREMENT OF ELECTRICAL RESISTANCE.
value of a resistance is determined by comparing it with a
known standard resistance are called comparison methods.
Measurements in which the value of a resistance is
determined by immediate reference to the fundamental
measurements of length, mass, and time are called absolute
metlwds.
2, Networks of Conductors. In the generality of cases
the conductor whose electrical resistance has to be determined
takes the form of a wire, strip, or rod of metal of uniform
cross-section, or a column of a liquid conductor of similar
form. A number of wires or conductors, so joined together
that their ends meet in certain common points, is called a
network of conductors. A network of conductors has a
common or resultant electrical resistance, which can be
expressed as a function of the separate or individual resist-
ances of the members forming the network.
As the majority of methods for the measurement of the resistances of wires
involve arrangements of networks, it will be useful to indicate the best
method of calculating the resultant resistance of a network from its con-
stituent resistances, and also the method of calculating the current flowing
through any constituent branch by the application of a known electromotive
force to the network.
The following method of calculating the resultant resistance
of a network of conductors was given by the Author in a
Paper read before the Physical Society of London, June 27,
1885 (see Phil. Mag., Sept., 1885, or Proc. Phys. Soc., London,
Vol. VIL, 1885) :
If at any two points in the network connection is made with a source of
electromotive force by conductors called respectively the anode and cathode con-
ductor, then, after a short period, depending on the self and mutual induction
coefficients of the various conductors, the total quantity of electricity arriving
by the anode will distribute itself throughout the network and settle down
into a steady flow. When this is the case, there is a certain definite difference
of potential between the anode or source-point and the cithode or sink-point,
and there is also a certain definite and constant strength of current in the anode
conductor and in every mesh or branch of the network. Call a and 7 the poten-
tials of these source and sink-points, and x the strength of the current in the
anode lead (that is, the whole quantity of electricity flowing per second
through the network), then (y a}/x measures the resistance of the network.
MEASUREMENT OF ELECTRICAL RESISTANCE. 195
We can imagine the network replaced by a single linear conductor or wire of
such sort that if the anode and cathode conductors are applied to its ends the
difference of potentials at the ends of this simple conductor and the strength
of the current flowing through it have the same numerical values, y, a, and x.
The resistance of this single conductor is then the same as that of the complex
network.
The resistance of the network is obviously some function of the resistances
of the separate conductors or wires which compose it, and is capable of being
calculated from them. Experimentally, the resistance of a complicated net-
work would best be determined by the measurement of the current-strength
in the anode lead and the difference of potential between the source and the
sink. Theoretically, it is interesting to examine the law of distribution of
currents in a network, and to reduce to a function of the separate resistances
the total resistance of the whole network between any two points.
In his treatise on "Electricity and Magnetism " Clerk Maxwell has treated
the general case to determine the differences of potentials and the currents in
a linear system of n points connected together in pairs by ^n(n 1) linear
conductors,* and has shown how to form the linear equations, the solution of
which gives the condition of the network when given electromotive forces
acting along some or all of the branches have established steady currents in
them.
The usual method of obtaining a solution for the distribution of currents is
the application of Ohm's law round the several circuits of the network,
controlled by the condition of continuity that there is no creation nor
destruction of electricity at the junctions.
Since the publication of the first edition of his treatise, Maxwell reduced
these two sets of equations to one set by the simple device of regarding the
real currents in the meshes of the network as the differences of imaginary
currents round each cycle or mesh of the network, all directed in the same
direction, and thus obtained by the application of Ohm's law a single set of
linear equations, the solution of which gives the required currents in each
branch. Maxwell's method is as followsf : If we have p points in space and
join them together by lines, the least number of lines which will connect all
the points together is p-1. If we add one line more we make a closed
circuit somewhere in the system that is to say, a portion of space is enclosed
and forms a cell, cycle, or mesh. Every fresh line added then makes a fresh
mesh, and hence, if there are I lines altogether joining p points, the number
of cycles or cells will be k = l-(p -1). Let such,a system of points and lines
represent conducting wires joining fixed points and forming a conducting
network. Let a symbol be affixed to each point which represents the electrical
potential at that point, and also a symbol affixed to each line representing the
* Maxwell's "Electricity and Magnetism," 2nd edition, Vol. I., p. 374,:
and 2826.
f This method was first given by Clerk Maxwell in his last course of
University lectures. It is alluded to in the second edition of his larger
treatise and in the Appendix of his smaller treatise by their respective editors,
Prof. W. D. Niven and Dr. W. Garnett, to whom it was communicated by the
present Author.
o2
19G MEASUREMENT OF ELECTRICAL RESISTANCE.
electrical resistance of the conductor represented by it. In such a diagram of
conductors the form is a matter of indifference so long as the connections are
not disturbed and lines are not made to cross unless the conductors they
represent are in contact at that point.
Consider a network (Fig. 1) formed by joining nine points by thirteen
conductors. Then there will be 13 - (9 - 1) = 5 cycles or cells. Let an electro-
motive force E act in one branch B, and give rise to a distribution of currents
in the network. Take a, /3, 7, 5, &c., to represent the potentials at the points,
and A, B, C, D, &c., the electrical resistances of the conductors joining these
points, and consider that round each cycle or circuit an imaginary current
flows, all such currents flowing in the same direction of rotation.
A circuit is considered to be circumnavigated positively if we move round it
so as to keep the boundary on the right hand. Hence, going round an area A
in the direction of the arrow is positive as regards the inside if we walk inside
the boundary-line, and negative as regards external space B if we walk in the
same direction round the outside. We shall consider a current as positive
when it flows round a cycle in the opposite direction to the hands of a watch,
Keturning then to the network, we consider that round each cycle an imagi-
nary current flows in the positive direction. The real currents in the
conductors are the differences of these in adjacent cycles or meshep, and the
imaginary currents will necessarily fulfil the condition of continuity, because
any point is merely a place through which imaginary currents flow, and at
which therefore there can be no accumulation nor disappearance of electricity.
Let x, y, z, &c., denote these imaginary like-directed currents. Then x- y
denotes the real current in the branch I, and similarly x-z that in branch H.
Then a-, y, z, &c., may be called the cyclic symbols of these areas. The cyclic
symbol of external space is taken as zero ; hence the real current in branch B
MEASUREMENT OF ELECTRICAL RESISTANCE. 197
Let an electromotive force act in the branch B. Let the internal resistance
of the source of electromotive force be included in the quantity B, representing
the resistance of the branch A. Then apply Ohm's law to the cycle x formed
by the conductors B, I, H, and we have
E-Bx = 7-a.
In this case x is the actual current flowing in the resistance B, and the poten-
tial at the ends of B is equal to the effective electromotive force acting in it,
less the product of the resistance of the conductor multiplied by the current
flowing in it. For the conductor I we have similarly
Hence x - y represents the actual current in I : it is the difference of the
imaginary currents flowing round the x and y cycles in the positive direction.
And for the conductor H we have also
Add together these three equations,
and we have, as the result of going round the cycle x, formed of conductors
B, I. and H,
/I- 2 H, ..... . . (1)
<a, , 7 having disappeared in virtue of these opposite signs.
The above equation (1) is called the equation of the x cycle, and we see
that it is formed by writing as coefficient of the cyclic symbol x the sum of all
the resistances which bound that cycle and subtracting the cyclic symbol of
-each neighbouring cycle multiplied respectively by the common bounding
resistance as coefficient, and equating this result to the effective electromotive
force acting in the cycle, written as positive or negative acjording as it acts
with or against the imaginary current in the cycle. This statement may be
called Maxwell's rule for the formation of the cycle or mesh equations.
Since there are k cycles or meshes, we can in this way form k independent
equations, and by the solution of these determine the k independent variables,
, y, z, &c. The value of the current in any branch is then obtained by simply
taking the difference of these variables belonging to the adjacent meshes, of
which the conductor or branch considered is the common boundary.
The rule for forming the cycle equations, as given above, is merely a modi-
fication of the two statements concerning current networks generally known
as KirchhofFs Laws or Corollaries. These laws are usually stated as follows :
(i.) In any network of conductors conveying steady electric currents the
algebraic sum of all the currents meeting at a common point is zero, or
S(C) = 0.
In applying the above rule the current magnitude or value must be considered
as algebraically positive if it flows to the common point, as negative if it flows
Jrom, it.
198 MEASUREMENT OF ELECTRICAL RESISTANCE.
(ii.) In any mesh of a network of conductors conveying steady currents, the-
sum of the products of the resistance of each conductor bounding the mesh
and the current conveyed by it, is equal to the sum of all the electromotive-
forces acting round the mesh, or
2(CR) = 2(E).
If we assume the existence of imaginary cycle electric currents, all circu-
lating round the several meshes of the network in the same direction, it is
obvious that this in itself implies the truth of (i.) ; and the second law (ii.)'
follows at once from an application of Ohm's law and the additive property
of electromotive forces.
Let us now consider the most general case possible, in which we have a
network composed of linear conductors sufficiently far apart to have no-
sensible mutual induction, and let there be electromotive fotces acting in
each branch or conductor. Let the system be considered to have arrived at<
FIG. 2.
the steady condition. Let x, y, z, &c., be the cyclic symbols or measure of the-
imaginary current circulating counter-clockwise round each mesh. Let
A, B, C, &c. (Fig. 2) be the resistances, and e 1} c. 2 , e 3 , &c., the electromotive forces
acting in each branch. These are reckoned positive when they tend to force
a current round the mesh counter-clockwise, and negative when they act in.
the opposite direction. Then the equation to the x cycle will be
The symbols of all the cycles are written down, putting in those of z, u, and
w with zero coefficients, as they are not adjacent cycles to that of x. We
shall have four equations similar to the above for the other cycles, y, z, w t
and u. These equations involving only first powers of the variables x, y, z, &c.,
are called linear equations, and the student of physics is constantly met by
the necessity for quickly obtaining the solution of such simultaneous linear
equations, so as to evaluate the variables in terms of the constants.
MEASUREMENT OF ELECTRICAL RESISTANCE. 199
In order that it may be possible to obtain a solution for the n variables in
n simultaneous linear equations, certain conditions must be satisfied, and these
conditions are determined by the relation between the constants.
The solution of linear equations is best effected by means of the method of
determinants, and a small knowledge of this department of higher algebra is
exceedingly useful to the student of electrical physics. The following elemen-
tary principles may be here explained :
Consider the two linear equations
l , ......... (i.)
2 .......... (ii.)
Multiply (i.) by 6 2 and (ii.) by b l} and subtract the results. We obtain
(a t b n azb t ) x = Ci& 2 C 2^i-
This result is symbolically written in the form
c, ft,
C 2 63
02 63
The solution of the equations expresses the value of x as the quotient of two
expressions called determinants.
A determinant may therefore be defined as an algebraical expression
which consists of the sum (algebraic) of a number of terms denoted by letters
or other signs, each of which is a product of certain elements. Into each
product or term every element enters only once, and the elements can be
arranged in a square or rectangular form consisting of columns and rows such
that every product is formed by taking one element progressively from every
row and every column once and multiplying together.
stands for the expression ay - b x, the minus sign occurring
Thus
before the product b x because the order of operation or sign of the term must
always be positive when the selection of elements proceeds forward i.e.,
from first row to second row, &c., or from first column to second column, &c. ;
and negative when the order of selection is reversed that is, from the second
row to the first row, or second column to the first column.
It can be similarly shown that if there are n linear equations of the type
200 MEASUREMENT OF ELECTRICAL RESISTANCE.
the solution for any variable a, is capable of being expressed as the quotient
of two determinants, thus :
p t 0-2 .... a n
Pn
a 2
a n
6.
The diflference between the determinants which form the numerator and
denominator in the solution for x n results from writing as numerator the
determinant of the n equations having the column p } , p z . . . p n substituted
for its nth column, and then writing down as denominator the determinant of
the n equations simply. For example, the solution of the three linear equations
ax + b +cz = d,
d b c
d } 6, c,
d z 6 2 c 2
with similar expressions for y and z, differing only in having as numerators
respectively the determinants
and
a b d
a, &, d,
a 2 6 2 d%
the denominator being in each case the same.
In each case the evaluation of these determinants is easy : a simple sym-
metrical process of taking products, according to the rule
a b c
g h i
suffices to give the equivalent of the three-row determinant in an ordinary
algebraic form.
MEASUREMENT OF ELECTRICAL RESISTANCE. 201
The properties of determinants enable us also very easily to evaluate a
numerical determinant of any order. The process consists in a gradual reduc-
tion in the order of the determinant by such transformations as will render
all the elements of the first row or column zero except the first. The deter-
minant is then reduced to the product of its leading elements and the
corresponding minor. The minor of any determinant is one formed from it
by omitting all the^elements in one row and one column and closing up all the
rest of the elements into one determinant. A repetition of this process lowers
the determinant one degree at each stage ; and finally, when it is resolved into a
numerical two-row determinant, a simple cross multiplication gives its value.
The process of evaluation of a numerical determinant is dependent on four
principles :
(1) That the value of a determinant is not altered if rows are changed into
columns, or columns into rows.
(2) The interchange of two rows or two columns reverses the sign of the
determinant.
(3) If every constituent in any row or column be multiplied by the same
factor, then the determinant is multiplied by that factor.
. (4) A determinant is not altered if we add to each constituent of any row or
column the corresponding constituents of any other row or column multiplied
respectively by an identical factor, positive or negative.
For example, suppose that the solution of a series of network equations
with numerical coefficients of resistance yields the determinant
5316
7892
2143
10 7 5 7
we proceed to operate on this as follows : Subtract the second column from
the first and write the remainder as a new first column, we get
2316
-1
1
3
Subtract the third row from the first and put the remainder as a new first
row, also add the third row to the second for a new second row, and we get
12-33
9 13 5
1143
3 7 5 7 |
Again, subtract the first row from the third for a new third, and subtract
three times the first row from the fourth row for a new fourth row, and we have
12-33
9 13 5
0-170
1 14 -2
202 MEASUREMENT OF ELECTRICAL RESISTANCE,
which is equivalent to the third order determinant
9 13 5
-170
1 14 -2
And a similar series of operations reduces this to
76 5
21 -2
which is equal to
-76x2-5x21=-257.
Accordingly, a series of simple subtractions and multiplications will effect
the evaluation of any numerical determinant, and enable us to solve a series of
linear network equations for the currents in all the branches when the
numerical values of the resistances of the conductors are given.
The linear current equations as written above give as solutions the values
of the cyclic symbols or imaginary currents round each mesh. To obtain the
actual current in any branch we should have to obtain the values of the cyclic
symbols or imaginary currents, for the adjacent meshes of which the given
branch is a common boundary, and then take their difference. Maxwell
ingeniously saves labour in this operation by taking as the symbol for one
B
FIG. 3.
mesh say x + y, and for an adjacent mesh y (Fig. 3), and then the real current
in the branch AB is *.
x + y-y=x.
And the simple rearrangement and solution of the network equation gives at
once as value for x the current in the resistance AB, which is the common
partition of the two meshes.
Keturning to the case when there is only one impressed electromotive force
in one branch, we see that in forming the cycle equations only one will be
equated to an electromotive force viz., the equation for the mesh containing
the impressed electromotive force in one of its branches. All the other equa-
tions will be equated to zero ; and accordingly the equation for the current in
any conductor will be of the form
EA rt _.i .
where A n is a determinant of the ?ith order, and A n _i is a first minor of this.
Referring to Fig. 1, we see that, by writing down the five equations of the
cycles x, y, z, u, w, we obtain equations by which to calculate the currents in
MEASUREMENT OF ELECTRICAL RESISTANCE. 203-
any of the thirteen branches, and the current in branch B will be
where A n is the determinant formed of the coefficients of the five equations,
and A ft _i is the first minor corresponding to the coefficient of x in the equa-
tion of the sc-cycle.
We also saw that if 7 and a are the potentials at the ends of the branch B,
E-Bz = 7-a.
Consider that part of the network which remains if the conductor B is
removed, and let us imagine that a current x continues to be forced into it at
7 and drained out at a. The total resistance of that part of' the network, not
counting B, is
J~y-.
~ x >
V
but this is equal to -- B.
Since the resistance of B may be anything, let it be zero ; then the total
resistance of the network between 7 and a will be
E
but
JB=0,
where the suffix and bracket denote that after the determinants are formed
from the cycle equations, according to Maxwell's rule, then in them B is put
equal to zero.
If we denote the determinant of all the w-cycle equations under the condi-
tion of B = by d n , and by d n -\ the first minor of this latttr, or the minor of
its leading element corresponding to the coefficient of x with the resistance of
the circuit containing the effective electromotive force put equal to zero, we
have for the total resit tance R of the network between the points at which the
current enters and leaves the expression
R= *-.
rf n -i
Since, then, as we have seen, the linear equations for the cycles can always
be solved by evaluating the determinants, it follows that in all cases, no
matter how complicated, the resistance of any network can be calculated by
simple arithmetic processes from the given resistances of the branches or
conductors which compose it. We have therefore here an interesting exten-
sion of Maxwell's method of calculating the currents in a network and the
potentials at the junctions to a method of calculating the combined resistance
of a number of conductors forming a network ; which method consists, as seen
above, in forming a certain determinant whose elements are formed of the
separate resistances of the branches, and dividing this determinant by another
of an order next below viz., the first minor of its leading elements ; and we
find that the resistance between any two points of any network of conductor?,
however complicated, is expressible as the quotient of a certain determinant
by another formed from it.
'204 MEASUREMENT OF ELECTRICAL RESISTANCE.
We shall proceed to illustrate this method by a few examples.
1. Find the resistance between the points 1 and 3 (Fig. 4) of a network
FIG. 4.
consisting of five conductors, whose resistances are A, B, C, D, E, joining four
points, 1, 2, 3, and 4.
Connect 1 and 3 by an imaginary conductor of zero resistance, and having
an electromotive force, e, supposed to act in it. Let x, y, z denote the cycles
or imaginary like-directed currents in the three meshes so formed, and write
down the current equations, according to Maxwell, for these three cycles
(A+B)as -Ay -Ez = e,
-Ax + (A + E + D)y -Ez = 0,
-Ex -Ey + (B + C + E)s=0.
Then, by what has been shown above, the resistance R between the points 1
and 3 of the network is given by the expression
(A + B), -A, -B
-A, (A + E + D), -E
-B, -E, (B + C + E)
(A + E + D), -E
-E, (B + C + E)
In dealing with numerical cases we need 110 longer introduce any notice of
imaginary electromotive forces, but proceed according to the following
rule :
TO DETERMINE THE RESISTANCE OF A NETWORK OF CONDUCTORS
BETWEEN ANY TWO POINTS ON THE NETWORK. Join these two points by
<i line whose resistance is supposed zero, and give symbols to the meshes of the
network so formed, calling the additional mesh produced by this added zero
conductor the added mesh. Then write doivn a determinant whose dexter
diagonal has for elements the sum of the resistances which bound each mesh t
beginning with the added mesh; and for the other elements of each row the
resistances, having the minus sign prefixed, which separate this mesh respectively
from adjacent meshes, zeros being placed for elements corresponding to non-
adjacent meshes.
MEASUREMENT OF ELECTRICAL RESISTANCE. 205
More explicitly, if we denote by x, y, z, &c., the meshes, x being the added
mesh, and by SR^, 2R y , 2R 3 , &c., the sum of the resistances which bound each
cycle, then these will be the elements along the dexter diagonal of the
determinant And if x and y are adjacent meshes, and Z R^ represents the
resistance of the common boundary, then - x R y will be the 'element in the
a;th row and yth column, and also in the 7/th row and xth column ; but if x
and z are non-adjacent meshes, then will be the element in the ceth row and
2th column, and also in the zth row and xth column. Having formed th:&
determinant, which we call the network determinant, we divide it by the first
minor of its leading element ; and the quotient is the resistance of the net-
work between the two points, joined by the zero-conductor forming the added
mesh. It is seen that, owing to the mode of formation of the network
equations, the network determinant is a symmetrical determinant that is r
one half of the determinant is the reflection, as it were, of the other half in
the diagonal considered as a mirror.
As a means of comparing the results of this method with other known
results, let ua take the exceedingly simple case of three conductors joining
two points in so-called multiple arc
Let 1, 2, and 3 (Fig. 5) be th three conductors joining two points A and B - r
FIG. 5.
heir respective resistances be r v r^, r$ ; then join A, B by a dotted line so
as to make one added mesh, and let the resistance of this added circuit be-
zero. Then, without writing down the equations to the cycles, we see that
the network determinant is
d n = r, -r, I
-r l r, + r. 2 - r. 2
\ -r 2 r 2 + r 3 \
The elements r,, r,4 r- 2 , r 2 + r 3 of the dexter diagonal are the sums of the
resistances which bound each mesh, x, y. and z, taking the added mesh x first.
The other elements of the first row are the resistances, with minus sign pre-
fixed, which separate the mesh x from mesh y and mesh z ; or are common to x
and y and x and z viz., r } and zero, because x and z are non-adjacent. And r
similarly, if m and n are any two meehes, then the element in the nth row and
with column is the resistance separating or common to the two meshes ; and
the element in the nth row and with column is identical with that in the mth
row and nth column ; zero being placed as an element if these meshes, m and
n, have no common boundary or circuit.
206 MEASUREMENT OF ELECTRICAL RESISTANCE.
The above determinant is easily evaluated. By adding the first row to the
second for a new second row, and this second row to the third for a new third
row, we transform the determinant easily into
r, -r
r 2 - r 2
r 3
-which is equal to r\r z rz.
The first minor of the leading term of the network determinant is
which is equal to r,r 2 + r 2 r 3 + r s r } ;
and hence the resistance of the network between A and B is
d n -
which is a known result. In these simple cases the above general rule is of
-course a less easy method of finding the combined resistance than the direct
application of Kirchhoff's corollaries of Ohm's law ; but whereas the general
FIG. 6.
method is alike applicable to the most complicated as well as to the most
pimple cases, the simple direct method requires twice as many equations, and
<loes not determine the direction as well as magnitude of the current in each
branch.*
As a simple numerical example we may take the case of a crossed square of
wires. Let twelve conductors join nine points (Fig. 6) so as to form a square
* The joint resistance of two conductors in parallel may be obtained by the
following single geometrical construction : Draw two straight lines perpen-
dicular to a common base line and at any distance apart. Set off on each
lengths proportional to the two resistances respectively. Join the top of each
line so set off with the base of the other line by a straight line, and from the
point where these diagonals cross drop a perpendicular on the common base
line. The length of the last perpendicular will represent to scale the joint
resistance of the two conductors. We leave the proof as an exercise to the
.student. (See The Electrician, Vol. XXVIII., p. 167.)
MEASUREMENT OF ELECTRICAL RESISTANCE. 207
divided into four squares, or a four-mesh network of conductors. Let the
resistance of each branch, as ab, be unity. It is required to find the combined
resistance between A and B. Number the meshes 2, 3, 4, 5 ; 1 being the
.added mesh formed by joining A B by a dotted line, making an additional
fifth mesh, the resistance of this additional ideal conductor being zero. Then
the network determinant is
4
-1
-2
-1
- 1
4
-1
-1
2
_ ^
4
-1
^<K
-1
-1
4
-i
-1
-1
4
The dexter diagonal has for each element 4 viz., the sum of the four
resistances, each to unity, which form each mesh or cell. And all the other
figures, say in the nth row, are the resistances (with minus sign prefixed)
separating the nth mesh from all other meshes, zero being placed in the
column corresponding to any mesh which has no common conductor or branch
with this wth mesh. The order in which the columns stand and also the rows
correspond to the order in which the meshes are numbered in Fig. 6.
FIG. 7.
The numerical value of this determinant is easily found to be 288 = 3 x 96 = c n .
'Now if we take the first minor of its leading element, we get a determinant
formed of the elements included in the dotted rectangle ; and taking this as a
separate determinant and evaluating it, we have its value
d n -i = 192 = 2x96;
hence the resist nice of the network between the points A and B is
d n 288 .
One more simple numerical case may be taken and compared with the
results of known methods.
Let a hexagon of conductors be taken (Fig. 7) having crossed diagonals all
meeting in the centre. Let the resistance of each side, as ab, be unity, and
208 MEASUREMENT OF ELECTRICAL RESISTANCE.
also let the resistance of each semidiagonal, as Oa. be unity. Then required
the combined resistance of this network of 12 conductors between the points
A and B diametrically opposite. Join the points A and B by a dotted line of
zero resistance, making an added mesh 1. Mark the other meshes 2, 3, 4, 5 r
6, 7. Then by forming the network equations it is easily seen that the net-
work determinant d n is
3-1-1-1
-1 3-1 0-1
-1 -I 3-1
-1 0-1 3 0-1
0-0003-10
0000-13-1
0-1 0-1 3 =d n .
The value of this determinant is 256.
The first minor of the leading element of d n is d n -i
= 3-10-100
-13-1000
0-1 3 0-1
-1003-10
0-1 3-1
0-1 0-1 3
The value of this last is 320.
Hence the resistance of the network between the points A and B is
R _
"
32u 5'
FIG. 8.
We can easily verify this result in the above symmetrical case, for the
hexagonal framework in Fig. 7 is traversed symmetrically by the current
flowing through it ; and hence no disturbance of the distribution of currents
will take place by separating it, as in Fig. 8. We break the connection
between the semi-diagonal conductors a, b and the mean diagonal A B, whilst-
MEASUREMENT OF ELECTRICAL RESISTANCE. 209
keeping them in contact with each other, the resistance of each branch still
remaining unity. It is then easily seen that the hexagon so arranged must
offer exactly the same resistance between the points A and B as in its original
form.
The combined resistance of a, b, and /, each equal to unity, between the points
C D is f , and the combined resistance of this with e and g in series is 2f ; and
hence the total resistance of the whole network between A and B is equal to
that of three conductors in multiple arc whose resistances are respectively 2f .
2, and 2f , which is equal to
1 _4
1 . J. _1 5'
2f 2 2|
the same result as obtained above.
These numerical examples show conclusively that, in cases in which the
resistance of a network can be obtained by simple direct methods, the results
coincide, as should be the case, with those obtained by the employment of the
general method ; but at the same time the general method is capable of
conducting easily to a solution in the most unsymmetrical cases. The general
rule will, for instance, just as easily give the determinants when the selected
points between which the resistance is required are not symmetrically placed,
but are say adjacent angles of the hexagon, in which case no such simple
direct method as employed above can be used.
A little practice will enable the student to apply the above
rules to very complicated cases of networks of conductors, and
to calculate the resultant resistance between any two points
of a network.
3. The Wheatstone-Kirchhoff Bridge. Slide Wire
Form. The arrangement or network of conductors called
Wheatstone's bridge has already been briefly explained in
principle (see 13, Chap. I.). It consists essentially of six
conductors joining four points (see Fig. 59, Chap. I.). In one
of these circuits is placed a source of electromotive force, and
in the other a galvanometer. In the laboratory the actual
apparatus takes many different forms. In its most simple
modification it is known usually in England as the slide
wire bridge, or, as Continental writers call it, the Wheatstone-
Kirchhoff bridge. In this form its most important portion
is a uniform straight metallic wire of platinum-indium alloy,
platinum-silver alloy, manganin (which must be surface-gilt),
or platinoid, This wire is stretched over a scale between
lUO MEASUREMENT OF ELECTRICAL RESISTANCE.
terminal blocks of copper, and may conveniently be one or
two metres in length. The scale in contiguity to it may be
either of boxwood, ebonite, or metal, and it should be divided
into centimetres and millimetres. The slide wire must be very
carefully selected, and its uniformity in electrical resistance per
centimetre of length tested as described in 5 of this chapter.
In the construction of a high-class instrument it is desirable
to employ a wire drawn of an alloy formed of 90 per cent,
platinum and 10 per cent, iridium. This alloy is very hard
and non-oxidisable by exposure to the air. An alloy of
platinum-silver may also be adopted having a composition of
66'6 per cent, silver and 33*3 per cent, platinum.
In cheaper instruments a German-silver or platinoid wire
is generally used, but both these last alloys tarnish slightly
when exposed to air. Manganin can be preserved from
atmospheric action only by being gilt on the surface. The
gilding must necessarily not be very thick, and in con-
sequence is somewhat easily rubbed off the manganin. The
extremities of the wire are screwed or clamped to massive
terminal blocks of high-conductivity copper.
If the wire is soldered to the terminals, care must be taken
that the solder does not affect the composition of the alloy at
the extreme ends of the wire. Thus, for instance, manganin
should not be soldered with any solder containing zinc, and
platinum alloys should not be soldered with any solder
containing lead.
The instrument must be provided with a travelling block or
slider, such that an electrical contact may be made with the
wire at any point by pressing a contact key. This contact
must be made by a knife-edge, and it is desirable that the
pressure of the finger should not apply the knife-edge directly
to the slide wire, but merely release a spring. Thus, in
Fig. 9, iow' is a portion of the slide wire, and EE' is a part
of the sliding block, K a knife-edge carried on the extremity
of a spring x t and P a finger-piece or trigger. A pressure
applied to P will release the knife-edge and permit it to make
MEASUREMENT OF ELECTRICAL RESISTANCE. 211
contact with the wire. It is easily seen that the pressure of
the knife-edge on the wire is determined by the elasticity
spring x carrying it, but not by the pressure of the linger
on the finger-piece. The object of employing the above
device is to prevent any undue pressure on the knife-edge
causing "nicks" or deformations in the slide wire if contact is
repeatedly made at one place on the wire. The knife-edge
should consist of a piece of the same alloy used for the slide
wire itself, carefully shaped to a wedge shape and soldered to
a metallic carrier spring. The block holding the contact
knife-edge should be capable of being traversed easily to and
fro along the base-board in such a way that the knife-edge
can make contact with the slide wire at any point in its
length, and the exact position is observed and recorded by an
indicating point, or vernier, moving over the divided scale.
FIG. 9.
The " bridge " arrangement is then completed, as shown in
Fig. 10, in which the third and fourth arms of the bridge
consist respectively of a variable standard resistance S and
the resistance E to be measured. A battery, B, consisting
of two or three dry cells, is connected to the ends of the slide
wire, and a movable coil galvanometer, G, between the knife-
edge on the slider block and the junction between the third
and fourth arms. Keys K x and K 2 are inserted in the battery
and galvanometer circuits respectively. The comparison
resistance may best be a dial or series plug pattern resistance
box. The resistance unplugged or inserted into the third arm
of the bridge should be as nearly as possible equal to the
'212 MEASUREMENT OF ELECTRICAL RESISTANCE.
resistance to be measured. Under these conditions, if the
slider is moved along the wire and trial contacts made with
the knife-edge at various places, a point, C, will be found at
which the galvanometer G- indicates no current when- the
knife-edge contact is made. The ratio of the resistance being
measured to that of the standard is then the same as that
of the resistances or lengths of the two sections Into which
the knife-edge divides the slide wire. Hence, if S is the
value of the standard in ohms and E that of the resistance
being measured, and if P and Q are the resistances or the
I V.,i|in.,iiiflniiii:.ir ,;. -.. ,-,.i,t ii..|.-..i'., .....fX,.- ; - ,. .,,. nTTTi! **j
^^^t- ^^^
3
B
^OJ-^
FIG. 10.
lengths of the uniform slide wire sections on the respectively
adjacent sides of the bridge arrangement, we have, when the
galvanometer current is zero,
P:Q = R:S,
or
If the electrical resistances of various lengths of the slide
wire are exactly proportional to those lengths, if the total
length of the slide wire is 1,000 millimetres, and the slide
wire reading at the knife-edge contact when the bridge is
MEASUREMENT OF ELECTRICAL RESISTANCE. 213
balanced is at x millimetres from one end of the wire, then
we have
P : Q = : 1,000 as.
Hence B -
Accordingly, we can determine the value of the unknown
resistance II in terms of the value of a known standard, S,
and the ratio of the lengths of the two sections of the slide
wire when the balance is obtained.
4. The Plug Pattern Resistance Bridge. In practice it
is generally much more convenient to employ a plug pattern
Wheatstone bridge for the measurement of resistances. In
this case the resistances which form the three arms of the
FIG. 11. Sectional View of Blocks, Bobbins and Coil in Series Pattern Plug
Bridge.
bridge are formed by adding in series the resistances of fixed
coils of wire contained in a box. This addition is effected -by
the insertion of coned metallic plugs into holes bored out
partly in one block of metal and partly in another adjacent
one.
The resistance coils may be arranged either in series or in
parallel, and the plugs may be arranged so as to short- circuit
coils or to interconnect the junction between any coil of the
series and a common or omnibus bar alongside the coils. In
Fig. 11 is shown the series system of short-circuiting arrange-
ment of plugs and blocks interconnected by resistance coils.
In this case we have a series of bobbins of insulated wire of
214 MEASUREMENT OF ELECTRICAL RESISTANCE.
various resistances, and one or more coils can be short-
circuited and cut out of series by the insertion of plugs
between the metal interconnecting blocks. In the second
arrangement (Fig. 12) the coils are also arranged in series, but
a junction can be effected between any interconnecting block
and a parallel common or omnibus bar, so that the resistance
between the bar and one end of the coil series can be varied
by steps. In this latter case it is customary to employ a
series of nine or ten coils of exactly equal value say ten
units, ten tens, or ten hundreds. The plug may be stepped
along from hole to hole, and thus insert a resistance of one,
FIG. 12.
two, three, four, &c., units, tens, or hundreds of ohms between
the end or terminal block and the common bar or block
alongside. In some cases the blocks are arranged for this
second pattern in a circle or dial (see Fig. 13), and in other
cases in a row or rows (see Fig. 14) so connected that the
resistances are joined in parallel and not in series, when one
or more plugs are inserted.
A " bridge " is constructed of a series of coils arranged so
as to form the two ratio arms of the bridge by having a
terminal placed in some position in the series, and another
sciic-s of resistances forming the measuring arm. These
MEASUREMENT OF ELECTRICAL RESISTANCE. 215
resistances may be arranged as follows : In the so-called
" Post Office " pattern of Wheatstone bridge the ratio arms
are each formed of a series of coils of 1,000, 100, 10, and 1 ohms
1
FIG. 13. Arrangement of Blocks and Colls in Dial Pattern Resistance Box.
resistance arranged in the series fashion. The measuring arm
is then made of a series of coils (generally of 1, 2, 3, 4, 10, 20,
30, 40, 100, 200, 300, 400, 1,000, 2,000, 3,000, 4,000 ohms in
FIG. 14. Arrangement of Resistances in a Conductivity Box.
series) ; and terminals for the battery, galvanometer, and
resistance to be measured, together with a contact key in the
battery and one in the galvanometer circuit, arc also added.
216 MEASUREMENT OF ELECTRICAL RESISTANCE.
The block pieces are of brass, generally mounted on an ebonite
slab, which forms the top of the box. The arrangement of circuits
in a series coil bridge is shown in Fig. 16, and the external
appearance in Fig. 15. The particular design illustrated is
that of Messrs. Nalder Bros, and Co.*
In using this bridge the operator connects the resistance
to be measured to the terminals marked L arid L, the
galvanometer to the terminals G G, and a battery of
three or four dry cells to the terminals 13 and I>. He
then removes one of the plugs from the one ratio arm
FIG. 15. Series Plug Pattern Wheatstoue Bridge.
series and one from the other ratio arm series. In so doing
it is desirable to have some notion of the value of the
resistance to be measured, and in general it is well, unless
the unknown resistance is suspected to be very large or very
small, to begin by a ratio of equality that is, the two ratio
arms are made 1 and 1, or 10 and 10, or 1,000 and 1,000
ohms by removing the plugs from the holes marked 1, 10, or
1,000 on each side. This done, the observer removes plugs
from the other or measuring arm series until, on pressing first
* See The Electrician, Vol. XLL, p. 596.
MEASUREMENT OF ELECTRICAL RESISTANCE. 217
the battery key and afterwards the galvanometer key, the
galvanometer indicates no current. The bridge is then said
to be balanced. It will generally happen that with integer
value coils of the three arms it is not possible to secure
a perfect or absolute balance. For instance, if the ratio arms
are 10 and 10 ohms, then with 230 ohms resistance un-
plugged on the measuring arm, the galvanometer may show a
small current in one direction through it, whereas with 231
ohms unplugged the galvanometer may show a small deflec-
tion in the opposite direction.
NAl OCR BROS CO. UONOON
Q:O;CCP:O:Q
^\^*+*l*J -x-v-r'O*' .^%^^*WV^.> lM ^^tWV J xx-^x.*V ^s*^/^^
FIG. 16. Arrangement of Circuits in Series Plug Pattern Wheatstone Bridge.
A further approximation to the true value of the unknown
resistance may be obtained as follows : If the galvanometer-
is one reading by a mirror and scale, note the small
steady scale deflection of the galvanometer when the
galvanometer and battery key are both held down and
the lower of the two measuring arm resistances is
unplugged. Thus, for instance, suppose that, with 230 ohms
out in the measuring arm, the steady scale deflection of
the galvanometer is 10 millimetres to the left. This small
deflection of the spot of light or indicating needle is propor-
tional to the galvanometer or bridge current under those
218 MEASUREMENT OF ELECTRICAL RESISTANCE.
conditions. Suppose, then, that the measuring arm is made
231 ohms and the galvanometer deflection is changed to 15
scale divisions to the right. We may deduce the true value
of the measuring arm resistance, which would exactly balance
this unknown resistance being measured, by a simple calcula-
tion. Since a change of one unit in the measuring arm
resistance changes the galvanometer deflection from +15 to
10, it is clear that, since the whole scale deflection change
is 25 divisions for the whole change from 230 to 231 ohms in
the measuring arm resistance, a value of the measuring arm
of 230 -f ohms, or of 2304 ohms, would exactly balance
the unknown resistance being measured. Hence, if the ratio
arms are 10 and 10, the resistance being measured is 2304
ohms. The above-described method, called taking right and
left galvanometer deflections, enables us to make an initial
approximation to the value of the unknown resistance.
When this is done a different ratio may be selected for the
ratio arm* The ratio may, for instance, be made 10 to 1 by
removing the plugs corresponding to 1,000 and 100 ohms in
the two ratio arms. Balancing again, suppose we find that
a value of 2,304 ohms unplugged out of the measuring arm
makes a scale deflection of one division to the left, and with
2,305 ohms unplugged in the measuring arm we obtain a scale
deflection of two divisions to the right ; then similar reasoning
shows that the exact balancing resistance would be 2,304*33 ohms.
Hence the resistance being measured is 230433 ohms.
In using a series pattern plug bridge the following pre-
cautions must not be neglected :
(i.) The plugs when not in use should never be laid on the
table, or be held in a hot hand, but should be placed in the lid of
the bridge box, which is generally lined with velvet or cloth.
(ii.) The greatest care should be taken to prevent the plugs
becoming permanently soiled, oxidised, or amalgamated with
mercury. If necessary to clean a plug, only a very careful
application of the finest glass-paper should be made.
MEASUREMENT OF ELECTRICAL RESISTANCE. 219
(Hi.) In putting the plug into a hole, give it a slight twist
to make it seat itself accurately in the coned hole, and, if the
box is a series plug pattern box, after each rearrangement of
plugs go over the other plugs in the same manner again to
see that there are no loose plugs. The plugs should, however,
not be put into the holes so violently that there is risk of
twisting off the heads in getting them out again.
(iv.) The ebonite slab carrying the brass blocks should be kept
carefully dusted, and the bridge when not in use should be put
away in its box with all the plugs loosely placed in their holes.
The advantage of the dial pattern of bridge (see Fig. 13)
is that there is only one plug to each decimal series of coils.
A resistance of to 9 ohms is introduced into the measuring
arm by merely moving the plug to the holes marked to
9 in the dial or group or row of blocks marked units.
A resistance of to 90 ohms or to 900 ohms is intro-
duced by placing a plug in one or other of the holes in the
block group marked tens or hundreds, and so on.
In using a dial pattern bridge to measure an unknown
resistance, set off first a ratio of 1 to 1 in the ratio arms, and
then systematically increase the measuring arm resistance by
changing the unit plug ; then move the ten ohm plug, next the
hundred ohm plug, from hole to hole progressively until a
resistance is found such that the galvanometer is deflected
one way for the lower and the opposite way for the higher.
Thus, suppose that with a ratio arm of 100 and 100 ohms we
find a resistance of 500 ohms in the balancing arm makes the
galvanometer needle fly to the left and 600 ohms makes it fly
to the right, we may try next increasing regularly from 500
to 600 by tens. If then we find left and right deflections for
550 and 560 ohms, we proceed to increase by units; and when
we find small left and right deflections for 553 and 554 ohms
we adopt the deflectional method and unequal ratio arms
already explained to determine the next decimal place or places.
In measuring any inductive resistance it is essential to
cluac the battery circuit of the bridge before the galvanometer
220 MEASUREMENT OF ELECTRICAL RESISTANCE.
circuit, in order to permit the currents in the various
branches to become steady. This is achieved without thought
by the employment of a double key (see Fig. 17), which closes
first the battery circuit B B, and afterwards the galvanometer
circuit G G.
In making careful measurements it is necessary to apply a
correction to the bridge reading for the temperature variation
of its own coils, and also for any error there may be in the
actual coil resistances.
The possessor of a plug pattern bridge should not take for
granted that it is correct, but should proceed to check its
readings as follows : A standard 1-ohm coil should be
connected to the bridge, using very thick copper rods or
strips of copper and mercury cups to make the connection.
FIG. 17. Wheatstone Bridge Combined Battery and Galvanometer Key.
The bridge reading should then be taken, using various ratio
arms say 1 to 1 ohm, 10 to 1 ohm. 1,000 to 100 ohms. If
the bridge is properly adjusted each of these readings, when
reduced, should give a value of unity for the known standard
1-ohm resistance. The maker of the bridge generally marks
on it the temperature at which it is correct in its readings,
and he will always furnish the purchaser with a statement of
the nature of the wire used for the coils and its temperature
coefficient. Thus, if the bridge coils are made of platinum-
silver wire, the temperature coefficient of which at about
15C. is 0'026 per cent, per degree, and if the bridge is
correct at 15C., then it follows that, if the bridge coils at the
moment of reading are at a temperature tG., the true value
of one unit of the bridge reading is 1+0 < 00026( 15) ohms.
MEASUREMENT OF ELECTRICAL RESISTANCE. 221
The real difficulty is the uncertainty as to the actual
temperature of the wire of the bridge coils at the moment of
measurement. A thermometer placed in the box containing
the coils merely gives the temperature of the air round the
coils, and if these have become internally heated by currents
passing through them, the actual temperature of the wire
may be, and probably is, very different from that of the air
outside them. To avoid this uncertainty, it is necessary that
bridges intended for very accurate work should be made up
with manganin wire properly aged, and that the coils of wire
should be wound on brass or copper tubes merely having one
layer of silk tape laid over it. The box containing all the
coils should be filled with an insulating oil which can be kept
stirred. In this manner it is possible to maintain the coils at
a temperature near to that at which the manganin has a zero
temperature coefficient, and at this temperature the coils
should be adjusted to be correct.
In the case of the measurements made in an electro-
technical laboratory, it will not often happen that a degree of
refinement is necessary in the resistance measurements which
will make it worth while to apply the above correction for the
temperature of the bridge coils. For very accurate work,
however, it has been proposed to employ coils of bare wire
wound on mica- frames.* The coils after winding are annealed
by passing a strong current through them. When in use they
are kept immersed in a fluid insulating oil which is well
stirred.
We may conclude this section with a description of a
standard form of Wheatstone bridge for very accurate
resistance measurements which has been designed by Prof.
H. L. Callendar and Mr. E. H. Griffiths.f
* See Mr. F. W. Burstall, " On the Use of Bare Wire for Resistance Coils."
Proc. Phys. Soc., Vol. XIV., p. 286.
f The following paragraphs describing the Callendar and Griffiths bridge are
taken by permission verbatim from a series of articles in The Electrician for
1898 by Mr. G. M. Clark, entitled " On the Measurement of Temperature :
an Application of the Measurement e>f Resistance." (The Electrician,
Vol. XXXVIII., p. 747.)
222 MEASUREMENT OF ELECTRICAL RESISTANCE.
A general view in its case is given in Fig. 18, and a view of
the top of the box in Fig. 19. It will be seen that, besides a
FIG. 18. Callendar ind Griffith's Resistance Bridge.
set of coils, the box has a bridge wire in addition. One arm
of the bridge is formed by the resistance to be measured and
MEASUREMENT OF ELECTRICAL RESISTANCE. 223
224 MEASUREMENT OF ELECTRICAL RESISTANCE.
part of the bridge wire, the rest of the bridge wire and the
necessary coils forming the other arm. As the back coils of
the bridge are equal, a pair of compensating leads (equal in
resistance to those leading to the resistance to be tested) may
also be introduced into this arm. It is therefore not
necessary to make separate measurements for the leads.
When the resistance to be tested is short-circuited, the bridge
should be in balance with the contact at the centre of the
bridge wire. Thus, by short-circuiting the bridge by the four
connectors shown at the right of Fig. 18, the zero of the bridge
can be readily tested at any time.
The coils of the bridge are thirteen in number. Eleven of
these form the ordinary working coils of the bridge. These
are arranged on the binary scale. The smallest coil, marked
A, has a resistance of 5 box units. The unit of the box is
0*01 ohm. The other coils are respectively 10, 20, &c., of
such units. The largest coil, L, is 5,120 units. Thus the
whole resistance of the box is a little over 100 ohms. Since
the back coils are equal, this is also the greatest resistance
that can be measured with the box. The other two coils are
marked respectively Cal. and <. The coil Cal. has a resistance
of approximately the box unit, arid is used in the calibration
of the bridge wire. The coil < has a resistance of 100 box
units, and is useful for the adjustment of platinum thermo-
meters. For if these are constructed so that their funda-
mental interval is 100 box units, then the calculation of the
platinum temperature is greatly simplified.*
A movement of two centimetres on the bridge wire corres-
ponds to the box unit. As it is easy to read this movement
by means of a vernier to ^mm., the least count of the bridge
is joW^ f the box unit, or O'OOOOl ohm. The contact
maker seen on the bridge wire is of a special design to permit
of this fine adjustment. It also, by its construction, renders
injury to the bridge wire impossible.
In calibrating the bridge wire all that is required is a rough
adjustable resistance, whose value need not be known. Having
adjusted this until the bridge is in balance with the slider at
one end of the scale, the plug Cal. is removed and the slider
moved until a fresh balance is obtained. The plug is then
replaced and the external resistance adjusted until the balance
* For pt = 100(R - RoVRi - R : and F. I. = RI - R = 100, then pt = H- R . If
the F. I. is not exactly 100, but differs only by a small quantity, then pt can
be found by the usual methods of making small corrections,
MEASUREMENT OF ELECTRICAL RESISTANCE. 225
is again attained at, or sufficiently near to, the same place
in the bridge wire, and the process is repeated until the whole
bridge wire has been traversed. We have thus a series of
steps on the bridge wire, each equal in resistance to one box
unit. The length of these steps has been read off on the scale,
so that if there are any errors in the scale, these have been
introduced into the calibration, and are therefore of no
consequence.
In the calibration of the coils a somewhat similar process is
followed. As each coil only differs from the sum of all that
precede it by five box units, a balance obtained with any one
coil can also be obtained with the preceding coils, together
with a length of bridge wire. Thus every coil in the box
can be readily determined in terms of the bridge wire. By
using different combinations of coils to measure any resis-
tance, there is a perpetual check on the calibration of the
whole box. Any change which takes place in the value of
any of the coils can be readily detected. It is, however, very
improbable that much will take place. These coils are of
naked platinum silver, and are wound on mica frames. By
lifting the box out of its case all the coils can be seen, and are
easily accessible. Coils so formed can be very thoroughly
annealed by passing a strong current through them, sufficient
to raise them to a red heat, after the coil has been wound.
They are thus entirely free from all strain. The bare wire
coils are immersed in a bath of non- volatile hydrocarbon oil
of high insulating power. This oil can be stirred, and there is
no doubt that the temperature indicated by a thermometer in
the oil is also the temperature of the coils themselves. The
temperature of the box can be rapidly raised or lowered if
necessary ; and as the coils follow these changes, the tempera-
ture coefficient of the coils can very readily be found.
The back coils of the bridge also consist of two naked
platinum silver coils wound together on the same rnica frame.
There is thus no chance of the two being at different tempera-
tures. A short length of wire on the top of the box joins the
two ends of these coils, and on this length is the galvanometer
contact. If the back coils are not equal the galvanometer
contact can be adjusted till equality in the back arms is
obtained. The galvanometer contact is a potential one only,
so that resistance through the contact is of no importance.
The top of the box is formed of white marble. This has
high insulating properties, and is not open to the same
Q
226
MEASUREMENT OF ELECTRICAL RESISTANCE.
objections as ebonite. Separate brasses are used for each plug,
so that the movement of one plug in no way affects the rest.
Each block and plug is also marked with its distinguishing
letter and value, so that in case of wear either can be refitted.
As no part of the plug is wider than the top of the plug hole,
no shoulder can be worn on the taper, and the wear is reduced
to a minimum. The contact resistance of these plugs is found
to be very constant. When not in use, the plugs are placed
in a spring rack lined with wash-leather, so that they are
always kept thoroughly cleaned.
The box case is constructed of a double copper box with
asbestos lining between. Thus the inner surface of this must
be at a very uniform temperature throughout. The top of the
box is protected by a glass case similar to a balance case. The
FIG. 20.
front of this is made to slide up or down. This serves the
purpose not only of keeping the instrument free from dirt and
dust, but also adds very considerably to the uniform distribu-
tion of temperature throughout the box. The terminals are
brought through the side of the case.
The bridge wire is connected in such a manner that its ten-
sion is not affected by changes in temperature. The coefficient
of expansion of platinum-silver is intermediate between that
of steel and brass. The rectangular framework carrying the
bridge wire has its two longer sides one of steel and the other
of brass. By placing the bridge wire in the correct position
it will suffer no further strain, no matter what temperature
changes it may be subjected to. These bars further tend
MEASUREMENT OF ELECTRICAL RESISTANCE. 227
to protect the bridge wire, so that there is but little danger of
differences in temperature existing in the bridge wire. Along-
side the bridge wire proper is stretched a second wire, on
which the galvanometer contact is made.
This contact is made through the contact maker, which is
shown in section in Fig. 20 and in plan in Fig. 21. ABA' is a
brass framework, which slides between the steel and brass
bars. A second block, FEE'H, is within the brass framework.
Springs at A and A' press the brass frame against the steel
bar, and springs at E and E' press the inner block against the
brass bar. Thus if the screw S is turned the inner block is
alone moved, for the pressure of the inner block against the
brass bar is that of the springs at E and E' only, whereas the
ilimimi mmiiiiii
Brass Bar
FIG. 21.
pressure of the framework against the steel bar is that of the
springs at A and A in addition. If the screw S is receded
instead of advanced, then the inner block is made to follow it
l)y long springs indicated by the dotted lines in Fig. 21. The
screw C clamps the bridge wire and galvanometer wire together
on to a short length of wire W, as shown in section in Fig. 20.
If it is desired to make a temporary connection only, then the
block G- must be pressed down. The spring MN releases the
bridge wire from the contact wire. If by mischance the screw
S is turned whilst the bridge wire is clamped by the screw C,
then the outer framework ABA alone moves, and it is thus
impossible with this form of contact maker to scrape or in any
way damage the bridge wire. At the same time a very sharply
defined contact is obtained.
Q2
228 MEASUREMENT OF ELECTRICAL RESISTANCE.
5. Portable Forms of Wheat stone Bridge and Testing
Sets. Trotter Bridge. Instrument makers have devised!
numerous forms of portable slide-wire and plug bridges suitable-
for laboratory and outdoor work. For the details of these the
trade circulars of the principal electrical instrument makers
may be consulted. In most of these arrangements the galvano-
meter is one with a movable nearly astatic double-magnetic
needle carried on a jewelled centre. The vibrations of the-
FIG. 22. Portable Form of Wheatstone Bridge.
needle are arrested by a stop which raises the needle off its-
steel centre-suspension point when the box lid enclosing the-
instrument is shut.
For rapid work, where great accuracy is not required, or
for obtaining a preliminary measurement of the resistance of
a wire afterwards to be more accurately measured, some of
these portable bridges are very useful. The resistances are
thrown into circuit, not by removing plugs, which may be-
MEASUREMENT OF ELECTRICAL RESISTANCE. 229
lost, but by a revolving contact arm making contact against
sfixed brass studs. The stud surfaces must be kept clean.
These instruments are arranged either for measuring ordinary
-and low resistance or for high resistances such as insulation.
(See Figs. 22 and 23.) In the latter case the battery is
replaced by a small continuous-current magneto machine,
giving a voltage of from 80 to 100 volts when the handle is
quickly turned.
FIG. 23.
A form of portable slide-wire bridge has been developed
'by Messrs. A. P. Trotter and J. Swinburne out of a simpler
form due to Major P. Cardew.* Two wires of nickel steel
.are stretched over a scale divided into equal parts. These
wires are connected together at one end by a bar of
negligible resistance. These wires are represented by the
lines b and a and c, d, e in Fig. 24. A length I is. set off one
>end of one wire, and a length c is set off the end of the
* See The Electrician, Vol. XXXVII., p. 691.
230
MEASUREMENT OF ELECTRICAL RESISTANCE.
other wire, so that the resistance of I is equal to that of c~
The scale extends over d and e, and the scale zero is at d~
The resistance to be measured is represented by the coil x.
A battery is joined in between the cross piece and the
junction a to x and a galvanometer between junctions I to a
and a slide which moves over the wire c, d, e and make*
contact at any place.
1
\
a
t b
I
FIG. 24.
Then it is obvious that, if the bridge is balanced so that
the galvanometer shows no current, we have
a+b
b c+d
where the letters stand for the resistances of the segments of
the two wires. If b = c and a = e + d, then the above ratio-
1 1 A X
is reduced to ~ = -,
6 d
or
a+l
Hence the length d on the slide wire is proportional to the-
resistance x if a-\-b/b is a constant ratio. Accordingly, by
MEASUREMENT OF ELECTRICAL RESISTANCE. 231
shifting the galvanometer con-
tact on the wire a b, so as to
give the ratio a/b any desired
value, we can make the ratio
a+b/b what we please.
When once this ratio is fixed,
the length of d, when the gal-
vanometer balance is obtained,
is proportional to x. Points may
therefore be marked off on the
wire a b, so that the segments
a and b have such values that
a + b/b=l or 10 or 100. If,
then, the resistance per unit of
length of the wire d e is known,
we have at once the value of x
given.
The Trotter bridge is made up-
in a portable form, as shown in
Fig. 25.
A useful implement to possess
in an electrical laboratory is a
pair of equal uniform platinum-
silver wires stretched parallel to
each other over a pair of divided
scales, both wires having contact
sliders moving over them and
terminal screws at each end of
each wire. The platinum -silver
wires may be replaced by plat-
inoid or manganin. They should
be about the size called No. 20
S.W.G. A thick strip of copper
should be provided for con-
necting across corresponding ends
of the two wires.
o
Q
5 s '
I-
r
i
232 MEASUREMENT OF ELECTRICAL RESISTANCE.
6. Theory of the Wheatstone Bridge, In connection with
the use of the Wheatstone bridge for resistance measurement,
we have to consider the best arrangement of the circuits so
that with a given galvanometer and battery the sensitiveness
of the arrangement may be a maximum. The six con-
ductors joining four points consist of two ratio arms or
resistances, the standard of comparison or balancing arm, and
the galvanometer and battery circuits. These can be shown
arranged symmetrically as in Fig. 26, instead of in lozenge
form as in Fig. 27.
Let the three meshes of the above network be supposed to be traversed by
imaginary cycle currents x + y, y, and z, then the real current through the
galvanometer circuit is x, and that through the battery circuit is s. Forming,
by Maxwell's rule, the cycle equations (see page 197), we have
Gy _ -P 0,
(G + Q + S) y -G(x + y)-Qz = 0,
(P + Q + B) z -
where G and B are taken as the respective resistances of the battery and
galvanometer branch, and E is the electromotive force of the battery.
Rearranging these equations, we have
= E . . . . (i.)
- P 2 = .... (ii.)
- Qz=0 .... (iii.)
Hence, solving these equations for x, we obtain
E(PS-RQ)
KQ+S), -Q
-P , -<P + Q),(P+Q+B)
(P + R + G), (P+R), -P
-G , (Q + S), -Q
where A stands for the determinant, in the denominator with the full
algebraic expression of which we are not for the moment concerned.
Accordingly, if PS-RQ = 0, that is, if the relation ? = ? holds good, then
Q S
the current through the galvanometer is zero ; the bridge is then said to be
balanced, and x = 0. The determinant A can be written out symmetrically
into the expression
(iv.)
The full expression for the current x through the galvanometer circuit of the
MEASUREMENT OF ELECTRICAL RESISTANCE. 233
.bridge, in terms of the electromotive force (E) of the battery and the
resistances (P, Q, R, S, B, G) of the six branches, is therefore
_ E(PS-RQ) __
'~ .bG(P T Ci + R + S) + B(Q + S)(P -I- R) -i- G(R + S)(F + Q) + RS(P + Q) + PQ(R+ S)
The question then arises whether for given values of P, Q, R and S the current
.x through the galvanometer will be greater if the battery circuit is connected
in between the junctions where (P and R) and (Q and S) meet and the
galvanometer in between the junctions where (P and Q) and (R and S) meet,
or vice versa.
If we consider the position of the galvanometer and battery exchanged
that is, if we write B instead of G and G instead of B in the above expression,
.(iv.), and call the result A lf we have for the value of A x - A the equations
-A = (G-B)(S-P)(R-Q).
FIG. 26.
FIG. 27.
The best arrangement of the battery and galvanometer therefore is that
which will make x a maximum, other arrangements remaining the same ; for
if the balance is nearly obtained, the galvanometer should show the greatest
possible deflection for a small defection from the fulfilment of the relation
PS = RQ. It will generally happen that the value of G, the galvanometer
resistance, is greater than that of the battery B.
Let us suppose the four resistances arranged in consecutive order of magni-
tude are denoted by S. R, Q, P. That is, assume
S>R R>Q Q>P,
or else S<R R<Q Q<P ;
then (S - P) and (R - Q) are both positive quantities or both negative ones, so
that their product is always positive. Therefore, in the expression given
-above Ai-A = (G-B) (S-P) (R-Q), Aj-A must have the same sign as
(G B). Accordingly, if G is greater than B, Aj will be greater than A;
.and hence sc will be less in value when the galvanometer and battery have
4he positions shown in Fig. 28 than when they are exchanged.
234 MEASUREMENT OF ELECTRICAL RESISTANCE.
We have therefore the following rule : Assuming the galvanometer to have
a greater resistance than the battery, the current through the galvanometer
G, when it and the four resistances S, R, Q, P in order of magnitude are
arranged so that the galvanometer is connected in between the junctions of
the two greatest resistances S, R and the two least resistances Q,-P, is greater
than when the battery occupies that position ; or the rule may be formulated
in another manner, as follows :
Of the two resistances, that of the lattery and that of the galvanometer, select
that which is greater, and connect it to join the junction of the two greatest to-
thai of the two least of the four resistances forming the arms of the bridge. Let
the remaining appliance occupy the conjugate position.
Thus, for instance, if we have to measure a resistance of the order of say 50
ohms, and we decide to adopt a ratio of 1,000 to 10 for the ratio arms of the
bridge, then, when the balance is obtained, the resistance in the measuring
arm will be about 5 000 ohms. Suppose that in the quadrilateral of resistances
we have two large and two small, as shown in Fig. 28.
FIG. 28.
In this case the rule above given shows that if the battery circuit B has a
ower resistance than the galvanometer circuit G, then the galvanometer and
battery should be connected as shown in Fig. 28. If, however, the battery
has a higher resistance than the galvanometer, then their positions should be
exchanged.
If the equations (i.), (ii.) and (iii.) for x, y and z are solved for z instead of X T
we obtain the value of the current through the battery circuit, and we find,
by the above methods the equation
^ I (P + R + G), (P + R)|
A
where A has the same value as in (iv.). Hence the ratio of x to z, or current
through galvanometer to current through battery, is
-P
-Q
(P + R + G), (P + R)
-G (Q + S)
PS- QR
S) + (P + R)(Q + S)
MEASUREMENT OF ELECTRICAL RESISTANCE.
235
It has been shown independently by Mr. Oliver Heaviside
(Phil Mag., Vol. XLY., 1873, p. 114) and by Mr. T. Gray
(Phil Mag., Vol. XII, 1881, p. 283), that if K is the resist-
ance to be measured, and B and G, the battery and galva-
nometer resistances, are fixed, the maximum sensitiveness
is secured if the other resistances P, Q and S forming the
bridge arms are selected so that
, and P 2 =
(For the proof of the above formulae the reader is referred to
" Absolute Measurements in Electricity and Magnetism," by
Prof. A. Gray, Vol. T., p 332.)
7. The Matthiessen and Hockin Bridge. We have
already explained that the slide-wire bridge can be used so
as to enable us to measure the difference in resistance between
two coils and not their ratio. In this arrangement four coils
are provided and connected with the bridge wire as shown
in Fig. 29.
FIG. 29.
We have, also, already proved (see page 149) that if the
coils A and B are exchanged in position, the resistance of
that length of the slide wire over which the slider contact
has to be moved to find a second balancing position after the
236
MEASUREMENT OF ELECTRICAL RESISTANCE.
coils are exchanged is equal to the difference in electrical
resistance of the two coils. This method of resistance com-
parison is due to Prof. G. Carey Foster,* and is invariably
used when comparisons have to be made between coils of
nearly equal value, one being a standard and the other a
coil of which the resistance is required with reference to
the standard.
We have already also described some of the mechanical
devices for effecting quickly the interchange of the coils A
and B. The simplest device for this purpose is to form a group
00
1
T-^a " p~
cl
yb
i
FIG. 30.
of 12 mercury cups, x, y, x', y\ 1, 2, 3, 4, 1', 2', 3', 4', which may
be made by holes bored out in a thick mahogany slab. These
mercury cups are connected, as shown in Fig. 30, by copper
strips about half an inch wide and one-eighth of an inch thick.
These strips are prevented from touching one another where
they cross by slips of mica inserted between them. The
coils to be compared are represented by A and B, and these
coils have their legs or terminal rods placed in mercury cups
x, y, x' y', which can be connected by thick copper fl -shaped
rods with the other cups, so that x is connected to 1, y to 3,
* See Journal of the Society of Telegraph Engineers, May 8, 1872.
MEASUREMENT OF ELECTRICAL RESISTANCE. 23 7
x r to 2', y' to 4', or else a; to 2, y to 4, x' to 1', ?/' to 3'. The
ends of the copper strips are connected up to a bridge wire-
and to two ratio arm coils E and S as shown.
To obtain very accurate results, all the coils A, B, E and
S must be placed in melting ice or in paraffin oil surrounded
by melting ice, to keep them at a known and constant
temperature. In the bottom of each mercury cup must be
placed an amalgamated copper dish, against which the ends of
the copper strips, fl-connectors, or coil terminals are placed. In
the Author's form of circular bridge (seepage 152) the mercury
cups are formed by slipping pieces of indiarubber tube on to
the ends of short cylinders of copper which are soldered to-
INDIA RUBBER TUBE
ICURY
FiG. 31.
the copper bars or strips (see Fig. 31). The ends of these-
cylinders being well amalgamated, the coil legs or connectors
are then well pressed down on them by weights or springs so
that a good copper-to-copper contact is made between well
amalgamated true copper surfaces immersed in mercury. A
joint such as this offers an exceedingly small and constant
resistance.
The process of taking a reading is then as follows : Let A
be a standard coil of known value at 0C. After the coils
have been kept immersed in ice for a sufficient time to ensure
that in each the whole wire is all at the temperature of
238 MEASUREMENT OF ELECTRICAL RESISTANCE.
melting ice, a bridge reading is taken by finding the balancing
point of the slider on the wire. The position of the coils
A and B is then exchanged and a second reading taken. The
resistance of that part of the slide wire between the two
positions of balance is equal to the difference between the
resistances of the known resistance A and the unknown
resistance B at 0C. For if E and S are the values,
of the resistances of the ratio arm coils, and A and B
the resistance of the coils the difference of which is
desired, and if p is the resistance of the slide wire and
connections at the side of A up to the point of contact of
the slider, whilst W is the whole resistance of the slide wire
and connections between A and B, we have the following
relation between these resistances when the bridge is
balanced :
S:K=A + /> :B + W-/>.
Supposing, then, the coils A and B interchanged in position
and that the reading p then becomes p, for a new position
of balance ; then :
S:E=B + p' : A+W />'.
Hence A ~B=p' p.
Accordingly, the difference in the resistances of A and B
becomes known when the slide wire is calibrated so that its
resistance per centimetre or per scale division is discovered,
and then, if A is a known resistance, the value of B is
accurately determined.
In the accurate comparison of standard coils or of unknown
resistances with a standard resistance, the great difficulty is
that of discovering the actual temperature of the wire
MEASUREMENT OF ELECTRICAL RESISTANCE. 239
corresponding to a certain evaluation or measurement. The
passage of a current, however small, through a wire heats it
and changes its resistance ; hence the very accurate comparison
of resistances is not easy to make unless the coils can be kept
immersed in crushed and melting ice for long periods of
time, or else can be placed in tanks containing a large
quantity of water or oil in a state of motion and at the
temperature of the air around them.
There are several methods by which this constancy of
temperature can be secured. If the supply of water to the
laboratory is from a constant town supply, it will generally
be found that, if a current of this town water is kept flowing
through a tank, after a time the temperature will be main-
tained at a nearly constant value, or at least within narrow
limits. The coils to be compared can be both immersed in
such a tank. Another way is to place both coils in a vessel
h'lled with an insulating oil, which is kept in motion by a
paddle driven by an electromotor, or by blowing air through
it with a bellows, or by hand stirring. In any case the
object must be to rapidly and thoroughly renew the layer of
liquid in contact with the metallic case of the resistance coil
or the wire itself, and it is only under these conditions that
we can assume that a thermometer placed in the liquid will
give even an approximation to the true temperature of the
wire. Then, after discovering the points of balance on the
bridge, the coils should be left for some time, and when
quite at the temperature of the bath should be once more
compared.
For the very accurate comparison of standard resistances a
special room should be set apart, and this room should
preferably be below ground, so as to be preserved nearly at a
constant temperature all the year round. No person should
be allowed in the room except the observer at the time the
measurements are being made. If it is necessary to place
the galvanometer scale at a distance, it can be read by means
of a telescope suitably fixed near the observer.
240 MEASUREMENT OF ELECTRICAL RESISTANCE.
8. The Calibration of a Slide Wire. In the use of a
standard wire bridge a preliminary operation is that of
the calibration of the wire to determine the true resistance
per centimetre length of the wire. The following method is
the one which is most convenient : Two resistances are
provided of nearly equal value at the same temperature. These
may be manganin wires, each having a resistance of 1 ohm
and soldered to suitable terminal rods. These wires should
be of sufficient diameter not to heat sensibly with the bridge-
currents. If they are not of exactly equal resistance,
then one of them will be greater. Let two plug resistance
boxes be provided, and let the terminals of these be connected
to the ends of the 1-ohm wires, so that when a high
resistance K is unplugged out of either box the resistance of
the 1-ohm wire and this high resistance in parallel can be
slightly varied. Thus, suppose the 1-ohm wire to have a
value of exactly 1 ohm, and that we place in parallel with,
it a resistance of 2,000 ohms. The joint resistance of the
two in parallel is
1_ _2,000_ 1_
JL_l_ "2,001 ~ 2,001'
1^2,000
or is diminished by nearly O'OOOS of an ohm. Hence, by
a series of trials we can adjust the parallel low and high
resistances so that the combined resistances consisting of the
two 1-ohm coils so shunted are of exactly equal resistance.
The high resistance shunts must be adjusted until the two-
combined resistances are brought into a condition of equality
as shown by the fact that when placed as coils A and B and
exchanged on the bridge the balancing point on the slide wire
is not changed.
This being done, let the two equal combined resistances be
furthermore made different by a known small amount by
shunting one of them with a resistance say of 1,000 ohms.
We have then two resistances which differ by a known
small resistance. For if each of the equal combined
MEASUREMENT OF ELECTRICAL RESISTANCE. 241
resistances is x ohms, the cue shunted with 1,000 ohms is
,andhence their differenceis then fa+
1,000 +
ohms. Let these two groups of coils be connected to the
Matthiessen and Hockin bridge as the coils A and B, and inter-
changed in position, the balancing point on the slide wire a b
(see Fig. 32) being found for each position. Let the distance
between the two balancing positions be y centimetres of wire.
We then know that the resistance of the length y of the slide
wire lying between the two points of balance is equal to the
known difference of resistance of the two coils viz., to
l ^ x } ohms. The coils P and Q in the Matthiessen
1,000 + n/
FIG. 32.
and Hockin bridge are then to be replaced by a wire of
platinoid a'b' about equal in resistance to the resistance of
each of the coils A and B taken together. This wire need not
be specially selected for uniformity. It is preferably in the
form of a slide wire stretched over a board with a divided
scale beneath it, and having a sliding contact piece to make
contact with any point in its length.
The connections are then made as in Fig. 32, the ends of
the galvanometer circuit being connected to the sliders on the
wires. The observer begins by moving the contact G- on the
top slide wire until a place of balance, 1, is found on the bridge
242 MEASUREMENT OF ELECTRICAL RESISTANCE.
slide wire a b as near as possible to one end of the bridge
wire. Then he .interchanges the coils A and B, and finds a
new balancing position at 2. The resistance of the lengths
between points 1 and 2 on the bridge slide wire is equal to
the resistance A-B. Then he changes the coils A and B
back to their original position, and moves the contact G to G'
until a place of balance is found at the same point 2 on the
bridge slide wire. Again he interchanges A and B, and finds
a new place of balance at 3. The resistance of the length
between 2 and 3 on the bridge slide wire is also equal to the
resistance A B. In this way, by changing alternately the
position of the coils and the point of contact G, we are able to
mark off the whole length of the bridge slide wire into little
intervals of length, 1 2, 2 3, 3 4, &c., each of equal
electrical resistance.
We can then from these values construct a table, by using
proportional parts, which will give us very approximately the
true resistance of each centimetre in length of the slide wire,
and thus give us the mean resistance per unit of length or
centimetre of the slide wire.
This calculation should be checked by increasing the differ-
ence between the coils A and B by a known shunting resist-
ance, so that the difference A B is just a little less than the
resistance of the whole slide wire. The constant application
of corrections for inequality in the slide wire is, however, so
troublesome, that in building a standard Matthiessen and
Hockin slide wire bridge it is worth while to take some pains
to secure a Wire of such uniformity in resistance per unit of
length that the correction to be applied for inequality in
resistance per centimetre is practically negligible. When the
resistance of the wire has been thus determined, we can at
once employ the bridge to measure the difference between a
standard resistance and a coil not differing from it by more
than the whole resistance of the bridge wire, and this method
of differences is more accurate for evaluating standard coils
than is the method of ratios.
MEASUREMENT OF ELECTRICAL RESISTANCE. 243
In this manner, given a standard 1-ohm coil, a standard
or known value 10-ohin coil, &c., the experimentalist can fix
the exact value at a known temperature of other coils intended
to represent 1 ohm, 10 ohms, &c.
9. To Determine the Temperature Coefficient of a
Standard Resistance Coil. If the observer possesses a
resistance coil the value of which, in terms of some standard
of reference, is known at a stated temperature, it is essential
to determine the temperature coefficient (T.C.), so that the true
resistance of the coil may be known at any other temperature.
In the case of the high-resistance alloys platinum-silver,
manganin, platinoid, &c., used in the construction of standard
coils for ranges of temperature from about 0C. to 25C., it
may be assumed that for all practical purposes the resistance
(K,) of the coil or wire at any temperature tC. is related to
its resistance (R ) at 0C., in the manner expressed by the
formula
In this case a is called the temperature coefficient. It is
generally expressed as a percentage per degree Centigrade of
the resistance at 0C. or at 15C.
In the case of pure metals or alloys taken over wider
ranges of temperature, the relation between the resistances at
different temperatures is less simple, and can generally only
be expressed in a graphical form by a curve of resistance in
terms of temperature. If E is the value of the resistance of
jp
the conductor at any temperature C., then ^ is the rate of
ctt
1 /7"P
change with temperature, and -~ Vis the rate of change per
unit of resistance at that temperature. The value of the
expression - - may be taken as the temperature coefficient
_Lt Ctt
corresponding to that temperature tC. It is usual to state
the mean temperature coefficient between certain extreme
temperatures. Thus, the mean temperature coefficient (mean
R2
244 MEASUREMENT OF ELECTRICAL RESISTANCE.
T.C.) between 0C. and 25C. must be known for every
standard coil possessed by the laboratory. Also its true-
resistance at 0C. Its resistance at tC. is then at once
calculated by the expression
Generally speaking, instrument makers mark on a coil the
temperature at which it has its nominal value. Thus, a
1-ohm standard may be marked as u correct at 15*4C." If r
then, the temperature coefficient is known or given, the true
resistance at any other temperature can be found provided it
lies within the limits of practical constancy of the tempera-
ture coefficient.
The temperature coefficient of a standard coil is most easily
determined as follows: >Select two coils of nearly equal value,
say A and B. Place both coils in crushed melting ice
contained in any convenient vessel, and let the coils remain
in this ice until it is practically certain all parts of the wire
of the coil are at 0C. Place these coils on a Matthiessein
and Hockin bridge (which may conveniently be the Fleming
or Nalder form of differential^bridge), and take the difference-
between the resistance of these coils in terms of the resistance
of the bridge wire unit. Thus, suppose at 0C. we have
A B =# divisions of bridge wire.
Next keep the coil B at 0C., but immerse the coil A in tap
water say at t*C. or the service water temperature, and keep it
there until it is practically certain all parts of the wire are
at the same temperature. Then again take the difference in
resistance of A and B on the bridge, and we have
A, B =:^ divisions of bridge wire.
Hence, by subtraction, A t A =.yx.
) I 'Y*
Accordingly, - - is the increment in bridge wire divisions
t
of the resistance of coil A when heated from 0C. to tC. If
p is the resistance of the bridge wire per unit of length, we
MEASUREMENT OF ELECTRICAL RESISTANCE. 245
Iiave the value of the temperature coefficient (a) of the coil
A between 0C. and 15C. given by the expression
100 ?/ x
== r ' 3 P-
A t
10, To Determine the Mean Temperature Coefficient of
a, Metallic Alloy in the Form of a Curve. The sample of
the alloy should be drawn into a wire of uniform diameter
and as far as possible of uniform resistance per unit of
length. It is then required to determine the mean tempera-
ture coefficient of the material. This is effected in the
following manner: A boxwood cylinder of about 2in. (or
5cm.) in diameter and Sin. in length has a deep and coarse
n
n
FIG. 33.
screw thread cut on it in the lathe. This screw tlireaa ma
Iiave a pitch of six or eight turns per inch. The opposite
sides of the cylinder should have deep grooves cut in them
and copper rods about T \in. (or 4mm.) in diameter attached
to the cylinder, as shown in Fig. 33. These rods may be
slightly flattened where they lie against the wood cylinder,
and be screwed to it. The rods are bent over, as shown in
the diagram, to form electrodes. The alloy must be drawn
into the form of a wire of diameter between No. 22 and
Xo. 30 S.W.G., and must be wound loosely on the boxwood
cylinder in the grooves. The ends of the wire must be
246 MEASUREMENT OF ELECTRICAL RESISTANCE.
soldered to the copper terminal rods. The cylinder is then
to be immersed in a copper vessel containing paraffin oil
enclosed in another vessel which contains water. The
resistance coil is connected with the resistance bridge by
means of thick stranded copper connecting leads. In the
first instance the copper vessel of paraffin oil may be
immersed in crushed ice and kept there until the paraffin
and the resistance wire immersed in it has a temperature of
0C. as taken by a correct mercury thermometer. The
resistance of the wire is then observed on the bridge by
taking either its difference from, or ratio to, a known
resistance. The resistance coil is conveniently connected to
the bridge circuit by having its copper legs placed in
mercury cups, which are in connection with the bridge by
thick flexible leads of stranded copper. In order to eliminate
the resistance of the leads a copper loop must be provided, the
total length of which is equal to the total length of the two
copper terminal rods of the coil, and it must be made of a
sample of the same copper wire. This blank, as it is called, is
placed in the mercury cups and measured, and the difference
in measurements taken when the resistance coil is in the
cups and when the blank is in the cups is the resistance of
the wire of the resistance coil.
The measurements having been made at 0C., the next step
is to make them at a temperature as near as possible to
100C. For this purpose the outer jacket of the copper vessel
is filled with water, which is made to boil. The paraffin oil
in the inner vessel must be kept well stirred and the tempera-
ture taken by a correct mercury thermometer. The double
readings are then obtained as before. Other readings may
then be taken at intermediate temperatures. The chief diffi-
culty in obtaining good results consists in ascertaining the
true mean temperature of the wire at the moment when the
resistance measurement is made.
A very extensive series of measurements of the above kind
were made by the Author in conjunction with Prof. J. Dewar
MEASUREMENT OF ELECTRICAL RESISTANCE. 247
in 1893, using metals of known purity and alloys of ascer^
tained composition. The measurements were made between
200C. and + 200C., using boiling liquid oxygen to provide
a temperature of 182'5C., a mixture of solid carbonic acid
in ether to create a temperature of 78'2C., melting ice to
give a temperature of 0C., and boiling water under a pres-
sure of 760mm. to fix a temperature of 100C. By this
means a series of observations of resistances of the same
metallic wire were taken at known temperatures, and the
results set out in a series of curves. These curves show that
the resistance of a wire of a pure metal steadily diminishes as
the temperature falls in such a manner as to indicate that
at or near the absolute zero of temperature ( - 273C.) the
resistivity of the metal would in all probability be zero. In
other words, it would become a perfect conductor. Values of
the ordinates of these curves showing the volume resistivity
of different metals at fixed temperatures between 150C. and
-f- 150C. are given in Table Y. at the end of this chapter.
The curves of temperature resistance (temperatures being
the abscissae) are in the case of some metals concave upwards
and in other cases concave downwards. The curves of the
magnetic metals iron and nickel are at first concave upwards
and rise very rapidly. At a temperature very near to that at
which the metals lose their marked magnetic qualities (the
magnetic critical temperature) the temperature resistance
curve has a point of inflexion and becomes concave down-
wards. The temperature coefficient thereafter becomes
greatly diminished. In the case of iron this change tem-
perature is near 780C., and in the case of nickel near 340C.
The variation of resistance with temperature in the case of
iron is therefore delineated by a curve not unlike its magnetisa-
tion (see Fig. 34).
The following table gives the values of the absolute volume
resistivity of a certain specimen of annealed iron wire as
observed by Dr. D. K Morris.* The absolute volume
* "On the Magnetic Properties and Electrical Resistance of Iron as Dependent
upon Temperature." D. K. Morris, Ph.D. Phil. Mag., Sept. 1897, p. 213.
248 MEASUREMENT OF ELECTRICAL RESISTANCE.
resistivities (/>) in C.G.S. measure have been calculated for
exact centennial temperatures by interpolation from the
observed values as given by Dr. Morris for numerous inter-
mediate temperatures. The change in resistivity per degree
( - in the neighbourhood of each century is also stated.
120,000
100,000
80,000
03
c5
60,000
| 40,000
20,000
X
^
/
/
f
/
/
./
/
/
2CO 400 600 800 1,000 1,100
Temp. Centigrade.
FIG. 34. Temperature Resistance Curve of Iron.
The temperature coefficient at any temperature (t) is obtained
by dividing - at that temperature by the absolute resistivity
(p t ) corresponding to that temperature.
Volume electrical resistivity of iron annealed at 1,150.
Magnetic critical temperature=77SC.
Centigrade temperature
t.
Volume resistivity in
C.G.S. units.
Change in resistivity
per degree Centigrade.
10,050
61
100
16,527
71
200
24,308
82
300
34,537
115
400
45,024
116
500
57,416
124
600
71,764
152
765
100,025
195
780
103,200
800
106,600
133
900
115,342
52
1,000
118,781
22
1,100
120,656
12
MEASUREMENT OF ELECTRICAL RESISTANCE. 249
The temperature coefficient at 0C. is 0'0057, and it rises
-to a maximum value of 0*0204 at 765C. and falls again to a
value 0-00244 at 1,000C.
Observations on the specific heat of iron seem to show a
remarkable similarity in variation to that of the resistance
temperature coefficient. According to M. Pionchon, the
.specific heat of iron can be calculated for any temperature
between 0C. and 660C. by the formula
7, = 0-1012 + O-OOOOSO^G* + 0-0 00000164* 2 .
Hence we have the specific heat of iron at various
temperatures as follows :
Temperature. Specific heat.
0C 01012
100C 0-1079
200C 0-1176
300C 0-1306
400C 01468
500C 01665
600C 0-1892
Also it has been shown that the average specific heat of iron
between 750C. and 1,000C. = 0-213,
between 954C. 1,006C. = 0-218, and
between 1,050C. 1,200C. = 01988.
If the above values are set out in a curve, we find that the
specific heat of iron rises to a maximum and falls again in a
very similar manner to the temperature resistivity coefficient.
'These remarkable changes in the temperature coefficient and
in the form of the resistivity curve are doubtless connected
with the changes in the internal energy which go on in iron
;at certain critical temperatures.
Many attempts have been made to express the relation
'between temperature and electrical resistivity by an algebraic
formula. Over moderate ranges of temperature for most
nnetals an expression of the form
250 MEASUREMENT OF ELECTRICAL RESISTANCE.
where p t is the resistivity at tC., p is the resistivity at 0C. r
and a and (3 are constants, will suffice to approximately
express the facts.
It is, however, clear, from the form of the resistance
temperature curve of iron given above, that no such simple-
formula will suffice over wide ranges. of temperature or when
including critical temperatures.
In some other cases, such as that of the alloy manganin,-
there is a well-marked maximum value of the resistivity
corresponding to a certain temperature, and in certain
specimens of bismuth a minimum value of the resistivity has
been found for a particular temperature. This is the case
also with graphitic carbon. Hence all simple algebraic
expressions, expressing the value of resistivity in terms of
temperature, can only be made conformable with the facts of
observation over a certain range of temperature, and such
expressions cannot safely be extrapolated to yield results
lying beyond the limits of temperature for which the formula
was originally constructed.
When a pure metal is fused there are always rapid and
generally large changes in the electrical resistivity in passing
from the solid to the liquid condition. Thus, when solid
mercury is heated up from 200C. to above +100C. it
melts at 40 C., and just beyond that temperature its resis-
tivity is increased nearly 4'1 times,* as shown in Fig. 35.
The temperature coefficient whilst solid is not very different
from that of other pure metals.
In the case of pure platinum Mr. J. Hamilton Dickson,
after discussing other formula?, showedf that the resistivity
of pure platinum could be very well represented in terms of
the centigrade temperature by an empirical equation of the
form (E + a) 2 =
* See Dewar and Fleming, " On the Electrical Resistivity of Mercury at the
Temperature of Liquid Air." Proc. Roy. Soc., June, 1896, Vol. LX., p. 76.
See also Cailletet and Bouty, Comptes Kendus, 1885, Vol. C., p. 1188, who-
found the ratio to be 4'08 times.
t " On Platinum Temperatures,*' by J. D. H. Dickson, M.A. Phil. Man. r
Dec., 1897, p. 445.
MEASUREMENT OF ELECTRICAL RESISTANCE. 251
where R is the resistance at the temperature C. and a, p,.
and b are suitably selected constants. He has found, by
comparison with actual observations made on a pure annealed
platinum wire by Profs. Fleming and Dewar over a range of
temperature of 200C. to +200C., that a formula of the
above kind can be made to express with considerable accuracy
the variation in resistivity of platinum between the above
-283 -200 -100 +1
M*
^
^
's
^ 80,OOC
QJ 70000
60,000
| 50,000
1
5 40,0(K
| 30,000
J 20,000
10,000
r
1
$^
y
^,,-'''
^
-283 -2CO -108
Temperature in Platinum Degrees.
+100
FIG. 35. Temperature Resistance Curve of Mercury.
limits of temperature. The formula will be seen to be-
equivalent to the statement that the square of the resistance
measured from an artificial zero is simply proportional to
the temperature also measured from an artificial zero. In
the case of the magnetic metals iron, nickel, and cobalt,
there are remarkable changes in resistivity at the temperatures
at which the magnetic qualities are suddenly altered which
prevent any empirical formula from adequately representing
252 MEASUREMENT OF ELECTRICAL RESISTANCE.
the temperature change in resistance over ranges of tempera-
ture which include these critical points.*
11. To Determine the Specific Resistance or the Resis-
tivity of a Metal or Alloy. The volume-resistivity of a
material is defined to be the resistance of a cube of the
material having a side of unit length, taken between opposed
faces of the cube at a defined temperature. The usual mcde
of stating the resistivity of metals and alloys is in C.G.S. units
or in microhms per centimetre-cube at 0C. In the case of
electrolytes or conducting liquids it is expressed in ohms
per centimetre-cube at 18C. In the case of materials of very
high resistivity, commonly called insulators, it is usual to state
the resistivity taken at 75F. in megohms or in mega-megohms
that is, in millions of megohms per centimetre-cube.
To determine the volume-resistivity of a sample of a metal
or alloy, it is desirable to possess it in the form of a carefully
drawn wire of uniform circular cross-section, Owing to the
-difficulty of determining the diameter of very fine wires, it is
found more convenient to determine and define the resistivity
of metals and alloys by the resistance in ohms per metre-
gramme at 0C. that is to say, by stating the ohmic resistance
at 0C. of a wire of circular cross-section having a length of
one metre and weighing one gramme.
* For a discussion of the chief formulae which have been proposed to
represent the variation in the electrical resistivity of metals, and especially
'platinum, with temperature, the reader may consult with advantage the
following papers :
"On Platinum Temperatures," by J. D. Hamilton Dickson, Phil. Mag..
Dec., 1897. Also
"Notes on Platinum Thermometry," by H. L. Callendar, Phil. Mag..
Feb., 1899.
With regard- to the temperature variation in resistance of magnetic metals,
consult
W. Kohlrausch, Wied. Ann., Vol. XXXIII., p. 42,
J. Hopkinson, Proc. Roy. Soc., Vol. XLV., p. 457,
Le Chatelier, Comptes Rcndus, Vol. CX., p. 283, and
D. K. Morris, Phil. Mag., Sept., 1897. ,
For a record of very careful work on the variation of the resistance of metals
with temperature, and the representation of results by a parabolic formula
of the type Rf/R = 1 + a U-, see Benoit, Comptes Rendus, 1873, p. 342.
MEASUREMENT OF ELECTRICAL RESISTANCE.
The relation between the resistance per centimetre-cube,
called the volume-resistivity, and the resistance per metre-
gramme, called the mass-resistivity, is as follows :
Consider a wire of uniform circular cross-section of s square
centimetres and of length I centimetres. Let the density of
the material be d, its electrical volume-resistivity in C.G.S. units-
be p, and the total resistance of the wire be E ohms. Then,
we have
~~s~'
also lsd=M,
where M is the mass of the wire in grammes.
Hence, if M=l, we have
lsd=l, ors= .
Id
Hence ltfR=pPd.
If the wire has a length of one metre or 100 cms. we have
5 ,
Accordingly, if p is the mass-resistivity, or resistance-
expressed in ohms, of a wire of circular section one metre-
long and weighing one gramme, we have
If the mass-resistivity is expressed in microhms per metre-
gramme (=10V) we have the rule : Microhms per metre-
gramme, divided by ten times density, is equal to resistivity per
centimetre-cube in C.G.S. units. Also, if the volume-resistivity
of the material, reckoned in microhms per centimetre-cube, is
denoted by />" we have
l,OOOp"=/>.
Hence 100p'=//W, <*'
Accordingly, the resistivity of a uniform wire in ohms per
metre-gramme is to the resistivity of the material in microhms
per centimetre-cube as the density is to 100. Or, again,,
-254 MEASUREMENT OF ELECTRICAL RESISTANCE.
since we have p" = p r =-, we see that the volume-resistivity
. a
can always be deduced from the mass resistivity when we
know the density of the material.
The mass-resistivity per metre-gramme can always be
-obtained b} 7 measuring the resistance and the mass of any
uniform sectioned wire of which the length is known. If, as
above, p stands for the mass-resistivity in ohms per metre-
gramme and p for the volume-resistivity per centimetre-cube,
and if E is the resistance in ohms of any uniform sectioned
wire of length I centimetres and mass M grammes, we then
.have
Also lOV =p W * d , or 10 V =pcl
,
M M
Hence a determination of the length (7), mass (M), density (rf),
and resistance (E) of any wire enables us to find the mass-
resistivity in ohms per metre-gramme (/o / ) and the volume-
resistivity in C.G-.S. units per centimetre-cube (/>) by the
-equations
Hence we have the following practical rules :
Given the resistance in ohms (R) of a uniform sectioned wire of length (I)
in centimetres and mass (M) in grammes, calculate the mass-resistivity (p'} in
-ohms per metre-gramme.
Answer. Multiply together 10,OCO times the mass in grammes and the
resistance in ohms, and divide the product by the square of the length in
centimetres ; the quotient is the ohmic mass-resistivity per metre -gramme.-
MEASUREMENT OF ELECTRICAL RESISTANCE. 255
Example. The resistance of a column of pure mercury 106*3 centimetres in
length, and weighing 144521 grammes, is one ohm at 0C. ; find the mass-
resistivity of mercury.
Answer. 12'789 ohms per metre-gramme at 0C.
Again, given the mass -resistivity in ohms per metre-gramme (//); find the
volume-resistivity (/>) in C.G.S. units per centimetre-cube.
Answer. Multiply the ohmic mass-resistivity by 100,000, and divide the
product by the density (rf).
Example. Given that the density of mercury at 0C. is 13 '595; find
the volume-resistivity in C.G.S. units, knowing the mass- resistivity to be
12'789 ohms per metre-gramme.
Answer. 94,070 C.G.S. units per centimetre -cube at 0C.
To determine the resistivity of a metallic material in the
form of a wire of uniform section, we must, therefore, find the
total resistance, length, mass, and density of the wire. The
density may be taken with appropriate samples on the whole
wire. It is convenient to proceed in the following manner :
If the length and diameter of the wire furnished is such
that the total resistance is not much less than one ohm,
the wire may be laid in a flat circular coil the turns of which
are prevented from touching each other by winding the wire
on a suitable bobbin or frame. The ends of the wire must
be soldered to thick copper terminal rods or leads by which it
can be connected to the bridge. The wire must be immersed
in a bath of paraffin oil kept continually stirred. The resist-
ance of the wire is then carefully taken at several tempera-
tures. It is best to take it at the temperature of the room
and also at or near 0C. by cooling the paraffin oil by ice. In
this manner the temperature-coefficient becomes known.
Having satisfactorily ascertained the resistance of the wire
at known temperatures, it is cut off close to the thick
terminal rods, and these are soldered together and the
resistance of the leads determined in order that a correction
may be applied for lead resistance. The length of the wire
used has then to be determined. This must be done without
in the least degree stretching the wire, and is best achieved
by pressing the wire gently into a shallow groove made with
a saw in the surface of a long board. This groove holds the
256 MEASUREMENT OF ELECTRICAL RESISTANCE.
wire straight and enables its length to be measured with arc
accurate metre scale. The length and resistance having
been found, the wire may be cut up into sections and the-
density or specific gravity found in the usual way. If the
wire is a fine wire it may be wound up into a sort of loose-
ball, and the specific gravity of the whole mass determined.
The great difficulty which here occurs is that of the removal
of all the air which is entangled in, or adherent to, the wire..
The best way to proceed is as follows : The hank of wire is-
suspended by a fine horse-hair from the beam of a delicate
chemical balance and the weight taken. Let this weight be
W grammes. The wire is then placed in distilled water and
well boiled, and allowed to remain in the water whilst the-
water cools. The wire is then weighed again in the water
without removing it from the water. Let the weight then be
W
W grammes. The density d is equal to . If the
wire is of such a material that it is chemically affected by
being boiled in water at 100C. the adherent air must be-
removed by gently heating the water and then placing it
under the receiver of an air pump and exhausting the air from*
around it. The water will then boil under a reduced pressure-
at a much lower temperature. The presence of any air-
bubble in contact with the wire when weighed in water will
render the apparent density too small. In both weighings
a correction must be applied by weighing the horse-hair
suspension alone and deducting this from the weight of the
mass. It is more difficult to get correct results the smaller
the mass of the wire. Hence the mass of the material
weighed should be as great as possible. The density d being
obtained and the mass M of the wire in grammes used for the
resistance measurement, as also the length I in centimetres r
we have the means of determining the mean cross-section s of
the wire for /scfcM.
M
Hence s=-.- 7 .
id
MEASUREMENT OF ELECTRICAL RESISTANCE. 25?
In the case of very line circular-sectioned wires a close
approximation can be made to the mean diameter of the
wire by measuring with a microscope-micrometer the mean
diameter in a large number of different places and positions
and taking the mean of all these measurements.
Having determined in one way or other the mean diameter
of the wire, we have the volume-resistivity p in C.G-.S. units
given by the equation,
-W-,
s M
MK10 9
Tables of the volume-resistivities of various metals and alloys
are given at the end of the present chapter. (See Tables I.,
II, III., IV., V. and VII.)
12. Determinations of Volume and Mass-Resistivity
of Metals and Alloys. Great labour has been expended on
the determination of the mass and volume-resistivity of
metals and certain standard alloys. Considerable differences
are, however, found in the values assigned by various
authorities to the volume-resistivities at 0C. of the various
metals. The reason for this is that exceedingly minute pro-
portions of impurity or other metals have an immense effect
upon the electrical resistivity. Some metals, such as iron,
have probably never yet been obtained in an absolutely
pure annealed condition.
The work on this subject to which reference is most often
made is that of Dr. A. Matthiessen, who published between
1860 and 1864 the results of numerous researches on elec-
trical conductivity recorded in the Philosophical Magazine,
in the Philosophical Transactions of the Eoyal Society, and the
Jieports of the British Association for those years.
For most electrical engineering purposes the constants of
greatest importance are those of the mass and volume-
resistivity of pure copper in its hard-drawn and annealed
258 MEASUREMENT OF ELECTRICAL RESISTANCE.
conditions. Matthiessen's value for the mass-resistivity of
pure hard-drawn copper is called Matthiessen's Standard.
Matthiessen's Standard is defined in the following state-
ment* :
The resistance of a wire of pure hard-drawn copper, one
metre long, weighing one gramme, is 0-1469 British Association
units at SWF.
Since the numerical value of a resistance measured in
standard or international ohms is, by authoritative definition,
equal to O9866 of the value of the same resistance stated in
B.A. units, the above may be modernised into the following
fundamental definition :
The resistance of a ivire of pure hard-drawn copper, one metre
long, and weighing one gramme, is '1449 3 standard ohms at
0C.
Since resistances are not conveniently determined at 0C.,
but better at 60F. or 15'55 C., the definition has again been
re-cast in form by the Committee on Copper Conductors
appointed to consider this question of Copper Conductivity
Standards-)- as follows :
Matthiessen's standard for hard-drawn high-conductivity
commercial copper shall be considered to be a 'wire of pure
hard-drawn copper one metre long and weighing one gramme,
whose resistance at 60F. is 0*153858 standard ohms.
Hard-drawn copper is defined as that which will not
elongate more than 1 per cent, without fracture.
The conversion from B.A. units at 32F. to standard
ohms at 60F. is made by employing a formula given by
*Briti&h Association Report, 1864, or Phil. Mag., Vol. XXIX., May, 3865,
p. 362.
t The Committee on Copper Conductors was organised in 1899 by writing
to the General Post Office and the Institution of Electrical Engineers and
inviting them to send delegates to meet the representatives of eight of the
principal manufacturers of insulated copper cables to consider and come to an
arrangement as to the standard to be adopted for Copper Conductivity.
The sittings of the Committee were held in London. The Secretary was
Mr. A. H. Howard. The recommendations of the Committee have been adopted
by the General Post Office and the chief cable manufacturing companies. The
Report of the Committee is published in the Journal, of the Institution of
Electrical Engineers, January, 1900, p. 169.
MEASUREMENT OF ELECTRICAL RESISTANCE. 259
Matthiessen for the temperature coefficient of copper, viz. :
n_
1-0-00215006 (* 32) + 0*00000278 (-32) 2 '
and the rule :
Resistance in B.A.U. X -9 86 6= resistance in standard ohms.
Hence, we have for hard-drawn copper wire the values below
for the metre-gramme resistivity (p'} :
p' (at 32F.)=01469 B.A.U.
p' (at 0C.) =0-1449 standard ohms.
P r (at 60F.)=0'1539 standard ohms.
Matthiessen also measured the mass-resistivity of annealed
copper in the form of wire. Annealed copper may exist in
various states of annealing, and in this condition its resis-
tivity 'is less by slightly variable amounts than in the
hard-drawn condition. The resistivity of annealed copper
was measured by Matthiessen at an earlier date (Phil.
Trans. Roy. Soc., 1860, p. 86), and he found that it showed
a conductivity greater than that of hard-drawn copper
by about 2-26 per cent, to 2*5 per cent. Although this is
undoubtedly correct for carefully annealed copper, it is a
result which cannot be obtained in practice with ordinary
commercial copper wire, as this latter is unannealed, or
hardened somewhat by bending and winding in the process
of manufacturing it into covered wire. In practice it
is found tli at the resistance of commercial annealed copper
wire is about 0-9875, or \\ per cent, less than that of
hard-drawn wire of the same length and section.
Matthiessen, however, gave a later value for annealed
copper as follows :
The resistance of a wire of annealed copper one metre long
and weighing one gramme is 0'1440 British Association
units at 32F.
In modern standard units the definition reads thus :
The resistance of a wire of annealed copper one metre long
and iveighing one gramme is ! 1421 standard ohms at 0C.
a
260 MEASUREMENT OF ELECTRICAL RESISTANCE.
The ratio of the numbers 01421 to 01449 is G'98025.
This value has accordingly been accepted by the Committee
on Copper Conductors, and the ratio of the resistivity of soft
or annealed to hard-drawn copper is taken at the above
value, so that
The resistivity of _ Q.ggQ.?- x the resistivity of pure
pure annealed copper ~ ' hard-drawn copper.
Hence the Committee have formulated the definition for the
standard for soft or annealed copper as follows :
Matthiessen's standard for annealed high-conductivity com-
mercial copper shall be considered to be a wire of pure annealed
copper one metre long and weighing one gramme, whose resist-
ance at 60F. is 0150822 standard ohms.
Employing the same temperature coefficient as for hard-
drawn copper, we have the following values for the metre-
gramme resistivity of annealed copper :
P ' (at 32F.)=01440 B.A.U.
P r (at 0C.)=01421 standard ohms.
p' (at 60F.) =01508 standard ohms.
It is to be noted that this standard for annealed copper is
based upon an assumption as to the relative conductivities of
hard and annealed copper. The figures given by Matthiessen
for this ratio vary considerably in different Papers. See Phil.
Trans., 1860, p. 86 ; Phil. Trans., 1864, p. 197 ; and Phil.
Mag., May, 1865, p. 363; also The Electrician, Vol. XLV.,
p. 59.
The next question with which we are concerned is the
equivalents of the above numbers in volume-resistivity. The
specific gravity of copper varies from 8'89 to 8'95, and the
standard value which is now accepted for high-conductivity
commercial copper is 8*912, corresponding to a weight of
5551b. per cubic foot at 60F. Hence, multiplying the values
for the metre-gramme resistivity by 100 and then dividing
by 8*912, we have the corresponding volume-resistivities in
MEASUREMENT OF ELECTRTCAL RESISTANCE. 261
microhms per centimetre-cube for pure commercial hard-
drawn and pure annealed copper as follows :
The volume-resistivity of pure hard-drawn copper at 0C. =
1'626 microhms per centimetre-cube, or 1,626 C.Gr.S. units.
The volume-resistivity of pure annealed copper at 0C. =
1-594 microhms per centimetre-cube, or 1,594 C.G.S. units.
A table giving the resistances of annealed copper wire
calculated on the basis of the above value is given at the end
of this chapter. (See Table XIII.)
The calculation of the resistivity at any other temperature
(0 requires a knowledge of the temperature coefficient (T.C.J
for copper. Matthiessen's formula for the reduction of the
resistivity at tY.(p t ) to the resistivity (p 3 J at 32F. was :
P&f=Pt (1-0-00215006 (*-32) + 0-00000278 (*-32) 2 ),
or approximately p t =p Q (1 + 0*00387 t'), if '= Centigrade temp.
It is now known that this correcting factor is rather too
small, owing to the improvement in the quality of copper
made since Matthiessen's time. Hence the Committee on
Copper Conductors have recommended that the average tem-
perature coefficient between the temperatures 30F. and 100F.
shall be that value obtained by Messrs. Clark, Forde and
Taylor, as given in a pamphlet published by them on Feb-
ruary 20th, 1899, viz., 0-00238 per degree Fahr., or 0*00428 per
degree Centigrade*, so that for Centigrade temperatures we
shall have pt=pQ ^ + 0-004280,
or P6QY.=P32. x 1*06665.
Since the date when Matthiessen's work was carried out
the most careful research carried out on the conductivity of
copper is that by Mr. T. C. Fitzpatrick, described in a Paper
read before the British Association at Leedsf in 1890.
Mr. Fitzpatrick's experiments on the conductivity of hard-
* This is precisely the same mean value for the temperature coefficient of
annealed copper as was independently obtained by Profs. Fleming and Dewar.
See Phil. Mag., Sept., 1893, p. 299. Messrs. Clark, Forde and Taylor's pamphlet
is published by " The Electrician " Printing and Publishing Co.
t See Report B.A., Leeds, 1890 ; Appendix IIT. to the Reports of the Com-
mittee on Electric*! Standards for 1890 : also The Electrician, Vol. 25, p. 608,
1890.
262 MEASUREMENT Of ELECTRICAL RESISTANCE.
drawn copper led him to confirm exactly Matthiessen's value
for the resistivity (per metre-gramme) of a wire of hard-drawn
copper wire taken at 18C., viz., O1571 ohms per metre-
gramme. Also, he found substantially the same percentage
difference as Matthiessen did between the metre-gramme
resistance of a hard-drawn copper wire and that of the same
wire when annealed and soft.
Mr. Fitzpatrick found, as others have done, great variations
in the specific gravity of copper, so that wires having the same
mass-resistivity per metre-gramme do not give the same
volume-resistivity per centimetre-cube at the same temperature.
Matthiessen therefore expressed all his results in mass-resis-
tivity, believing it to be more accurate and affording a better
definition of the real conductivity.
In addition to the determination of the conductivity of
copper, Matthiessen carried out very elaborate researches on
the electrical conductivity of different metals and alloys,
researches which are justly regarded as classical. At various
times numerous other observers have obtained values for the
volume-resistivities of different metals and alloys.
A table of resistances of platinoid and manganin wires of
various sizes is given at the end of this chapter. (See
Tables XII. and XIII.)
As regards the metals, with the exception of silver, copper
and mercury, and one or two others, such as tin and gold,
obtained without much difficulty in a state of chemical purity,
it is found that the greatest differences exist between the
electric conductivities as found by different observers. This
is due partly to the influence of minute proportions of
impurity, and the all but impossibility of obtaining certain
metals, such as iron, in a state of absolute chemical purity.
It is also due to differences in physical condition. Even
in the case of platinum and nickel, which are capable of
being prepared almost, if not quite, perfectly pure, the
greatest differences are found in the values assigned by
different observers to the electric conductivity. In the tables
MEASUREMENT OF ELECTRICAL RESISTANCE. 263
at the end of this chapter are given Matthiessen's results for
the principal metals reduced to express them in terms of the
standard ohm; also values obtained from a very extensive
series of observations made in 1892 and 1893 by Fleming
and Dewar.* (See Table V.)
In these last-mentioned researches great care was taken to
obtain the metals in the highest state of chemical purity.
These materials were drawn into uniform wires and the
diameters of these wires measured by a micrometer method
as described in the above-mentioned papers. Hence the
measurement made was a volume-resistivity determination.
The resistances of these various wires were measured over a
range of temperature lying been -f 200C. and -200C., this
latter temperature being obtained by the use of liquid air. The
temperatures were measured by means of a platinum thermo-
meter. A table of densities (see Table I.) of the principal
metals is added to enable inass-resistivity to be converted to
volume-resistivity.
The differences which occur in the values assigned by
different authors and experimentalists to the volume-resistivity
of the various metals are in some cases very great.
It appears as if, in some metals, very considerable pro-
portions of impurity or changes in physical state make but
little difference in the electric conductivity, whereas in the
case of other metals very great differences are created in the
electric conductivity by the presence of mere traces of other
metals. Matthiessen showed that metallic alloys may be
broadly divided into two classes :
(i.) Those in which an admixture or alloy composed of them has a very much
higher resistivity than either or any of the constituents. To this class belong
alloys of copper, silver, gold, aluminium, platinum, nickel and most other metals.
(ii.) On the other hand, alloys which consist only of two or more of the
following metals, viz., lead, tin, zinc, and cadmium, have a conductivity which
is nearly the mean of those of their constituents, and may be roughly calcu-
lated from the proportions in which the elements are mixe l.f
In the case of alloys of these last four metals (ii.), the resultant or mean
conductivity C can be calculated by the formula
n_ c^ + caifr + &c.
v l + y. 2 + &c. :
* See Phil. May., Oct. 1892 aud Sept. 1893. t Matthiessen, B.A. Report, 1864.
264 MEASUREMENT OF ELECTRICAL RESISTANCE.
while Cic 2 , &c., are the specific conductivities of the constituents, and v^v-^ &c.
are the volumes of the respective constituents.
For alloys containing only two or more of the above-named metals, viz.
zinc, lead, tin and cadmium, the mean density D of the alloy is also obtain-
able from the densities d^, Ac., of the constituents, and their relative
volumes ?; 1 t > 2 , &c., by a similar formula, viz. :
Vi + V>2 + &C.
The alloys formed with metals of class (i.) with one another have a much
inferior conductivity to that of any of the components, but as the percentage
of one component rises to 100 the conductivity of the alloy rises also very
quickly to that of the pure metal.
Alloys of metals taken partly from class (i.) and partly from class (ii.) have
a specific gravity and conductivity which is always less than that of the mean.
If a metal of class (ii.) is alloyed with a considerable percentage of a metal
from class (i.) the conductivity is not much altered, but if a metal from
class (i.) is alloyed with a very little of a metal from class (ii.) the conductivity
is very much reduced. Hence we find an immense effect produced by the
presence of a little zinc in reducing the conductivity of pure copper, or of
lead in reducing that of pure silver. Accordingly large variations may be
expected in the determinations of resistivity in the case of chemically-
prepared metals which are not easily prepared pure.
The reader may be referred to the following Papers and
sources of information for additional knowledge on the subject
of resistivity measurement :
" The Specific Eesistance of Pure Copper." By Messrs. J. W.
Swan and Ehodin. The Electrician, Vol. XXXIII., p. 803.
As the mean of a number of determinations of the volume -resistivity made
with hard-drawn and annealed copper the authors find the following values
for the resistivity (p ) at 0C. in C.G.S. units and the temperature coefficient (a).
Hard-drawn copper p = 1603 a = 0'00408.
A nnealed copper p - 1563 a = 0'00416.
The density of the copper at 15C. was 8'96.
" The Electrical Conductivity of Aluminium." By Messrs. J. W.
Eichards and J. A. Thomson. The Electrician, Vol. XXXVIII.,
p. 801.
The authors find the volume resistivity at to be as follows :
Hard-drawn aluminium p = 2684
Annealed aluminium p - 2659
"The Electric Conductivity of Steels." By M. Campredon.
The Electrician, Vol. XXVIIL, p. 845.
The author gives a useful table of the electric conductivity of steels of
given composition. The resistance of a wire linin. diameter and 1 kilometre
MEASUREMENT OF ELECTRICAL RESISTANCE. 265
long at 15C. would be 21 ohms if of copper and 125 ohms if of iron. The
resistivity of steel is lower in proportion as the purity and softness is greater.
Manganese is the element which has the greatest effect in raising the
resistivity.
" The Electric Eesistance of Copper at Low Temperatures."
By Wroblewski. The Electrician, Vol. XXI., p. 432.
" Electric and Thermal Conductivity." By H. F. Weber.
The Electrician, Vol. VII., p. 6.
A remarkable connection is established between the electrical conductivity
(K), the thermal conductivity (H), and the specific heat per unit of volume
TT
(S). This relation is =a + 6S. where a and 6 are constants.
K
" Electric Conductivity and Atomic Volume." By W. P.
Granville. The Electrician, Vol. XXI., p. 381.
An attempt to establish a relation between these quantities.
"The Electrical Resistivity of Silicon." The Electrician,
Vol. XL., p. 580.
"The Conductivity of Cement and Concrete." By Dr. St.
Lindeck. The Electrician, Vol. XXXVI., p. 788.
Useful data on the electrical conductivity of road-making materials.
13. Determination of Low Resistances by Fall of
Potential. For the determination of very low resistances
many of the above-described bridge methods are not
applicable. If it is desired to measure the resistance of a
dynamo armature or transformer coil or short length of
electric lighting cable, the uncertain resistance at the contacts
of any conductors used in connecting the resistance to be
measured to other circuits would perhaps be greater than
the whole resistance to be measured.
In the case of such low resistances one method which may
be adopted is that of measuring the resistance by the fall of
potential down it when a known current is sent through it.
The resistance to be measured is joined in series with a known
low resistance standard, say one-tenth or one-hundredth of an
ohm. A suitable adjustable resistance is then added in series
with the two above-mentioned resistances, and a few cells of
266 MEASUREMENT OF ELECTRICAL RESISTANCE.
a primary or secondary battery are employed to send a
current through the circuit. The terminals of a high
resistance galvanometer, or a galvanometer having a resist-
ance of 1,000 or 2,000 ohms in series with it, are then
connected, first to the terminals of the known low resistance
and next to the terminals of the unknown low resistance.
In each case the galvanometer deflection is noted. It is
desirable to reduce the current in the circuit to such a value
that neither of these galvanometer deflections is very large.
The ratio of these scale deflections then gives us the ratio of
the unknown to the known deflection, on the assumption,
which must previously be justified, that the deflections of the
galvanometer are proportional to the current flowing through it.
The methods of testing the correctness of this assumption
in the case of the galvanometer used will be given in the
chapter on CURRENT MEASUREMENT. Meanwhile, assuming it
to be the case, let G- denote the galvanometer constant, or the
number by which the scale deflection of the galvanometer
must be multiplied to give the current in amperes flowing
through it. Let K^ be the galvanometer resistance, R s the
resistance of the known standard, and K the resistance to
be determined. Also let V s be the potential difference (P.D.)
between the terminals of the standard resistance, and V
that between the ends of the unknown resistance. If, then,
D g and D are the galvanometer scale deflections in the two
cases, we have, by Ohm's law,
, . and =: ,
since the current in the main circuit is everywhere the same.
Hence, from the above equations,
D_E pp p D
TT fp 01 K=::K rf
D s li s D s
Accordingly, the value of the resistance being measured is
given as the product of the value of the standard resistance
i and the ratio of the two scale deflections D and D,.
MEASUREMENT OP ELECTRICAL RESISTANCE. 267
In practically measuring, for instance, the resistance of a
dynamo armature, we must first give a rough guess at the
probable order of the resistance. Let it be ascertained to be
something of the order of O'Ol of an ohm. We should
then select as a standard resistance a resistance strip
having a resistance of 0*01 ohm. This may be a suitable
strip or strand of manganin or platinoid. The strip is then
joined in series with the armature by connecting it to the
brushes or terminals, and a few dry cells may be employed to
send a current through the circuit. The ends of a pair of
wires are then connected to the terminals of the standard
resistance strip, and a pair to the terminals of the armature.
These last ir ay preferably be pressed into contact with opposite
sections of the commutator by being placed under the brushes,
if the armature being measured is a continuous-current
armature. The other ends of these wires are conveniently
brought to a set of six mercury cups mounted on a board,
so that, by changing the position of a pair of copper bridge
pieces, either of the potential wires can quickly be brought
into connection with the galvanometer.
It is necessary to make both the measurements quickly
after one another, and to ascertain that the main current
has not altered in the meantime. It is best, therefore, to
take several readings of the values of D and D, alternately.
If, say, D is taken first, and we find a value D x , and then D,
is taken, and after an equal interval D is taken again, and
we find a value D 2 , the scale reading which must be taken
for D is half the sum of D! and D 2 , or its mean value, and it
may be assumed that this is the proper value corresponding
to D,. In any case, a large number of such readings should
be taken and the value ultimately accepted, for the ratio of
I) : D, should be the mean of a large number of observations.
An essential condition of success in this method is that the
galvanometer circuit shall be so high that its connection as a
shunt on one of the low resistances does not sensibly alter
the potential difference of the terminals of the latter.
268 MEASUREMENT OF ELECTRICAL RESISTANCE.
15. Measurement of Low Resistances by the Matthies-
sen and Hockin Bridge. We may employ the slide wire
bridge with a carefully calibrated or uniform slide wire to
compare together two resistances which are small, one of
them having a known value. Let the resistances be arranged
in bridge form as in Fig. 36.
Let PE be the slide wire extended electrically by the
resistance coils A and C, -and let a battery of a few dry
cells be joined up to points x and y. Let ab and'cd be
the low resistances to be compared joined in so as to complete
the four arms of the bridge. Let G be a galvanometer of high
or not very low resistance but great sensitiveness, and let
FIG. 36.
contact keys be inserted in the galvanometer and battery
circuits. The following operations are then performed :
Connect the galvanometer G in between the sliding contact
on the bridge wire and the point a. Find a point Q x on
the slide wire such that the galvanometer shows no current.
Then we have
xa, A+PQ, ,, xa A+PQ t
^ = 0+02? e ^ = A+0+Pfi'
where xa stands for the resistance of the conductor between
points x and a, and A stands for the resistance of the
conductors between the points x and P, and so forth for the
other points.
We then connect the galvanometer in between points b and
the slider, and find a second position of the slider at which the
(i.)
MEASUREMENT OF ELECTRICAL RESISTANCE. 269
galvanometer indicates no current. Similarly we have,
(iii) xl = A tJ Q2 > whe
xy W
Hence from (i.) and (ii.) we find
&==*&-*=
Also in the same way we find
where Q 3 Q4 are the balancing positions on the slide wire
when the galvanometer is connected to the points c and d
respectively.
Accordingly, we find the ratio of ab to Ho be
cd Q 3 Q 4 '
In other words, assuming the uniformity of the slide wire,
we have
The resistance between ab _
The resistance between cd
The length of the slide wire between Q, and Q 2
The length of the slide wire between Q 3 and Q, 4
It may so happen that the resistances A and C will have
to be changed between the readings, so as to make all the
balancing positions come on the. slide wire. If in the case
of the four readings of the resistance A takes the values A lf
A 2 , A 3 and A4, and the same for the resistance C, then, pro-
vided A 1 + C 1 = A 2 +0 2 , the four equations will take the form
l xa j
'
ay . + xy
. -d hence <* = (A 2 -A 1 + Ql Q 2 ),
where W, as before, is the constant resistance
270 MEASUREMENT OF ELECTRICAL RESISTANCE.
In 'the same way we can find that
*-*?(A 4 -A,+Q,Q 4 ).
Hence o6_A a -A 1 +Q 1 Q 11
^-A.-AS+QA-
If A t = Ag = A 3 = A 4 , the last equation reduces as before to
If, then, cd is a known low resistance, we obtain the value
of db in terms of cd and the ratio of two lengths of a uniform
slide wire.
The accuracy of the above method is not dependent upon
the absence of any variation of the battery current. It can
be carried out with the current supplied from public supply
circuits if necessary.*
15. The Kelvin Double Bridge. The Kelvin double
bridge is an arrangement of nine conductors joining six
points and having a source of electromotive force in one
branch and a galvanometer in another.
Let P, Q, E, S, B, G, a, b, c (Fig. 37) be the nine conductors,
B being the battery branch and G- the galvanometer branch
Let the above letters stand for the respective resistances of these
branches. It will be seen that if the conductor c is cut at any
point x the arrangement then becomes a simple Wheatstone's
bridge. It is always possible to find some point x in the con-
ductor c dividing c into two segments, a and /3, such that the
point x and the two points x 1 and # 2 are all at the same potential.
When this is the case we must have the relation a = -. For,
__ __ ft t>
* The above method was reproduced in The Electrician, July 1, 1898,
Vol. XLL, p. 320, as a new method due to Messrs. Miiller and Wallau. It
was, however, described many jears previously in Maxwell's Treatise on
" Electricity and Magnetism," and is due to Messrs. Matthiessen and Hockin,
MEASUREMENT OF ELECTRICAL RESISTANCE. 271
under the above conditions, the current along the conductor a
must be the same as the current along b. Also, for the same
reason, we must have the relation
1
Or, since a + /3=c, the above becomes
P+- a
Q+
B
C
If, then, we make a-f l c, we have
X 2
FIG. 37. Diagram of Kelvin Bridge.
Under this last condition the Kelvin bridge becomes
modified into a form called the Thomson (Kelvin) and Varley
272 MEASUREMENT OF ELECTRICAL RESISTANCE.
slide. This latter instrument may be described in principle
as follows :
Let two slide wires XY, XT' (Fig. 38) be stretched over
scales parallel to one another. Let a battery B be attached
to the terminals of one slide wire, XY, so as to create a fall
of potential down it. Along the wire XY a slider is arranged
to move having double contact edges, so as to make contact
at two places, nn' on XY, separated by a constant resistance
or length of slide wire, nn'. Let the resistance from X to n
be P, that from Y to n' be Q, and let nn' be c. The second
slide wire X'Y' must have a resistance equal to a + b=c, and
FIG. 38. Diagram showing arrangement of Conductors in Kelvin and Varley
Slide.
it has a slider m running on it and making contact at any
point, and thus dividing it into two sections a and ~b. A pair
of adjustable resistances B, and S, are connected to the points
X and Y, and from their common junction, t, a galvanometer
having a resistance G is connected in between the slider m
and t. The double contact slider nn' has its contacts con-
nected to the ends of the wire X'Y'.
In Fig. 38, showing the diagram of the above arrangement
of circuits, the letters denoting resistances are the same as
those used in Fig. 37, showing diagrammatically the form of
the Kelvin bridge.
MEASUREMENT OF ELECTRICAL RESISTANCE. 273
Iii the laboratory the practical form of this double
bridge is known as the Kelvin and Varley slide. In this
instrument (shown in Fig. 39) the slide wire XY consists of
101 coils of wire in series, each of 1,000 ohms. The common
junctions of these coils are brought to terminal pins on the
top board of the instrument, which is generally an ebonite
slab. The wire X'Y' is represented by a similar series of
100 coils of 20 ohms each so that the whole resistance of
XT' =2,000 ohms = that of two coils of XY. The double
contact piece nn f is represented by a double branched
revolving arm which as it moves round makes contact with
FIG. 39 Kelvin and Varley Slide.
a pair of studs including between them two of the 1,000 ohm
coils in series. This interval of 2,000 ohms corresponds with
the resistance c in the diagrams.
The resistances to be compared are the R and S in the
diagrams, and these are represented in practice by a plug
resistance box and the unknown resistance to be determined.
The revolving contact arms of the two resistance boxes, which
represent the wires XY and X'Y' are then moved round
to touch the various contact pins until positions are found
where the galvanometer connected in circuit as indicated
shows no current.
274 MEASUREMENT OF ELECTRICAL RESISTANCE.
If It is the unknown resistance and S is the standard or
resistance of the plug box, we have
E
S
If the point n is indicated by a scale reading N\ on the first
box and the point m by a scale reading N 2 on the second box
we have P= 1,000 K,_ ohms,
and a= 20 N 2 ohms.
Also, we have Q = 1,000 (99 - NJ,
and 1= 20(100-N 2 ).
Accordingly P + ? = 1,000 N x + 10 N 2 ,
and Q+l =1,000 (99 -2^) + 10 (100-N 2 )
= 100,000 -(1,000 N x +10 N 2 );
E 1,000 K + lONa
QY
100,000 -(1,000 Ni + 10
FIG. 40.
The theory of the Kelvin bridge is as follows : Referring again to Fig. 37,
it is easy to show that the absence of a current in the galvanometer circuit
necessitates a certain relation between the values of the various resistances.
Assign letters x + y, y, z, and w to denote the imaginary cycle currents in the
meshes of the bridge arrangement (see Fig. 40) and consider the network so
formed of the nine conductors.
MEASUREMENT OF ELECTRICAL RESISTANCE. 275
Let imaginary currents x + y and y circulate clockwise round the circuits
bounded by the resistances R, G, P, a and G, &, Q, S. Then the actual current
through the galvanometer is x. Form, as before described, the cycle equations
by the method of Maxwell, and we have
ay cio = 0.
Re-arranging terms, we have the four equations in x, y, z, w as follows :
The solution for x (the galvanometer current) is then
(S + Q + 6), -b, -Q
(R + P + a), -a, -P
-(a + 6), (a + b + c), c
where D in the denominator is a determinant whose value does not concern us*
The above equation writes out into
x = ^(a + b + c) (RQ -SP) + c (R6 -Sa)}.
Hence the condition that the galvanometer shall show no current, or that x
shall be zero, is that the relations RQ = SP and R6 = Sa must simultaneously
hold good. If, however, c is a very small resistance, then the galvanometer
current will be very nearly zero if RQ = SP, even though R6 is not quite equal
to Sa.
Accordingly, in the Kelvin double bridge we have a double relation which
must hold good in order that the bridge may be balanced. We must have
- = - as a relation between the resistances P, Q, R and S, and also - =^ as a
Q S So
relation between the resistances a, b, R and S.
16. Modifications of the Kelvin Double Bridge for Low
Resistance Measurement. Practical Forms. The Kelvin
double bridge can be arranged so as to be a convenient instru-
ment for measuring low resistances, such as lengths of electric
arc light carbons or short lengths of copper cable. One form
which it then takes is as follows :
The resistance to be measured is clamped in between
massive clamps, GI C 2 , fixed on a board, and contact knife
edges, e 1 e 2 , arranged to press against it, intercepting any
required length of the conductor. A slide wire, AI A^ is
fastened to the same board, and on it move two sliders, ^ v%>
*2
276 MEASUREMENT OF ELECTRICAL RESISTANCE.
one or both of which are movable, which can make contact
with the wire at any position. In the centre of the board
are two plug resistance boxes of series pattern, having re-
sistances 10, 10, 100, 3,000 ohms each, and each provided
with two plugs. The galvanometer Gr and battery B (which,
should be a couple of storage cells) are connected in as shown.
The resistances in Fig 41 are lettered to correspond with,
those in Fig. 37.
In the first place, the plugs are inserted so as to make the
resistances E and S in the same ratio as a to b, viz., either
10 : 10, 10 : 100, or 10 : 1,000. The sliders ^ and v 2 are then
moved until the galvanometer shows no current. Calling the
FIG. 41.
ratio of K : S = a : I = n, we then have P = Qw. If the slide-
wire has been calibrated so that its resistance per centimetre
of length is known, we have at once the resistance of P in
terms of a certain length of slide wire, v l t- 2 .
Another form of the Kelvin bridge adapted for the purpose
of low resistance measurement has been devised by Mr. J. H..
Beeves.* In this apparatus A and E (see Fig. 42) are two
massive pieces of copper, which can be joined by a plug
when desired. To one is connected the wire or bar EFGH of
which the resistance is to be determined, and to the other a.
*See Proc. Phys. Soc. Lond., Vol. XIV., p. 166.
MEASUREMENT OF ELECTRICAL RESISTANCE. 277
comparison wire ABCD of known resistance per unit of
length. A pair of contact edges K and M make contact with
the wire FG at two places L and N of known distance apart.
It is convenient to make the distance LN equal to one metre.
A pair of connecting wires BO, CT are soldered to the wire
BC intercepting a known resistance, which may be con-
veniently O'Ol ohm. The same board or another carries a
calibrated slide wire, a&, the terminals of which are con-
nected to anJ K.
A pair of adjustable resistances x and y are connected to
M and T. These last may be ordinary resistance boxes, one
say y, is 1,000 ohms, and the other is a series plug box
Galvo.
ft
x||y
^ Battery J.
x' ^
O, . b '
M * ^T
? B . II P'H ["
FIG. 42.
reading from 1 to 5,000 ohms. Between the junction of
x and y and the slider on the slide wire is joined in a galvano-
meter, and a battery is connected to the terminals I)
and H. If the plug P is removed so that the blocks A and E
.are not connected, the arrangement is an ordinary Wheatstone's
bridge. The slider s can be then adjusted so as to divide the
slide wire into two segments a and & such that the resistance
-a is to that of b as x is to y. This being done, the plug P is
inserted to connect A and E. The arrangement then becomes
a Kelvin double bridge. If the resistance of the wire under
4est between L and N" is called E, and if that of the standard
wire between B and C is called r, we can then further adjust
278 MEASUREMENT OF ELECTRICAL RESISTANCE,
x and y so that the galvanometer shows no current. When
this is the case we have again
r y
If the wire under test is a copper wire, then we know from
the tables of wire resistances approximately the resistance of
one metre length of it. Calling this resistance ~R V we choose
x l as the value of the resistance unplugged out of the box
represented by %, so that ^ = l . If y is made 1,000 ohms, and
V r
Eemoving the plug and making the bridge an ordinary
one we find a position of the slider so that the slide wire is
divided into sections a and b, and when the balance is obtained
b + r y r
n "P T*
or - = ! - approximately,
where R is the true resistance of the wire between L and K".
Next, inserting the plug P and passing a stronger current
from the battery, we find a new balancing position by altering
x l to # 2 but keeping a and b the same. Then, since - =
b r
nearly, we have
R 2fe <n 3fe i
= - , or R= r very nearly.
r y y
In any case the value of R so obtained is much nearer to the
true value of the resistance of the metre length of the wire
than R r
If the value of x 2 is not very different from x 1 the value
r may be taken as the true value of R, but if # 2 differs
y
considerably from x^ then we must begin over again, and,
employing x% as the resistance in branch x, obtain a new
position of the slider and new values for a and b.
MEASUREMENT OF ELECTRICAL RESISTANCE. 279
In carrying out the test the battery employed should be
such that a small current can be sent from it when the bridge
is being employed as a simple bridge, but a much larger current
when as a double bridge. This is best achieved by employing
a couple of secondary cells in series with a resistance which
can be more or less short circuited as required. This
resistance may be a simple length of platinoid wire with
terminals at each end so arranged that the resistance can
be short-circuited by bringing the ends together.
The above method enables us to measure with great ease
and accuracy the resistance of a metre length of ordinary
copper wire of, say, No. 16 S.W.G., and deduce the volume
or mass-resistivity from the observations. It is, therefore, of
great utility when only a short sample of bare wire is obtain-
able. It may be employed also to measure the resistance of
short lengths of strand copper cable or copper rod. The
sensibility of the method is that an accuracy of 01 per
cent, can be obtained, or, in other words, by this means the
resistance of a yard or two of bare copper wire of No. 16 or
No. 14 S.W.G. can be as accurately measured as a resistance
of the order of an ohm or more can be measured on the
ordinary plug form of Wheatstone's bridge.
17. Modifications of the Ordinary Wheatstone's Bridge
for Low Resistance Measurement. A simple yet effective
bridge arrangement for measuring low resistances is that
devised by Mr. E. H. Housman.* The principle of the
method consists in making an ordinary bridge measurement
in two stages in such a manner that the value of a low
resistance standard of O'OOl or even O'OOOl of an ohm can
be compared with a standard one-ohm resistance with an
accuracy of about one-tenth per cent. This test can be
carried out with an ordinary plug Wheatstone's bridge,
using with it a movable coil mirror galvanometer of fairly
high sensibility, say, giving a scale deflection of 1mm. at a
* See The Electrician, Vol. XL., p. 300, December 24, 1897
280
MEASUREMENT OF ELECTRICAL RESISTANCE
metre distance per microvolt at the galvanometer terminals.
The method requires the possession of a one-ohm standard
resistance, which will carry safely a current of one or two
amperes for a few seconds without sensible heating. For
this purpose a Xo. 18 bare manganin wire, wound on a
frame but otherwise exposed to the air, may be employed.
This wire resistance standard should terminate in thick copper
connecting rods. The standard should be very carefully
compared, by any of the methods already described in this
chapter, with an ordinary small current one-ohm standard
resistance of platinum-silver or manganin of known value.
Let us suppose, then, that a low-resistance standard in the
form of a manganin strip has to be measured, and that its
FIG. 43. Diagram of Housman Bridge Arrangement.
resistance value is something of the order of O'OOOl of an
ohm. This strip will be provided with current terminals in
the usual way and also with potential terminals. Let the
resistance ' of the strip to be tested be taken between the
potential terminals and called R 2 - It is then to be joined in
series with a second resistance or strip, having a resistance
(denoted by 11Q of about O'Ol ohm, and with the one-ohm
resistance standard, whose exact value will be denoted by S.
These three resistances must be joined up in series by stout
copper rods or strips, and connected to a plug resistance,
which may be an ordinary resistance box, as shown in Fig. 43.
MEASUREMENT OF ELECTRICAL RESISTANCE. 281
The first stage in the process is to measure the ratio of
the resistance of the O'Ol ohm strip (R,) with contacts and
connections plus the resistance of the strip under test
(iy to the resistance of the one-ohm standard S. Let
P i ~p
Lzlf^srek The one-ohm standard, S, should be provided
k>
with double terminals, two for current entrance and exit,
.and two for potential terminals, between which its resistance
is known. The Wheatstone bridge employed with the above
resistances, RI, E 2 and S is used merely as a potentiometer
wire, the side AB, or the ratio arms, being used as one
branch, and BC, or the measuring arm, being used as the
other branch. When this bridge arrangement is connected
with a galvanometer, as shown in Fig. 43, and with a single
storage cell, the cell sends a current of about two amperes
.along the circuit E 2 +Ri-f-S. Since the ratio of R 2 +R t to
.S is about 1 : 100, it can be determined with an accuracy
of 1 to 10,000 when a suitably sensitive galvanometer G is
employed, connected across between the terminals B and E,
as shown in Fig. 43.
The second stage in the process is to shift one galvanometer
.connection from E to F and one battery connection from
I) to E. The storage cell used should be one which can for
;a short time send a current of 200 amperes or so without
injury. The arrangement in the second case is again a
.simple bridge, but in this last form the circuit Rj + R^ is
traversed by about 200 amperes No contact which was
included in the first stage is altered, but we can now
measure the ratio of E 2 to E r This is again a ratio of about
1 to 100. Hence we can find with great accuracy the ratio
p
^ -^ = I. Accordingly, we have, by the first measurement,
.and by the second one =5.
Hence,
282 MEASUREMENT OF ELECTRICAL RESISTANCE.
The contact resistances are all eliminated. If the galvano-
meter is one having a resistance of 100 ohms, and giving a
scale deflection of 1 mm. at 1 metre distance with 1 micro-
volt, we can measure the ratio of R 2 to (^1 + ^2) with an
accuracy of 1 in 10,000.
The connections of the bridge wire or bridge circuit ABC
to the series of three resistance S p R^ E 2 should be made as
small as possible. If, for instance, Rx^O'Ol ohm, R 2 0*0001
ohm, then in the measurement the arm AB may be 10 ohms
and the arm BC may be 1,000 ohms. The fall in potential
down each side will be 2 volts. Hence, if a current of
200 amperes is flowing through Ei + R 2 =0 > 010 ohm, it is clear
that a change in resistance of T ^th of the '0001 ohm
resistance, or of '0000001 ohm, or of one-tenth of a microhm,,
will produce a potential change of nearly 20 microvolts on
the galvanometer terminals, and hence produce 20mm. scale
divisions deflection, which it is impossible to avoid detecting.
This method is therefore one which can quite easily be put
into practice in any laboratory possessing a good plug
resistance bridge and a sensitive galvanometer.
When once a low resistance strip is obtained, the value-
of which is accurately known at any temperature, then it is
easily copied and others reproduced from it.
Bridge methods, speaking generally, have a great advantage
over methods for the comparison of resistances which depend
upon the measurement of the relative value of the fall of
potential down conductors to be compared when traversed
by the same current, in that, in the case of bridge measure-
ments, slight variations in the value of the currents passing
through the network do not affect the accuracy of the
result.*
* See The Electrician, Vol. XLTf, p. 354, 1898, for remarks by Prof.
H. L. Callendar " On the Bridge Method of Comparing Low Resistances,"
in which the advantages of bridge over potentiometer methods of com-
paring low resistances are upheld. For a trenchant criticism by the same
writer on the subject, see also The Electrician, Vol. XLI., 1898, p. 501 and.
p. 631.
MEASUREMENT OF ELECTRICAL RESISTANCE. 283-
18. Measurement of High Resistances by Direct
Galvanometer Deflection. The measurement of high
resistances, or resistances of the order of a megohm.
or upwards, cannot be well effected by any of the above
described bridge methods. The method by which it is
generally achieved is by observing the current which can be
sent through a calibrated galvanometer of great deflectional
sensibility, but good zero-keeping quality, by a battery of
high electromotive force placed in series with the galvanometer
and with the resistance to be measured. If the resistance to
be measured is placed in series with the galvanometer and
with a battery of small secondary cells, we have then a
circuit of which the resistance is made up of the resistance
to be measured (which may be reckoned as megohms and
denoted by II), the internal resistance of the cells denoted by
r v the resistance of the galvanometer (represented by r), and
that of the connections by r% these last three being measured
in ohms. If, then, E is the electromotive force of the battery
in volts, and A the current in amperes which flows through.
the circuit, we have
If the battery is composed of secondary cells, and the-
connections are of copper wire and not long, then 7*1 and r&
may be neglected in comparison with 10 6 B, arid we have
\= E
10 6 E+r"
Under these circumstances the galvanometer will give a
deflection S such that A = GS, where Gr is the galvanometer-
constant for steady currents. The galvanometer must, for
this purpose, be a highly sensitive mirror instrument, with
either movable needle or movable coil, placed at a distance,,
say, 2 metres, from a scale divided into millimetres. On the
scale the sharp image of a portion of an incandescent lamp
filament is focussed so that any deflection of the coil or
284 MEASUREMENT OF ELECTRICAL RESISTANCE.
needle can be carefully measured in terms of the scale
deflections. In the case of such a mirror galvanometer the
deflections will be proportional to the current flowing through
the galvanometer. The first step, therefore, is to determine the
galvanometer constant. This is best done by the employment
of a potentiometer. A fall of potential is created down a long
fine wire of high resistance laid over a divided scale, and this
fall of potential is adjusted by means of a Clark cell, so that
the fall of potential per scale division is known. For the
details of this process the reader is referred to the descrip-
tion given of the potentiometer and its uses in Chapters I.,
III. and IV.
Suppose the potentiometer is so adjusted that we have
a fall in potential of O'OOl volt per scale division of the
scale over which the wire is laid. The terminals of the
galvanometer are then connected through a resistance of
several thousand ohms with twc points on this slide curve
and the distance between these points adjusted until the
galvanometer gives a convenient deflection. Thus, suppose
the galvanometer has a resistance of 6,000 ohms and we place
in series with it 4,000 ohms and find that when the terminals
are connected to two points on the slide wire separated by
20 scale divisions we have a galvanometer deflection of
40 divisions. Then we know that the potential difference on
the terminals of the galvanometer is 20 X O'OOl volt= 0'02 volt
and the resistance of the galvanometer circuit is 10,000 ohms.
Hence the current through it is (0-02-^-10,000) amperes.
If G is the galvanometer constant, then
40G = (0-02-=-10,000),.
or G = 20,000,000 = 20 X l(?'
or '05 of a microampere, per scale division. A determination
of G should be made for a great many different values of S
(the galvanometer deflection) and the mean value taken.
In the next place we must determine, by means of the
potentiometer, the value of the electromotive force (E) of the
MEASUREMENT OF ELEOTRLCAL RESISTANCE. 285
battery. This can be done in the way described in
Chapter IV., in which are given methods for the
measurement of electromotive force. Having thus deter-
mined the value of G and E, and knowing the value of the
galvanometer resistance r, we can calculate the value of
E in the expression
-&-> ;.,
In this test the electromotive force E should be produced
by a number, say, 50 to 100, of small secondary cells, so
that it can be measured with a good voltmeter. It may
even be the circuit pressure of an electric supply circuit if
it is sufficiently constant.
If neither potentiometer nor voltmeter is at hand, but
merely a battery of cells and resistance boxes of the ordinary
type, we may proceed as follows :
Let <j be the galvanometer resistance, and s be the resist-
ance of a shunt across its terminals. Then the total resistance,
(j v of the shunted galvanometer is
(IS
Employing one cell of the battery, send first a current
from it through the shunted galvanometer and a resistance,
r v in series with it. Let r be the internal resistance of the
cell and e its electromotive force. If, then, the resulting
galvanometer deflection is d v and if G is the galvanometer
constant, or the number by which the galvanometer deflection
must be multiplied to give the current in amperes producing
that deflection, then, by Ohm's law, we have
or
386 MEASUREMENT OF ELECTRICAL RESISTANCE.
Next alter the resistance r\ to r% and obtain a corresponding
scale deflection, d%, of the galvanometer ; then
or rdz+rA+dtf! ..... (ii.)
Eliminating from (i) and (ii.), we have
If the resistance r 2 is so adjusted that the second deflection
,dz=%d lt then we may reduce the equation (iii.) to
r=(r 2 -2r 1 )-g v
Hence the internal resistance of the cell becomes known
under the conditions that it is sending a very small current.
In the next place, let a battery of n cells be joined in series
with the galvanometer and the large resistance to be measured
of which the value in megohms may be denoted by E. Let
-the galvanometer deflection then be d 3 . Hence we have
Gd 3 . (iv.)
Change the number of cells to n', and obtain another galvano-
meter deflection d^ then
Eliminating r - from (iv.) and (v.), we have
(jT
''(d^ d 3 )r
.'Substituting in (vi.) the value found above by equation (iii.)
for r, we obtain the value of the resistance E. in megohms in
terms of the scale deflections and the resistances of the
galvanometer and cells.
The assumption made that each cell has the same internal
resistance must be tested by measuring the internal resistance
MEASUREMENT OF ELECTRICAL RESISTANCE. 287
of various cells, and if they differ, as they probably will do,
then the mean value of all must be taken.
The method, however, cannot be regarded as affording
more than an approximation to the value of the high
resistance unless each of the cells has absolutely the same
internal resistance and electromotive force. This is never
the case in any actual battery. If, however, we employ a
battery, say of 50 moderately large secondary cells which
have been about half discharged, and in which each cell is
in good order, the voltage of each cell will be very nearly
2 volts and the internal resistance of the whole battery will be
negligible in comparison with that of a galvanometer having
a resistance of say 5,000 ohms. In this case the equations
become reduced as follows :
Let a single secondary cell be first applied to create a
current through the shunted galvanometer in series with a
resistance. Then, taking the same symbols as before, we have
(vii.)
Xext let the high resistance be placed in series with the
battery of n cells and the galvanometer be unshunted, and we
have
nc n 7 / ...
Hence, from (vii.) and (viii.) we obtain
lu%
or, if the high resistance is measured in ohms, then
. ,. ,
The most satisfactory method is, however, to standardize
the galvanometer by the potentiometer, and then to measure
288 MEASUREMENT OF ELECTRICAL RESISTANCE.
by the same means the actual value of the high electromotive
force employed to transmit the currents through the high
resistance.
The apparatus therefore required for this measurement
consists of three parts : First, the sensitive high-resistance
galvanometer combining good zero-keeping quality and pro-
portionality of deflection to current or constancy of deflectional
constant over the useful range of the scale. These qualities
must not be taken for granted, but be carefully proved to-
exist. The galvanometer should have various electromotive
forces applied to its terminals by the potentiometer, and the-
ratio between the observed scale deflection and the potential
difference of the terminals observed. This ratio should prove
to be constant. In the next place, when the circuit is opened,,
the galvanometer needle or coil should return accurately to
the same zero position. If it does not, the galvanometer is no
use for the present purpose. In the next place a good
potentiometer is required by means of which to make the
above-described calibration and to determine the galvanometer
constant at any moment. In the third place a battery of
small secondary cells is required. This is most conveniently
provided in the form of a series of trays containing rows of
lithanode cells made up in large test tubes. For most work
in measuring insulation frolh 6 to 12 trays will be required,,
each containing 25 cells. These trays should be exceedingly
well insulated by being placed on ebonite legs or paraffin
blocks. High resistance keys are also required. The insula-
tion of the galvanometer itself is a matter of importance, and
it should be supported on three ebonite blocks in which the
levelling screws rest.
The above apparatus serves for the measurement of the
insulation resistance of cables or of highly insulating
materials such as indiarubber or gutta-percha,
19. Measurement of Insulation Resistance. Let it be
desired to measure the insulation resistance of the dielectric
MEASUREMENT OF ELECTRICAL RESISTANCE. 289
of a cable or insulated wire. The method of procedure is as
follows :
A large tank is provided of sufficient capacity to contain
one or more coils of the wire or cable to be tested. For
laboratory purposes it is convenient to have a galvanised iron
tank about 3ft. wide, 3ft. long, and 2ft. deep, and to rest it
upon a wooden platform on castors for facility of movement.
The coil of cable is placed in the tank, and the tank filled up
with water. The two ends of the cable are kept well above
the surface of the water and must be prepared by stripping
FIG 44. Use of Price's Guard Wire.
back for some distance the plait or tape outer covering so
as to expose the indiarubber (I.E.) or gutta-percha (G.P.)
insulation. The two ends of the copper conductor are also
bared and twisted together. Bound the exposed length of
I.B. or G.P., which should be a foot or more in length, is
twisted a fine wire, G, called a guard wire. This should be
put on at about Gin. from the outer end of the insulation.
The cable then presents 'the appearance shown in Fig. 44.
C, C' are the exposed copper ends connected by a wire W.
I, I' are the exposed indiarubber or gutta-percha surfaces, the
290
MEASUREMENT OP ELECTRICAL RESISTANCE.
tape or protective covering being neatly stripped off and the
ends connected by the guard wire G. T,T is the tape or twist-
covered complete cable which remains under water in the tank.
The connections are then made as follows : One terminal
of the battery is connected to the tank or to a metal plate
placed in the water. The other terminal is connected to one
terminal of the galvanometer, and the remaining terminal of
the galvanometer G (see Fig. 45) is connected to the copper
wire iv of the cable. The guard wire g short-circuits the galvano-
meter. It is best to insert a key in circuit with the battery
and to place this next to the tank. The battery and galvano-
meter should be well insulated by placing them on ebonite
FTG. 45. Testing Insulation of Cable.
slabs or blocks of paraffin. The use of the guard wire is as
follows : If any leakage of current takes place over the cleaned
surfaces of indiarubber, this current would, unless prevented,
pass through the galvanometer and be added to the true
conduction current or flow through the dielectric of the cable.
The guard wire, however, arrests the leakage current and
conducts it harmlessly past the galvanometer.*
* This ingenious yet simple means for annulling the effect of the leakage
current over the exposed dielectric ends of a cable under insulation test is
called Price's Guard wire, being due to Mr. W. A. Price (see Electrical Review,
Vol. XXXVII., p. 702, 1895). It is described also in a Paper by Mr. R. Apple-
yard on Dielectrics (see Proc. Phys. Soc., Lond., Vol. XIV., p. 256 ; or The
Electrician, Vol. XXXVII., p. 159). See also, Prof. W. E. Ayrton, " Some
Developments in the Use of Price's Guard Wire in Insulation Tests," Phil.
Mag., April, 1900, Vol. XLIX., p. 343.
MEASUREMENT OF ELECTRICAL RESISTANCE. 291
In making such an insulation test it will be found that if
the material of which the dielectric of the cable consists is
indiarubber, gutta-percha, okonite or any of the usual insulators,
the deflection of the galvanometer does not remain constant
when the same electromotive force is continuously applied.
It will be seen to decrease with the time during which the
battery is kept in circuit. If the cable is at all a long one,
then at the moment of first making contact there will, in
addition, be a rush of current into the cable. In the case of
very large cables this rush is so violent that it is better to
short-circuit the galvanometer for a moment whilst putting
-down the battery key, and then to withdraw the galvanometer
short-circuit i mmediately.
If we operate in. this manner we shall find that the
galvanometer deflection decreases from moment to moment
in a manner which indicates that the insulation resistance is
increasing with time. It is the custom to define the insula-
tion by stating its value in megohms after one minutes
electrification, naming also the electromotive force of the
battery and the temperature of the cable.
In the case of such materials as indiarubber and gutta-
percha, and probably in the case of most dielectrics, the
apparent insulation resistance is a function of the electro-
motive force and of the time during which it acts. The,
.apparent resistance increases with the time of application of
the electromotive force, and in some cases it decreases also
slightly as the electromotive force is increased, even if taken
.after the same interval. The insulation resistance decreases
markedly with rise of temperature.
Hence the voltage, temperature, and time of electrification
must always be stated, or else the numerical value of the
insulation resistance is a meaningless number. Thus a cable
may be marked as having an insulation resistance of 300
megohms per mile tested with 600 volts after one minute's
-electrification on application of the electromotive force, the
insulator being at a temperature of 75Fahr. Such a
u2
292 . MEASUREMENT OF ELECTRICAL RESISTANCE.
statement is precise, but tlie mere statement that the insula-
tion resistance is 300 megohms per mile is a very imperfect
description of the actual insulation quality of the cable.
The relation between the strength of the current flowing
through a non-metallic conductor and the electromotive force
producing it is in general much less simple than in the case
of metals.
In addition to the metals and alloys formed of them, which are called
the metallic conductors, we have bodies such as carbon, selenium, tellurium,
phosphorus, certain metallic oxides and sulphides, &c. which are non-metal? r
and yet in certain states are electrical conductors. These are called non-
metallic conductors. They are generally characterised by the property of
existing in two or more allotropic conditions, in which their electrical
conductivity differs widely. Carbon exists in three forms, as diamond r
charcoal and graphite. In the first state it is a good insulator, in the second
a poor or indifferent conductor, and in the third a fairly good conductc r.
Selenium, also, can exist in two allotropic forms, and is remarkable from the
fact that light falling on it when it is in one of these forms causes a sudden
and considerable diminution in resistance. For the most part, the electrical
volume-resistivity of all these non-metallic conductors is much higher than
that of any of the metallic conductors. '.
The third class of conductors comprises such substances as indiarubber,
gutta-percha, mica, glas?, ebonite, etc. These are all substances of very high
electrical resistivity, and are generally called insulators. They have a volume -
resistivity enormously greater than any metallic or non-metallic conductor.
They are usually termed non-conductors, but may also be denominated a*
dielectric conductors. This class includes numerous solids and liquids.
The fourth class of conductors comprise the conducting liquids. These are
called electrolytes,. In their case the process of conduction is accompanied by
an evident chemical decomposition of the material, and it is described as
electrolytic conduction, the liquids themselves being spoken of as electrolytic
conductors. It is a difficult matter to give a precise answer to the question,
AVhat is an electrolyte 1
A fifth class may be said to comprise the gaseous conductors ; and although
there is some evidence that in their case the process of conduction is ele c-
trolytic in nature, it may be well to retain them at present in a distinct
sub-division. Gases at ordinary pressures are good insulators, but if subjected
to an electromotive force exceeding a certain limit, they pass into the
conductive condition.
As examples of these five classes of conductors, we may select copper,,
graphite, mica, melted silver chloride, or an aqueous solution of sodic
cliloride, and hydrochloric acid gas.
It may be that these divisions are not sharply marked. The conduction in
the case of glass may be electrolytic, and also in the case of gases. On the
MEASUREMENT OF ELECTRICAL RESISTANCE. 293
other hand, the process of conduction may be of a' similar nature in all the
five sub-divisions, and even in the metallic conductors may be electrolytic.
The action of temperature on the conductivity of the substances in the
various classes is very different. In the case of metallic conductors, if ihey
are pure metals, increasing their temperature always increases their resistivity,
and lowering the temperature towards the absDlute zero indefinitely decreases
the resistivity. As regards metallic alloys, some of these, such as manganin,
have a maximum resistivity at a certain temperature, above which they
decrease in resistance as temperature rises, and below which they also decrease
in resistivity, but not probably indefinitely, and there is no indication, as in the
case of pure metals, that it would become zero at the absolute temperature.*
la the case of the non-metallic conductors, increase of temperature lowers the
resistivity. As regards graphite there is clear indication that it has a
minimum resistivity corresponding to a certain temperature near a dull red
heat.t
The class of dielectric conductors are distinguished by the
fact that rise in temperature always reduces their electric
resistivity, and this rate of decrease in some instances is very
marked. Thus, in the case of glass .we have an exceedingly
large .negative temperature co-efficient ,J as shown in the
following tables :
Volume-resistivity of Glasses in C.G.S. Units per Centimetre-
cube.
BOHEMIAN GLASS. FLINT GLASS.
Temp.
60C G xlO 22
100C 2 xlO 21
130C 2 xlO 20
160C. ...... 2-4 xlO 19
174C. 8-7 x 10 18
60C 1-02 xlO- 4
100C 2 xlO 2 *
120C 4-68 xlO 22
140C. 1-06 XlO 22
160C. 2-45 XlO 21
180C. 5'6 xlO 20
200C. 1-2 XlO 20
Another characteristic of some dielectric conductors is that
the resistivity is a function of the electromotive force with
* For a theory as to the cause of the greater average resistivity and
smaller temperature cc-efficient of alloys compared with that of the metals
composing them, see a Paper by Lord Rayleigh in The Electrician, Vol. XXXVII.,
p. 277.
t See The Electrician, Vol. XXXVIII., p. 835, Mr. J. C. Howell, " On the
mductivity of Incandescent Lamp Filaments."
See Mr. Thomas Gray, Proc. Roy. Soc. Lond., January 12, 1882.
294
MEASUREMENT OF ELECTRICAL RESISTANCE.
which it is measured. This is shown by the results in the
following table, obtained by measurements made at the works
of Messrs. Siemens Bros. & Co.*
Resistance of Certain Dielectrics under various Electromotive
Forces or Voltage after One Minute's Electrification.
Dielectric. Voltage.
Kesistance. Dielectric. Voltage.
Resistance.
f 150
... 3,468
r 150
... 2,813
300
...3,366
Lead-covered
300
... 2,674
Gutta-percha.^
750
1,050
... 3,267
... 3,117
impregnation
cable
750
1,050
... 2,541
... 2,224
1,500
... 3,086
(C class).
1,500
... 2,057
Vl,800
... 3,021
d,800
... 1,798
f 150
... 8,054 ;
r 150
... 2,602
High insula-
tion india-
300
750
1,050
... 7,916 ,
... 7,470
... 7,268
Lead-covered
impregnation
cable
300
750
1,050
... 2,492
... 2,425
... 2,345
rubber.
1,500
... 6,705
(A class).
1,500
... 2,274
1,800
... 6,245
,1,800
... 2,212
( 150
... 513
Ordinary 300
... 462
indiar ubber. 1 750
419
U,050 ... 355
The above figures show beyond question that the resistance
of certain dielectrics after one minute's action of the impressed
electromotive force or voltage decreases as the voltage
increases. The same variation has been found to exist after
electrification for other intervals. Hence it must not be
hastily assumed that in the case of any dielectric the current
flowing through it under different electromotive forces is in a
constant ratio to the electromotive force. The current flow
in amperes or micro-amperes per volt of impressed electro-
motive force is not constant. The actual current flowing
* The figures were given by Mr. A. Siemens at the Institution of Electrical
Engineers, during a discussion on a Paper by Sir W. H. Preece on " The
Specification of Insulated Conductors." See Journal Inst. Elec. Eng.,
Vol. XXL, p. 217.
MEASUREMENT OF ELECTRICAL RESISTANCE. 295
through a dielectric conductor at any instant after an
impressed electromotive force has been applied to it is a
complicated function of the time from closing the circuit, the
temperature and the impressed electromotive force, and the
usual custom of denominating the ratio of the electromotive
force (measured in volts) to the current (in amperes) through
the dielectric after one minute's application of that electro-
motive force, the ohmic resistance of the dielectric, is a
perfectly arbitrary or conventional proceeding. The properties
of dielectrics will be more fully considered in a later chapter
in the section dealing with capacity measurement.
Returning to the practical test of insulation, we may add
that it is necessary in these tests to provide a sufficient
electromotive force in the form of a well-insulated battery
In cable factories it is usual to set up in a room a battery of
600 to 1,200 Leclanche cells arranged in groups, in series,
and placed on well-insulated platforms of paraffined wood
standing on oil insulators. From this battery insulated wires
run to the testing room, so that any required electromotive
force up to 1,800 volts or so is available for testing purposes.
In a laboratory it is more convenient to employ small
secondary cells set up in test-tubes and arranged in trays of
10 cells. The most convenient form of cell is the lithanode
secondary cell. These cells consist of glass tubes about 1 inch
in diameter and' 4 inches high, and each contain two plates.
They should be charged when required with a small current,
and no greater current than one-tenth of an ampere taken
from them. The trays of cells should be arranged in a
portable cupboard and terminal wires from the various sets
of cells or from each cell brought out to insulated terminals
on the outside.
The insulation tests of ordinary indiarubber-covered cable
as used in electric lighting work are always made with an elec-
tromotive force of 300 volts to 600 volts, and the resistance
taken after one minute's electrification. Previously, however,
the cable must be allowed to lie in water for at least 24 hours,
296 MEASUREMENT OF ELECTRICAL RESISTANCE.
so that the final result is stated in the form of a certificate
appended to each coil of cable that it has been tested with
600 volts applied for one minute after 24 hours' soaking in
water.
In making a critical examination of a dielectric material
the cable or insulated wire must be supplied in coils of known
length, say, one-quarter or half-mile coils. The insulation
tests enable us then to state the results as so many megohms
per mile ,of cable.
It is to be noted that if, for instance, the test of 440 yards
of cable showed its dielectric to have an insulation resis-
tance of 4,000 megohms, then the insulation is at the rate of
1,000 megohms per mile.
Each coil of cable after testing should then have a certifi-
cate appended to it as follows :
Certificate of Insulation Test.
Length of this Coil yards or miles.
Gauge of Copper Wire .........S.W.G.
Natu re of Insulation .
Temperature of Coil when Tested
Insulation Resistance megohms
per mile at ..F. when tested
with volts after one minute's electrification
and hours' soaking in water.
Daie of test
Test made at Laboratory, by
For electric light wiring no wire should be employed which
has not thus been tested, and the certificates of each coil
of wire as used by the contractor should be demanded by
the clerk of works or consulting engineer. No wire should
be employed of less insulation than 300 megohms per mile
at 7oF. after 24 hours soaking in water, the test being made
with 600 volts and resistance taken after one minute.
In the case of dielectrics such as paper or jute impregnated
with oil or resins or various other dielectrics, which are not
in themselves waterproof, the cable must be covered with
a continuous sheath of lead in order to protect them. In
MEASUREMENT OF ELECTRICAL RESISTANCE, 297
this case, also, a test in water is necessary in order to
ascertain whether the lead covering is perfect.
20. Measurement of Dielectric Resistance by Time of
Falling to Half Charge. A usual method of measuring the
insulation or dielectric resistance of a substance of very high
resistivity is to connect it between the earth arid a charged
conductor, which is otherwise perfectly insulated, and then
observe the time taken for the conductor to fall in potential
by a known fraction or, say, to half its value.
As a first simple approximation to a theory, assume that
.the capacity r of the perfectly insulated conductor is C, and
that it is charged to an initial potential V, and connected to
earth through a resistance, E, of large value. After a time,
t seconds, let the potential of the conductor be v, and after a
further small time, dt, let it be v dv ; then the time rate of
change of potential at that time is - -~. If the capacity of the
(JLt
conductor is C, the electric quantity in it at that instant is Cv,
and the time rate of change of the charge or quantity is
C^; hence, this also must be the rate of leakage or
current flow through the dielectric resistance. If K is this
resistance we have, if Ohm's law is obeyed,
v _ f <dv dv _ dt
iT dt' I 'V-~OK'
Hence, integrating each side of the equation, we obtain
where A is the constant of integration. If t = 0, then v =
where V is the initial voltage.
Hence log e - lo&V = - ^,
or
298 MEASUREMENT OF ELECTRICAL RESISTANCE.
If we use ordinary logarithms to the base 10, then we have
0-4343*
it =
where 04343 is the modulus or factor for converting
Napierian to ordinary logarithms. If T is the time in
seconds taken to fall to half potential, then V/ / z; = 2, and
Iog 10 2- 0-30103, and
p 04343T T _ 10T ,
Cx 0-30103 "0-693C" 7C
Hence E is obtained as the quotient of a time by a capacity.
If C is measured in microfarads, then E will be measured or
given in megohms.
In the above proof two things are assumed : First
that the resistance strictly obeys Ohm's law, and, secondly,
that the capacity is constant and independent of the
voltage. In the case of actual dielectrics and condensers
neither of the above assumptions is strictly in accordance
with fact
In applying this method the difficulty is to find a voltmeter
or electrometer which is itself sufficiently well insulated. No
electrostatic voltmeter or electrometer is so absolutely insulated
that if charged and left to itself it will not lose charge,
neither is any condenser or body having capacity similarly
free from leakage. We may, however, proceed| in practice as
follows : A condenser or body having capacity is charged to a
known voltage and connected to the voltmeter. The arrange-
ment is then left insulated and the time of falling to half
charge or half potential is noted. Thus a Kelvin multicellular
electrostatic voltmeter, having its terminals closed by a half
microfarad condenser, may be placed on a sheet of ebonite
and charged, say, to 100 volts, and left insulated. We note
the time T (in seconds) taken by the voltmeter to fall to
50 volts. Then the internal leakage resistance E of the volt-
meter and condenser, taken together, can be calculated by the
MEASUREMENT OF ELECTRICAL RESISTANCE. 299
10T 1
formula above given, viz., R=_ _, from which, if C = ^
(microfarad), we find R = "^-T, where R is the insulation
resistance in megohms, T the time of falling to half charge in
seconds, and C the capacity in microfarads.
The insulator or dielectric whose insulation resistance is
required is then joined across the terminals of the voltmeter
and the experiment repeated. Let T' be the time in seconds
required then to fall to half charge. The combined insulation
resistance of the insulator and the voltmeter and condensev
9Q
is R' megohms when R' = ~^T'. If, then, R" is the resistance
/
per se of the substance tested, we must have ^+^7=^7;,
. It K lv
RR'
or ir=- =-7, for the total conductivity found in the second
jU-j-R
experiment must be the sum of the conductivities of the
body tested, and of the voltmeter and condenser taken
together.
The above method is only practicable and useful in those
cases in which the insulation resistance of the condenser and
voltmeter and body tested is so high that the time required in
any case for the charge of the system to fall to half its initial
value is a considerable number of seconds say 15 or 20 at
the very least. If the potential falls to half value in a, much
less time, the power of observing it accurately is much
diminished.
If, however, a highly insulated quadrant electrometer is
available, and an air condenser of considerable capacity, the
method may be used with success to determine the insulation
resistance of glass or porcelain telegraph insulators and long
lengths of highly insulated cable. The difficulty which
besets this method is that the internal leakage of the volt-
meter or condenser and other supports is due to films of dirt
or moisture. It is not certain (in fact, very doubtful) that
dirt or moisture films of this kind obey Ohm's law. The
330 MEASUREMENT OF ELECTRICAL RESISTANCE.
formula for calculating resistance by this leakage method
is worked out on the assumption that all the conductance
which takes place does so in accordance with Ohm's law
in other words, that the resistance is independent of the
voltage. This is not quite, the case for any dielectric, and
there is no proof that it is the case for surface films causing
leakage. The method, therefore, must be applied with care
and discrimination.
In estimating the insulating value of a dielectric it is
necessary to consider not only the mere insulation resistance,
but also the dielectric strength or voltage required to pierce
the insulation. This is an important matter in connection
with cables for high-pressure currents and porcelain insulators
for carrying bare high-pressure electric wires.* Any report
on the insulating po\ye,r of a cable or dielectric should
comprise the results of tests as to the average electro-
motive force required to pierce a known thickness of the
insulation.
21. Cardew's Differential Method for Measuring High
Resistance. This method consists in comparing together
the rate of leakage from the two quadrants of a quadrant
electrometer. The quadrants are connected respectively to the
two poles of a highly insulated battery of about 400 cells.
For this purpose the most convenient battery to use is a
form of small water battery devised by Lord Kelvin, con-
sisting of a large number of copper-zinc couples attached
to an ebonite slab, and so arranged that when dipped into
water the drop of liquid held by capillarity between adjacent
copper-zinc slips forms the exciting fluid of each couple. A
battery of about 500 couples of this form provides an
electromotive force sufficient for the test.
The terminals of the battery are connected to the two
quadrants of the electrometer, and the needle is connected
* See N. M. Hopkins on " Testing Insulators for High Pressure Overhead
Service," The Electrician, Vol. XXXVIII., p. 432.
MEASUREMENT OP ELECTRICAL RESISTANCE. 301
to the .earth. The battery must be highly insulated by
placing it on paraffin blocks. If, then, the quadrants are
connected also to earth through two high resistances of equal
magnitude, the leakage from each, quadrant will be the same,
and the needle will remain at zero. If one of these resistances
is an adjustable one, the other may be determined in terms
of it.
In starting the test, the centre of the battery should be
earthed for one moment, which will bring the needle to zero.
As comparison resistances lengths of silk or string have been
found convenient. Thus, a white embroidery silk was found
to have a resistance of 250,000 megohms per inch, and a
green thread, partly silk, partly cotton, 10,000 megohms per
inch, an ordinary measuring tape 1,400 megohms per inch,
and a piece of wet tape 64,000 ohms per inch. These
materials, however, are all more or less hygroscopic. Prob-
ably better standards would be found by using capillary glass
tubes filled with liquids of definite composition, which do not
act upon glass. The method, however, is of great sensibility,
and useful for rapid qualitative comparisons of insulation
power.
22. The Practical Measurement of Electric Light Wiring
Insulation. The Ohmmeter. In measuring the insulation
resistance of the electric light wiring of a building, it is
now the custom to employ some form of Ohmmeter. The
principle of this instrument is as follows : Let there be
two coils. of wire, C, c, through one of which, C, flows a current
passing through a conductor, E, the resistance of which is to
be measured, and another coil, c, of high resistance connected to
the terminals of the conductor. Let these coils be placed
with their planes or axes at right angles, to each other..
Then, in the case of each coil there will be a magnetic field
proportional at any point to the current flowing, through
it. Hence, at some common point in the field of the two COLS
(see Fig. 46), there will be two magnetic forces, one pro- .
302
MEASUREMENT OF ELECTRICAL RESISTANCE
portioiial to the current through the conductor and one at
right angles to it proportional to the voltage fall down the
conductor. Hence the resultant magnetic force will have
a direction which depends upon the relative magnitude of the
components or their ratio to one another i.e., upon the ratio
of the potential fall down the conductor to the current
through it. In other words, the direction of this resultant
magnetic force will depend upon the resistance of the con-
ductor so connected to the coils. If, then, a small magnetic
needle, n s, or piece of soft iron is placed at that point, its
direction may be indicated on a scale, and the scale may
be graduated so as to show at a glance the resistance of
the conductor in ohms.
FIG. 46. Theory of the Ohmmeter.
In order to apply this principle to the measurement of
insulation resistances we require a source of high electro-
motive force. It is universally recognised that an insulation
test is entirely insufficient if made with an electromotive, force
loss than the working or circuit electromotive force. Hence,
if the electric light wiring of a building is put in for use at
200 volts the insulation resistance must be tested with
200 volts at least.
In a well-known form of ohmmeter by Evershed, the
electromotive force for testing is supplied by a small hand-
driven magneto machine, which provides the necessary
pressure, (see Fig. 47). One coil of the ohmmeter is connected
in series with the copper conductor of the insulated wire and
MEASUREMENT OF ELECTRICAL RESISTANCE.
303
the armature of the magneto machine, the remaining terminal
of the generator being connected to a good earth by being
joined to gas or water pipes. When the handle of the magneto
machine is turned, a current at an electromotive force of
200 volts is operative on the dielectric of the insulated cable
and the series coil of the ohmmeter, and completes its circuit
through the earth. The other or volt coil of the ohmrneter
FIG. 47. Evershed's Ohmmeter.
has its ends connected respectively to the copper conductor
and the earth, or is a shunt across the series coil and magneto-
armature in series with that last coil. Hence, if the insula-
tion is perfect- when the magneto-machine handle is turned
at the proper speed no deflection of the needle of the
ohmmeter will be seen. If, however, the insulation is not
perfect, but if a current flows through the dielectric either
304
MEASUREMENT OF ELECTRICAL RESISTANCE.
uniformly or at some faulty place, the series coil has a current
in it and the ohmmeter needle deflects. The scale or dial of
the ohmmeter is divided so as to indicate directly in megohms
the insulation resistance. It is possible to make use of the
service pressure itself as a testing pressure in measuring
the insulation resistance of electric light wiring. This may
be done as follows*:
The portion of the circuit to be tested is separated from
the main circuit by removing the fuses. Let ABCD (see
Fig. 48) be the portion of the circuit to be tested, and let the
terminals J K be those of the dynamo or secondary battery
or street service which normally supplies the electric current.
w
Earth
FIG. 43.
Provide a milliampere meter or other sensitive calibrated
galvanometer and connect it in series with a resistance
between the terminals A and J. Then connect the terminal
K to earth through a lamp, W. The galvanometer or milli-
amperemeter will then show a current if there is leakage or
conductivity through the dielectric of the wiring system
ABCD, and if the galvanometer has been calibrated for
small currents the numerical value of this resistance may be
* The method here described is due to Dr. Oscar May. See The Electrician,
Vol. XXXVIII., p. 81 ; see also a critical letter, ibid., p. 128.
MEASUREMENT OF ELECTRICAL RESISTANCE. 305
determined knowing the voltage between the main GH and
the earth.
It is to be noted that the testing pressure we are really
here using is not the ordinary service pressure between the
terminals J and K, but the voltage between J and K when
this latter is connected to the earth through a lamp. Hence
the determination of this voltage must always be made at the
time by means of a voltmeter of sufficiently high resistance
(or say by an electrostatic voltmeter) not to disturb this
potential difference. The main GH should always be the
positive main, because the negative main on a public supply
service by continuous current is nearly always dead-earthed,
especially if bare copper strip carried on glass insulators
of certain descriptions is used as part of the distribution
system.
The method therefore must be applied with discrimination.
23. Insulation Rules for House Wiring. The various
electric lighting companies and insurance offices have
different regulations as to the minimum insulation resistance
which should be indicated on test under the working pressure
by electric light wiring. This is generally defined as so many
megohms per lamp. If, then, there are n incandescent lamps
(reckoned, say, in 8 c.p. lamps or their equivalent) in the
building, the total insulation resistance between the copper
conductors and the earth must not be less than this limiting
number divided by n. It is generally specified that these
tests shall be carried out with a voltage equal to double the
working voltage and the reading taken after not less than
one minute's application of the E.M.F., all lamps being in
and switches on. Thus, for instance, the limiting values
for various electric lighting corporations and fire insurance
companies are as follows :
For some calculations dealing with problems on the measurement of
insulation resistance and leakage currents from insulated conductors, and
especially in connection with 3- wire systems, the reader is referred to a paper
by Mr. A. Russell in The Electrician, Vol. XLL, p. 206 ; also Vol. XXXIV., p.7.
306 MEASUREMENT OF ELECTRICAL RESISTANCE.
Minimum Insulation Resistances allowed per Lamp in Installa
tions of Incandescent Lamps* by various Authorities.
Lightng
Glasgow Corporation ............ 60
Manchester ........................ 50
Scarborough Electric Lighting ) ^
Company ........................ j
Brighton Corporation ............ 20
Liverpool Corporation, Phoenix ( 19 .-
Fire Office, Lloyds ............ j
Bradford Corporation ............ 10
The lead ing Insurance Companies,
including Guardian, Sun, North
British, London, Liverpool and
Globe, Alliance, London As-
surance, Royal Exchange and
others.
Leakage not to exceed
of total
current. = 6 megohms
per lamp for 100-
volt 8 c.p. lamps.
Institution of Electrical Engi- ) 10 megohms per ampere
neers latest regulations j of maximum use.
2$. Measurement of the Resistance of Liquids.
As all liquids which conduct at all do so in virtue of
electrolysis, special difficulties are introduced into the
resistance measurement of liquids by the counter electro-
motive force of polarisation due to the ions liberated on
the electrodes. The possibility, therefore, of obtaining
accurate information as to the resistance of a column of
an electrolyte depends upon the completeness with which
these disturbing effects of electrolysis can be eliminated.
One obvious method is to employ an alternating electromotive
force, so that in the column of liquid there is no unilateral
flow of electric quantity, but the electrolytic effects due to a
current for one moment in one direction may be annulled by
an equal current in the opposite direction the next instant.
* For a chart showing the regulations for insulation resistance of electric
light wiring enforced by various authorities see The Electrician, Vol. XXXII.,
p. 265,
MEASUREMENT OF ELECTRICAL RESISTANCE. 307
A plan due to F. Kohlrausch is to employ with an ordinary
Wheatstone's bridge a small induction coil instead of a
simple battery, and in place of the galvanometer to use a
telephone. The secondary currents from the induction coil,
which are created at each make-and-break of the primary
circuit, are equal in total quantity i.e., the time integrals
of the two secondary currents are equal. Hence, on the
whole, polarisation is absent.
The liquid resistance to be measured may be contained
in a vessel of any suitable shape forming an electrolytic cell,
''-:::"-:^~":^;H;^ : - |. : -- ;; : ::::: : . . -..:.,,-
FIG. 49. Kohlrausch's Bridge for Liquid Resistance Measurement.
the cell having two electrodes by which it is connected with
the bridge circuits. These electrodes are formed of sheet
platinum, which should be covered with a deposit of
platinum black (sie below). In Fig. 49 are shown diagrams
of the usual arrangements. The bridge is a simple slide
wire bridge, and the induction coil is set in operation by a
few dry cells.
After connecting the electrolytic cell to the proper
terminals of the bridge, and setting the induction coil in
x2
308 MEASUREMENT OF ELECTRICAL RESISTANCE.
action, the slider is moved until no sound is heard in the
telephone. As this point of silence is not sharply marked,
but reached by slow gradations of sound, the observer will,
unless he possesses very sharp hearing, have some difficulty
in deciding exactly the point of balance. The method, in
fact, tests the acuteness of the observer's hearing as much as
it tests the resistance of the electrolytic cell. The ability to
distinguish an exact position of the bridge slider correspond-
ing to silence in the telephone depends also upon the nature
of the electrodes used in the electrolytic cell. If these are of
bright sheet platinum they must be much larger in area than
if covered with a deposit of platinum black. This is due to
the deposit on them of the products of electrolytic decomposi-
tion and is called the " polarisation of the electrodes." This
polarisation creates a counter electromotive force in the
circuit. It is not altogether absent even when alternating
currents are employed, and in this last case it operates to
produce an effect as if the inductance of the circuit in which
it exists had been increased. The point of balance on the
bridge when so used is often affected by the capacity and
inductances of the four arms of the bridge arrangement.
The platinizing of platinum electrodes with platinum black
is best done with the platinizing solution employed by
Lummer and Karlbaum for their bolometer strips, and the
same solution is very useful for coating platinum electrodes
for use in electrolytic cells. It consists of 1 part of PtCl 4 to
0-008 of lead acetate and 30 of water.
The solution is used as an electrolyte in an electrolytic cell
with platinum electrodes, the cathode or negative plate being
the one on which a deposit of platinum black is required.
The electrolysing current must be adjusted until on the
chemically-clean platinum cathode is deposited an adherent
dull platinum black deposit. To ensure wetting the electrode
so prepared with water they should be treated first with a
drop of alcohol. A thick deposit of platinum black should
be secured, Platinum electrodes covered with this dull
MEASUREMENT OF ELECTRICAL RESISTANCE. 309
black deposit of platinum black are less easily polarisable
than ordinary sheet platinum and hence give better defined
readings when used with a telephone induction coil and
bridge.
If ordinary bright sheet platinum is used for electrodes,
these are easily polarised or covered with a deposit of
liberated gaseous ions, and these polarisation films, as they
are called, are strongly adherent to the platinum and create
between the electrodes a potential difference which forms a
counter electromotive force. Since the counter electromotive
force cannot exceed 2 volts to 2'5 volts, its presence is most felt
at or near the balancing point of the bridge, and it operates to
prevent the development of a sharp or well-defined condition
of silence in the telephone in this bridge circuit. If the
electrodes are covered with a deposit of platinum black they
are less polarisable, and hence better defined bridge readings
can be obtained.*
A method due to Messrs. Stroud and Hendersonf is, in
many respects, more satisfactory than the use of a bridge with
telephone and induction coil. Their method depends upon
inserting in the two arms of a bridge two glass tubes, T 1 , T 2 ,
of different lengths, having terminal cups of the same size.
These tubes are filled with the electrolyte the resistance of
which is to be measured. In the terminal cups are placed
cylinders of sheet platinum covered with a deposit ot
platinum black. The two tubes form, therefore, electrolytic
cells identical in every way except in that one contains a
longer column of liquid than the other. The dimensions of
this column of liquid are easily obtained by measuring the
length and mean inner diameter of the glass tubes. These
electrolytic cells are arranged as the two arms of a bridge,
* See F. Kohlrausch, Annals Phys. Chew., 60, 2, pp. 315-322, 1897 ; or Science
Abstracts, Vol. I., p. 338.
t " On a Satisfactory Method of Measuring the Resistance of Electrolytes
by Continuous Currents." By Prof. W. Stroud and J. B. Henderson. Tke
Electrician, Vol. XXXVIIL, p. 49 ; also Proc. Phys. Soc. Lond., Vol. XV.,
p. 13, Oct. 30, 1896,
3iO MEASUREMENT OP ELECTRICAL RESISTANCE.
the shorter tube being in series with a resistance box, II (see
Fig. 50). The two other arms of the bridge are made up with
high metallic resistances, P and Q, of about 20,000 ohms each.
The galvanometer used must be a sensitive galvanometer of
high resistance, say 1,000 ohms or more. The battery, 1>,
should consist of a number of cells giving an electromotive
force of at least about 30 volts. It can conveniently consist
of 20 dry cells in series.
The measuring operation consists in altering the resistance
II until the galvanometer shows no current. When this is
the case, the resistance of E must be identical with that
FIG. 50. Stroud and Henderson's Bridge Arrangement for Liquid
Resistance Measurement.
of a column of the electrolyte equal to the difference in
length between the two columns forming the two cells. Since
the electromotive forces of polarisation are equal, and since
the two columns of liquid are traversed by equal currents, the
effects of electrolysis in the two arms of the bridges exactly
neutralize each other. If then the two tubes are of the same
diameter and graduated in centimetres along their lengths, we
can at once deduce the resistance of a column of the liquid of
known length and section, and hence determine its volume-
resistivity.
OF ELECTRICAL RESISTANCE.
A modification of this method, due to Fitzpatrick (see
Brit. Assoc. Report, 1886, p. 328), which has been constantly
in use at the Cavendish Laboratory, Cambridge, overcomes all
difficulties due to polarization. It consists in employing a
revolving current-reverser, driven by a small water motor,
which rapidly reverses the direction of the battery current
flowing through the bridge. The direction of connection of
the galvanometer is reversed about the same time, but not quite
at the same instant, the galvanometer circuit being closed a
little later than the battery circuit and opened a little earlier.
If the galvanometer needle is made heavy, so as to have a
long period of vibration, these continual reversals do not
affect its steadiness, but the result is to eliminate altogether
effects due to polarization, and to make it quite as easy
to measure an electrolytic resistance as to measure a metallic
conductor. The reverser consists of a drum on which are
fixed brass sectors with wire brushes touching them. The
drum resembles a dynamo commutator, only alternate
segments are connected to metallic bands at each end. The
segments which belong to the galvanometer circuit are
rather less wide than those which belong to the battery
circuit.
In measuring the absolute value of the resistivity of an
electrolyte it is usual to place it in a glass containing vessel
or tube having platinised platinum electrodes. Once for all a
careful measurement is made of the resistivity of some pure
electrolyte, such as potassic chloride, of known concentration.
This is done in a rectangular or tubular vessel of such shape
that the dimensions of the mass of liquid and the distribution
of current through it are known. Afterwards any other
electrolyte can have its resistivity determined by being placed
in a cell of any form and the ratio of the resistances
determined when the cell is first filled with the standard
electrolyte and then with the electrolyte under test.
It is not unusual to express the conductivity of elec-
trolytes in terms of a fraction (say 10"" 8 ) of that of mercury,
312 MEASUREMENT OF ELECTRICAL RESISTANCE.
For many purposes, however, it is better to express it in
ohms or megohms per centimetre-cube.
In the tables on pp. 327, 329 are given the values of the
volume-resistivity of electrolytes of various kinds. The
aqueous solutions of the acids and many aqueous solutions of
salts or hydrates have a minimum resistivity corresponding to
a certain dilution or concentration. The temperature of the
electrolyte very greatly affects its conductivity. It will be
seen from the tables that the temperature coefficient of an
electrolyte is generally about three to four times greater
tnan that of a pure metal.
25. The Absolute Measurement of Electrical Resist-
ance. The determination of the value of an electrical
resistance in absolute measure, or its direct recovery in terms
of the units of length and time, is an operation not likely to
be conducted in an ordinary electrical testing laboratory.
Space cannot here be granted to review in detail all the
various processes which have been suggested. The student
desirous for information on this question may be referred for
full information to the following advanced treatises on
electricity and magnetism :
CLERK MAXWELL. "Treatise on Electricity and Magnetism."
Vol. II., Chap. XVIII., 2nd Ed.
E. MASCART and J. JOUBERT. "Electricity and Magnetism."
Translated by E. Atkinson. Vol. II., Chap. VII.
A. GRAY. " Absolute Measurements in Electricity and Magne-
tism." Vol. II., Part II., Chap. X., p. 538.
G. WIEDEMANN. Electricitdt, Vol. IV., p. 910.
The various methods used for the absolute measurement of
resistance have also been critically discussed by Lord Kayleigh,
Phil. Mag., Vol. XIV., 1882, and by Mr. E. J. Glazebrook,
B.A. Report, 1890. See also The Electrician, Vol. XXV., p. 544.
Amongst the processes there described for the absolute
determination of an electrical resistance is one due to
Lorenz which, from its simplicity, has been made the
starting point for the construction of an apparatus by
MEASUREMENT OF ELECTRICAL RESISTANCE. 313
Prof. J. V. Jones which is likely soon to be found in the
possession of every well-equipped electro- physical laboratory.
This apparatus enables an observer to re-determine for him-
self in absolute measure the value of a low resistance, and
that with not greater expenditure of time than would be
incurred in making a mere comparison experiment.
The general theory of the Lorenz method of determining
a resistance in absolute measure may thus be described :
If a metallic disc is caused to rotate in the mean plane
of a coil concentric and co-axial with the disc, and if a
current passes through the coil, an electromotive force is
created in the disc. If brushes touch the centre and
circumference of the disc, and if from these connections are
led away to make contact with two points on the circuit,
which includes the coil, then it is possible to so adjust the
resistance between these contact places that no current flows
through the disc in other words, the electromotive force set
up in the disc may be made to exactly balance the potential
fall down the resistance in series with the coil. If, then, E
is the resistance of this conductor and C the current through
it and the coil, and if M is the co-efficient of mutual
inductance between the coil and the disc, and n the speed
of revolution, the electromotive force set up in the disc is
equal to MCw, and the fall of potential down the conductor
is EC. Hence, when there is equilibrium, MO/i = EC, or
E = M?i. The measurement of the resistance is therefore
reduced to the calculation of a co-efficient of inductance from
the measured dimensions of the coil and the disc and the
observation of a speed of revolution.
In Fig. 51 the points and M are the centre and circum-
ference of the disc, and XY is the resistance of which the
absolute value is to be determined. The real apparatus as
designed by Prof. J. Y. Jones* is represented in Fig. 52.
* For a full description of the theory and practice of the method the reader
is referred to Papers by Prof. J. V. Jones in The Electrician of 1890 and 1895
Vol. XXV., p. 552, and Vol. XXXV., pp. 231 and 253.
314 MEASUREMENT OF ELECTRICAL RESISTANCE.
The metallic disc is driven at a uniform speed by an electric
motor. Contact is made against the centre and circum-
FIG. 51.
FIG. 52. The Jones-Lorenz Apparatus for Absolute Resistance
Determinations.
t'erence of the disc by brushes, and these are connected
through a galvanometer with the ends of the resistance
MEASUREMENT Otf ELECTRICAL RESISTANCE. 3 15
being measured. The axis carrying the disc carries also a
speed indicator, which is preferably an arrangement for
making an electric contact every revolution of the disc.
This is made to print dots on a fast-running paper tape on
which also series of parallel dots are printed by a standard
clock. The speed of the disc can then be accurately determined.
The coil consists of a wire wound specially in grooves in
a marble ring, on the outer edge of which is cut a screw-
groove. The calculation of the mutual inductance of the
coil and disc once effected becomes a constant of the
instrument.
For the details of the machines already designed and made
under the direction of Prof. J. V. Jones the reader is referred
to the following Papers by Prof. Jones : " Suggestions
towards the Determination of the Ohm in Absolute Measure,"
a Paper read before the British Association at Leeds in
1890. (See also The Electrician, Vol. XXV., p. 552.)
In this Paper the details of the theory are set out. Reference is also made
to a Paper, by the same author, read before the Physical Society in 1888,
(see Phil. Mag., Jan., 1889), in which the theory of the calculation of -the
mutual inductance of a disc and co-axial coil of single layer is given.
Also, by the same author, a Lecture on this subject was
given at the Eoyal Institution, London, in May, 1895, entitled
" The Absolute Measurement of Electrical Resistance." (See
The Electrician, Vol. XXXV., p. 231.)
In this Lecture the details of an improved Lorenz apparatus are described.
A well-constructed Lorenz apparatus was made for the
McGill University, Montreal, and a description of the design
will be found hi The Electrician, Vol. XXXVIL, p. 267, as
well as a perspective view of the machine (see Fig. 53), A
careful determination of the absolute value of the Board of
Trade standard ohm was made by Profs. Ayrton arid Jones in
1897, with the above described Montreal Lorentz apparatus
and the results of these experiments are recorded in The
Electrician, Vol. XL,, pp. 149-150 (see also Science Abstracts
Vol. 1., p. 24).
316 MEASUREMENT OF ELECTRICAL RESISTANCE.
MEASUREMENT OF ELECTRICAL RESISTANCE. 317
A Paper by Prof. Ayrton in The Electrician, Vol. XL.,
p, 149, entitled " Our Knowledge of the Value of a Kesistance,"
gives the facts on which are founded the opinion that the
Board of Trade standard ohm, which is intended to represent
as nearly as possible the International ohm, or a resistance of
106*3cms. of mercury 1 sq. mm. in section at 0C., may in fact be
equal to 106'33cms. or may be in error by three or four parts
in 10,000. Hence we cannot say that this official standard
ohm really represents 10 9 absolute C.G.S. units of resistance
with a greater accuracy than three or four parts in 10,000 or
0*03 per cent. The mean of nine absolute determinations of
the value of the Board of Trade wire standard ohm showed
that its real value is, in all probability, 1-00026 true ohms
the true ohm being 10 9 absolute C.G.S. units.
The reader desirous of information on the relative value of
the experimental methods which have been adopted for the
absolute determination of resistance and the absolute measure-
ment of the resistivity of mercury may be referred to two
important reports made by Mr. E. T. Glazebrook on behalf of
the Electrical Standards Committee of the British Association
(see Brit. Assoc. Pteports, 1890 (Leeds) and 1892 (Edinburgh);
also The Electrician, Vol. XXV., pp. 543 and 588, and Vol.
XXIX., p. 462).
Values which have been obtained by various observers for
the ohm in terms of the dimensions of a column of pure
mercury at 0C. are given in Table XV. following (p. 335).
26. Resistance of Conductors to Alternating Currents.
If a metallic conductor, in the form of a wire or rod, is
traversed by an alternating electric current, it is well known
that the current does not distribute itself uniformly over the
cross-section of the conductor, but concentrates itself more
or less at the surface. The result is to make the effective
resistance of the conductor greater for alternating currents
than for continuous, because the periodic current, so to speak,
makes less use of the conductor- Hence we need a correction
318 MEASUREMENT OF ELECTRICAL RESISTANCE.
which must be applied to the true or ohmic resistance in cal-
culating the resistance of a conductor to alternating currents.
Assuming the currents to be simply periodic and the conduc-
tor a round metallic rod, Lord Rayleigh in 1886 gave a
formula for calculating the resistance to alternating currents.*
Another formula and method was given by Lord Kelvin in
1889, f and he gave a table calculated for conductors of round
section of certain diameters, and for certain frequencies.
The above formulae are, however, in a form which does
not render them very convenient for laboratory calculation.
M. E. Hospitalier has, however, reduced Lord Kelvin's
formula to a very convenient table.
If we denote the resistance to alternating currents by R A and
that to continuous currents by II , then for round-sectioned
rods as wires the two quantities are related by the general
expression p _;,p
k being a numerical constant which depends upon the
frequency n and on the diameter d.
In the case of wires made of the same metal but of
different diameters k has the same value for equal values
of the product nd 2 . Hence we can make a table showing
the values of k corresponding to various values of nd 2 .
M. E. Hospitalier, assisted by M. A. Potier, has calculated
the following table, which is correct for copper having a
resistivity of 1,597 C.G.S. units.*
nd\ k
1-0000
20 1-0000
80 1-0001
180 1-0258
320 1-0805
500 1-1747
720 1-3180
980 1-4920
1,280 1-6778
1,620 T8628
2,000 2-0430
2,420 2-2190
2,830 2-3937
5,120 3-0956
8,000 3-7940
18,000 5-5732
22,000 7-3250
* Phil. Mag., May, 1886. See also " The Alternate Current Transformer,"
Fleming, Vol. I., third edition, p. 294.
t Presidential address to the Institution of Electrical Engineers, 1889.
t See The Electrician, Vol. XXXII., p. 277, >r L' Industrie Electrize, 1893,
p. 563.
MEASUREMENT OF ELECTRICAL RESISTANCE. 319
As an example of its use, let us apply it to the following
problem :
What will be the resistance to alternating currents having
a frequency of 80, of a round-sectioned copper rod 2cms. in
diameter. Here d = 2, n = 80 ; hence nd* = 80x4 = 320.
From the above table we see that, corresponding to nd 2 = 320,
/j = 1*0805. Hence, if the ohmic resistance of the rod is, say,
3 ohms, then its resistance to the above periodic currents
is 3*2415 ohms. If the exact value of the product ?icf 2
required is not in the above table, it can be obtained by
interpolation or by setting out the figures in a curve. In
Table XVI., at the end of this chapter, are given the values
of the ohmic and alternating resistance for stranded copper
cables for a frequency of 100. For other non-magnetic metals
besides copper the table in the text (p. 318) may be made
available by employing a factor to find k equal to the values
for copper of nd* multiplied by 1,597/p, where p is the resis-
tivity in C.G.S. units.
Hence, for a round metal rod of diameter d, and made of
a material having double the specific resistance of copper,
in order to find its resistance to alternating currents of a
frequency n, we should have to find the value of k in the
above table corresponding to a value - , and not simply
nd 2 , as for copper. Accordingly, the higher the resistivity of
the material the less different is the alternating from the
continuous current resistance.
( .320 )
TABLE I Atomic Weights and Densities of Metals.
The quotient of density multiplied by 1,000 by atomic weight gives a number
called the atomic density, and is proportional to the number of atoms per
centimetre-cube.
Metal.
1
Atomic
weights.
a.
Density.
Water =1.
Atomic
density
Atomic
volume
1
H = l
= 16
d.
Xd/a.
= a{d.
Lithium
Beryllium ...
Sodium
Li
Be
Na
7
9-1
23
7
9-0
23-05
0-589- 0-598
1-85
0-974
85
203
42
11-8
4-86
23-6
Magnesium . .
Aluminium . .
Potassium ...
Calcium
Mg
Al
K
Ca
23-9
27-0
39-0
39-9
24-3
27
39-11
40
1-743
2-56 - 2-583
0-875
1-566- 1-584
73
95
22-5
39-5
13-76
10-56
44-96
25-28
Titanium . . .
Chromium . . .
Manganese. . .
Iron ....
Ti
Cr
Mn
Fe
48-0
52-0
54-8
55-9
48
52-1
55-1
56-0
6-8 '
7-33
7-8 - 8-1
130
134
142
7-0
7-0
7-1
Nickel
Ni
58-7
58-7
8-3 - 9-0
148
6-94
Cobalt
Ho
59-4
59-5
8-5 - 8-9
148
6-94
Copper .
On
63-2
63-6
8-9 - 8-95
141
7-10
Zinc
fin
64-9
65-3
6-9 - 7-2
108
9-12
Arsenic
Rubidium ...
Strontium ...
Molybdenum
Ruthenium...
Ehodium . . .
Palladium ...
Silver
As
Rb
Sr
Mo
Ru
Rh
Pd
Ap
74-9
85-2
87-3
95-7
101-4
1027
106-2
107-6
75
85-5
87-66
103
106-5
107-92
2-54'"
8-6
110 -11-4
11-0 -11-2
11-3 -12-1
10-4 -10-57
29
89-5
110-5
108
110
97-5
12-96(?)
56-1 (?)
34-56
11-13
9-05
9-12
9-12
10-04
Cadmium . . .
Indium
Tin
Cd
In
Sn
111-7
113-4
117-3
112
113-7
119
8-54- 8-66
7-2 - 7-4
7-3
77
64
62
12-96
15-53
16-20
Antimony ...
CaBsium
Sb
Cs
119-6
132-7
120
132-9
6-72
1-88
56
14
18-16
70-5
Barium
Cerium
Ba
O
136-4
139-9
137-4
140-2
4-0
6-73
29
47-5
34-25
20'8
Tungsten . . .
Osmium
Iridium
W
Os
Tr
183-6
190-3
192-5
193-1
19-261
22-43
22-4
105
117
116
9-53
8-49
8-6
Platinum ...
Gold
Pt
An
194-3
196-8
195
197-3
20-3 -22-1
19-3 -19-5
106
98
9-12
10-04
Mercury
HP
199-8
200
13-596
68
14-56
Thallium ...
Lead
Tl
Ph
203-7
206-4
204
20695
11-8
11-3 -11-4
58
55
17-20
18-24
Bismuth
Thorium . . .
Uranium . . .
Bi
Th
U
208-0
232-0
239-8
208
232-6
9-8 - 9-9
10-97-11-23
18-4
47
48
77
21-34
20-84
13-03
The atomic weights under column (0 = 16) are the numbers published by
the American Chemical Society's committee on atomic weights (Journal
American Chemical Society, Vol. XVII.), revised to January, 1894.
The atomic weights under column (H = l) are those given by Professor
T. E. Thorp ("Manual of Inorganic Chemistry," Vol. I.).
MEASUREMENT OF ELECTRICAL RESISTANCE. 321
TABLE II.
Electrical Mass-resistivity of Various Metals at 0C., or Re-
sistance per Metre-gramme in Standard Ohms at 0C.
(Matthiessen.)
Metal.
Resistance at 0C. (in
Standard Ohms) of a
wire one metre long
and weighing one
gramme.
Approximate
temperature co-
efficient near
20C.
Silver (annealed)
0-1523
0-1657
0-1421
0-1449 (Matt
0-4025
0-4094
0-0757
0-4013
1-9337
0-765
1-058
0-9618
2-2268
2-3787
12-8554
12-885
0-00377
0-00388
hiessen's Standard)
0-00365
0-00365
0-00387
0-00389
0-00354
0-00072
Silver (hard drawn)
Copper (annealed)
Copper (hard drawn)
Gold (annealed)
Gold (hard drawn) .. .
Aluminium (annealed) ...
Zinc (pressed)
Platinum (annealed)
Iron (annealed)
Xickel (annealed)
Tin (pressed)
Lead (pressed)
Antimony (pressed)
Bismuth (pressed)
Mercury (liquid)*
* Matthiessen's value (12'885) for the electrical mass-resistivity of liquid
mercury is too high by nearly 1 per cent. The value now accepted is
12*789 international standard ohms per metre-gramme at 0C. The values
for nickel and bismuth are also much higher than are obtainable now with
pure electrolytic metals. The temperature coefficients given by Matthiessen
are also, in all cases, smaller than those now adopted for pure metals.
322 MEASUREMENT OF ELECTRICAL RESISTANCE.
TABLE III.
Electrical Volume-resistivity of Various Metals at 0C., or
Resistance per Centimetre-cube in C.G.S. Units at 0C.
This Table is calculated from the results of experiments made by
Matthiessen, employing the values given by Jenkin in his Cantor Lectures
(Society of Arts, 1866) for the resistance in B.A. units of a uniform circular-
sectioned wire of the metal 1 metre long and 1 mm. in diameter taken at 0C.
The figures given by Jenkin have been reduced to standard ohms and C.G.S.
units by multiplying by - x 0'9S66 x 10 5 =77,485.
Metal.
Volume Resistivity
at 0C. in C.G.S. Units.
Silver (annealed)
Silver (hard drawn) . .
Copper (annealed)
Copper (hard drawn) . .
Gold (annealed)
Gold (hard drawn)
Aluminium (annealed)
Zinc (pressed)
Platinum (annealed) ..
Iron (annealed)
Nickel (annealed)
Tin (pressed)
Lead (pressed)
Antimony (pressed)
Bismuth (pressed)
Mercury (liquid)
1,502
1,629
1,594
1,630*
2,052
2,090
3,006
5,621
9,035
10,568
12,429!
13,178
19,580
35,418
130,872
94,896t
* The value (1,630) here given for hard drawn copper is about one-quarter
per cent, higher than the value now adopted, viz. : (1,626). The difference Is
due to the fact that either Jenkin or M atthiessen did not employ precisely the
same values as at present employed for the density of hard-drawn and annealed
copper in calculating the volume-resistivities from the mass-resistivities.
t Matthiessen's value for nickel is much greater than that obtained by the
Author, as shown in Table IV.
t Matthiessen's value for mercury is nearly 1 per cent, larger than the value
now adopted as the mean of the best results, viz. : 94,070.
MEASUREMENT OF ELECTRICAL RESISTANCE. 323
TABLE IV.
Electrical Volume-resistivity of Various Pure Metals at 0C.,
or Resistance per Centimetre-cube at 00. in C.G.S. Units.
(Fleming and Dewar, Phil. Mag., September, 1893.)
Metal.
Resistance at
0C. per centi-
metre-cube in
C.G.S. Units.
Mean tempera-
ture coefficient
between 0C.
and 100C.
Silver (electrolytic and well)
annealed)* j
1,468
0-00400 '
Copper (electrolytic and well)
annealed)* j
1,561
0-00428
Gold (annealed)
2,197
0-00377
Aluminium (annealed)
2,665
0-00435 ^
Magnesium (pressed)
4,355
0-00381
Zinc
5,751
0-00406
Nickel (electrolytic)*
6,935
0-00618
Iron (annealed)
9,065
0-00625
Cadmium
10,023
0-00419
Palladium
10,219
0-00354
Platinum (annealed)
10,917
0-003669
Tin (pressed)
13,048
0-00440
Thallium (pressed) ...
17,633
0-00398
Lead (pressed)
20,380
0-00411
Bismuth (electrolytic)f
110,000
0-00433
Mercury (Pure)
94 070
0-00098
* The samples of silver, copper and nickel employed for these tests were
prepared electrolytically by Mr. J. W. Swan, F.R.S., and were exceedingly
pure and soft. The value for volume-resistivity of nickel as given in the
above table (from experiments by J. A. Fleming) is much less (by nearly
40 per cent.) than the value given by Matthiessen's researches.
t The electrolytic bismuth here used was prepared by Messrs. Hartmann
and Braun, and the resistivity taken by J. A. Fleming. The value is nearly
20 per cent, less than that given by Matthiessen.
Y2
324
MEASUREMENT OF ELECTRICAL RESISTANCE.
TABLE V.
Electrical Volume-resistivity of Pure Metals at Various
Temperatures.
(From experiments by Fleming and Dewar.)
Tempera- Specific Resistance in C.G.S. Units.
ture
(Centi-
grade).
Silver.
Copper.
Gold.
Alu-
minium.
Mag-
nesium.
Zinc.
Nickel.
- 150C.
580
515
960
900
1,625
2,270
2,400
- 100C.
890
860
1,360 1,485
2,585
3,430 3,645
- 50C.
1,195
1,210
1,770
2,075
3,485
4,585
5,130
0C.
1,468
1,561
2,197
2,665
4,355
5,751
6,935
+ 50C.
1,775
1,895
2,605
3,255
5,205
6,925
8,915
+ 100C.
2,070
2,215
3,030
3,845 6,010
8,115
11,210
+ 150C.
2,360
2,560
3,440
4,420 ! 6,790
9,345
13,820
+ 200C.
2,885
2,890
3,840
5,000
7,540
10,590
16,630
i
Tempera-
Specific Resistance in C.G.S. Units.
ture
(Centi-
grade).
Iron.
Cad-
mium.
Palla-
dium.
Plati-
num.
Tin.
Thal-
lium.
Lead.
-150C.
2,325
4,210
4,205
4,760
5,080
6,275
8,515
- 100C.
4,360
6,115
6.290
6,890
7,650
10,155
12,340
- 50C.
6,590
8,045
8,300
8,945
10,350
13,930
16,390
0C.
9,065
10,023
10,219
10,917 i 13,048
17,633
20,380
+ 50C.
11,770
12,060
12,055
12,910
15,895
21,225
24,555
+ 100C.
14,765
14,315
13,840
14,820
18,870
24,770
28,900
+ 150C.
18,110
16,725
15,545
16,690
21,990
28,100
33,470
+ 200C.
21,960
19,325
15,215
18,535
25,155
31,635
38,000
MEASUREMENT OF ELECTRICAL RESISTANCE.
325
TABLE VI.
Electrical Conductivity of Metals at C. in Absolute and
Arbitrary Units.
Absolute conductivity is measured in mhos. The mho is the reciprocal of
the ohm, and the mho-conductivity is obtained by dividing 10 9 by the volutne-
resistivity in C.G.S. units.
Metal
Mho-conductivity at 0C.
1 mho = conductivity of a
centimetre-cube of
material having a volurne-
resistivity of 1 ohm.
Arbitrary conduc-
tivity. Annealed
electrolytic silver
= 100atOC.
Silver (electrolytic\
annealed) J
681,198
100
Copper (electrolytic)
annealed) /
640,615
94-04
Gold (annealed)
455,166
66-81
Aluminium (annealed)
Sodium (pressed at)
20 C }
37.5,234
253,973
55-08
37-43
Magnesium
229,616
33-71
Zinc
171,381
25-16
Calcium (at 18C.) ...
Nickel (electrolytic) . . .
Potassium (at 20C.)
Lithium (at 20C.) ...
Indium
150,818
144,196
141,990
129,428
112,400
22-14
21-17
20-85
19-00
16-50
Iron
110,314
16-19
Cobalt
106,140
15-58
Oa^rninm
99,770
14-64
Palladium
97,857
14-64
Platinum
91,600
13-44
Tin
76,640
11-25
Thallium
56,712
8'32
Lead. ..
49,067
7-20
Strontium (at 18C.)
Arsenic
45,708
32,425
6-71
4-76
Antimony
31,471
4-62
Mercury
10,630
1-56
Bismuth .
9,091
1-33
326 MEASUREMENT OF ELECTRICAL RESISTANCE.
TABLE VII.
Volume-resistivity of Alloys of known Composition at 0C.
in C.G.S. Units per Centimetre-cube.
Mean temperature coefficients taken at 15C.
(Fleming and Dewar. )
Alloy.
Resis-
tivity
at 0C.
Tempera-
ture
coefficient
at 15C.
Composition in
per cents.
Platinum-Silver
31 582
0-000243
Pt337, As667
Platinum- Iridium .
30,896
0-000822
Pt 807, Ir 207
Platinum-Rhodium
21,142
0-00143
Pt907,Khl07
Gold-Silver,
6,280
0-00124
Au907,Agl07
Manganese-Steel
67,148
0-00127
Mnl27,Fe807
Nickel-Steel .
29 452
0-00201
Ni 4-357
Germ an -Silver ..
29 982
0-000273
Cu, Zn Q NL
Platinoid*
41,731
0-00031
Manganin
46,678
o-oooo
/Cu84%,Mnl2%,
Aluminium- Silver
4 641
0-00238
I Ni4%
Al 947, As 67
Aluminium- Copper
2,904
0-00381
v /o' 5 **/o
Al 947, Cu 67
Copper- Aluminium ...
8,847
0-000897
Cu 977, Al 37
Copper - Nickel - Aluminium
Titanium- Aluminium
14,912
3,887
0-000645
0-00290
/Cu87%,Ni6-7%,
1 A16-5%
* Platinoid is an alloy first produced by Martino, the composition being
said to be similar to that of German silver, but with a little tungsten added.
It varies a good deal in composition according to manufacture, and the resis-
tivity of different specimens is not identical. The electrical properties of
platinoid were first made known by Dr. J. T. Bottomley, F.R.S., in a Paper
read at the Royal Society, May 5, 1885.
MEASUREMENT OF ELECTRICAL RESISTANCE.
TABLE VIII.
327
Electrical Volume-resistivity of Various Liquids in Ohms er
Centimetre-cube.
I. FUSED SALTS.
Substance.
Kesistivity.
Remarks.
Observer.
Plumbic chloride Pb
Clo
0-376
F. Braun
Silver chloride AgCl
Sodic nitrate NaN0 3
Zinc chloride ZnCl 9
0-392
0-817
109-3
at 600C.
W. Kohlrausch
F. Braun
F. Braun
II. AQUEOUS SOLUTION OF ACIDS.*
Solution having maximum conductivity at 18C.
Acid.
Resistivity.
Temperature Coefficient.
Nitric Acid N0 3 H....
1-28
0-014 \
Hydrochloric Acid HC1
Sulphuric Acid H 2 S0 4
Tartaric Acid C 4 H e 6
Acetic Acid C 2 H 4 9 ...
1-32
1-36
100-0
618-4
0-0155! . ,
0-0169 as given by
0-0192 [G.Wieaemann.
0-0174J
III. AQUEOUS SOLUTIONS OF SALTS AND HYDRATES.*
Salt.
Resistivity.
Specific
Gravity.
Temperature Coefficient.
Potassic Hydrate KHO
1-84
0-0225\
Potassic Iodide KI
2-29
1-70
0-014
Ammonic Chloride Am
Cl
2-36
1-078
00155
Silver Nitrate AgN0 3 ...
Sodic Chloride NaCl ...
Hydro -potassic Car-
4-48
4-66
2-18
1-201
0-0211
0-0234
as given
by G.
Wiedemann.
bonate KHCO S
8-54
1-15
0-0199
Copper sulphate CuS0 4 ! 29-37
1-208
0-0241
Zinc sulphate ZnS0 4 ...
21-35
1-286
t
* The above Table contains only the resistivity values corresponding to the
maximum conductivity in the case of the aqueous solutions of salts and acids.
328
MEASUREMENT OF ELECTRICAL RESISTANCE.
TABLE IX.
Electrical Volume-resistivity of Various Badly Conducting
Liquids in Megohms per Centimetre-cube.
Substance.
Resistivity in
megohms per c.c.
Observer.
Ethylic Alcohol
0-522
Pfeiffer.
Ethylic Ether
1-175 to 3-760
W. Kohlrausch.
Benzine
4700
Water
(1-446 at 14C.
Pfeiffer.
Absolutely pure water
approximates probably
to
5'222 at 18C.
1 25-0 at 18C.
F. Kohlrausch.
c Estimated value by
Kohlrausch and
I Heydweiler.
All very dilute aqueous
salt solutions having a
concentration of about
0-00001 of an equiva-
lent gramme- molecule*
per litre approximate to
- 1-00 at 18C.
{From results by F.
Kohlrausch and
others.
* An equivalent gramme-molecule is a weight in grammes numerically
equal to the chemical equivalent of the salt. For instance, one equivalent
gramme- molecule of sodic chloride is a mass of 58'5 grammes, since NaCl
= 58-5.
MEASUREMENT OF ELECTRICAL RESISTANCE.
329
TABLE X.
Volume-resistivity of Solutions of Copper and Zinc Sulphate of
Various Densities at IOC. in Ohms per Centimetre-cube.
(Ewing and MacGregor.)*
SULPHATE OF COPPEB.
Density.
Resistivity.
Density.
Resistivity.
1-0167
164-4
1-1386
35-0
1-0216
134-8
1-1432
34-1
1-0318
98-7
1-1679
31-7
1-0622
590
11829
30-6
1-0858
47-3
1-2051
29-3
1-1174
38-1
(saturated)
...
SULPHATE OF ZINC.
Density.
Resistivity. Density.
II
Resistivity.
1-0140 182-9 1-2709
28-5
1-0187 140-5 1-2891
28-3
1-0278 111-1
1-2895
28-5
1-0540
638
1-2987
28-7
1-0760
50-8
1-3288
29-2
1-1019
421
1-3530
31-0
1-1582
33-7
1-4053
32-1
1-1845
321
1-4174
33-4
1-2186
303 1-4220
33-7
1-2562 29 2
1
^saturated)
...
* Trans. Roy. Soc., Edin., Vol. XXVII., 1873.
The resistivity values obtained by various observers for electrolytic con-
ductors do not agree at all well. The above values are not quite in accord
with other results.
330 MEASUREMENT OF ELECTRICAL RESISTANCE.
TABLE XI.
Electrical Volume-resistivity of Dielectrics expressed in Millions
of Megohms (Mega-megohms) per Centimetre- cube, and in
Megohms per Quadrant-cube i.e., a Cube whose side is
10" cms.
Substance.
Resistivity.
Temperature.
Cent.
Mega-
megohms
per c.c.
Megohms per
quadrant-
cube.
Bohemian Glass
61
84*
450*
1,020
1,630
2,280
9,000*
10,900
11,900
16,170
20,000
28,000*
34,000*
061
084
45
1-02
1-63
2-28
9-0
10-9
11*9
16-17
20-0
28
34
60
20
24
60
15
15
28
24
15
15
20
46
46
Mica
G utta-percha
Flint Glass at 60 C
Glover's Vulcanised India-
rubber
Siemens' ordinary pure
Vulcanised India-rubber
Shellac
India-rubber
Siemens' High Insulating
Fibrous Material
Siemens' Special High
Insulating India-rubber
Flint Glass at 20 C
Ebonite
Paraffin
The values of the resistivity of various dielectrics given in the above Table
can only be taken as approximate. In most cases the observers have not
stated the time of imposition of the electric stress. Values marked (*) are
those given by experiments by Profs. Ayrton and Perry : " On the Viscosity
of Dielectrics " (Proc. Roy. Soc., March, 1878), " after several minutes'
electrification."
The temperature coefficients of the resistivities of dielectric conductors are
very large ; in most cases far larger than those of the pure metals, and
the apparent resistivity is also a function of the value and of the time of
operation of the electromotive force.
MEASUREMENT OF ELECTRICAL RESISTANCE. 331
TABLE XII.
Resistances of various sizes of Platinoid Wire.
(London Electric Wire Company, Ltd.)
Size.
Diameter.
Resistance (approximate).
: L.S.G.
Inch.
m/m.
Per Ib.
Per 1,000 yards.
Ohms.
Ohms.
8 '
0-160
4-064
0-1241
28-852
10
0-128
3-251
0-3031
45-084
12
0-104
2-642
0-6957
68-292
14
0-080
2-032
1-9869
115-416
16
0-064
1-626
4*8520
180-338
18
0-048
1-219
15-3312
320-601
19
0-040
1-016
31-7952
461-664
20
0-036
0-914
48-4602
569-952
21
0-032
0-813
77-6480
721-368
22
0-028
0-711
132-4272
942-192
23
0-024
0-610
245-3280
1282-392
24
0-022
0-559
347-4720
1526-184
25
0-020
0-508
508-7280
1846-656
26
0-018
0-457
775-3680
2279-808
27
0-0164
0-417
1125-2160
2746-440
28
0-0148
0-876
1696-4880
3372-264
80
0-0124
0-315
8442-8000
4803-984
32
0-0108
0-274
5982-7200
6332-904
34
0-0092
0-2337
11362
8727-120
36
0-0076
0-1930
24398
12789-640
38
0-0060
0-1524
62805
20518-560
40
0-0048
0-1219
153333
32060-160
42
0-0040
0-1016
317904
46166
44
0-0032
0-0813
784280
72136
46
0-0024
0-0610
2453280
128239
47
0-0020
0-0508
5087280
184665
332 MEASUREMENT OF ELECTRICAL RESISTANCE.
TABLE XIII.
Resistances of various sizes of Manganin Wire.
(London Electric Wire Company, Ltd.)
Size.
Diameter.
Resistance (approximate).
L.S.G.
Inch.
m/m.
Per Ib.
Per 1,000 yards.
Ohms.
Ohms.
14
0-080
2-032
2-027
117-85
16
0-064
1-626
4-952
184-17
18
0-048
1-219
15-652
327-42
20
0-036
0-914
49-475
582-00
22
0-028
0-711
135-175
962-00
24
0-022
0-559
354-700
1560-25
26
0-018
0-457
791-475
2330-00
28
0-0148
0-376
1731-750
3442-50
30
0-0124
0-315
3514-250
4907-50
32
0-0108
0-274
6107-250
6467-50
34
0-0092
0-2337
11597-750
8912-50
36
0-0076
0-1930
24904-500
13060
38
0-0060
0-1524
64100
20955
40
0-0048
0-1219
156525
32875
42
0-0040
0-1016
324550
47150
44
00032
0-0813
792375
73675
MEASUREMENT OF ELECTRICAL RESISTANCE.
333
3 il
I
I
1
OQ
111
GO i-H
s
CO <M CO t-
o
<M b- CO O CO
Cq^H
i-H (M CO
^
CO CO
OQ CO
"<H co f<
<NCOCOOOOCO<Ni-l
r^ (M rH
kO
00 tM O CO t^ 00
OCCCCt^COOS^OO
(M O "* X O CO CM rH O
^ <M i 1
fI
o <M oo ^ oq
t>OCOr-(^O5<NrH^
obrHcbcbdb4cb<irH
00 rji r- 1
co (?q -I
r> co GO o co p so
O O rH CN CO 1*
X O t- l> O
rHrHi lrHC<lGt>l>-i I
OrHrHCOXOOOCMOOO
O O O O ' G<1 G<l
(~) f^ {^} f_^ <^ ^^ ^^
ooooooooo
as
pOOpO^-irHrHrH
OOOOOOOOO
w ,
ai^
llifH
t-O<MOOCOpppp
rH <M CO -T"
CO 05 O O O O
OrH-rHcboobciOOO
O
( 334 )
Ill
i i l> !>
COCDCDOOt>-CCOi i OCO
CO
i i TH co -^ T-HCMCOOCMCOOOC;
OOCOO
00
iH rH Cq TJ1 t*(M 00 <M CO D- (M Oi CO O l> CO TH 00 -* (M O CO
i ir-i T-H i i co o r-((Mcoooq^co
a a
CO"^QOOCOCOTHTHOOCO(MrHOOOOr-iOOOOOOOOC
o i i co a
OOOQOCOr-
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O
(M rH
OOOOrHOOOOOOOOC
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d&
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t CO rH CM
rH O b-
rH CD US <* t- CO ^ t- t* (M C5 05
C5
^^ ^D ^^ ^D "* O^ CO *-O 00 T"H rH CO CO O^ *O "^^ CO CO <^ GO ^H ^^ O^ C^ ^H 1C
OOOOpOOOOOOOOOTH^OOrHr-iCprHnHCpO^)
ooooooooooooooooooooooooooc
g
ll
s
s
ooooooooooooooooooooooooooc
-2 '
CM TH ;
CqCOTHXOrHrHrHCqCOTHOr-HrHC<lCO-HHrHCMCOTHa;
CM CO TH CM CO TH CO 00 O CM CM CO TH CO 00 O CM CO TH O 00 O TH O OO O OC
OOOpOOpOrHrHOOOpOrHrHOOOOT-lOOOTHC
OOOOOOOOOOOOOOOOOOOOOOOOOOC
to
OD TH CO
iOTHrHTHOOOCNOt^ CO CO *O CO
O
OCOr>COCOC5O5CDOOOCOTHOOO5t-b-
rH rHCMCOTHb-OrHCMTHt-OCOCOiOOOCNOOOOOqOOOCOG:
rH rHi ICQ 'rHCMrHrHCMTHOC
gH
f*l
CO TH CO <M
rHCMCO^OOOrHrHCOCOOSiO
rHt^COt--COOC5CO(7q<Nr-
THCOCOi lOOrHOOOrHO
s
^^<M rH CJ^CM rH -~-^-^.~~^ ^ -^.
^c^^t^i^i^^t^^^^o^Grcrcrorcrt^^^t^t^"
MEASUREMENT OF ELECTRICAL RESISTANCE. 335
TABLE XV.
The Value of the Ohm.
Observer.
Date.
Method.
Value of
B.A.U.
in ohms.
Value of
100 centi-
metres of
mercury
in ohms.
Value of
ohm in
centi-
metres of
mercury.
Lord Rayleigh
Lord Rayleigh
G.Wiedemann
Mascart
1882
1883
1884
1884
1887
1887
1882
1888
189U
1890
1891
1885
1888
1890
Rotatin^ coil
0-98651
0-98677
0-98611
0-98644
0-98660
0-98665
0-98686
0-98634
0-94133
0-94096
0-94071
0-94061
0-94074
0-94077
0-94067
0-94067
0-94056
0-94074
0-94054
0-94076
0-94076
o 1 u t e^>
3ments
3d with
i silver >
s issued
lens or
f )
K'6-24
106-21
106-19
106-33
106-32
106-32
106-29
106-27
106-32
106-31
106-32
106-30
106-33
106-30
106-28
10537
106-16
105-89
105-98
106-24
106-03
105-93
Lorenz method
Rotation through 180
Induced current . .
Rowland
Mean of several
methods
Kohlrausch ...
Glazebrook . . . j
Wuilleumeier
Duncan and
Wilkes
Damping of magnets
} Induced currents . . .
Lorenz
Jones
Lorenz
Strecker . . .
Mean
0-98653
f An absolute deter-'
mination of resist-
ance was not made.
The value 0-98656
has been used
Mean
Hutchinson ...
Salvioni
Salvioni
H.F.Weber...
H.F.Weber...
Roiti
1884
1884
1885
1889
1883
1885
Induced current
Rotating coil
...
Mean effect of induced
current
/ Abs
measur<
compar
Germar
wirecoi'
by Sien
Streckei
Himstedt
Dorn ... .
Damping of a magnet
Damping of a magnet
Lorenz method
Wild
Lorenz
336
MEASUREMENT OF ELECTRICAL RESISTANCE.
TABLE XVI.
Table of Resistance of High Conductivity Bound Copper
Conductors to Alternating and Continuous Currents.
Size of stranded
cable.
Area in
square inches.
Kesistance in ohms per 1,000 yards.
To continuous
currents.
To alternating
currents.
Frequency 100 ^
per second.
7/18
00126
1-974
1-974
7/17
0-0172
1-452
1-452
7/16
0-0225
1-108
1-108
7/15
0-0285
0-878
0-878
7/14
0-0351
0-712
0-712
19/18
0-0351
0-712
0-712
19/17
0-0477
0-524
0-524
19/16
00624
0-401
0-401
19/15
0-0789
0-318
0-318
19/14
00973
0-257
0-257
19/13
0-1289
0-194
0-195
19/12
0-1645
0-153
0-155
19/11
0-2048
0-122
0-1247
19/10
0-2500
0-100
0-1034
37/16
0-1227
0-204
0-2041
37/15
0-1551
0-162
0-104
37/14
0-1913
0131
0-1334
37/13
0-2534
0-099
0-1024
37
0-3000
0-083
0-087
37/12
0-3235
0-077
0-081
37/11
0-4000
0-063
0-068
37/10
0-4905
0-051
0-057
61/15
0-2582
0-097
0-1004
61/14
0-3185
0-078
0-082
61/13
0-4218
0-060
0-065
61
0-5000
0-050
0-056
61/12
0-5385
0-046
0-052
61
0-6000
0-041
0-048
61/11
0-6476
0-039
0-0465
61
0-7000
0-0357
. 0-0435
61/10
0-8167
0-0305
0-0391
91/13
0-6354
0-0385
0-0458
91
0-7500
0-0330
00412
91/12
0-8111
0-0305
0-0391
91
0-9000
0-0277
0-0370
91/11
1-0000
0-0250
0-0350
MEASUREMENT OF ELECTRICAL RESISTANCE. 337
TABLE XVII.
Materials Used for Electrical Resistances.
Material.
Resistance in microhms per centimetre-
cube at 0C.
Copper (hard drawn) . . .
Iron (annealed)
German Silver
Platinoid
Manganin
Eesista
Beacon
Eureka
Cast Iron
Steel
Graphite
Arc Lamp Carbon
Plumbago and Stour-
bridge Clay, about
equal parts mixed and
well baked.
Saturated Solution of
Sulphate of Copper.
Saturated Solution of
Sulphate of Zinc.
Dilute Sulphuric Acid,
1-2 density.
Sodic Sulphate Solution,
15 per cent. salt.
From
About
About
1-626
9-0
20-0 to 30-0
40-0
42-0 to 46*0
76-0
80-0
40-0
80-0 to 100-0
15-0 to 50-0
300-0 to 400-0
3,000 to 4,000
100,000
29-3 xlO 6
33-7 xlO 6
l-24x!0 6
11-37 xlO 6
microhms.
CHAPTER III.
THE MEASUREMENT OF ELECTRIC CURRENT.
1. Classification of Electric Currents. Electric currents
may be either unidirectional that is, flowing continually in
one and the same direction, or alternating that is, periodi-
cally changing their direction.
The character of a current in a conductor is determined
by the nature of the field of magnetic force associated with
the conductor when it forms part of a circuit in which a
current exists. If the direction of the field when tested
in any manner at any point outside the conductor is always
in the same direction, as indicated, say, by the behaviour of a
small magnet held in the field, the current is said to be
unidirectional or continuous. If the direction of the field
periodically changes, the current in the conductor is said to
be alternating or periodic.
A continuous current may be either uniform or unvarying,
or it may be intermittent or pulsatory. An alternating current
may, in the same manner, be steadily periodic, or it may be
variable and periodic.
Alternating currents are furthermore divided into monophase
and polyphase. In the first case the periodic current exists
in a single circuit ; in the second case the circuit in which
the current is created is a complex circuit, each elementary
circuit of which is traversed by a periodic current, these
various currents differing in phase that is to say, not chang-
ing their directions at the same instant, but preserving a
constant phase difference with respect to each other.
z2
340 THE MEASUREMENT OF ELECTRIC CURRENT.
In the measurement of electric currents we are concerned
with the determination of a quantity capable of having
direction as well as magnitude. The magnitude or, as it is
sometimes called, the strength is measured by the degree
to which some measurable physical effect is produced. The
three most important physical effects accompanying or
constituting an electric current are : (i.) The production of
heat in the conductor; (ii.) the production of a magnetic
field around and in the conductor; and (iii.) the production
of an electrolytic effect in liquid conductors of a certain
kind forming part of the circuit.
Other things being equal, the heating effects of an unvary-
ing current increases as the square of the current when
measured in either of the other two ways. That is to say,
if there be two currents which, when respectively passed
through the same circuit, produce magnetic forces at any one
point in the ratio of 1 : x, they produce in the same time
chemical decompositions of a given electrolyte inserted in
the circuit which, measured by the masses of a liberated ion,
are in the ratio of 1 : x. These two currents, however, will
produce in any part of the conducting circuit quantities
of heat which are in the ratio of 1 : x 2 . Two currents are
said to have the same mean square value if they produce in
the same time and in the same conductor the same total
quantity of heat.
If a current is periodic or alternating, its effective or virtual
value, estimated in its equivalent of continuous current, is that
of the unvarying and unidirectional current which will pro-
duce in the same conductor the same heat in the same time.
This effective value is also called the root-mean-sqiiare (RM.S.)
value, because it is equal to the square root of the mean of
the squares of the instantaneous current values taken at
equidistant and very near intervals of time throughout one
complete cycle. The true mean (T.M.) value of a current is
the arithmetic mean of its instantaneous values taken at
equidistant intervals of time throughout any period.
THE MEASUREMENT OF ELECTRIC CURRENT. 341
We have, therefore, three methods of measuring a current,
which may be called respectively the thermal, the magnetic,
and the chemical methods.
The definition of the absolute unit of current in magnetic
measure is thus given :
Let a thin conducting wire be bent into a circle having
a radius of r centimetres, and let the pole of a very long
linear magnet of strength m be placed at the centre, the
other complementary pole being at a considerable distance.
Then, if the mechanical force on the magnetic pole placed
at the centre is measured in absolute units of force (in dynes),
and is represented by /, the absolute magnetic measure of the
current (C) is determined by the relation
The absolute electromagnetic (C.G.S.) unit of current is
therefore the current which, when circulating in a circuit of
unit radius, exerts on a unit magnetic pole placed at the
centre a force of 2?r dynes. The practical unit of current
(the ampere) is one-tenth of the above electromagnetic unit
in magnitude.
The Standard or International Ampere, as already explained, has been
officially defined as the current which, when passed through a solution of
nitrate of silver, made according to a certain specification, deposits 0*001118
of a gramme of silver per second on the cathode.* As previously pointed out,
there is reason to believe that the unit of current called the International
ampere is smaller by about 1 part in 1,000, or 1 part in 800, than the unit of
current or ampere defined as one-tenth of the absolute C.G.S. unit of current.
This view is confirmed by the discrepancy between the values of the mechanical
equivalent of heat, or, as it should be called, the dynamical value of the
specific heat of water when determined mechanically and electrically. In the
determination of the above equivalent by electrical methods, values obtained
by Griffiths exceed those of Rowland, made by mechanical or frictional
methods, by about 1 part in 400 at all temperatures between 15deg. and 20deg.
on the nitrogen gas thermometer siale. Those of Schuster and Gannon exceed
those of Rowland at 19'ldeg. on the same scale by 1 part in 500. Since the
current enters as a square, it follows that the above discrepancies would be
reconciled by the substitution of O'OOlllQl or 0-0011194 for the electro-
chemical equivalent of silver, instead of O'OOlllS, as now adopted.
* For the electro-chemical equivalents of other metals see Table II., p. 420,
at the end of this chapter.
342 THE MEASUREMENT OF ELECTRIC CURRENT.
A careful series of experiments by Patterson and Guthe at Michigan in
1898,* showed that the most probable value of the ampere-second silver
equivalent is 0*0011192 gramme, and hence a corresponding change must be
made in the E.M.F. at 15C. of the Clark cell, which is thereby reduced to
1'4327 International volts, instead of 1'4342, as now accepted.
Dr. K. Kahlef has investigated carefully the silver voltameter, and finds
that the electro-chemical equivalent obtained for silver varies slightly with
the age of the nitrate of silver solution. He states that with a freshly pre-
pared solution the ampere-second equivalent is very nearly 0'001182 gramme,
and with an old solution 0*001193 gramme. Some small degree of uncertainty
therefore exists as to the actual relation between the International and the
True or theoretical ampere, similar to that which occurs in the case of the
International and True ohm.
2. The Measurement of Current by the Electrolysis
of a Solution of Copper Sulphate. Standardisation of an
Ammeter. The employment of a solution of sulphate of
copper as the electrolyte enables an electrochemical deter-
mination of a current to be made with less initial outlay than
when silver is used. With certain precautions a high degree
of accuracy can be obtained. In order that any great degree
of exactness may be reached in the measurement of a current,
it is essential that the current shall be as nearly as possible
constant. To standardise an ampere-balance or ammeter
that is to say, to determine the true value in international
amperes corresponding to an observed scale reading we
proceed as follows :
The current should be provided from large secondary
cells which have been slightly discharged that is, about
10 per cent, of their full charge taken out. The ammeter or
ampere-balance to be standardised should be joined in series
with the cells and with a regulating wire resistance and a
carbon rheostat (see page 81), by which to make very small
variations in the resistance of the circuit:
This circuit must also include an electrolytic cell contain-
ing a solution of sulphate of copper. The electrolytic cell
found most convenient is a round glass jar about 30cm. high
* See Proc. Amer. Assoc., 47, pp. 154-175, 1898 ; also Science Abstracts^
Vol. II., pp. 39 and 762.
t Zeitschr. Instrument^., 18, 1898, pp. 229-240 and 267-276.
THE MEASUREMENT OF ELECTRIC CURRENT. 343
and 20cm. in diameter. This is placed on a slab of wood
at the sides of which are two vertical wooden rods carrying
brass forked strips which project over the top of the jar
(see Fig. 1). One of these forks may have three prongs
and the other one two. To these prongs are clamped by
brass clamps the copper anode and cathode plates. Each
plate can be separately removed from the solution. It is
convenient to make the two-prong brass fork the cathode.
To these forks large screw terminals are attached. The
solution placed in the electrolytic cell is made by dissolving
ioh~fol~~fol"
FIG. 1. Voltameter for Current Measurement by the Electrolysis of
Copper Sulphate.
pure re-crystallised sulphate of copper in distilled water
until a density of 1*15 or 1*18 is obtained. One per cent.
by volume of pure sulphuric acid is then added. This
addition of free acid is absolutely necessary to obtain good
results. No satisfactory determinations can be made with
neutral solutions of sulphate of copper. In any case the
density of the solution should be between I'l and 1*2.
The copper plates should be cut from high-conductivity
pure electrolytic copper, and should be 15cm. long and
5cm. wide. The corners of the plates should be neatly
344 THE MEASUREMENT OF ELECTRIC CURRENT.
rounded off and all burr on the edges removed. Each
plate should be stamped with a number in one corner for
recognition, and have a hole near the top edge by means of
which the plate can be handled with a wire hook.
The number and size of these plates to be employed in
each experiment is determined by the current to be measured.
To obtain an adherent and regular deposit of metal on the
cathode plate, it is necessary that the surface exposed should
exceed 20 sq. cm. per ampere. An exposed cathode surface
of 50cm. per ampere gives excellent results.*
If, then, the cathode plates are of the dimensions above
given and are placed in the electrolyte 10cm. deep, the
exposed surface on each plate, assuming both sides used,
will be 100 sq. cm., and each plate will be good for
2 amperes. The plates selected as cathodes have then to
be clamped to the cathode fork so that each row is included
between two rows of anode plates, and the number so selected
that the above-mentioned current density is not exceeded.
These preparations being complete, the cathode plates have to
be very carefully cleaned and weighed. The cleaning is best
performed by placing the plates in a flat porcelain dish and
covering them with strong commercial nitric acid. This
immediately evolves copious nitrous fumes, which are very
deleterious, and hence the process should be conducted in the
open air or in a well-ventilated fume cupboard. The experi-
mentalist should carefully avoid inhaling the nitrous vapours.
The plates having been left in the acid for a few minutes,
or until the acid boils violently, are fished out by the aid of
a stout copper wire and dropped into a large jug of clean
water. Each plate should then present a clean, bright salmon-
coloured surface, without a trace of brown oxide upon it on
either side. If the plates are newly cut from sheet copper it
will generally be necessary to give them a good scouring with
emery-cloth and water before treatment with the nitric acid.
* See Mr. A. W- Meikle, " On the Electrolysis of Copper Sulphate in Stan-
dardising Electrical Instruments." Proc. Phys. Soc. of Glasgow University,
Jan. 27, 1888.
THE MEASUREMENT OF ELECTRIC CURRENT. 345
Unless the plates are chemically clean the electrolytically
deposited copper will not adhere to them.
The plates, having been cleansed and washed copiously,
are then to be dried between clean white blotting paper as
quickly as possible, and completely dried in an air oven
or in a dessicating vessel. When thoroughly dry, each plate
must be weighed on a good chemical balance, and its weight
recorded. In so doing, the plate must not be touched with
the fingers, but be handled by a clean copper wire thrust
through the hole in the plate. When dried and weighed
the plates should, as soon as possible, be placed in the
electrolytic cell and the experiment commenced. The circuit
must be completed so that the same uniform current flows
through the ammeter to be calibrated, and the electrolytic
cell and the weighed plates must be made the cathode or
negative pole of the cell so that the current deposits copper
upon them. The time when the circuit is closed must be
noted on a good chronometer, and the current must be kept
perfectly constant, as indicated by the observed reading of
the ammeter, for a time varying from one to four hours.
The circuit is then opened, and the time of so doing is noted.
The weighed plates should then at once be removed from
the electrolytic cell, be washed copiously in water, and be
again dried and weighed. The deposit of electrolytic copper
should be a bright, clean and adherent film of metal. The
increase in weight of each plate is noted, and the total
deposit of copper in an observed time thus found. The
increase in weight in grammes per second can then at once be
calculated, This last figure, divided by the electro-chemical
equivalent of copper, gives the mean value in amperes of
the current, or true time average of the current during the
experiment.
It was found by experiments conducted in Lord Kelvin's
laboratory at Glasgow University that the electro-chemical
equivalent of copper varies with the temperature of the
electrolyte and with the current density. Hence, in reckoning
346
THE MEASUREMENT OF ELECTRIC CURRENT.
out results the proper electro-chemical equivalent must be
employed as given by Mr. Meikle. The electrochemical
equivalent in grammes per ampere-second is a number not far
from 0-000328, and it diminishes very slightly both with rise
of temperature and increase of cathode surface per ampere.
The Electro-chemical Equivalent of Copper in grammes per
ampere-second.
Area of cathode
surface in
square centims.
per ampere.
Temperature of electrolyte.
2C.
12C.
23C.
28C.
35C.
50
100
150
200
250
300
0003288
0003288
0003287
0003285
0003283
0003282
0003287
0003284
0003281
0003279
0003278
0003278
0003286
0003283
0003280
0003277
0003275
0003272
0003286
0003281
0003278
0003274
0003268
0003262
0003282
0003274
0003267
0003259
0003252
0003245
If accurate results are to be obtained, the following precautions must be
taken in the employment of the copper voltameter as a means of measuring
the time integral of a continuous current :
No satisfactory results can be reached unless the copper sulphate solution
contains free sulphuric acid. On the other hand, copper plates placed in this
solution lose in weight at a rate depending on their immersed surface. The
plates must, therefore, be most carefully freed from all traces of oxide before
being used as the weighed places. The anode plates should also be cleaned,
but it is not necessary that they should be of such pure copper as the
cathode plates. If, however, the electrolyte is to be frequently used, it is
desirable to employ electrolytic c >pper for both sets of plates. It is
important to round off the edges and make the cathode plates very smooth,
so as to avoid producing a rough deposit of copper or one nodulous or uneven
The plate is then not so easily dried, and there is a risk of small particles of
copper being detached.
It need hardly be said that in conducting the observations a good and
correct watch or chronometer must be used for determining the time durin g
which the experiment lasts.
The copper voltameter may be advantageously employed in evaluating a
steady continuous current and in standardizing an ampere-balance, but it is
not so well adapted for current measurement when the current cannot be
kept constant for considerable periods of time.
With the above precautions, however, there is not the slightest difficulty in
determining the true value of a steady unidirectional current of the order of
10 amperes to within one quarter per cent., and with a little care to within
one part in a thousand.
THE MEASUREMENT OF ELECTRIC CURRENT. 347
3. The Measurement of Current by the Electrolysis
of Silver Nitrate. The measurement of the time integral
of a current when the current is of the order of about one
ampere or so, is best effected by the employment of a solution
of nitrate of silver, as silver has a higher atomic weight than
copper, and, moreover, is a monad element. Hence the mass
of silver deposited by a given current is nearly three times
that of the copper deposited in the same time. Accordingly
there is more mass to weigh, and hence, on that account, a
greater possibility of accuracy when dealing with small
currents.
On the other hand, the materials used are expensive
compared with the copper method, and there is con-
siderably greater difficulty in washing and drying the
silver deposit. From a neutral or nearly neutral solution
of silver nitrate the deposit of silver on a platinum cathode
is apt to be nodulous, crystalline or non-adherent. This
irregular deposit occludes small particles of the salt or
solution and it is not easy to wash the deposit so as to
secure perfect removal of the salt without washing away
some of the metal.
The full detailed specification for performing the operation
of electrolysis of silver nitrate in current measurements has
already been given (see Chap. I., p. 57), hence there is no need
to repeat the details.
A very careful investigation by Dr. K. Kahle (see Science Abstracts, Vol. II.,
p. 41, or Zeitschr. Instrumentk., 18, p. 229, 1898), was conducted with the
special object of seeing how far the silver voltameter can be relied upon
for standardising current. In the course of 115 measurements the amount
of silver deposited by the same current acting for 40 minutes varied
from G'97134 grammes to 0'97473 grammes. With great care an accuracy
of 1 part in 10,000 can be obtained. A clean platinum surface receives
rather less deposit than an existing surface of silver, and fresh solutions of
silver nitrate deposit less easily than old ones. To free the silver deposit of
all silver nitrate solution repeated cold water washing and one final washing
in water at 80C. is necessary.
Dr. Kahle' s value for the mass of silver deposited per ampere-second is
0-0011193 from an old solution and '0011182 from a freshly- prepared
solution.
348 THE MEASUREMENT OF ELECTRIC CURRENT.
The reader is referred for further information to the
following original Papers :
LORD RAYLEIGH and MRS. SIDGWICK. " The Electrochemical
Equivalent of Silver." Phil. Trans. Roy. Soc. Lond.,
1884.
K. KAHLE. "The Silver Voltameter and Standard Cells."
ZeiUchrift fur Instrumentenkunde, 18, 1898, pp. 229, 267.
H. S. CARHART. " Standards of Measurement." Science, 8,
p. 326, 1898.
G. W. PATTERSON and K. E. GUTHE. " Electrochemical
Equivalent of Silver." Proc. Amer. Assoc., 47, p. 154, 1898.
T. W. RICHARDS, E. COLLINS and G. W. HEIMROD. " Electro-
chemical Equivalents of Silver and Copper." Proc. Amer.
Acad., 35, p. 123, 1899. Science Abstracts, Vol. III., p. 332.
G. F. C. SEARLE. " The Silver Voltameter." The Electrician,
Vol. XXIX., p. 111., 1892.
Mr. Searle here discusses the various advantages and disadvantages in
using different salts of silver.
FIG. 2. Silver Voltameter for Current Measurement.
The practical details to which attention must be directed
in making a current determination by the silver voltameter
are referred to in the above-mentioned article by Mr. Searle.
The deposit is best made upon the internal surface of a
carefully cleaned platinum bowl (see Fig. 2). The anode
should be a plate of pure silver wrapped in white filter paper.
THE MEASUREMENT OF ELECTRIC CURRENT. 349
The washing, drying and weighing of the silver deposit are
to be conducted in accordance with the specification given
on p. 58, Chap. I. of this volume.
4. Standard Current Measuring Instruments. Although
the official or practical method of determining the value of a
current is based upon an electrolytic definition, it is more
convenient in ordinary work to rely upon a standard current
measuring instrument which operates in virtue of the mag-
netic properties of a current-conveying conductor. These
instruments may be of such a form that the absolute measure-
ment of a current can be made when the geometrical form of
the circuits is determined. In this case it is called an absolute
standard current-measuring instrument. Of this type are-
the absolute tangent galvanometer, or the absolute electro-
dynamometer or absolute current balance.
On the other hand, the instruments may be so constructed
that, whilst the same current invariably gives the same-
indication, the ampere or absolute value of the current cannot
be determined until the instrument has been standardised by
passing through it a current the value of which is electro-
lytically determined. To this latter class belong the various
forms of ampere-balance and standard electro-dynamometer
already described in Chap: I.
It will seldom happen that it is necessary in an ordinary
electro-technical laboratory to make an original re-determina-
tion of the unit current by means of an absolute instrument,,
but it may be convenient to collect here a few elementary
principal facts involved in the construction of absolute
galvanometers.
Magnetic Fields of Current-conveying Conductors of Various
Forms. (i.) Single Circular Conductor. If a very thin wire
is bent into a circle of one turn, the mean radius (r) of
the circle being large compared with the diameter of the
wire, and if a uniform current is sent through the conductor,.
350 THE MEASUREMENT OF ELECTRIC CURRENT.
the magnetic force (F) in C.G.S. units at the centre is given
by the expression
where A is the current in amperes through the conductor and
r is the mean radius of the circle in centimetres. If the
point P selected is not at the centre of the plane of the
circle, but is a point on the axis or line drawn through that
centre at right angles to the plane of the circle, and distant x
centimetres from the centre, then the magnetic force there is
given by the expression
r J^A r-
*~~ 10 (r 8 +*)*'
If we write ^for \/r 2 +# 2 , the above becomes
F _27rA r 2
= 10 u*
where A is the current in amperes through the coil. The
above formula may also be written
where 6 is the angle subtended by the radius r at the point P.
The expression for the magnetic force due to a circular
current at a point not on the axis is more complicated, and
for the detailed proof of the following formulae the reader
must be referred to other sources of information. (See
Mascart and Joubert's " Electricity and Magnetism," English
translation by Atkinson, Vol. II., p. 90, 736 et seq.)
Let r be the radius of a thin circular wire carrying a current, and x and y
the co-ordinates of a point P outside its plane, the centre of the circle being
the origin and the axis through the centre perpendicular to the plane of the
circle taken as the axis of x. Let X and Y be the components of the
magnetic force at P parallel respectively to the axes of x and y, when one
absolute or C.G.S. unit of current ( = 10 amperes) flows through the wire. Let
M 2 =r 2 +a; 2 , as above. Then it can be shown that, if y is small compared
with u, we have, approximately,
THE MEASUREMENT OF ELECTRIC CURRENT. 351
The above expressions hold good on the assumption that powers of the
ratio y/u above the fourth may be neglected.
The resultant magnetic force at the point P outside the axis is given by
the value of N /X 2 + Y 2 , and the inclination 6 to the a-axis by tan 6 = Y/X.
If the point P is taken in the plane of the circle, then the force at any
point not far removed from the centre by a distance y is given by making
# = in the above expressions for X and Y. We have then, approximately,
4r 5
Y=0.
The above formulas are only true when y is, very small compared with r.
When this is not the case Y is no longer zero.
(ii.) Solenoid. Let insulated wire be wound closely in one
layer over a cylinder of length 21, so as to cover the whole
cylinder. Let r be the mean radius of one circular turn.
The magnetic force at any point on the axis of the cylinder
may be considered to be the sum of the actions due to a
number of circular currents. Take the centre of the cylinder
FIG. 3.
as origin, and consider the force at a point P (see Fig. 3) on
the axis due to one single circular turn at C occupying a
length Sx on the cylinder. Let the distance CP = x. Suppose
there are N turns of wire on the cylinder ; then the number
of turns per unit of length is N/2J, and the number in a length
$x is-^r^' Hence the magnetic force in absolute units due
to this single turn when a current of A amperes traverses the
wire is given by the expression
df
201
v i "" j
Accordingly, the magnetic force at P due to the whole
solenoid is
352 IHE MEASUREMENT OF ELECTRIC CURRENT.
where #=the distance of P from the nearest face of cylinder
=AP.
Omitting the constant of integration the value of the integral
x
Let us call the above integral the cosine of an angle, say 0.
Hence,
2xNA/ a+2l a \ 27rNA
~M-U*+(a+2/)s -V^r~20r )S *~ )S *')>
where and <' are the angles subtended by the radii of the
two circular ends of the cylinder at P.
Suppose we take the point P in the centre of an infinitely
long solenoid, and call the length of the cylinder L. Then
cos < approximates to 1 and cos <' to 1 . Hence, at the
centre of the long solenoid we have a magnetic force F given
by the equation
-p _ 47rNA _ 1 i ampere-turns
= TOL~" length
Or, the magnetic force in the centre is equal to 47T/10 times
the ampere-turns per unit of length of the solenoid.
The above equation holds true approximately for a solenoid
the length of which is, say, 20 times its diameter except at
regions close to the ends.
It is easily seen that, in the case of a long solenoid, the
force at the centre is just double that at the mouth or
entrance to the solenoid, taking the points on the axial line.
The above formula is also very nearly true for a self-closed
or endless solenoid. The calculation of the magnetic field at
points not on the axis outside cylindrical solenoids or circular
conductors conveying currents involves mathematical pro-
cesses of a difficult kind, and the reader must be referred to
advanced treatises on the subject.
5. Absolute Galvanometers. An absolute galvanometer
consists of a coil of insulated wire wound in such a form that
THE MEASUREMENT OF ELECTRIC CURRENT. 353
the field due to a current through it can be calculated at an
assigned point. If this coil is arranged so that the coil field
at the stated point is at right angles to a known and constant
field, such as that of the earth, at the same point, then the
ratio of these field strengths can be determined by placing at
that point a small magnetic needle and observing its direction.
Let C (Fig. 4) be a circular coil of wire, and let F be the
magnitude and direction of its field at the point P. Let the
coil be arranged so that F is at right angles to the magnetic
field H due to the earth ; then if a small magnetic needle is
suspended freely at P, it will set its axis in a direction
inclined to the magnetic meridian by an angle 6, such that
FIG. 4.
F/H tan 0. The current through the coil, reckoned in
amperes, is proportional to the magnetic force F at any point.
Hence, if G is a constant depending on the geometrical form
of the coil, we may write
F = GA.
Hence,
G
The quantity H/G- is called the galvanometer deflectional
constant.
Accordingly, if the space distribution of magnetic force
due to the current in the coil is of such a nature that every-
where in the region occupied by the magnetic needle it is
at right angles to the magnetic force due to the earth and of
AA
354 THE MEASUREMENT OF ELECTRIC CURRENT.
constant value, the deflections are strictly proportional to the
tangents of the angles of deflection, and the instrument is
called a tangent galvanometer.
Suppose, for instance, that an exceedingly large circular coil of wire of one
turn has a very small horizontal magnetic needle hung exactly at the centre
of the coil. Let the needle not exceed in length one-hundredth of the
radius (r) of the coil. Let the coil be placed with its plane in the magnetic
meridian. Then the magnetic force F at the centre of the coil due to a
2?r A
current of A amperes flowing in the wire is F = j~ - Hence, for this coil
G = 2?r/10r ; and if the magnetic needle takes a deflection under a terrestrial
horizontal force H we have A= * tan 6.
2ir
An arrangement of this kind constitutes an absolute tangent galvanometer,
because we can determine the value of the current absolutely from measure-
ments of r H, and 0.
Consider next the case when the magnetic needle is placed with its centre
at a point on the axis outside the plane of the circular coil of one turn, and has
aO
60
a length not very small compared with the radius of the coil. Let the current in
the wire be 10 amperes or a unit (C.G.S.) current. Let ab (Fig. 5) be the coil seen
in section and let the magnetic needle ns have a length 2 and be placed with
its centre at P, at a distance x from the centre of the coil. Let each pole
of the needle have a strength, m. Then each pole is acted upon by two
forces wXi mY 1} ?ftX 2 mY 2 , the values of X and Y being determined by the
co-ordinates of the pole, and areas stated in equations (i) and (ii) in 4 on p. 350.
This system of forces resolves itself into one resultant force and one resultant
couple. If, however, the centre of the neeile is constrained to remain at P,
then we need only consider the couple. This couple may be called D, and it
has a value such that
D = ml (X x + X 2 ) cos - ml (Yj + Y 2 ) sin 0.
By substituting the proper values of Xj. YI, &c., obtained from the equations
above mentioned on p. 350, it is not difficult to show that
1):
D
4
"64
THE MEASUREMENT OF ELECTRIC CURRENT. 355
la the above equation r is the radius of the coil and u? = r 2 + x z , and it is
assumed also that I is so small compared with u that we may neglect powers
above the fourth of the ratio l/u. Also, M is written for 2ml or the moment
of the magnet.
If the coil is placed with its plane in the magnetic meridian, then the
opposing or controlling couple due to the earth is MH sin 0. If the coil
consists of many turns of insulated wire wound on a square-grooved circular
frame, then in place of the factor 2?r-j we have to write a more complex
function G, which is obtained as follows :
Let the windings of the coil be in a square groove having a length 26
parallel to the axis of x and a depth 2c = r"-r' parallel to the radius of the
coil. Let there be n turns of wire per unit of length of the groove. Consider
first, one single layer forming a short solenoid or diameter 2r. It has already
been shown that the magnetic force at P due to unit current in this coil
would be expressed by
. . ,-
r 2 + (x + 6) 2 V r 2 + (x -
To obtain the magnetic force due to the whole of the windings we have to
integrate the above expression between the limits r=r" and r = r' and obtain
the value of Gr from the expression.
G = 2irn a
Keturning to the expression for the value of the couple D
exerted by the unit current on the needle placed with its
centre at P. It is seen that if the ratio l/u is so small that
we can neglect powers of it above the second, then we can
make the correcting factor in the square bracket due to the
finite length of the needle reduce to unity, either by making
45C 2 = r 2 or by making 1 5 sin 2 $=0.
The first condition is complied with by placing the centre of
the needle at a distance from the plane of the coil equal to
half the radius r, and the second by making the reading
as nearly as possible in the neighbourhood of the angle
= VE =
AA2
356 THE MEASUREMENT OF ELECTRIC CURRENT.
We may, then, summarise the above results as
follows :
If a coil of insulated wire wound in a square-sectioned
groove is placed with its plane in the magnetic meridian, and
is traversed by a current of A amperes, it exerts a magnetic
couple on a needle placed with its centre at a point on
the axis of the coil which is determined by the equation for
D given at the bottom of p. 354 Let this equation be written
where G is the coil constant or value of the magnetic force
due to unit C.G-.S. current (10 amperes) in one turn of the coil
at a point on the axis, and K is a correcting factor for the
distribution of the force at points not on the axis. This
couple is balanced against the couple MH sin due to the
action of the terrestrial magnetic force on the needle. Hence
we have
A _10Htan0
=
If the needle is placed with its centre at a distance from the
plane of the coil equal to r/2, then the correcting factor K is
reduced to a value
on the assumption that powers of l/r above the fourth may
be neglected. If the length of the needle is not greater than
say one-twentieth of the mean radius of the coil, then K
becomes sensibly zero and the tangents of the deflections of
the needle are proportional to the currents flowing through
the coil.
If the tangent galvanometer consists of a single circular
coil of mean radius r, and having the wire wound in n turns
in a square-sectioned groove of widtli 2a and radial depth 21,
also haying a magnetic needle of length 21 placed at us\
THE MEASUREMENT OF ELECTRIC CURRENT. 357
centre, the value for the current in amperes (A) creating a
deflection is approximately given by the equation
A lOrH /-, . I a 2 1 b* 3 / 2 \ A , 15 Z* . 2 <\ .
A = _ M+ _ _ JM + _sm 2 0) tana
2wn \ 2 r- 3 r 2 4 r 2 / \ 4 7^ /
In the above equation it will be sufficient to take 21 as
equal to 0*82 of the full length of the magnetic needle.
(See F. Kohlrausch, " Physical Measurements.")
A tangent galvanometer of the above type is employed
generally in the Postal Telegraph Department.
Helmholtz Standard Tangent Galvanometer. A better
and more practically convenient form of tangent galvano-
meter is that devised by Von Helmholtz. In this instru-
ment there are two large circular coils of insulated wire, the
wire being either wound in a square groove in the edge of a
wooden ring or wound in one layer on the edge of a ring
which forms the frustrum of a cone. These coils are fixed at
a distance apart equal to the mean radius of either coil of
wire. If the wire windings lie on the frustrum of a cone the
cone angle is selected so that the apex of the cone is the mid-
point between the coils. Every turn of wire then complies
with the condition that it is separated from another equal
circular turn in the other coil by a distance equal to the
radius of either. This latter arrangement of the winding is
most suitable for an absolute instrument. These coils are
fixed to a base so that, whilst remaining at the fixed distance
apart, they can be turned round on axes perpendicular to and
passing through the mid-point. At the middle point is
placed a compass-box containing a short magnetised needle
having attached a long aluminium index needle moving over
a circular scale of degrees. Otherwise the magnetic needle
may be suspended by a fibre of cocoon silk and have attached
to it & mirror. If the compass needle has the ordinary jewel
centre suspension some device should be added to lift the
needle off its pivot when not in use. The length of the needle
should not exceed one-twelfth of the radius of either coil.
358 THE MEASUREMENT OF ELECTRIC CURRENT.
To use the instrument it is placed at a distance from all
iron or magnets, and the current to be measured is conveyed
to it through a length of concentric cable, or through insulated
wires twisted together. The current then flows through the
coils in such a manner as to produce a uniform field in the
space between the coils. The needle then takes a deflection,
the tangent of which is proportional to the current. The
instrument must be so oriented that if the current is reversed
the angular deflection of the needle from the plane of the
meridian is in both cases the same in amount though opposite
in direction.
If, then, the dimensions and disposition of the windings is
known, the value of the current can be calculated when the
magnitude of the earth's horizontal magnetic force H is
known at that place. Yery roughly speaking, this has a value
lying between 0*15 and 0*18 C.G.S. units in Great Britain ;
but its value at any given spot in a laboratory may be greatly
affected by the neighbourhood of iron pipes or masses of iron.
Hence, a standard tangent galvanometer can only be employed,
for purposes where accuracy is required, in a special room set
apart for its use and where facilities also exist for determining
the value of H as often as required. This constant can,
however, be determined with a fair degree of approximation
as follows :
Provide a cylinder of steel carefully magnetised longitudi-
nally and measure (in cms.) its length I and mean diameter d.
The moment of inertia I of this cylinder round an axis through
its centre and perpendicular to its own axis of symmetry is
12 + :
where W is the weight of the cylinder in grammes. If this
cylinder is suspended in a paper stirrup by a few threads of
floss silk and set in vibration round a vertical axis, it is easy
to determine, from the time taken to execute, say, 50 complete
vibrations, the time t of one vibration. If, then, M is the
THE MEASUREMENT OF ELECTRIC CURRENT. 359
magnetic moment of the magnet, it can be shown that
t = 2 7r ^/^-.*
Hence, MH=^.
Then let this magnet be placed in a position with its axis
in a horizontal line passing at right angles to the meridian,
through the centre of the tangent galvanometer needle, and
with its centre at a distance D centimetres from the needle-
pivot. Observe the deflection produced on the galvanometer
needle. It can be shown that
M DV, .ItfV 1
= I j_ + - i
M_D 3 /.
H~~2V
2DV tan0 '
where L is the " magnetic length " or distance between the
poles of the cylindrical magnet and D the distance of the
centre of the deflecting magnet from the centre of the
galvanometer needle ; and the assumption is made that L/D
is a quantity so small that its squares and higher powers can
be neglected.
From the two equations for MH and M/H we can find at
once the value of H, by taking two sets of observations with
the magnet at different distances, D 1 and D 2 , from the
galvanometer needle and then eliminating L from the two
equations so obtained, viz. :
M I
M
from which L may be eliminated.
The above equations may be written
"
* See the Appendix of a book entitled "Magnets and Electric Currents,
by J, A, Fleming.
860 THE MEASUREMENT OF ELECTRIC CURRENT.
from which we obviously have
M_ 1 D^tan^ D 2 5 tanfe
H~2 IV-D 2 2
Hence the ratio M/H is easily calculated when D r D 2 , 9 V 62
are found.
Having, then, the value of the ratio M/H and that of the
product MH, we obtain at once the value of H.
The values of G (the coil constant) having been calculated
as already explained, and H determined as described for the
locality, we can obtain the ampere value of a current creating
any observed galvanometer deflection.
Standard galvanometers in which fixed coils and magnetic
needles are used are, however, almost useless as exact measur-
ing appliances unless placed in buildings set apart for the
purpose, into the construction of which no iron enters. In
ordinary laboratories warmed with iron hot-water pipes or near
engines and boilers or machinery, the value of the local
terrestrial magnetic force is so constantly varying in amount
and direction that the standardization of the instrument
changes almost from moment to moment. Hence the use
of the tangent galvanometer under these circumstances as an
instrument of precision is as impossible as would be the use
of the balance if the mass of the standard weights of com-
parison were changing from moment to moment.
6. The Electro -dynamometer. A most valuable substi-
tute for the standard galvanometer in the precise measurement
of current is the standard electro-dynamometer. In this
instrument, as in the commercial form, there are two coils
of wire, one fixed and the other movable. In standard
instruments both these coils take the Helmholtz form that
is to say, they consist of two equal separate circular coils
placed with their planes parallel to one another and fixed at a
distance equal to the radius of either. The movable coil is
suspended by a bifilar suspension consisting generally of the
THE MEASUREMENT OF ELECTRIC CURRENT.
361
two wires by which the current enters and leaves this movable
coil. The coils are held normally with their axes at right
angles and centres coincident. When one and the same
current is passed through the coils, the electrodynarnic forces
tend to turn the coils so that their axes are more in the same
direction, and this torque is resisted by the bifilar torque.
The theory of the electro-dynamometer has been given by
Clerk Maxwell (see "Electricity and Magnetism," Vol. IT.,
p. 337, 2nd edition). The reader is also referred to an
excellent series of explanatory articles by Mr. G. R C. Searle,
FIG. 6.
on the determination of current in absolute measure in The
Electrician, Vol. XXVII. and Vol. XXVIII, for 1892. From
these sources the following abbreviated analysis has been
taken :
Consider, in the first case, the electro-dynamometer to
consist of two coils only (see Fig. 6).
Let the inner coil a be the suspended coil, and let its
diameter be small compared with the outer or fixed coil A.
Let G be the galvanometer constant of the large coil, i.e., the
magnetic force at the centre due to unit absolute current
362 THE MEASUREMENT OF ELECTRIC CURRENT.
flowing in it. Hence, if i is the current flowing in both
coils when joined in series, the magnetic force over the central
region of the large coil is nearly equal to Qi.
Let g be the total area enclosed by all the windings of the
small coil ; then gi is the magnetic moment of the small coil.
Hence, when the latter is held so that the angle between the
axes of the coils is <f>, the magnetic couple or torque on the
small coil is i 2 Gg cos 0. If the large coil is placed with its
plane in the magnetic meridian there is also a couple due to
the earth's force acting on the small coil and equal to giK sin 0.
The bifilar suspension produces a restoring couple, which may be represented
by ju sin 0, since for small angular displacements it is proportional to the sine
of the displacement. Hence the equation of equilibrium of the small coil,
hung in a uniform magnetic field H and supported by a bifilar suspension, is
i 2 Gg cos <f> = igU sin + P sin fa
or tan = i 2 Gg/(igH + ft).
It is always possible to make th eterm igR negligible compared with /j. ; so
that approximately we have
If we then take four observations of the deflection of the small coil, first by
reversing the direction of the current through the small coil alone and then
through the large one alone, and call the several observed angular displace-
ments of the small coil fa, 02, 03> 04> it is easy to see that, since
tan 0! =
and tan 2 =
we have & = (tan fa + tan 2 W2G# ;
and therefore, also,
i 2 = (tan 0! + tan 2 - tan 3 - tan 4
Hence, i is determined in terms of the tangents of the deflections and the
constants of the instrument, viz., M, G and g.
The constants for any instrument can be found as follows : Let M be the
mass of the suspended coil. Then /* = XM. Let T be the time of a small
vibration of the suspended coil, and K its moment of inertia. Then
m <
1-u,,*, XM -
Affix to the movable coil a bar of mass M', of which the moment of inertia
K' is known, and observe the time T' of a small vibration of the new system.
Then,
Hence, from the two above equations, we have
47r 2 K'M
/* =
M(T' 2 -T 2 ) + M'
THE MEASUREMENT OF ELECTRIC CURRENT. 363
In the next place, we have to determine G and g. Suppose the fixed coils
have the Helmholtz form, and consist of two coils of mean radius A fixed with
centres at a distance B = A/2. Then the magnetic force at the central region
for unit current in the coils = G is such that
n _ 47rnA 2
\j __ _-
or, if B = A/2, G = - 32?m
Also, g stands for the total area included by all the windings of the small
coil. If a is the mean radius of the small coil that is, the radius from the
centre to the centre of gravity of the windings, it can be shown that
where h is the radial depth of the windings supposed to be placed in a
rectangular groove, and n' is the number of turns.
If we substitute the above values of n, G and g in the equation for i, we
arrive at the following result :
2 _ *jv\ ft. / A 2 M'A
where the symbols have the meanings below :
x = observed scale deflection.
d = distance of scale from mirror on movable coil.
B=half distance of fixed coils.
A = mean radius of fixed coil.
a = mean radius of movable coil.
M = mass of movable coil.
M' = ma<3s of inertia bar.
K' = moment of inertia of the above bar.
T,T' = times of vibration of movable coil with and without inertia bar.
n,n' = number of turns of wire on fixed and movable coils respectively.
Maxwell gives (" Electricity and Magnetism," Vol. II.) the full theory of
the action of one circular coil upon another, and shows that if there be two
circular coils whose axes intersect at an angle 0, then the co-efficient of
mutual induction M can be expressed in a series of zonal harmonics, such that
M = GiiP 1 (0) + G 2 2 P 2 (0) + &c., where the constants are G 1} G 2 , &c. The
quantities P 1} P 2 , called zonal harmonics, are functions of cos 6 of the form
P (0) = l, Pi(0) = cos0, P 2 (0)=i(3cos 2 0-l), P 3 (0) = |(5cos 3 0-3cos0), &c.,
and have been tabulated and calculated out numerically for various values
of 0.*
The quantities GI, G 2 , &c., are found as follows : Maxwell shows (loc. cit.)
that if any point be taken on the axis of a circular current, the magnetic force
See Prof. John Perry, Phil. Mag., Dec., 1891,
364 THE MEASUREMENT OF ELECTRIC CURRENT.
at that point, F, due to unit current in the coil can be expressed in terms of
the distance x of the point from the centre and certain functions of the radius
of the coil and the distance of a point of reference on the axis. Consider the
case of a circular current of radius A, and take any point as origin on the
axis at a distance B Let C 2 = A 2 + B 2 . Then the magnetic f orce F at any
point at a distance x from the centre of the circle where x is small compared
with C may be expressed by
F = GI + 2G 2 a- + 3G 3 aj 2 + &c. ;
or, if x is large compared with C, by
F= 2^ 3^ %3
Off* a 4 X 5
We have already shown that the magnetic force at a point at distance x
from the centre on the axis of a circular current is given by the formula
27TIA 2
F= - a-
Hence, if we expand the above expression in ascending or descending powers
of x and equate the co-efficients to those of the above series, we have the
values of G and g as follows :
G 1 = 2 7 rA 2 /C 3 , G 3 =47rA 2 (B2 - |A 2 )C 7 ,
G 2 =37rA 2 B/C 5 , G 4 =57rA 2 B(B 2 - f A 2 )/C 9 .
- |A 2 ).
Now in the Helmholtz pattern electro-dynamometer, when we are considering
the magnetic force at the centre, we have B = A/2, and, as a consequence, all
the terms vanish in the expansion for M between the first and fifth. In
other words
M = Gtf ^(0) + G 5 ? 5 P 5 (0) +
We need not generally take account of terms beyond the fifth. Hence
also if the deflection < of the movable coil is small, and since <f> = ir/2-0,
it is easy to show that P 5 (0) = . cos nearly. Under these circumstances
144
G 5 = - _ Gi/A 4 , and if a single suspended coil is placed at the centre of the
090
pair of fixed coils, then g. = gO^i- Then we have
M = Gtf! sin {l - 27a 4 /lCOA 4 }>
and the couple or torque experienced by the movable coil when both are
traversed by a current i is
i^=G 1 g l cos 0{l - 27a 4 /100A 4 }.
Hence the factor (1 - 27a 4 /100A 4 ) comes in as a correcting factor to the term
Gg cos0 in the equation of equilibrium of the movable coil.
Space does not permit us to enter more fully into
the detailed theory of the electro-dynamometer, but the
THE MEASUREMENT OF ELECTRIC CURRENT. 365
mathematical reader is referred to the following sources of
information :
For the full mathematical treatment of the action of
circular currents on each other see Maxwell, " Electricity
and Magnetism," Vol. II., Chap. XIV., 2nd edition.
Also Mascart and Joubert, " Treatise on Electricity and
Magnetism." translated by Atkinson, Vol II., Chap. IV.
And A. Gray, " Absolute Measurements in Electricity and
Magnetism," Vol. II., part 2.
In addition, the above-mentioned series of articles by
Mr. Searle on " Current Measurements " in The Electrician,
Vol. XXVII. and XXVIII, may be consulted.
As an instance of the use of the electro-dynamometer and
calculations connected therewith the reader may consult a
paper by Mr. Dugald McKichan " On the Number of Electro-
static Units in one Electromagnetic Unit," Phil. Trans. Eoy.
Soc, 1873.
7. Current Balances. Dr. Joule was one of the first
persons to construct an amperemeter in which a current was
measured by observing the apparent increase or decrease in
weight of a coil carrying a current produced by the mutual
electrodynamic action of another coil conveying a current
placed parallel to it. The much more elaborate current
balances of Lord Kelvin have already been fully described
(see Chapter I.). In these latter instruments the movable
coil is placed between two fixed coils.
In order that stability may be secured, it is necessary that
a displacement of the movable coil from its position of rest
should not decrease the electrodynamic forces acting upon it.
If we place two fixed circular coils parallel to each other, as
on the Helmholtz galvanometer, and a smaller movable coil
is held between them so that the planes of all three are
parallel, then, by suitably arranging the direction of the
currents, we can create a force tending to move the movable
366
THE MEASUREMENT OF ELECTRIC CURRENT.
coil parallel to itself. Maxwell points out that if the
diameter of the fixed circular coils is to the distance between
their planes as 2 : \/3, then they will produce a nearly
uniform force on a much smaller circular coil placed between
them and with its plane parallel to those of the fixed coils.
FIG. 7.
FIG. 8. Pellat's Ampere Balance.
A form of standard ampere balance has been designed by M.
Pellat for the Laboratoire Central d'Electricite in Paris. It
consists (see Figs. 7 and 8) of a fixed horizontal solenoid
and an enclosed smaller solenoid attached to the beam of a
balance. When a current is passed through the two coils in
THE MEASUREMENT OF ELECTRIC CURRENT. 367
series it tends to turn round the movable solenoid so as to
bring the axes of the coils more into colineation. This torque
is resisted by weights put upon the scale pans of the balance.
If H is the value of the earth's horizontal magnetic field
parallel to the axis of the fixed coil, and if A is the current
flowing through the coils, then the resultant magnetic force
in the interior of the large coil parallel to its axis is
F = BA+H.
If the magnetic moment of the movable coil is M, then
M-B'A.
Hence the couple acting on the movable coil when it is in
equilibrium is
C-MF-KK'A'+K'HA.
If the current in the fixed coil is then reversed, the couple
becomes
C'- -BB'A 2 +B'HA.
Hence C-C'=>2BB'A 2 , f
If the couples are produced by weights W and W put in the
scale pans attached to the movable coil, then these weights
are proportional to the couples, and we have
A =
where K is some single constant. If the coil dimensions are
measured K can be calculated. The value of K for the
Pellat balance in the Laboratoire Central in Paris is
K = 0*217682 in terms of the ampere and gramme.
8. Working or Laboratory Amperemeters. It would be
of little use to describe the multitudinous forms of commercial
ampere or ammeters which have appeared and disappeared in
the last 20 years. Broadly speaking, in addition to the
standard instruments already described, the practical elec-
trician has need of three classes of current-measuring
368 THE MEASUREMENT OF ELEGTRIG CURRENT.
direct-reading instruments called respectively galvanometers,
table or portable ammeters, and switchboard ammeters. Table
or portable ammeters are employed for the numerous occasional
measurements of current in practical units made anywhere or
everywhere in the laboratory, and those of the third class
only in fixed positions and on certain circuits.
It is necessary that the above two classes of instruments
should give at once, by a direct-scale reading, the approxi-
mate value of the current in amperes. The first class, or galva-
nometers, are not usually direct-reading. They are 'mostly
employed to indicate the mere presence or absence of
a current in a circuit, and when the ampere value of
FIG. 9. The Weston Portable Ammeter.
their indications is required they have to be standardised.
The necessary qualifications for a good portable or table
ammeter are (i.) that it should be dead-beat that is to say,
its indicating needle must come immediately and without
oscillations to the scale reading corresponding to the current
passing ; (ii.) it should have no dead or undivided part of the
scale ; and, (iii.) if possible, the scale divisions for equal
increments of current at various portions of the scale should
be equal in other words, the scale should be equi-divisional.
No laboratory instruments fulfil the above requirements, as
far as continuous currents are concerned, so well as the
Weston instruments. In these ammeters (see Fig. 9) there
THE MEASUREMENT OF ELECTRIC CURRENT. 369
is a well-aged magnet which produces a constant magnetic
field. In this field is held a circular coil of wire carried on
an axis revolving in jewelled centres. The control is produced
by a steel spiral spring, like the hair-spring of a watch.
In all but the ammeters for very small currents the
greater portion of the current in the circuit containing the
ammeter passes through a shunt, so that the above-mentioned
coil only carries a very small portion of the current. The
terminals of the instrument are marked + and so as to
FIG. 10. General Design of Hartmann and Braun Hot Wire Ammeter.
show how the connections should be made. The instruments
are made in various grades, to read from milliamperes to
hundreds of amperes, the readable range in each instrument
being about 1 to 1,500. These instruments are not, however,
available for alternating-current measurement. For this last
purpose, a convenient form of ammeter is that depending on
the heating of a wire, and therefore called a hot-wire ammeter.
A good form of hot-wire ammeter is that of Hartmann and
Braun (The Electrician, Oct. 6, 1899). In this instrument (see
Figs. 10 and 19) a fine wire is stretched between two fixed
370 THE MEASUREMENT OF ELECTRIC CURRENT.
points, and is heated by the whole or part of the current to
be measured. The wire, therefore, extends and "sags/' and
the indicating portion of the instrument is a device for accu-
rately measuring this sag. The advantage of this arrangement
is that the sag is greater than the mere longitudinal extension
of the wire. This is easily proved as follows :
Let an inextensible thread of length 21 be fastened between two supports
at a distance 21, and held, therefore, in a straight line. Let one of these
supports move towards the other by a small distance, 2x, which is equivalent
_ L-x
FIG. 11.
to assuming a small increment of length, 2x, to be made in the thread. The
thread, therefore, will sag down. Let s be the amount of the sag. Then, as
seen from Fig. 11, we have the equation
or s*+x* -21x^0.
If x is small compared with I, we may neglect x 2 in comparison with 2lx, and
we have
Hence it will be seen that s is very much greater than x provided I is much
greater than x. For instance, if 1 = 100mm. and x = 1mm., then s = 141mm.
nearly.
Fm. 12.
A means of still further multiplying the extension of a wire may be found
by allowing the sag of one wire to create a still greater sag in a second. Thus,
suppose two wires, each of length 21, are arranged as in Fig. 12, connected
to three fixed points, a, 6, c.
THE MEASUREMENT OF ELECTRIC CURRENT. 371
Let the wire cd have its end d attached to the middle point of ab. Let the
wire ab increase by a small length 2x. Then, if s is its sag, we have
or 2xl+x 2 =s 2 ,
or, if x/l is small, s=
Then, in the same way, for the second wire we have, if s' is its sag,
or, if xl is small compared with xl?,
s'
Hence, s' is very much greater than x.
Thus, if <e = 0'lmin. and Z = 100 s' = 21mm. nearly, or the extension is
multiplied 210 times.
In the Hartmann and Braun hot-wire ammeter the wire is
mounted between fixed insulated pivots, on a plate of metal
having the same coefficient of expansion for heat as the wire.
The sag of the wire is measured by causing it to create
rotation in an indicating needle, the movement of the needle
being resisted by a steel spiral spring which brings it back to
zero.
In the case of ammeters for small currents the whole
current passes through the wire and heats it. In the case of
ammeters for larger currents, the main portion of the current
passes through a shunt. The instrnments are very dead beat
and the scale reading is most open at the point at which
greatest accuracy is required. The vibrations of the needle
are checked by attaching to the needle shaft a light circular
disc of copper which moves between the closely placed poles
of a strong horse-shoe magnet, thus creating "magnetic
friction" by reason of the eddy currents set up in the disc
whenever rapid rotation of the disc takes place.
These instruments are available both for direct and
alternating currents, and have many practical advantages.
There is, however, a dead portion of the scale below which no
scale divisions are engraved ; the lower limit of the scale
reading is approximately 10 per cent, of the upper limit.
Thus an ammeter reading to 100 amperes would be useless
BB2
372 THE MEASUREMENT OF ELECTRIC CURRENT.
for measuring less than 10 amperes (see The Electrician, Vol,
XLIIL, p. 839).
For switchboard purposes very popular instruments are
those called the Edgewise instruments (see Fig. 13). In this
case the scale is a curved circular band, and the needle end
projects through a slit in it and has its end turned over so as
to be seen against the scale. The instruments take up less
room on a switchboard than the circular type, and are more
easily read from the floor level.
FIG. 13. Kelvin Edgewise Switchboard Ammeter.
For a full discussion of the advantages and disadvantages
of various forms of ammeter for switchboard purposes the
reader is referred to a paper by Mr. Blakie on " Instruments
for Switchboards," in The Electrician, Vol. XLL, p. 209.
9. Calibration of Laboratory Ammeters. No com-
mercial instruments can be taken to be absolutely correct in
their scale indications no matter what the makers of them
may assert. The practical electrician must proceed first to
standardise them in order to obtain the true or most probable
THE MEASUREMENT OF ELECTRIC CURRENT. 373
real ampere value of any scale-reading by an independant
measurement. For this purpose no appliance is so convenient
as the potentiometer already described (see Chapter I., 13
p. 134) aided by appropriate standard current-carrying resist*
ances. For by this means the measurement of a current is
reduced to the measurement of a resistance and the electro*
motive force of a standard cell, both of which are tolerably
permanent values for given well-made instruments. Hence, the
standardisation of an ammeter is conducted as follows :
The ammeter A (see Fig. 14) must be joined up in series
with a low resistance standard K of such type that it can
FIG. 14.
carry, without injurious heating, the maximum currents to be
passed through the ammeter. In series with this should be
another adjustable rheostat for varying the current passed
through the ammeter, and also a carbon rheostat C for
making very small adjustments in the current. From the
potential terminals of the standard low resistance are brought
two potential wires, which are connected with the potentio-
meter wire a 5, as shown in the diagram The potentiometer
is first set by means of a Clark or Weston cell so that the fall
of potential down the slide- wire is of known amount, obtained
by regulating the current flowing from the working battery
through the slide-wire.
374 THE MEASUREMENT OF ELECTRIC CURRENT.
If, for instance, a Clark cell is employed, the temperature
of which is 15C. and the corresponding E.M.F. 1434 volts,
the sliding contact is set to make contact at that division on
the slide-wire marked 14,340, and the current down the
slide-wire regulated until the reading galvanometer shows no
deflection. When this is done, the potential wires connected
to the ends of the low resistance are substituted for the
connections to the Clark cell, and the fall of potential down
the low resistance is read off directly on the potentiometer
slide-wire. Hence, knowing the value of this low resistance,
we have at once the true current through the resistance, and,
-2
1 23456
SCALE READING
NL s A 10 11 1
FIG. 15. Ammeter Error Curve.
therefore, that through the ammeter. We can, therefore,
write down two columns of figures, one of which gives the
observed scale-reading of the ammeter and the other the
true ampere value of the corresponding current. The
difference between these two figures is the error of the
ammeter corresponding to that scale-reading.
We can then make an error curve for the instrument as
follows : Let the various scale readings be plotted out as a"
horizontal line (see Fig. 15) and, corresponding to each, let
a line be erected the length of which is the error of the
ammeter at that reading, the said line being drawn upwards
THE MEASUREMENT OF ELECTRIC CURRENT. 375;
the error is positive and downwards when the error is
negative. Thus if, corresponding to an abscissa 20, denoting
a. scale-reading of 20 amperes, the error is +2'2, we draw
the line representing 2 '2 upwards, and the true ampere value
of the current when the ammeter needle points to 20 on the
scale is 20+ 2*2 = 22*2. If,, on the other hand, the error is
negative, the line is to be drawn downwards, and the
true ampere value corresponding to 20 divisions would be
20 -2-2 = 17-8 amperes.
, Every working ammeter in the laboratory should in this
manner have an error curve drawn for it which should be
repeatedly verified. The error curve should be taken with
ascending as well as descending values of the currents, since,
in certain types of ammeter, particularly those containing soft
iron masses moved in a magnetic field, there is often con-
siderable hysteresis error. The ammeter will not give the
s^ime reading for the same current value if it has previously
been used with a different and much larger or much smaller
current.
, Hence, in checking an ammeter it is not sufficient. to
determine its scale inaccuracy for one cycle of current
values : we must know how far the instrument gives the
same scale-readings for the same current values independently
of the values of the currents previously passed through it
At the same time, its zero-keeping quality and dead-beatness
can be noted.
' If the ammeter is one intended for use with alternating
currents, an investigation must be made to determine how far
the readings are affected by change in frequency of the
current.
There is no better method of doing this than by calibrating,;
first of all, a Siemens' electro-dynamometer and delineating
for it a curve showing the torsion in scale degrees corres-
ponding to various continuous currents passed through it. :
In so doing, it is essential to place the instrument in such
a position that the movable coil when in its zero position;
376 THE MEASUREMENT OF ELECTRIC CURRENT.
shall not be affected by the earth's magnetic force. In order
that this may be the case the instrument should be so oriented
that the axis of the movable coil when in its zero position is
in the direction of the local magnetic meridian. To test this
try reversing the direction of the current through the movable
coil alone, and ascertain if the torsion required to restore the
movable coil to the sighted position is the same in both cases-
When the instrument has been calibrated for direct currents,
it may be used with alternating currents of various
frequencies; and employed in series with the ammeter to
be tested to calibrate it and to detect if the ammeter reading
varies with the frequency.
10. Direct Measurement of Current by the Potentio-
meter. The majority of commercial ammeters are so liable
to change of errors that, in order to avoid the expenditure of
time in constantly calibrating them, it is better in many cases
to rely on the potentiometer directly as a means of measuring
current directly. Thus, in the case of the measurement of
current through an incandescent lamp, it is necessary to be
able to determine a current which may have a value approxi-
mately of half an ampere or so to within 1 per cent, at least.
No commercial ammeter can be depended upon to measure or
indicate correctly a current of this order with the above-
mentioned accuracy. Hence incandescent lamp currents are
far better measured by inserting in series with the lamp a
resistance adapted for carrying 1 ampere to 10 amperes and
measuring with the potentiometer the fall of potential
down this resistance. If the resistance has a value of
1 ohm and is made of manganin, we can, by its aid, deter-
mine the current value with great ease to within one-tenth
of 1 per cent.
These measurements may take a little longer than when
made with a direct-reading ammeter, but they can be
depended upon when made to be accurate within the above-
named limits.
THE MEASUREMENT OF ELECTRIC CURRENT 377
In the same manner, in measuring large currents, such as
those given by large dynamos, it is much better to pass the
current through a resistance strip of one-thousandth of an
ohm resistance and determine the current by the fall of
potential down the strip.
A stock of low-resistance current-carrying resistance strips
and a potentiometer is thus a more profitable investment of
capital for an electrical laboratory than the purchase of a
large number of commercial ammeters of different kinds.
The measurement of the large currents sent out from
continuous-current stations is most accurately effected by the
direct measurement of the fall of resistance down a low-
resistance strip or strips, the resistance values of which have
been carefully determined in absolute measure by a Jones-
Lorenz apparatus.
If a low-resistance strip of known value is not at hand,
then a resistance can be constructed by joining in parallel a
known number of wires of measured resistance. Thus, if
a resistance capable of carrying 1,000 amperes is to be made,
it can be constructed by joining in parallel 100 wires each
having a resistance of one-tenth of an ohm and each capable
of carrying 10 amperes. In making these arrangements a
large margin must be allowed in the carrying capacity of the
single wires. It does not follow that, if one single bare wire,
say of platinoid, No. 36 S.W.G-. size, will carry, without undue
heating, one-quarter of an ampere,- that 100 of these wires
closely laid in parallel will carry 25 amperes. Owing to the
diminution in the radiative power of each wire by its
proximity to others, the final temperature of each wire will
be much higher, and therefore a less total safe current-
carrying capacity results.
11. Current-carrying Capacity of Wires. In the con-
struction of resistances used for the purpose of causing a
definite fall in voltage in a current passing through them it is
necessary that the rate of generation of heat shall be so
378 TEE MEASUREMENT OP ELECTRIC CURRENT.
related to the rate of dissipation that the wire does not rise
in temperature by an amount sufficient to seriously affect its
resistance, or else one of the factors required for the current
measurement viz., the resistance of the measuring portion of
the circuit is uncertain. The heat generated per second in
a bare wire in air by the passage through it of a steady
current having a value of A amperes is mechanically equal to
A 2 E joules, where E is the resistance of the wire. This
energy is dissipated or conveyed away from the surface by
radiation and convection, and every surface at a certain
temperature has a certain emisssivity, which is defined as the
energy passing out per second per square centimetre. The
true emissivity is a function of the difference of temperature
of the surface of the wire and that of the surrounding vessel
or enclosing surface. If the wire is in a vacuum, the
dissipated energy is wholly radiant, except in so far as there
is conduction out of the ends of the wire. In the case of
wires exposed in the air, energy is removed by air convection
as well as by radiation, and convection in this case forms an
important part of the heat loss.
Let w stand for the total energy removed from the wire
per second per square centimetre of surface, whether by
radiation or convection. Then, when a state of thermal
equilibrium is reached, we have the equation
where D is the diameter and L the length of the wire, which
we will suppose to have a circular section. Also, if p is the
electrical resistivity of its material, we have
10 9 E=-1
7T,
where E is the whole resistance of the wire in ohms and p
its resistivity in C.G.S. units.
THE MEASUREMENT OF ELECTRIC CURRENT. 379
If the diameter d of the wire is measured in millimetres,
we obtain from the above two equations another, viz.,
A 9 1^0 91AJ<* A -I rfff\
A 2 = l-7r 2 l(W, or A =1,570
P
This equation tells us the value of a current in amperes
(A) which will bring a circular-sectioned wire of diameter d
millimetres to a temperature at which it will be losing
energy at a rate equal to w joules per second from each
square centimetre of its surface.
Suppose, for instance, that w = Ol, or that the surface rate of
loss of energy is one-tenth of a watt per square centimetre, and
that the wire has a diameter of 1 mm. ; then we should have
A = 1,570 /JL, or p A 2 = 246,490.
\ 10/3
Experience shows that when a bare metallic wire is
radiating O'l watt per square centimetre, its surface tempera-
ture would be about 60C. if surrounded by air at 15C.
If we assume the wire to be of copper, then at 60C. its
resistivity p would be about 2,000 C.G.S. units. Hence the
current carried would approximate to 11 amperes.
It is generally the custom to specify the diameter of wires
in mils, the mil being one-thousandth of an inch. If the
resistivity r is measured in microhms per cubic centimetre
at the final steady temperature, and d is the diameter in
mils, then the above formula for the current carried can be
transformed into
A 1,570 fad*
8,000V r
If the rate of loss of energy w reaches one watt per square
centimetre of surface for a bare wire, it is far too hot to touch,
and is probably at a temperature of about 400deg. If w has
a value of 01, then the wire is just hand-hot, or, perhaps, at
about 60C. At the above temperature (60C.) the resistivity r-
of copper will be 25 per cent, greater than its resistivity at.
380 THE MEASUREMENT OF ELECTRIC CURRENT.
0C. and that of iron 36 per cent., but for platinoid and most
resistance alloys, only about 2 per cent, greater.
Inserting in the formula these values for r and w we have
the following convenient but rough empirical formulae for the
safe currents in amperes A, carried by round bare wires, of
the stated materials, having a diameter of d mils, viz. :
For copper,
A =
-A
V
For platinoid or German silver, A= /_
V 5,
500
For iron,
A =
OOP
d*
The above formulae only apply to bare wires in air, the
wires being either straight or coiled into very open spirals.*
The following table, embodying experimental results, shows
the safe current-carrying capacity of some common sizes of
bare wires of copper, iron, brass and German silver in loose
or open spirals :
Safe Current-carrying Capacity in amperes of Bare Wires,
ivound into Open Spirals.
Size of wire
in B.W.G.
Diameter
of wire in
inches.
Safe currents carried. Final temperature
not exceeding 60C.
Copper.
Brass.
Iron.
German
silver.
10
12
14
16
18
20
0-134
0109
0-083
0-065
0-049
0-035
50 amps.
i-
? ::
9
30
19
15
10
7
5
19
16
10
8
5
4
16
13
8
6
4
3
It will, therefore, be seen that the current density or amperes
per square inch of section can be very much greater in fine
wires than in large ones. In all cases, however, the surface
* These formulae cannot be applied to extreme cases, such as that of a wire
one mil in diameter, but apply generally to ordinary laboratory sizes of wires.
THE MEASUREMENT OP ELECTRIC CURRENT. 381
of a bare wire in air should approximate to 10 sq. cm. per
watt expended on it, if the temperature is not to rise above
the point at which it is possible to touch the wire with the
hand.
The result of investigation has been to show that the
emissivity of a bare cylindrical wire is not merely a function
of the temperature difference between its surface and that of
the surrounding envelope, but is also dependent on its form.
Prof. Ayrton and Mr. H. Kilgour have deduced the following
laws from observations on nine platinum wires varying
between l'2mm. and 14mm. in diameter.*
1. For any temperature the emissivity is higher the finer
the wire.
2. For each wire the emissivity increases with the tempera-
ture, the rate of increase being greater the finer the wire.
3. The effect of surface on the total loss of heat per square
centimetre per second per 1C. excess of temperature
increases as the temperature rises.
These authors find that for platinum wires of different
diameters the emissivity e, or loss in heat in calories per
square centimetre of surface per second per 1C. excess of
temperature above the enclosure, can be expressed by the
formulae
At 100C, e = 0-0010360 + 0120776 dr\
At 200C., e = 0-0011113 + 0-0143028^- 1 ,
At 300C., e = 0-0011353 + 0-016084 d~\
where d is the diameter in mils. Hence, whilst the simple
theory above given, in which the emissivity is taken as
constant, leads to the conclusion that the current required to
maintain a wire of given material at a given temperature
varies as the diameter of the wire raised to the power of
three-halves, as a matter of fact, for very thin wires, the
current is more nearly proportional to the diameter simply.
* See Ayrton and Kilgour, " On the Thermal Emissivity of Thin Wires in
Air," Proc. Roy. Soc., November 19, 1891 ; or The Electrician. Vol. XXVIII.,
page 119.
382
THE MEASUREMENT OF ELECTRIC CURRENT.
Iii 1884, Sir W. H. Preece gave some measurements of the
currents required to fuse fine bare platinum wires Gin. in
length and of various diameters. These currents were found
to be as follows :
Diameter of the Wire
in inches.
Fusing Current in
amperes.
0-00050
0-00075
o-ooi
0-002
0-003
0-277
0-356
0-437
0-790
1-150
It will be seen that these fusing currents are much more
nearly proportional to the first power of the diameter of the
-wire than to the three-halves power of the diameter. For
wires of copper varying in diameter (d) from 8 mils to
30 mils he found the observed values of the currents (A)
required to make the wires just visibly red hot in the dark
(temperature about 500C.) were in very fair agreement with
the values calculated from the formula
A = 0-14587 Vd*.
For Swedish wrought-iron wires of diameters varying from
] mils to 60 mils the same current could be calculated from
the formula
A = 0-035755 *J&,
and for German silver wires between 8mm. and 25mm. in
diameter from the formula
A = 0-056376 J3*.
These experiments made it evident that, whilst for round
bare wires in air of diameters between Sjmils and 60 mils
the currents required to keep them at constant temperatures
could be calculated from a formula of the form current
= (constant} X (diameter) , this law does not hold good for
wires of much smaller diameter, such as 1 mils to 3 mils, for
in this latter case the current varies more nearly as the
diameter.
THE MEASUREMENT OF ELECTRIC CURRENT. 383
In connection with this subject a knowledge of the current
required to fuse short bare wires of different materials and
various diameters in air is practically important. Sir W. H.
Preece has given a table (see Table L, end of this chapter)
of fuse currents for wires of different sizes of iron, copper,
lead and tin.
The reader may be referred to the following papers for
additional information on the heating of conductors by
electric currents :
PROF. G. FORBES. British Association Report, 1882.
SIR W. H. PREECE. " On the Heating Effects of Electric
Currents." Proc. Roy. Soc., April, 1884, or The Electrician,
Vol. XII., p. 518.
PROF. G. FORBES. " On the Diameter of Wires to Prevent Over-
heating by Electric Currents." Proc. Inst. Elec. Engineers,
London, April, 1884; also The Electrician, Vol. XIII. r
pp. 16, 39, 63, 82.
J. T. BOTTOMLEY, The Electrician, VoL XII., p. 541.
A. E. KENNELLY. " On the Heating of Conductors by Electric
Currents." The Electrician, Vol. XXIV., p. 142.
12. Calibration of a Galvanometer by the Potentio-
meter. The Measurement of Very Small Currents. When
using a sensitive galvanometer for many purposes it becomes
necessary to know the absolute value in amperes of the small
current causing an observed deflection. The most simple
method of calibrating any form of mirror or deflectional
galvanometer is as follows :
Unless the galvanometer Gr has a high resistance, say
2,000 ohms and upwards, it must have a resistance, E, of
known value joined in series with it, and the resistance of the
galvanometer coil itself must be measured. A potentiometer
wire, a b, is then set or adjusted by means of a Clark cell, Ok,
so that there is a known fall of voltage down the wire per centi-
metre. In the absence of a potentiometer it is always possible
384
TEE MEASUREMENT OF ELECTRIC CURRENT.
to improvise an equivalent by stretching a fine uniform
platinoid wire along a 2-metre scale and attaching to the ends of
the wire a single secondary cell. The galvanometer may then
be employed in connection with a Clark cell to discover the
length of the wire down which there is a fall in potential
equal to the voltage for the moment of the Clark cell. Thus,
suppose the connections made as in Fig. 16, and that the
Clark cell has an E.M.F. of 1434 volts at 15C. at that
temperature, and that we find the fall of potential down
80cm. of the wire is equal to 1434 volts ; then the fall of
potential per millimetre of the wire is 1434/800 volts.
FIG. 16.
This done, remove the Clark cell, attach in series with the
galvanometer the known resistance K, and join up the ends of
the galvanometer to any two points on the slide- wire separated
by such a distance that the resulting galvanometer deflection
is the one the current value of which is required.
Let the galvanometer have a resistance G ohms and be joined
in series with a resistance E ohms; let L be the length a x of the
slide- wire down which there is a fall of potential equal to the
voltage V of the Clark cell ; and let I be the length of slide-
wire separating the terminals of the galvanometer circuit
when the galvanometer deflection is 8. Then the value of A
THE MEASUREMENT OF ELECTRIC CURRENT. 385
the current in amperes through the galvanometer which
produces this deflection 8 is
A_
~
Hence the galvanometer constant k is equal to A/8.
The conditions of success are that the value of the resist-
ance K+G must be very large compared with the resistance
of the length I of the slide-wire, so that the addition of the
galvanometer in parallel with a section of the slide- wire does
not sensibly affect the current flowing through the slide-wire.
The galvanometer constant should, in the above manner,
be determined for a number of different deflections, and it
must not be taken for granted without proof that the constant
is constant. If, however, the deflectional constant has been
found, the galvanometer may be employed for the measure-
ments of large currents by being shunted.
If the terminals of a galvanometer having a resistance
G ohms are joined by a resistance of S ohms, called a
shunt, then the combined resistance of the galvanometer
SG
and shunt is ^ -^ ohms. If a steady current A amperes
is sent through the system, it is divided in the inverse
ratio of S and G, and the galvanometer is traversed by a
current a, such that
S
S + G'
Hence, A=fl*t
o
But if the current a produces a deflection, 8, and corre-
sponding to this deflection we have a constant, K, we then
have
A galvanometer is usually provided by the maker with
a set of shunt coils so adjusted for use with it that, by
cc
386 THE MEASUREMENT OF ELECTRIC CURRENT.
connecting each shunt coil in turn across the terminals
of the galvanometer, one-tenth, one-hundredth, or one-
thousandth of a current is sent through the galvanometer
when the shunted galvanometer is connected in a circuit.
A universal shunt-box has been designed by Prof. W. E.
Ayrton and Mr. Mather which is capable of being applied
to any galvanometer. The principle may be explained by
reference to the diagram (Fig. 17).
Let G be a galvanometer having its terminals ab shunted
by a resistance consisting of a long fine wire. Let B be
a battery having one terminal connected to a and the
other to a point, #, on the shunt wire. Then, if the
FIG. 17. Diagram illustrating the principle of the Ayrton-Mather
Universal Shunt-Box.
resistance of the galvanometer is G, and that of the wire ab
is nGr, and the resistance of the fraction of the wire ax
is wG, and if C is the current flowing out of the battery
and c the current flowing through the galvanometer, we
obviously have
Hence the fraction of the current flowing out of the battery
which passes through the galvanometer is independent of
the resistance of the galvanometer. Accordingly, if we
make n=9 and ra = l, c = OlC; if we make n = 9 and
m = 0*l, c = 0'01C, and so on.
THE MEASUREMENT OF ELECTRIC CURRENT. 387
If, then, the shunt wire db remains fixed, but an arrange-
ment exists by which the point x can be shifted so as to
make ax successively equal to one-tenth, one-hundredth,
&c., of ab, we shall have a shunt which can be applied
to any galvanometer. It must be noticed, however, that
the movement of the point x alters the total resistance
between a and x, and therefore affects the total resistance
of the circuit, and, as a consequence, the value of the
main current, unless some adjustment is made to keep it
constant. In the actual arrangement, the shifting of the
FIG. 18. Ayrton-Mather Universal Shunt-Box.
contact point x from place to place along the shunt line
is achieved either by a plug and block arrangement or by
a rubbing contact (see Fig. 18).
In connection with this matter it may be well to point
out that in the ordinary shunt arrangement, in which the
galvanometer is provided with a series of shunts, the
resistances of which are respectively ^, ^, -g^, &c., of that
of the galvanometer, we must not assume that, because steady
currents are divided in decimal ratios by the shunts, that
therefore sudden impulsive currents or instantaneous dis-
charges, as when the galvanometer is used ballistically, are
cc2
388 THE MEASUREMENT OF ELECTRIC CURRENT.
likewise so divided. Mr. Hockin showed many years ago
that the application of the shunt affected the logarithmic
decrement or damping of the galvanometer, and hence the
instantaneous swing or throw is less than it should be if
the shunt merely acted to divide the discharge in the inverse
ratio of the resistance of the galvanometer and shunt.
13. Alternating- Current Measurement. It has already
been explained that in the case of alternating or periodic
currents we are concerned with either the instantaneous value
(i) of the current, or with its maximum value (I), or with
its root-mean-square (RM.S.) value, and, occasionally, with
the true-mean (T.M.) value. Generally speaking, the measure-
ment of an alternating current implies the determination of
its root-mean-square value, and most alternating-current
ammeters and methods give us this value. In order, there-
fore, that an instrument may be useful for alternating-current
measurement, it must be based on some principle such that
the actual mechanical force, couple or displacement measured
varies as the square of the instantaneous value of the current.
We may avail ourselves therefore of the heating power of the
current, or of the mechanical force between two conductors
traversed by the same current, or of the mechanical force
between conductors connected to the ends of the circuit
traversed by the current, as a means of constructing an
ammeter for periodic current measurement, because in each
of these cases the observed effects, whether heat pro-
duction or mechanical force, varies as the square of the
current at any instant, and is therefore independent of its
direction.
We have already described the construction of the instru-
ments of the electro-dynamometer class, such as Siemens'
electro-dynamometer or the Kelvin ampere balances, which
depend for their action upon the mechanical forces existing
between fixed and movable conductors traversed by the same
current. In using these types of instruments for alternating-
THE MEASUREMENT OF ELECTRIG CURRENT. 389
current measurement the condition of success is that the
periodic time of the alternating current must be small
compared with the free time of vibration of the movable part
of the instrument.
There is, however, another very important matter concerned
in the proper construction of an instrument of this class in
order that it may be available for alternating-current
measurement. The instrument must have no metal parts or
plates or case near to the coils traversed by the alternating
currents. For if there are such metal parts, then the
alternating currents in the fixed coils will set up local or
eddy currents with these metal parts, and these eddy currents
will be nearly in opposition as regards phase with the
currents producing them. Hence the eddy currents will
react upon the movable coil, and will make the mechanical
force upon it different from that which it would be if the
eddy currents were absent. This defect may be masked by
the opposing action of the currents in the fixed and movable
portions of the circuit, and it will in general be more marked
if there is a difference in phase between the currents in the
fixed and movable circuit. In any case, it is a possible source
of serious error, and any electro-dynamometer instrument
intended to measure alternating currents which is included
in a brass case or has brass or metal parts near the coils
should be viewed with suspicion as regards its instrumental
accuracy. The Kelvin ampere balances intended for
alternating current measurement have their coils wound oil
cores of slate, marble or porcelain, and the bases on which
the instruments are mounted are also non-metallic.
The most suitable form of Siemens electro-dynamometer is
that called the "Workshop" form, in which the coils are
mounted on a wooden base. Even here the instrument
maker often fixes the coils to the base by metal straps.
These should be removed and ebonite straps used to hold the
fixed coil in place. Instrument makers are far too fond of
enclosing electrical measuring instruments in lacquered brass
390 THE MEASUREMENT OF ELECTRIC CURRENT.
cases, which look nice but often injuriously affect their
performance and accuracy.*
The measurement of a large alternating current is best
effected by some suitable instrument of the electro-dynamo-
meter type. This must previously have been calibrated by
passing through it a continuous current of known value, as
determined by the potentiometer method, and an error curve
constructed for the instrument as above described. The
instrument may then be used to measure the B.M.S. value of
an alternating current since the numerical value of the latter
is that of the continuous current which produces the same
dynamometer reading.
The most useful type of hot-wire alternating-current
ammeter is that in which the current to be measured passes
through a strip resistance of negligible inductance, and from
the ends of which connections are made to a very fine wire
which is heated by the small portion of the current shunted
through it. If the wire is in an enclosure of constant
temperature it soon comes to a final steady temperature,
which produces a definite elongation of the wire. This
expansion is measured by measuring the sag of the wire, its
ends being attached to fixed points. Instruments of the
above kind are manufactured by Hartmann and Braun (see
Eig. 19), and a self-recording hot-wire ammeter is in use,
designed by Holden and Pitkin, in which the current to be
measured passes through and heats a number of fine wires of
platinum or platinum silver arranged in parallel, the sag or
extension of these wires being detected and measured by a
multiplying gear which actuates a pen moving over a revolving
drum.
The measurement of small alternating currents, such as the
magnetising currents of transformers, is best accomplished by
. * As an instance of the kind of error that may thus result, the reader is
referred to a Paper by the Author in the Proc. of the Institution of Electrical
Engineers, Vol. XXL, p. 666, 1892, entitled, "Experimental Researches on
Alternate Current Transformers," in which reference is made to the results of
measurements made with a certain brass-cased wattmeter which were found
to be in some cases in error by nearly 50 per cent.
THE MEASUREMENT OF ELECTRIC CURRENT. 391
measuring the fall of potential down a known resistance by
means of an electrostatic voltmeter or quadrant electrometer
which has been previously standardised by continuous
voltage. Thus, for instance, if we have to measure an alter-
nating current, say, of about the magnitude of 0*25 ampere,
a resistance can be constructed of four strands of No. 36 bare
platinoid wire capable of carrying without sensible heating
0*25 ampere, the total resistance being, say, 400 ohms. This
resistance may be in the cage form described on p. 80. Then
the fall in potential down this resistance produced by the
current will be nearly 100 volts, and can be measured to
FIG. 19. Hartmann and Braun Hot- Wire Ammeter.
within one-tenth per cent, by means of a standardised Kelvin
multicellular voltmeter, the only condition necessary for so
doing being that we must be able to afford to drop 100 volts
in the voltage of the current used. In those cases in which
this cannot be done an air-core alternating current trans-
former must be employed to effect a transformation.
If a transformer is constructed without an iron core, the
two windings of which have their turns intermingled and in
the ratio of 'N l to N 2 , then if to the secondary terminals we
connect an electrostatic voltmeter, the scale reading of this
392 THE MEASUREMENT OF ELECTRIC CURRENT.
will be N^N^ times or fractions of the voltage on the primary
terminals. If, then, the fall of pressure down the resistance
through which the current to be measured is flowing is too
small to be measured, say on a Kelvin multicellular voltmeter,
we can, by employing an air-core transformer, raise this
voltage to a readable value by using a transformer of the
kind mentioned having its primary and secondary turns in a
known ratio. This transformer should be made with circuits
having as large an inductance as possible. It is desirable,
however, to calibrate the transformer directly by taking a
series of readings, within the range of the same voltmeter if
possible, of the observed voltage on the primary and
secondary terminals.
The same arrangement viz., an air-core transformer may
be employed as shown by Mr. A. Campbell* to measure
currents directly by transformation. In an air-core trans-
former the ratio of the maximum value of the primary
current I x to that of the secondary current I 2 is
where K 2 and N are the resistance and inductance of
the secondary circuit and M the mutual inductance, and
p = 27r times the frequency. Hence, if pN is large compared
with ~R%, the ratio of the currents is always N/M, and indepen-
dent of frequency.
By using an air-core transformer with the secondary
circuit, made of thick wire and a large number of turns, so
that the ratio R 2 /N is at least 50, then, for a frequency of
even 50 ^ the ratio of the currents is at most 1 per cent-
different from that which it would be for infinite frequency.
This ratio of current transformation may, however, be found
experimentally.
Thus, for instance, suppose it is required to measure an
alternating current of about 1,000 amperes, and we have
* Proc. Phys. Soc. Lond., Vol. XIV., p. 279.
THE MEASUREMENT OP ELECTRIC CURRENT. 393
only a Kelvin ampere balance and a Siemens' electro-
dynamometer available, each reading up to 100 amperes.
We may construct an air-core transformer having an
approximate transformation ratio of 10 : 1 by making it with
a thick wire core capable of carrying 1,000 amperes, and
a coil of 10 times as many turns capable of carrying
100 amperes. The transformer has then to be calibrated
by sending through the dynamometer and the thinner circuit
a current, say, of 10 amperes, and joining the thicker circuit
up in series with an adjustable resistance and the Kelvin
balance. Suppose that, when the reading of the dynamometer
is 10, the Kelvin ampere balance reads 98*2, we then know
that the current transformation ratio is 9*82 to 1, and we
can read the value of any current passing through the thick
coil by taking the readings of the dynamometer placed in
circuit with the thinner coil and multiplying by 9*82.
Mr. Campbell has shown that iron ring core transformers
may be .used in the same way provided that the resistance
of the secondary circuit is sufficiently low.
Convenient forms of electrostatic voltmeter for measuring
alternating currents by means of the fall of potential down a
resistance have been devised by Mr. G. L. Addenbrooke.*
He constructs a quadrant electrometer with two double
quadrant plates each formed of a pair of quadrant-shaped
plates. A paddle-shaped aluminum needle is suspended
between the plates by a very fine flat phosphor bronze strip
(see Fig. 20). The needle carries a mirror as usual. One
quadrant is connected to the needle and the two quadrants
are connected to the ends of the resistance through which
passes the current to be measured. The instrument can be
rendered so sensitive that a deflection of 100mm, of a spot
of light at 2 metres scale distance, can be obtained with
only 1 volt fall of potential down the resistance. The instru-
ment, therefore, can be used as an electrostatic voltmeter
* See a Paper read before the International Congress of Electricians at
Paris, 1900 ; also The Electrician, Vol. XLV., p. 901.
394 THE MEASUREMENT OP ELECTRIC CURRENT.
for the measurement of small potential differences, and also
by association with a resistance strip it becomes an alter-
nating current ammeter.
For the measurement of the small alternating currents pass-
ing through a transformer on open secondary circuit (magnetiz-
FIG. 20. The Addenbrooke Electrostatic Voltmeter.
ing currents) the instrument is especially useful. It can be
calibrated by the employment of a battery of Clark cells. Since
the deflection is approximately proportional to the square of
the potential difference at the terminals of the instrument,
the deflections increase very rapidly with the voltages. Some
form of low-potential electrostatic voltmeter, such as the one
THE MEASUREMENT OF ELECTRIC CURRENT. 395
above described, is a valuable acquisition in an electrical
testing laboratory.
14. Wave Form Measurements. One of the most
valuable methods of investigating the effects due to alternat-
ing currents consists in delineating the wave form that is,
drawing a curve to represent the mode of variation of the
periodic current or currents and their relative phase differ-
ence. This process is called alternate current wave form
tracing, or wave delineation. The results are generally
expressed by taking a horizontal line to represent the
uniform flow of time, and at distances measured from an
origin representing the time or epoch, ordinates are set up
representing to scale the instantaneous value of the current
strength. The curve defined by their upper ends is the
current wave form. Innumerable methods have been devised
for drawing this wave form curve, but there are two which
must be particularly described. These are called the
point-by-point method and the oscillograph method.
The first-mentioned method originated with M. Joubert
in 1880, and can be carried out in any laboratory possessing
an alternator, or at any place to which alternating current
is supplied, provided a synchronous alternating-current motor
is at hand. The second method necessitates the possession of
a more expensive and special device, called an oscillograph.
If we desire to know the current wave form of an
alternator which is supplying a certain circuit, we may
attach to the shaft of the alternator an insulating disc
preferably made of a material called stabilit. This disc has a
narrow brass strip inserted in its periphery. The strip may
be in width about 1 per cent, to 2 per cent, of the
periphery of the disc. Against this disc two insulated springs
or narrow brushes press, so that when the disc revolves
the springs are conductively connected during the moment
the brass strip is passing under them. The brushes are
carried on a rocking lever which moves over a divided
396
THE MEASUREMENT OF ELECTRIC CURRENT.
scale, so that they can be shifted round through a known
and measured angle. This arrangement is called a revolving
contact-maker. It can easily be fitted to any alternator
shaft The following arrangement of circuits are then made.
In the circuit, the current in which is to be delineated, is
inserted a resistance, E, of known value (see Fig. 21), and one
end of this resistance is connected to one of the brushes a
of the contact-maker c, and the other, 5, to one terminal of
an electrostatic voltmeter, V. The other terminal of the
voltmeter is connected to the other brush, but arrangements
are made for inserting in between a variable number of
R
YWWWW
FIG. 21.
small (lithanode) secondary cells B. The needle of the
voltmeter is thus caused to give a reading at any required
part of the scale according to the number of cells in use
whenever the brushes are connected together. The terminals
of this voltmeter are connected to a condenser K having a
capacity of about 0'5 microfarad, to act as a reservoir or
flywheel.
If now the alternator is set in operation, and the brushes
occupy a fixed position; every time the brushes are inter-
connected by the revolving brass strip, the voltmeter is put
momentarily in connection with the ends of the resistance,
and after a few revolutions the condenser becomes charged
THE MEASUREMENT OF ELECTRIC CURRENT. 397
to a potential depending upon the phase of the current
at the instant when this contact takes place. The volt-
meter reading therefore indicates this potential, plus or minus
that due to the cells of the battery B, according as they are
connected to act with or against the fall of potential down
the resistance. By taking the voltmeter readings as the
springs or brushes are shifted over degree by degree through
an angle covering the whole period, and correcting each
observation by adding or subtracting the cell voltage, we
obtain a series of values for the fall in pressure down the
FIG. 22.
resistance corresponding to regular time intervals during one
complete period.
Generally speaking, at least 20 observations should be
taken at equal intervals during the period. These are then
plotted out in a curve and give the wave form (see Tig. 22).
They may also be plotted out in the form of a polar curve (see
Fig. 23) in which radial lines are drawn at angular intervals
representing the time intervals of the observations and
lengths set off along these proportional to the instantaneous
value of the current. The polar curve defined by the ends
398 THE MEASUREMENT OF ELECTRIC CURRENT.
of these radii vectores has the property that, if we take its
area and find the radius of a semi-circle having the same
area, this last radius is to the same scale as the root-mean-
square (K.M.S.) value of the current.*
If the alternator supplying the current is not accessible,
the same process may be carried out by employing a small
synchronous motor to drive the contact-disc in step with
the distant alternator. A small synchronous alternating
motor is practically a small alternator. A good type of
machine to employ for this purpose is the one represented
in Fig. 24. The motor is a small Kapp alternator having
eight magnet poles and an armature consisting of an iron
wire core wound over with eight armature bobbins. The
field magnets are excited by an independent continuous
current, and the armature is connected through a resistance
with the circuit supplying the alternating current under
investigation. The motor is brought up into step with the
supply circuit by passing a strap round its shaft and
spinning it up to speed like a top. When in step it will
continue to run, and will drive the contact-disc on its shaft
* For the proof of this propostion see " The Alternate Current Transformer,"
Fleming, Vol. I., 3rd edition, p. 193.
THE MEASUREMENT OF ELECTRIC CURRENT.
399
so that the circuit of the brushes is closed for an instant at
an assigned moment during the phase once during every
to
3
revolution. The process of obtaining graphically the wave
form of the alternating current supplied by the circuit
400
THE MEASUREMENT OF ELECTRIC CURRENT.
is then carried out as above described, using, however, the
contact-disc on the motor instead of one on the inaccessible
alternator.
An example of an alternating current wave form plotted
out by the point-by-point method is given in Fig. 25.
The great labour involved in slowly delineating a current
wave form by this method led many inventors to devise
methods which are susceptible of greater rapidity. In some
FIG. 25.
cases these take the form of self-acting potentiometers, in
which the instantaneous value of the periodic electromotive
force or difference of potential being studied is balanced
against the fall of potential down a slide-wire. In this case
the galvanometer in the potentiometer circuit is replaced
by a very sensitive relay, which operates a mechanism
moving the contact point on the slide- wire one way or
the other until the current in the relay circuit is zero. A
very ingenious instrument of this kind has been devised
by Prof. Callendar, and another by Prof. Eosa.
THE MEASUREMENT OF ELECTRIC CURRENT.
401
In the Callendar instrument the essential parts are a
form of potentiometer, the contact along the wire being
shifted one way or the other by a couple of small motors'
The contact-piece carries a pen which records a curve on
a slowly revolving drum covered with paper. The contact
is driven by the action of a delicate relay, which starts either
one motor or the other in revolution unless the current
FIG. 26. Rosa's Alternating Current Curve Tracer. Revolving Contact.
through the relay is zero. The relay takes the place of the
usual galvanometer used with the potentiometer. Hence, if
the instantaneous voltage of a periodic current is balanced
against the fall of potential down the potentiometer slide-
wire the mechanism will make the pen follow the variations
of the periodic voltage as this last varies. The alternator
or synchronous motor is provided with a contact-disc and
brushes as above described, and these brushes are slowly
shifted over by an automatic gearing through an angle equal
LID
402 THE MEASUREMENT OF ELECTRIC CURRENT.
to one complete period. The pen then draws on the drum
the curve corresponding to the wave form of this periodic
voltage.*
The instrument designed by Prof. E. B. Kosaf is not
very dissimilar. In it the fall of potential down a
potentiometer wire is balanced against the difference of
potential between the ends of a resistance traversed by the
alternating current and by means of a revolving contact
maker with displacable brushes (see Fig. 26). A single value
of this periodic potential is selected at an assigned instant
during the period for balance. The shifting contact on the
potentiometer is coupled to a pantograph, which draws the
wave form curve on a uniformly revolving paper-covered drum
(see Fig, 27.)
The other method, making use of an instrument called the
Oscillograph, designed for giving a complete view of the
whole curve at once, is due originally to M. A. Blondel,
who first described it in 1892.
The oscillograph has been given a very practical and
improved form by Mr. Duddell. An oscillograph may be
defined as a galvanometer, the needle or coil of which has
such a small periodic time of vibration that it is able to
follow accurately the variations of a periodic current which
runs through its cycle of values in as little as one-hundredth
of a second ; the deflections of the needle being proportional
to the current. As a laboratory instrument the Duddell
oscillograph J has many advantages. It is made as follows :
On a base board is fixed a nearly circular electromagnet (see
Fig. 28) the coils of which are preferably excited by current
at a pressure of 100 volts. This magnet creates a strong
magnetic field between two pole pieces. In this field are
stretched two loops of flattened phosphor bronze wire, which
* See Prof. H. L. Callendar on " An Alternating Cycle Curve Recorder,"
The Electrician, Vol. XLL, p. 582.
t "An Electric Curve Tracer," bv Prof. E.B.Rosa, The Electrician, Vol. XL.
p. 126.
J Made by the Cambridge Scientific Instrument Company.
THE MEASUREMENT OF ELECTRIC CURRENT.
403
fcO
J
DD2
404 THE MEASUREMENT OF ELECTRIC CURRENT.
are kept in tension by a spring. These loops are fixed in the
field so that, if traversed by a current, one wire is forced
forward by the magnetic force and the other forced back.
The straps have attached to them a very small mirror, and
the space in which they move is filled with oil. The time of
free vibration of the mirror is either -a^jth of a second in
one form of the instrument, or Trnhnjth of a second in another
form. The first form of instrument is called the projection
form. In it a ray of light from an arc lamp is made to fall
upon the mirrors attached to the strips, and is reflected back
on to another mirror, which is given a rocking action by a
small synchronous motor, the rocking taking place round an
axis perpendicular to the reflected ray and parallel to the
plane of movement or vibration of that ray. The result of
the combined action of the mirrors is to reflect a spot of light
on to a screen which has a motion in two directions, its
displacement horizontally from the zero position being
proportional to the phase angle and its displacement
perpendicularly being proportional to the current in the
oscillograph strips. Accordingly, the spot of light executes a
motion on the screen which, in consequence of the persistence
of vision, is seen as a luminous curve delineating the wave
form of the periodic currents passing through the strip of the
oscillograph. The oscillograph is furnished with two strips
or loops in order that we may delineate two periodic curves
at once. It has also a fixed mirror to project a horizontal
datum line on the screen. In the high-frequency instrument
this reflected ray of light from the mirrors on the oscillograph
wires is received on a uniformly moving photographic film or
plate and photographs upon it an exact reproduction of the
wave form of the current through the strip.
In using the instrument to delineate the forms of current
and potential difference of the carbons of an alternating
current arc lamp, or motor, or other appliance, we attach the
terminals of one strip through appropriate resistances to the
points between which exists the periodic potential difference
THE MEASUREMENT OF ELECTRIC CURRENT. 405
FIG. 28. -The Duddell Oscillograph.
406
THE MEASUREMENT OF ELECTRIC CURRENT.
to be delineated, and we attach the terminals of the other
strip through resistance to the ends of a non-inductive
resistance in series with the circuit of the apparatus, which
is traversed by the current to be studied. We then obtain
on the oscillograph screen or plate two curves, which
represent the periodic current and potential difference in
question.
The projection pattern of the Duddell oscillograph has
sufficiently large mirrors attached to the wires that the light
reflected from them will project distinct curves upon a screen
at a distance of about 6ft. In the high-frequency instrument
the mirrors are necessarily much smaller, and it can only be
used as a visual or photographic instrument.
The following are the approximate data of the two types
of Duddell oscillograph:
High-frequency
Projection
pattern.
pattern.
Resistance of the field coils at 15C....
Magnetising current
360 ohms.
0*25 amp.
180 ohms.
0*5 amp.
Working temperature of oil for correct
dampincr
30 to 35C.
30 to 35C.
Periodic time
O'OOOl sec.
0-0005 sec.
Normal working current in strip
Resistance of each strip
0'05 to 01 amp.
2 ohms.
0'5 amp.
1 ohm.
Ditto with fuses
10 ohms
3 ohms.
As it is impossible to recapitulate here a description of
more than a fraction of the methods which have been
suggested or employed in alternating-current curve tracing,
the reader may be referred for further information to the
following original Papers and Memoirs, most of which
references are taken from a comprehensive Paper on oscillo-
graphs by Mr. W. D. B. Duddell.* The references are, for
the sake of convenience, divided into groups according to the
methods which they describe, and they have, as far as
possible, been made complete.
* Read at the British Association Meeting at Toronto, 1897.
Report, 1897 ; or The Electrician, Vol. XXXIX., p. 636.
See B.A.
THE MEASUREMENT OF ELECTRIC CURRENT. 407
I. Methods Depending on Foint-by-Point Observation and
Plotting a Curve.
M. JOUBERT. Journal de Physique, 1880.
H. MORTON and B. F. THOMAS. Jour. Amer. Assoc. Ad. of Science,
1880, or Trans. Am. Last. Elec. Eng., Vol. IX., p. 263.
DUNCAN, HUTCHINSON and WILKES. Elec. World., Vol. II., p. 160.
H. J. RYAN. Trans. Am. Inst. Elec. Eng., Vol. VII., p. 1.
L. DUNCAN. The Electrician, Vol. XXVIII., p. 61 ; Trans. Am.
Inst. Elec. Eng. Vol. IX., p. 179 ; or Elec. Eng. of New
York, Vol. XIX., p. 192.
F. BEDELL, K. B. MILLER, and C. F. WAGNER. Trans. Am.
Inst. Elec. Eng., Vol. X., p. 497.
J. A. FLEMING. The Electrician, Vol. XXXIV., p. 460.
W. M. HICKS. The Electrician, Vol. XXXIV., p. 699.
B. A. FESSENDEN. Elec. World, Vol. XXVIII., p. 688.
II. Self-Registering Methods by which a Continuous Curve
is Drawn.
A. BLONDEL. La Lumiere Electrique, Vol. XLL, p. 401 ; Vol.
XLIV., p. 185 ; Vol. XLIX., p. 501 ; The Electrician, Vol.
XXVIL, p. 603.
W. E. AYRTON. British Assoc. Report, 1895.
BARR, BURNIE and RODGERS. The Electrician, Vol. XXXV.
p. 719.
MANJAN LUTOSLAWSKI. Electrotechnische Zeitschrift, Vol. XVII.,
p. 582.
H. L. CALLENDAR. The Electrician, Vol. XLL, p. 582.
E. B. ROSA. The Electrician, Vol. XL., pp. 126, 221, 318.
III. Optical or Projection Methods
(a) With metal diaphragm as the moving part :
Q. FROHLICH. Electrotechnische Zeitschrift, Vol. VIII., p. 210 ;
Vol. X., pp. 65 and 345.
E. THOMSON. La Lumiere Electrique, Vol. XXVIL, p. 339.
C. ROLLEFSON. Eel. Electrique, Vol. L, p. 461.
408 THE MEASUREMENT OF ELECTRIC CURRENT.
(6) With a soft iron needle as the moving parts :
A. BLONDEL. Comptes Rendus, Vol. CXVL, pp. 502, 748.
H, J. HOTCHKISS and F. E. MILLS. Physical Review, Vol. III.,
pp. 49, 358; Vol. IV., p. 128.
F. J. A. McKiTTRicK. Trans. Am. Inst. Elec. Eng., Vol. XIII.,
Nos. 6 and 7.
(e) With a coil of wire carrying the observed currents as the moving part :
E. GERARD. Bull, de 1'Acad. de Belgique, 1888 ; Phil. Mag.,
Vol. XXIX.
H. BECKER, G. LAHMEYER and G. D. PICARD. La Lumiere
Electrique, Vol. XXXI., p. 16.
G. S. MOLER. Physical Review, Vol. I., p. 214.
(d) With the plane of polarization of a beam of light as the moving part :
A. C. CREHORE. Physical Review, Vol. II., p. 122 ; Vol. III.,
p. 63.
J. PIONCHON. Comptes Rendus, Vol. CXX., p. 872.
(e) With cathode ray in vacuo as the moving part :
F. BRAUN. Weid. Ann., Vol. LX., p. 552.
(/) With stream of mercury as the moving part :
E. L. NICHOLS. Jour. Amer. Assoc. Ad. Science, Vol. XLIL, p. 57.
(g) Miscellaneous methods :
LIPPMAN. 1875. The Electrician, July 17, 1896. (Uses a
capillary electrometer.)
P. JANET. Comptes Rendus, Vol. CXVIII., p. 862 ; Vol. CXIX.,
pp. 58, 27, 399. (Uses a chemical method.)
IV. Oscillograph Methods.
A. BLONDEL. Proc. French Association for the Advancement of
Science. 1898.
H. ABRAHAM. Comptes Rendus, Vol. CXXIV., p. 758.
W. D. B. DUDDELL. The Electrician, Vol. XXXIX., p. 636.
DUDDELL and MARCHANT. Journal Inst. E.E., Vol. XXVIII., p. 1.
THE MEASUREMENT OF ELECTRIC CURRENT. 409
The most convenient instrument for ordinary laboratory
work will be found to be the projection form of Duddell
oscillograph. In using it, a powerful parallel beam of light
from a lantern containing a hand-regulated arc lamp with
good vertical and horizontal slow-motion screws is thrown on
the mirrors of the oscillograph, and a cylindrical lens fixed in
front of the mirrors focuses the ray when reflected on to a
sheet of tracing paper laid over a curved glass screen. On
this tracing paper is then seen, when the oscillograph is in
operation, one or two bright sinuous lines of light, which are
the wave forms of the currents passing through the oscillo-
graph wires. If one of these currents is proportional to the
electromotive force in, or the potential difference of, the ends
of a circuit, and the other is part or the whole of the current
in that circuit, then the two sinuous lines will properly
represent the variation of current and voltage, and the
curves can be traced on the paper and investigation can be
made of their form and phase difference. The oscillograph
method has one enormous advantage over the point-by-point
method, in that the observer is enabled to see a transient
change in the wave form. The oscillograph shows at a
glance the whole of one wave, and a change anywhere is
instantly visible.
15. The Use of Transformers in Alternating Current
Measurement. The measurement of alternating currents of"
moderate value may be carried out as already described by
electrodynamic or hot-wire instruments. It often happens
however that measurements are required of alternating
currents haviDg very large or very small values. It is then
possible to bring these within the compass of instruments
found in every well-equipped laboratory by employing
transformers. Thus, for instance, a large alternating current
may be measured by passing it through a low resistance strip
of known value and measuring the potential difference of the
ends of the strip by means of a step-up transformer and an
410 THE MEASUREMENT OF ELECTRIC CURRENT.
ordinary electrostatic voltmeter reading, say, from 60 to
100 volts.
It has been shown by Mr. A. Campbell* that for the
purpose it is necessary to use a transformer with a well closed
iron, circuit and a primary coil of low resistance and large
inductance. This primary has its terminals connected to the
ends of the low resistance strip through which the current to
be measured is passing, and its secondary terminals connected
to an electrostatic voltmeter. The transformer may con-
veniently have a transformation ratio of 1:100.
As an example of the details of an appropriate transformer
Mr. Campbell (loc. cit.) gives the following specification :
The primary coil may consist of 100 turns of No. 16 wire,
and the secondary of 10,000 turns of No. 40 wire, the coil
consisting of iron stampings having a total weight of T5 kilos.
In the case of the above transformer the variation of the
transformation ratio from the value 10 was T9 per cent, at a
frequency of 39 and 0'8 per cent, at a frequency of 86.
Such a transformer can, of course, be adjusted to have any
required transformation ratio at a fixed frequency. If it is
to be used for varying frequencies, then compensation may
be introduced by the employment of a very small additional
transformer having its primary in series with that of the
main transformer and its secondary joined in reverse direction
with that of the secondary of the main transformer. In this
case the small transformer can have its turns so adjusted that
an increase in frequency causes it to deduct a little from the
secondary voltage of the main transformer, and keep the
resulting voltage transformation ratio constant.
The above device enables us to make use of an electro-
static voltmeter, reading from, say, 60 to 150 volts, to
measure alternating currents covering a wide range in value.
\ The advantage of the method is that it introduces no
sensible inductance into the circuit of the current to be
measured, and that it is applicable to very large currents,
* Proc. Inat. Elec. Eng., April, 1901.
THE MEASUREMENT OF ELECTRIC CURRENT. 411
such as those which would have to be measured in testing a
large alternator.
We have already mentioned the use of an air-core trans-
former to transform alternating currents in known ratios
(see page 392), but the method of measuring the volt fall
down a low resistance strip by means of a suitable trans-
former combination and an electrostatic (preferably reflecting)
voltmeter is more convenient. It need hardly be said that
the electrostatic voltmeter used should be carefully calibrated
in position by means of a potentiometer, a Clark cell and
a divided resistance.
16. Measurement of the Frequency of an Alternating
Current. Frequency Tellers. In many alternating current
investigations it is necessary to know the periodicity of the
current. If the alternator is accessible this can easily be
done by ascertaining the speed. If, however, the alternator is
in a distant station some appliance is necessary which will
measure the frequency of the current as it is supplied on the
circuit. Instruments for doing this are called frequency
tellers. For this purpose several devices have been invented.
In Campbell's frequency teller* a soft iron strip is so held in a
frame that it can be caused to protrude more or less from a
holding block. The end of the iron strip projects over an
electromagnet with laminated core, through the coils of which
passes the alternating current to be estimated. The iron
strip has a natural free period of vibration, and if the attrac-
tive impulses which act on it, due to the period magnetisa-
tions of the electromagnet, agree in frequency, the amplitude
of vibration of the strip becomes considerable.
The instrument includes a slow-motion arrangement for
pushing the iron strip more or less in or out of the clip which
holds it at one end and an indicating needle which magnifies
the motion. The observer makes the movement until the
sound or visible oscillations of the vibrating iron strip is a
* See The Electrician, Vol. XXXVIL, p. 437.
412 THE MEASUREMENT OF ELECTRIC CURRENT.
maximum, and then he reads off on the scale of the instru-
ment the frequency of the current passing through the coils
of the electromagnet. The instrument is graduated by
applying to it currents of various frequencies, and is said to
read frequency to within 0'2 per cent,
In another modification due to C. Kinsley* the free period
of the strip is altered, not by varying its length, but by
sliding along it a non-magnetic rider or weight.
A third variety of frequency teller, suggested originally by
Profs. Ayrton and Perry,f consists of a stretched wire placed
between or over the poles of an electromagnet. The wire
may be of iron, and the magnet coils may be traversed by
the current to be examined. In this case the periodic attrac-
tive impulses set the wire in vibration if its free period is in
concordance with that of the currents or is some harmonic
of it. The free period of the wire is determined by its length,
diameter, density and tension, arid is expressed by the equation
where /=the periodic time, / = the length of wire, r = the
semi-diameter, 8 = the density of the wire, and T = its tension
in dynes. Hence, if T is varied by using different stretching
weights, the free period of vibration of the wire may be made
equal to that of the exciting current of the magnet, and
when this is the case the vibrations of the wire become a
maximum.
The periodic current may be sent along the wire and the
magnet may be a permanent magnet. In this case, however,
the determination of the frequency is complicated by the
variable rise in temperature of the wire produced by the
current. Hence it is better to pass the current examined
through the coils of the magnet and use an iron wire or wire
with small iron armature attached to it, varying the tension
* See The Electrician, Vol. XL., p. 258.
t See " Laboratory Notes on Alternate Current Circuits." Proc. Inst. E. E.
Vol. XVIII., p. 310.
THE MEASUREMENT OF ELECTRIC CURRENT. 413
on the wire until unison is produced between its free period
of vibration and that of the current through the magnet coil.
A fourth method depends upon the use of a telephone
If an alternating current is passed through a magneto
telephone receiver its diaphragm is set in vibration, and it
emits not only a fundamental note corresponding to the
frequency of the current, but a series of higher harmonics.
The note of the telephone may be examined by testing it
with a sliding resonator tube and varying the length of the
column of air until resonance is produced. The resonator
tube length is altered until two lengths are found which both
exalt the note of the telephone. The periodicities corre-
sponding to these lengths are then known from the formula
y=n\
where X is the wave-length and V the velocity of sound
at the then temperature of the air. The length of the
resonator tube which then resounds is obviously one-quarter
of a wave-length.
Thus, if the length of resonator tube is 20cm., we know
that the wave-length is 80cm., and hence the frequency n is
*"* , where t is the temperature of the air. Hence,
80
at 15C. n = 427.
If, for instance, two resonator tube lengths are found, one
19'lcm. and the other 16*5cm., corresponding to frequencies
of 420 and 480, then these are harmonics, and the greatest
common divisor viz., 60 is the frequency of the fundamental.
For most electrical laboratory purposes, a carefully
calibrated Campbell frequency teller will be found to be
a most useful instrument, and will give the frequency of
usual alternating periodicities within at least 0'5 per cent.
17. The Measurement of the Phase-difference of
Periodic Current Phasemeters. An important measure-
ment in connection with alternate-current working is the
determination of the phase difference of two currents. If
414 THE MEASUREMENT OP ELECTRIC CURRENT.
two equi-periodic currents follow a simple sine law of vari-
ation, then the angular interval between their maximum or
zero values expressed in degrees, taking 360 to represent
the complete common period, is called their phase difference. If
the two currents can be passed in part or in whole through
the two wires of a double oscillograph, then a simple
inspection suffices to give the required information. It may
be, however, that the observer does not possess an oscillo-
graph, and then he may proceed by other means to obtain
the desired knowledge. One method is by the use of a
soft iron needle, as suggested by Lord Rayleigh.* Let two
circular coils of wire be prepared suitable for carrying the
two alternating currents which are to be examined as regards
difference of phase or lag. Let us, in the first place, assume
that these currents are simple periodic currents, or that they
are sine-curve curves ; in other words, let the instantaneous
value i of either current be represented by an expression of
the form,
i = I sin pt,
where I is the maximum value and p = 27rn, n being the
frequency and t the time reckoned from the instant when
i is zero. Let the two currents have the same frequency
but different maximum values, and let their phase difference
be represented by an angle 0. It is required to determine <.
The two currents are then represented by the equations
i = I sin pt,
*' = I'sin(/rt-0).
Hence, the root-mean-square (E.M.S.) value of i is I/\/2, and
that of i' is F/V2.
Suppose, then, that the two currents are passed through the
above-mentioned coils, and that these are placed with axes
in one line and paralled to each other. At some point
between them is placed a short soft iron needle (say 2cm. in
length), suspended by a torsion wire or glass fibre and
* Phil. Mag., May, 1897 ; or The Electrician, Vol. XXXIX., p. 180. j
THE MEASUREMENT OF ELECTRIC CURRENT. 415
carrying a mirror so that its deflections can be observed by a
mirror and scale method as usual. The upper end of the
torsion fibre should be carried on a torsion head so that it may
be twisted round through a known angle. The needle must
be so placed that its axis makes an angle of 45deg. with the line
joining the centres of the coils. First let one current, i, be
passed through one coil. It will create an alternating mag-
netic field, and this field will exert a couple or torque on the
soft iron needle proportional to I 2 . This can be measured
by the twist necessary to be given to the torsion head to bring
the needle back to the original position, or, if the deflection
is small, by observing simply the deflectional angle of the
needle.
Next, let the other current be passed alone through its coil,
and again observe the angle of deflection or torque acting on
the needle. It is proportional to I' 2 .
In the third place, let both currents be passed at once
through their coils, and let the joint field act on the soft iron
needle. Then the deflecting couple is proportional to
I 2 + 1' 2 211' cos 0.
Hence, if the first observed deflection or torsional angle is 9,
the second 9', and the third 6", we have
I' 2
where a is some constant depending on the torsion value of
the suspension. Hence, if the fields due to each current
oppose each other,
. O+V-O"
COS0 = -- . .
2 +/06 1
Thus, suppose 9 = 9 ' = 40 and 0" = 26J, then cos < = 0'67,
= 48deg. If the two equi-periodic currents considered do
not follow a simple sine law of variation, then their zero
points have not the same phase-difference as their maximum
416
THE MEASUREMENT OF ELECTRIC CURRENT.
values. Lord Kayleigh shows, in the original Paper, that
even if the currents do not follow the sine law, or are not
simple periodic currents, the above expression for cos <f> gives
us what is called the power-factor of one current with respect
to the other.
If, then, one of the currents is proportional to the voltage
of a current and the other to the current flowing in it, the
value of cos obtained as above is a factor which, if multi-
plied by the K.M.S. values of the current and voltage, will
give the true power being taken up electrically by the circuit.
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1
IT
7
FIG. 29.
Instruments for indicating the phase difference of two
simple periodic or harmonic currents are called phasemeters.
One convenient form is that invented by Von Dolivo-
Dobrowolsky.*
If two circuits are wound on a frame at right angles to
each other (see Fig. 29), and if a disc of soft iron having an
indicating needle attached is suspended at the centre, then, as
is well known, if there is any difference of phase between
periodic currents of equal frequency passing through the two
coils, then there will be a torque tending to rotate the iron
* See The Electrician, Vol. XXXIII., p. 610.
THE MEASUREMENT OF ELECTRIC CURRENT.
417
disc- This torque can be resisted by the action of a spiral
spring, and the instrument can be graduated by trial to show
on a dial (see Fig. 30) the phase difference of the currents.
If i and i' are the instantaneous values of the equi-periodic
currents, and if <p is their difference of phase, then the torque
T acting on the disc is proportional to n* sin 0. If one of
these coils is a high resistance inductionless coil, and is
connected to the terminals of any alternating current circuit,
then the current through that coil will be proportional to the
potential difference of the ends of the said circuit and in step
FIG. 30.
with it. If the other coil is traversed by the current entering
the above-named circuit, then the indications of the phase-
meter are proportional to ^esin^>, where <j> is the angle of
phase difference of the current i and the voltage e of the
circuit. If the voltage is always the same, then the indica-
tions of the instrument are proportional to the idle current,
i sin 0, passing into the circuit, and the direction of deflection
shows whether this idle current lags or leads.
The phase-meter may be graduated for a given frequency
and RM.S. value of the voltage to read directly on the dial
the ampere value of the idle current passing through it.
E B
418 THE MEASUREMENT OF ELECTRIC CURRENT.
Hence such an instrument is useful, in an alternating current
station, to indicate at a glance the so-called wattless current
passing out into a circuit.
Eeferences to appliances and methods for measuring phase
difference will be found in the following Papers :
J. TUMA. Science Abstracts, Vol. I., pp. 148 and 266.
The author employs a soft iron needle and an arrangement of two coils at
right angles carrying the two currents. Otherwise the principle of the
apparatus is the same as in the instrument of Lord Rayleigh above described.
MOLER and BEDELL. The Electrician, Vol. XXXIII., p. 210,
Describes an optical phase indicator.
VON DoLivo-DoBRowoLSKY. See The Electrician, Vol. XXXII.,
p. 40, and Vol. XXXIII., p. 610, for description of soft iron
disc phase meter.
E. ARNO. Eel. Electr., Vol. XX., 1899, p. 225; also Science
Abstracts, Vol. III., p. 71.
This writer describes an instrument which is a combination of a Weber
dynamometer, having separate coils, and an instrument to produce a rotating
magnetic field, having separate coils fixed at right angles, and a closed movable
circuit placed inside them.
THE MEASUREMENT OF ELECTRIC CURRENT.
419
TABLE I.
Fuse- Wire Currents. (SiR W. H. PBBBCE.)
Melting currents
in amperes.
Approximate gauge of wire in B.W.G. fused by the
stated currents in the case of the metals
Tin.
Lead.
Copper.
Iron.
1
36
35
47
40
2
34
32
43
36
3
30
28
41
33
4
26
26
39
31
5
24
24
38
29
10
20
20
33
24
15
18
18
30
22
20
17
17
27
20
25
16
16
26
19
30
15
15
25
18-5
35
14-5
14
24
18
40
14
13
23
17-5
45
13
12-5
22-5
17
50
12
12
22
16
60
11-5
2/15
21
15
70
10-5
2/14
20
14
80
10
2/13
19
13-5
90
9-5
3/15
18-5
13
100
9
4/16
18
12
120
8
3/13
17-5
2/15
140
2/10
4/14
17
2/14
160
4/13
4/13
16-5
2/18}
180
3/11
4/12
16
2/13
200
4/12
5/13
15
2/12
250
5/12
5/12
18}
5/16
EE2
420
THE MEASUREMENT OF ELECTRIC CURRENT.
TABLE II.
Electro-chemical Equivalents.*
Elements.
T3
~
^ rj
rS 00*
Atomic
weight.
Chemical
equiva-
lent.
Electro-
chemical
equivalent
in milli-
grammes
per coulomb
Coulombs
per
gramme.
Electro-
chemical
equivalent
in grammes
per ampere
hour.
Electro-Positive.
Hydrogen
Potassium
H 1
K 1
1
39-04
1
39-04
0-010384
0-40539
96293-00
2467-50
0-03738
1-45950
Sodium
Na 1
22-99
22-99
0-23873
4188-90
0-85942
Aluminium
Al 3
27-3
9-1
0-09449
1058-30
0-84016
Magnesium
M" 2
23-94
11-97
0-12430
804-03
0-44748
Gold
An 3
196-2
65-4
0-67911
1473-50
2-44480
Silver
Ap 1
107-66
107-66
1-11800
894-41
4-02500
Copper (Cupric) ...
(Cuprous). .
Mercury (Mercuric)
,, (Mercurous)
Tin (Stannic)
(Stannous) ...
Iron (Ferric)
,, (Ferrous)
Nickel
Zinc
Cu 2
Cu 1
Hg*
Hgi
Sn 4
Sn 2
Fe 3
Fe 2
Ni 2
Tin 2
63
63
199-8
199-8
117-8
117-8
55-9
55-9
58-6
64-9
31-5
63
99-9
199-8
29-45
58-9
18-64
27-95
29-3
32-45
0-32709
0-65419
1-03740
2-07470
0-30581
0-61162
0-19356
0-29035
0-30425
0-33696
3058-60
1525-30
963-99
481-99
3270-00
1635-00
5166-4
3445-50
3286-80
2967-10
1-17700
2-35500
3-73450
7-46900
1-10090
2-20180
0-69681
1-04480
1-09530
1-21330
Lead
Ph 2
206-4
103-2
1-07160
933-26
3-85780
Electro- Negative.
Oxygen
O 2
15-96
7-98
0-08286
Chlorine
ni 1
35-37
35-37
0-36728
Iodine
P
126-53
126-53
1-31390
Bromine
Br 1
79-75
79-75
0-82812
Nitrogen . .
N 3
14-01
4-67
0-04849
* Taken by permission of " The Electrician " Publishing Company (Ltd.) from
the " Electrical Trades' Directory and Handbook."
CHAPTER IV.
THE MEASUREMENT OF ELECTROMOTIVE FOKCE.
1. Electromotive Force Measurement. Being provided
with a standard of electrical resistance and means for defining
or obtaining an electric current, the value of which in amperes
or recognised units is known, we can obtain the consistent
unit of electromotive force by measuring the fall of potential
down the unit of resistance when the unit current flows
through it. In practice we may proceed to recover the
practical unit of electromotive force, called the International
or standard volt as follows :
Prepare a coil of manganin wire which has a resistance of
one International ohm. This wire should be of a gauge
or cross section sufficient to carry a current of 1 or 2
amperes without sensible heating, and should preferably
consist of a bare manganin wire of about No. 16 S.W.G.
wound on a wooden frame. The best form for this coil is to
construct a short skeleton wooden drum about Sin. in
diameter on which may be wound in grooves the necessary
length of some 18ft. to 20ft. of the bare manganin wire.
The drum may be made by putting eight wooden pegs
into holes bored near the circumference of two circular
wooden discs lOin. or llin. in diameter. Instead of winding
on the drum a length of wire having an exact resistance of
1 ohm, it will be sufficient to measure with great care the
resistance of the length of wire actually wound on it, provided
its resistance is nearly 1 ohm. The ends of the wire
422 MEASUREMENT OF ELECTROMOTIVE FORCE.
should be silver-soldered to stout copper rods which form the
terminals, and between these rods the resistance must be
accurately measured.
This resistance coil is then to be joined up in series with
a Kelvin deciampere-balance, which has been previously
most carefully standardised by silver deposit (see Chapter III.,
3, p. 347), and a current having a known value in Inter-
national amperes is then sent through this resistance. The
product of the values of the known current and known
resistance gives us, then, the value in International volts of
the potential difference between the copper terminals of the
resistance coil.
In this manner we recover or create a known voltage
between two points. It is, however, more convenient to
preserve a standard voltage in the form of a standard Clark
or Weston cell (see Chapter I., 8, p. 86), and to employ the
known voltage obtained as above mentioned to evaluate the
electromotive force of the cell. This can be done in the
following manner :
The standard cell to be checked is joined up in series
with a very sensitive galvanometer and a wire of high
resistance say of 10,000 ohms the two being placed as a
shunt across the ends of the above-mentioned 1 ohm
resistance. It is well to insert a key, so as to close the
circuit of the cell only when required. A current is then
passed through the Kelvin deciampere-balance, a carbon
rheostat, and the manganin resistance in series with it, and
is adjusted to have such a value approximately 1/5 amperes
that, when it flows through the manganin 1 ohm resist-
ance, it creates a fall of potential down it equal to the
electromotive force of the Clark cell. The Clark cell must be
so joined up (see Fig. 1) that its positive or mercury pole is
in connection with that end of the manganin resistance by
which the current enters it.
When this arrangement of apparatus is complete the experi-
mental measurement consists in adjusting the current through
MEASUREMENT OF ELECTROMOTIVE FORCE.
423
the ampere balance until the galvanometer in series with the
Clark cell shows no deflection when the key K is down.
This being the case, the product of the observed ampere-
balance current and the resistance of the manganin wire E
is equal to the value of the electromotive force of the Clark
cell at the temperature of the day. The Clark cell should
be provided with a thermometer by means of which its
temperature can be taken. In this manner the recovered
standard of voltage can, so to speak, be transferred to a
standard cell and be rendered permanent.
In an electrical testing laboratory the cells used as stan-
dards of electromotive force should be checked at intervals
so as to re-determine their absolute electromotive force values.
A Kelvin Deciampere-balance.
E, 1 ohm Manganiu Resistance.
G High-resistance Galvanometer.
Cfc Clark or Weston Standard Cell.
K Key.
r Resistance of 10,000 ohms.
C Adjustable Carbon Rheostat.
Fm. 1.
It was by a method of the above kind that Lord Eayleigh
made his original measurements of the electromotive force of
the Clark cell. An account of his work is found in a Paper
by Lord Kayleigh and Mrs. H. Sidgwick in the Phil. Trans.
of the Eoyal Society, Part II, 1884, entitled "On the
Electrochemical Equivalent of Silver, and on the Absolute
Electromotive Force of Clark Cells." In this Paper Lord
Eayleigh first describes the construction of an absolute
ampere-balance for the evaluation of the current in absolute
measure. This consisted of two fixed circular horizontal coils,
the distance between their planes being equal to the radius
424 MEASUREMENT OF ELECTROMOTIVE FORCE.
of either of them. Between these coils was supported another
smaller circular coil, with its plane horizontal and its centre
on the line forming the centres of the fixed coils, and
midway between them. This third coil was suspended from
the beam of a weighing balance, as shown in Fig. 20, p. 71,
Chapter I. The movable coil had the current led into and
out of it by flexible leads. The current to be measured was
passed through all three coils in series, so that the electro-
dynamic forces tended either to lift or lower the movable coil
and thus decrease or increase its apparent weight. By
reversing the current through the fixed coils the direction of
the force could be reversed, and hence half the difference
between the apparent weight of the movable coil when the
current through the fixed coils is reversed gives the force in
gravitation units exerted by the fixed upon the movable coil.
The general theory of the instrument is as follows : Consider 'first two
coils only viz., a fixed and a movable co-axial coil. Let n, ri be the respective
number of turns of wire on each, i, i r the current in each, and M the
coefficient of mutual induction. Then the attraction or repulsion between the
coils, in absolute units is equal to
,
dx
where x is the distance between the parallal planes of the coils.
The full expression for the attraction between two parallel co-axial circular
coils of mean radii A, a, and with centres respectively at distances B, 6 from
a point on their common axis, is given by Maxwell ("Electricity and
Magnetism," Vol. II., 304) :
LetC 2 =A 2 + B 2 . Then
.
do C V. C C
where a and 6 are supposed to be small compared with A.
In the present case there are two fixed coils, and if we take the origin mid
way between them, then
.
Also, approximately, for the fixed coils we have B 2 = |A 2 .
Hence ^ = 6w^ x 0'2862.
db A 2
In other words, the force of attraction / of the fixed coils on the movable is
given by /= hnn'i?a?IA z , where h =6?r 2 x 0*2862, and i is the current through
the coils.
MEASUREMENT OF ELECTROMOTIVE FORCE. 425
Accordingly, if ft is the ratio of the galvanometer constants of the coils
that is, if 3= , we have /= hBPi?n' s ln.
An
In the coils used by Lord Rayleigh
A=24-81016cms. n' = 225
a = 10'2473cms. n = 242
For the elaborate details of the process of weighing the
movable coil and reducing the results to calculation we must
refer the reader to the original Paper by Lord Eayleigh,
which is an example of accurate scientific research of the
most perfect kind.
Having obtained the means of defining in absolute
measure a steady electric current, this current was passed
through a resistance, and the fall of potential compared, as
above described, with the electromotive force of a Clark cell
when not sending current.
Ck
ll -
** > Cy Cy "A/WWWWWW
A Ampere-balance- I Kj, Rg Resistance Boxes.
K Resistance Coil. X Commutator.
Ck Clark Cell. L Two Leclanche" Cells.
G Galvanometer. |
FIG. 2.
In the above arrangement, as employed by Lord Eayleigh,
it was not found convenient to alter the main current flowing
through the ampere-balance when once started; hence the
fall of potential down the resistance was not exactly equal to
the electromotive force of the Clark cell. A compensating
electromotive force was, however, introduced as follows:
Let A (see Fig. 2) be the ampere-balance and E the resistance
through which the current traversing the balance is flowing.
'Let Ck be the Clark cell and G a sensitive galvanometer of
426 MEASUREMENT OF ELECTROMOTIVE FORCE.
high resistance. Then L is another battery, say of two
Leclanche' cells, the terminals of which are short-circuited by
a large resistance consisting of the coils in two resistance
boxes E- 1 , E 2 . A derived circuit is taken from this Leclanche
cell circuit, as shown in the figure, so as to insert an assisting
or opposing electromotive force in the Clark cell circuit, which
can be varied as to direction by a commutator X and as to
magnitude by varying the resistances B p K 2 . unplugged out
of the circuit of the two resistance boxes subject always to
the condition that E 1 + K 2 = 10,000 ohms. In this way the
current flowing out of the Leclanche cells is kept constant,
but a variable fraction of their electromotive force can be
used with or against that of the Clark cell Ck, so as to bring
the current in the circuit of the galvanometer G to zero.
Then, knowing the resultant electromotive force in the
galvanometer circuit, which is equal to the product of
the main current and the resistance R, we have only to find
the ratio between the electromotive force of the Clark cell and
that of the fractional part of the Leclanche cells. This can
be done at once by the use of a potentiometer, as described
in a subsequent section of this chapter, with any required
degree of accuracy.
By the above process, Lord Bayleigh* found the electro-
motive force of the Clark cell, at 15C., to be 1/435 volts, and
at tG. it is given by the equation
E, = 1-435{1 - 0-00077(^-15)} volts.
Later experiments decided the Board of Trade Committee
on Electrical Standards to recommend that the value of the
Clark cell electromotive force be taken as T434 International
volts at 15C. If, however, the electrochemical equivalent
of silver per ampere-second is taken as 0-001119 gramme,
instead of 0*001118 gramme as adopted by the Board of
Trade, then the corresponding value of the electromotive
* " The Clark Cell as a Standard of Electromotive Force," by Lord Kayleigh.
Trans. Roy. Soc., Part II., 1885.
MEASUREMENT OF ELECTROMOTIVE FORCE. 427
force of the Clark cell will be a number nearer to 1*432 true
volts at 15C. The Board of Trade values of the electro-
motive force of the Clark cell at various temperatures are
given in Table I. at the end of this chapter.
2. Practical Recovery of a Standard or Known Poten-
tial Difference. If the electrical laboratory possesses, as it
should do, a Kelvin deciampere-balance, the most convenient
practical method of recovering a known potential difference
is to standardise this balance most carefully by passing a
constant current through it of about 4 or 5 amperes, and
then determine by the copper sulphate method of electrolysis
the absolute value of this current with all the precautions
described in Chapter III.
Having standardised the balance, it may be employed to
measure the ampere-value of a current sent through a resist-
ance of known value say, 1 ohm constructed of manganin
wire of a sufficient cross-section not to be sensibly heated by
the current. If it is desired to obtain a known electromotive
force or potential difference of high value such, for instance,
as 2,000 volts then the ampere-balance must be one which
is suitable for alternating as well as for continuous currents.
A wire resistance must then be made having a known value
of 2,000 ohms or thereabouts, and an alternating current of
1 ampere, measured by the balance, must be passed
through it. The exact difference of potential between the
terminals of the high resistance then becomes known.
Generally speaking, however, the expense of constructing a
large current-carrying resistance of 2,000 ohms will be an
obstacle to the employment of this method. There is no
question, however, that it is the most satisfactory process for
conducting with certainty the calibration of high-tension
voltmeters.
The wire resistance must be so constructed as to be as
little inductive as possible. This may be done as follows:
An ebonite or fibre or pasteboard tube has wound upon it a
428 MEASUREMENT OF ELECTROMOTIVE FORCE.
silk-covered manganin wire, or, if bare wire is used, a silk
thread must be wound between the convolutions to prevent
them from touching each other. The coil so prepared is
covered with one layer of mica or shellac paper and another
layer of wire wound upon it in an opposite direction. The two
layers of wire are joined up at one and the same end, so that if
a current is sent through the two layers in series it flows in
opposite directions round each layer. A double-layer coil so
constructed is practically non-inductive, or but little induc-
tive. When traversed by a current there is little or no
magnetic field in the neighbourhood of the wire. A series of
FIG. 3. Skeleton Wooden Drum with Bare Manganin Wire wound
non-inductively on it.
such coils may be joined up in a frame and used as the
current-carrying resistance. It is exceedingly useful to
provide for the testing laboratory a number of resistances
made in this manner of No. 16 S.W.G. manganin wire having
resistances of 1 ohm, 10 ohms, 100 ohms, 1,000 ohms and, if
possible, 2,000 ohms. This size of wire will carry safely
1 ampere for a short time with but little change in resistance.
Instead of winding silk-covered wire on a tube, it is better
to wind bare wire on a skeleton bobbin made by joining
. together two round wooden discs by a number of wooden rods,
as shown in Fig. 3. The turns of wire should be kept apart by
MEASUREMENT OF ELECTROMOTIVE FORCE. 429
a paraffined silk thread or cord wound between them. The
wire should be wound double, two wires being wound on in
parallel and these joined up at one end. The whole wire is,
therefore, nearly non-inductive, and the bobbin can be
immersed in a vessel of paraffin oil, by which means its
temperature can more easily be kept constant and ascertained.
3. The Potentiometer Measurement of Electromotive
Force. Various forms of potentiometer have already been
described in Chapter I. Whatever form the instrument takes
it consists essentially of a resistance, which may be a series of
coils or a long wire stretched over a divided scale. Down
this resistance a uniform fall in potential is made by means
of a battery working through a rheostat in series with the
wire. This battery is called the Working Battery. The
working battery should consist of one or more lithanode
secondary cells of ample size. The cells should be highly
insulated by being placed upon pieces of ebonite. The cells
should be well charged, and then about 25 per cent, of the charge
taken out by discharging the cell slowly. No good results
can be obtained when using a fully and freshly charged cell,,
because there are then irregular changes in its electromotive
force. The cells should be joined up in series with the
potentiometer wire through a carbon plate rheostat.
The wire rheostats in which wire is wound off one cylinder
on to another, or in which a contact spring presses against a
wire wound in a helix on a cylinder, give trouble in dusty
rooms, because the dust gets under the contact and creates a
variable resistance. Whatever form of rheostat is used, the
aim must be to cause a perfectly steady current to flow through
the potentiometer wire or resistance, and be so adjusted as to
value that the wire is not sensibly heated. If a long stretched
wire is employed as the potentiometer wire, the greatest care
must be taken to secure uniformity in its resistance per
centimetre of length, and this uniformity must be proved and
not taken for granted.
430 MEASUREMENT OF ELECTROMOTIVE FORCE.
The potentiometer is set, or the current in the wire brought
to a standard value, by means of a standard cell preferably
a Weston cadmium cell made in the Eayleigh H-form, as
then temperature correction is negligible. If a Clark cell is
employed, it must have a thermometer placed in it, or in the
water bath in which it stands, in order that its temperature
may be known and the proper correction applied to its
nominal value at 15 C. The standard cell must have its
positive pole connected to that end of the potentiometer wire
to which the positive pole of the working battery is attached.
The other pole of the cell is connected through a high
resistance galvanometer, or through a sensitive galvanometer
with a high resistance in series with it, to a slider or contact
maker on the potentiometer wire. The electromotive force of
the standard cell being known, it is clear that, if a point is
found on the potentiometer wire at which, when connected,
the galvanometer shows no current, the fall of potential down
the length of potentiometer wire thus intercepted must be
equal to the electromotive force of the cell The current in
the potentiometer wire can be so adjusted that the fall of
potential down it can be read off directly on a divided scale
placed against the wire. Thus the electromotive force of the
standard cell is, say, 1434 volts ; the potentiometer current
can be adjusted by the rheostats to make the fall of poten-
tial down the 1,434 division of the wire equal to the above
value.
When this is the case the potentiometer becomes direct
reading, and any other electromotive force or potential
difference falling within the range of the potentiometer wire
can be measured at once by merely attaching the terminals
of a circuit formed of the galvanometer in series with this
new source of electromotive force to two points on the poten-
tiometer wire so selected that the galvanometer shows no
current. The positive terminal or highest potential point of
this source of electromotive force must be joined to that end
of the wire nearest to the positive terminal of the working
MEASUREMENT OF ELECTROMOTIVE FORCE. 431
battery. The source of electromotive force may be another
cell, or it may be a difference of potential between two points
on another wire traversed by a continuous current.
4. Measurement of Small Potential Differences.
To measure an electromotive force or potential difference of
about 1 volt or less we attach wires to the terminals of
this source of electromotive force (E.M.F.) or potential
difference (P.D.), and connect them as above described to the
potentiometer, and when it is set we can read off at once on
its scale the value of the E.M.F. or P.D. The potentiometer
is thus easily employed to give us the terminal voltage of a
primary or secondary cell, or the value of a current flowing
through a known low resistance, or of a very small current
flowing through a known higher resistance, provided always
that the P.D. to be measured is less than the whole fall down
the potentiometer wire. In making a number of measure-
ments of this kind the setting of the potentiometer must be
continually tested by coming back on to the Clark or other
standard cell.
In all practical forms of potentiometer, such as Crompton's
or Elliott's, there is a double pole switch on the instrument
so arranged that, without disturbing the galvanometer con-
nections, any cell or terminal wires from any circuit can be
quickly substituted for the standard cell in the galvanometer
circuit. Hence there is no loss of time in continually
re-checking the setting of the potentiometer current, and, if
it has varied, bringing it back to its original value by a touch
of the rheostat.
The potentiometer is especially useful in measuring
small E.M.F.s, such as that of a thermo-electric couple.
The Author designed for certain low temperature, re-
searches a combined resistance bridge and potentiometer
by means of which a thermo-electromotive force could be
measured and immediately afterwards the resistance of a
platinum wire giving the temperature of the junction. The
432 MEASUREMENT OF ELECTROMOTIVE FORCE.
arrangements of this combined bridge-potentiometer are as
follows :
A length of 2 metres of bare manganin wire (No. 36
S.W.G.) is stretched over a scale (see Fig. 4). This wire has
a resistance of 26*576 ohms and a diameter 0*0193 centimetre.
Over the slide wire moves a slider contact P. The other two
arms of the bridge consist of a resistance coil, C, of manganin
wire of 5,000 ohms, and a platinum wire used as a platinum
thermometer. The bridge is provided with current from a
2-cell lithanode battery, B, and a Pitkin-Holden galvano-
meter, G-, having a resistance of 4 ohms, is used with it. In
the diagram (Fig. 4) XZWY is the 2-metre slide wire
having its ends attached to terminal blocks X and Y. B is
the 2-cell battery which is connected through a current
reverser, D, with the ends of the slide wire, having interposed
between one terminal and the block Y either a resistance, E 2 ,
of 200 ohms when used as a bridge, or a resistance E 1? E 4 and
E 3 when used as a potentiometer. E x is a variable resistance
of about 5,000 ohms, R 4 a resistance of 18,200 ohms, and E 3 a
resistance of 10x25*576 ohms, divided into four sections
having ratios of 1, 2, 3 and 4 in magnitude. The galvano-
meter is connected to terminals U and V when the
instrument is used as a bridge and P is the slide contact
maker on the wire ; the other two arms being the 5-ohm coil
C and the platinum wire P x used as a thermometer.
When the instrument is used as a potentiometer the
thermo-couple or other source of E.M,F. is joined in
series with the galvanometer between the slider P and the
end of the resistance coil E 4 . In this case the fall of potential
down the slide wire is measured by the Clark cell Ck. In
order to make the changes of connection rapidly a seven-cup
mercury switch is employed, so that by shifting a pair of
copper forks all the necessary changes of connection are made
instantly.
Eeferring to the diagram, ic will be seen that if we connect
the mercury cups 4 to 5 and 1 to 7 the arrangement is a
MEASUREMENT OF ELECTROMOTIVE FORCE.
433
FF
434 MEASUREMENT OF ELECTROMOTIVE FORCE.
Wheatstone bridge. If we connect cups 3 to 4 and 6 and 7
it is changed to a potentiometer to measure E.M.F., and if
we connect cups 2 to 3 and 6 to 7 we can set the potentio-
meter by the Clark cell.
This form of combined bridge and potentiometer, devised
by the Author,* is of great use in measuring thermo-electro.
motive forces from single couples, and at the same time the
temperature of the thermo junction may be obtained from the
value of the resistance of a platinum wire, P p wound round it.
The instrument may be adapted for a variety of uses in
measuring E.M.F.S which are functions of temperature.
Potentiometers in which the whole or part of the resistance
is an exposed slide wire have the disadvantage that dust
settles on the wire, and then the sliding contact, by which the
connection to the galvanometer shunt circuit is made, is
uncertain in resistance. It must be borne in mind that, as
the position of balance is approached, the effective E.M.F.
in . the galvanometer circuit becomes vanishingly small,
and hence is unable to break through a dust or oxide
film and express itself as a deflection of the galvanometer
coil. Accordingly, for workshop purposes a potentiometer is
preferable which has no slide wire, but in which the resistance
inserted in the circuit of the working battery is wholly of
insulated wire coils included in a box.
A useful form of potentiometer, in which an external or
exposed slide wire only forms a 150th part of the whole
potentiometer resistance, is made by Messrs. Elliott Bros.,
and consists essentially of 149 coils of wire joined in series
with each other, and with a slide wire equal in resistance
to one of them. A perspective view of the instrument is
shown in Fig. 5, and a diagram of connections in Fig. 6.
Each of the 149 sections or coils is about Sin. in length,
and they are all adjusted so as to be absolutely equal in
* See Phil. Mag., July, 1895, p. 95. " On the Thermo-electric Powers of
Metals and Alloys between the Temperature of Boiling Water and the Boiling
Point of Liquid Air." By J. A. Fleming and J. Dewar.
MEASUREMENT OF ELECTROMOTIVE FORCE.
435
resistance one to the other. The slide portion of the wire
KM (Fig. 6) is extremely short, as can be seen in Fig. 5,
and is equal in resistance to one coil. Inequalities in the
drawing of this wire are compensated for by dividing the
scale, over which arm L travels, so that the individual
!FiG. 5. Elliott Potentiometer.
divisions of the divided wire EER are exactly multiples of
the divisions on the scale. As an example, the fall of
potential over 140*7 sections of the divided wire is exactly
five times that over 28 divisions of this wire, and 14
divisions on the scale.
PP2
436
MEASUREMENT OF ELECTROM011VE FORCE.
A reference to Fig. 6 shows clearly how the arrangement
is effected in practice. AB are two terminals, to which the
working battery i.e., the one accumulator cell should be
attached. At C is a small fuse, which serves to protect the
slide wire from injury should too high an E.M.F. be applied
to A and B by accident. DE are the galvanometer terminals,
and across these is connected a short circuit key X, which in
F G F, Gi F 2 G 2
mm
FIG. 6. Diagram of Connections in the Elliott Potentiometer.
its normal, or free, position keeps the galvanometer short-
circuited, and thus protected against violent deflections. A
d'Arsonval galvanometer should always be employed in all
these tests. F, G-, F p G 1 , F 2 , G 2 , &c., are the terminals to
which wires leading to the various sources of potential
differences to be compared should be attached. A multiple
double-pole switch V permits of the two common bars Hand
MEASUREMENT OF ELECTROMOTIVE FORCE, 437
I being connected to any pair of, these terminals at will.
EEE is the divided wire, which is laid round in a circular
position, and divided in 149 parts of equal resistances, small
contacts being placed at each of these 149 points. The
whole of this part of the divided wire, which, of course, is the
essential part of the whole apparatus, is perfectly protected
from mechanical injury by being inside the case.
At one extremity of this wire N" at the 149th contact it
is connected to O, a small fine adjustment rheostat, and so on
to P and Q, two other adjustable rheostats in series, and so
proportioned that the total resistance value of is rather
greater than that of one section of P, and that the total value
of all the sections of P are slightly greater than that of one
section of Q. P, Q, and O are not adjusted in any definite
values they serve simply as adjustments. In practice the
whole of Q, P, and are approximately 200 ohms altogether.
The divided wire itself, EEE, being about 30 ohms resist-
ance, one end of rheostat Q is joined to terminal B.
The other extremity of the wire EEE is taken up through
the top of the instrument at K, where it is led round a curved
segment, and where the moving contact arm L can travel over
it. A scale is fixed to the top of the instrument, and a
pointer is attached to L, so that when the moving contact is
on the stud K, the pointer attached to the arm L stands at
zero on the scale. When the arm L is moved till the pointer
stands at the figure 10, then the moving contact has passed
over a length of the divided wire exactly equal in resistance
to any of the other 149 sections between K and N. A
contact J can travel round the circle of the divided wire and
make contact with any of the 149 small contacts fixed to it.
This contact J is attached to a large toothed wheel, the edges
of which can be seen in Fig. 5 on the right and left of the
instrument. This affords a ready means of shifting the
position of contact J, and its position with reference to.JT
and K can be seen through a small window in the front of
the instrument, through which a number shows corresponding
438 MEASUREMENT OF ELECTROMOTIVE FORCE.
to the number of the contact on which J lies ; a device is
provided to cause J to make contact definitely on either one
or other of any pair of adjacent contact studs on the divided
wire. A wire is led from J to one on the galvanometer
terminals E.
The travelling contact on arm L is connected through a
small key W to the bar of the multiple switch, the other bar
H being connected to the second galvanometer terminal D.
The key is provided with a small clamping device, so that it
can be kept down if desired, and the galvanometer deflections
manipulated with key X. Care must be taken that no source
of E.M.F. is attached by mistake to terminals F, G-, &c., as,
in the event of the key W being clamped down and switch V
being in these terminals, a comparatively powerful current
might flow through the galvanometer and the slide wire,
probably damaging both. The key W, therefore, should only
be clamped down when making a series of tests where there is
no chance of a wrong connection having been made outside
the instrument.
It will be seen that there exists always between A and B
a closed circuit through which the current furnished by the
working battery passes from A through C to M, K, RRR,
N, 0, P, Q, and so to B. This circuit is of variable resistance,
owing to the adjustment of rheostats O, P, and Q ; but in all
cases the whole of the wire ERR is in circuit.
To make an JK.M.F. measurement we proceed as follows:
Fig. 7 illustrates the connections. The working battery
is connected to AB as usual, the standard cell and
resistance to FG. The small separate resistance box is
employed, the two terminals marked " Potentiometer " being
connected to FG, wires attached to the source of E.M.F. to
be measured being connected to terminals on this box, accord-
ing to the various ranges used. The terminals marked
" Potentiometer " have between them a small fractional part
of the whole resistance in the box. Setting the figure 143 at
the window, and arm L at 4 on the scale as before, when a
MEASUREMENT OF ELECTROMOTIVE FORCE.
439
balance is obtained with a multiple switch on the standard
cell at FG, then each movement of the toothed wheel means
0*01 volt, and O'OOOl corresponds to the small whole divisions
on the scale.
Suppose an E.M.F. of about 100 volts is to be measured,
the positive wire should be joined to the terminal marked
-h on the separate resistance box, and the other to the
terminal marked 150. Then, having balanced as above, the
instrument is direct reading in volts that is to say, if a
balance is obtained with 101 at the window and arm L at
FIG. 7. The Elliott Potentiometer and Divided Resistance arranged for
Measuring Voltages.
5-3 on the scale, then the E.M.F. under test equals 101'53
volts. For readings using the + to 15 terminals on the
separate resistance box, the readings must be divided by 10 ;
if using terminals -f- to 300, readings must be multiplied
by 2 ; if using + to 600, multiply by 4.
Supposing it is desired to determine exactly an E.M.F. of
about 2-2 volts. Obviously, if the standard cell is balanced
with 143 at the window and 4 on the scale, the range of the
potentiometer is insufficient to compare this directly. If the
440 MEASUREMENT OF ELECTROMOTIVE FORCE.
terminals + to 15 on the separate resistance box are used,
then the E.M.F. of 2 -2 volts would balance with figure
showing at the window. For great accuracy, the following
method may be adopted : Connect two accumulator cells in
series to AB ; then with switch V (Fig. 6) on FG-, correspond-
ing to the terminals of the standard cell, adjust P, Q and
so that a balance is obtained with 71 at the window aud
arm. L at 7 on the scale (1*434/2 = 0:717). Assuming that
the E.M.F. of the standard is taken at 1434 volts at the
working temperature, then let wires be brought from the
source of E.M.F. to be tested to terminals FG-; then, if a
balance is obtained on moving the multiple switch to FG,
with 111 at the window and arm L at 4 on the scale, the
value of the E.M.F. under test = 1, 114 X 2 = 2-228 volts that
is to say, with the standard balanced at the position corre-
sponding to half its value, all readings at the window and
scale must be double to obtain correct values in volts.
This process can be carried further, but not more than 6 volts
should ever be applied to AB.
In workshop potentiometers it is desirable to avoid the
employment of any slide wire, however short, and to construct
the whole potentiometer of coils of wire contained in a box.
In the case of a potentiometer designed by the Author, the
instrument takes the form of a box having on the ebonite or
marble top surface a set of block contacts arranged in circles,
and each set associated with a radial arm contact like one of
the simple forms of Wheatstone bridge. There are two sets
of concentric block contacts, arranged as in Fig. 8, and a pair
of concentric brass rings to which the radial arms connect the
plugs. Under the top of the box are a series of coils inter-
connecting the blocks, as in a dial pattern "Wheatstone bridge,
the only difference being that each dial is double. There are
three double dials, the coils in between the blocks of the first
dial being each of 10 ohms, those between the blocks of the
second being 1*0 ohm, and those of the third being each 01
of an ohm.
MEASUREMENT OF ELECTROMOTIVE FORCE.
441
The several dials are so joined up that they form one
resistance divided into two sections, but of such a nature that
increasing the resistance of one section decreases by an equal
amount the resistance of the other section. There are 10
blocks to each dial and, accordingly, the maximum resistance
which can be created in either section is 99*9 ohms ; and, no
matter how the dial radial arms are set, the joint resistance of
the two sections always has the same value, viz., 99*9 ohms.
FIG. 8. A Single Dial of the Fleming Potentiometer.
If, then, a single secondary cell is connected to the ends of
this divided resistance, and a high resistance galvanometer
and standard cell are connected to the terminals of one
section of the resistance, it is possible to move the radial
arms in such a manner that the relative magnitude of the
resistances of the two sections is varied, but the total value
of the two sections remains the same.
Let the standard cell be a Helmholtz calomel cell, which
is constructed to have an E.M.F. of 1 volt. Then it
442 MEASUREMENT OF ELECTROMOTIVE FORCE.
is possible to adjust the value of one section of the
resistance by moving the radial arm so that the high
resistance galvanometer indicates no current when the
secondary cell is connected to the terminals of the whole
resistance. For this is the case when the fall of potential
down the section of the resistance to which the galvanometer
is a shunt is 1 volt, and this is so when the sections of the
resistance have a certain ratio near equality.
Suppose, then, that another cell is substituted for the
standard cell, and again the radial arms are so moved that
the galvanometer shows no current. This movement of
the radial arms will not alter the value of the current
flowing through the whole resistance, but will alter the
ratio of the resistances of the two sections. This ratio
may be made such as to bring the galvanometer to zero
once more.
Let K x be the resistance of that section of the whole
resistance to which the galvanometer is a shunt when the
standard 1-volt cell is in series with the galvanometer, and
let K 2 be the resistance of the same section when the second
cell is substituted for it. Let us suppose the total constant
resistance of the two sections of the box is 99*9 ohms.
Let V be the E.M.F. of the cell being tested. Then
it is clear that, since the standard cell has an E.M.F.
of 1 volt, the volt-fall down the whole resistance in the
box is equal to 99'9/K r Hence the E.M.F. V of the cell
tested against it must be equal to IV^i volts.
Accordingly, if the secondary cell attached to the ends
of the whole resistance is large and very constant in
E.M.F., there is no need to have rheostats and other
complications to keep the potentiometer current constant.
The only pieces of apparatus necessary for measuring any
E.M.F. are the standard 1-volt cell, a high resistance gal-
vanometer and keys, the divided resistance above described,
and a large secondary cell which has been charged and
then partly discharged.
MEASUREMENT OF ELECTROMOTIVE FORCE.
443
5. The Calibration of a Low-Tension Voltmeter.
Suppose it is desired to calibrate or check the scale
accuracy of a voltmeter reading, say, from zero up to 150
volts, by reference to the potential difference of a standard
cell, we proceed as follows : A resistance, r 1 r a r 3 (see Fig. 9)
must be provided, which is generally called a volt-box, con-
sisting of a number of bobbins of manganin wire contained
in a box. These coils of wire are arranged in series so as to
form a resistance of 10,000 or 20,000 ohms, which is divided
V Voltmeter.
B Testing Battery.
G High-resistance Galvanometer.
i r 2> r s Divided Resistance.
a, b Potentiometer Wire.
Ck Clark Cell.
b Potentiometer Working Cell.
FIG. 9. Potentiometer Arrangement for Checking Voltmeter.
in certain ratios by terminal attachments. Thus one set of
terminals may be so arranged that the whole resistance is
divided into two sections in the ratio of 99 : 1, another set
in the ratio of 9:1, another 999 : 1, and so on. This
resistance is joined across the terminals of the voltmeter V
to be checked, and a proper potential difference applied by
means of secondary cells B to give any required reading of
444 MEASUREMENT OF ELECTROMOTIVE FORCE.
the voltmeter, For this purpose a set of 100 small lithanode
cells are very convenient, giving any required E.M.F. from
2 to 200 volts.
Suppose, for instance, we require to check a voltmeter,
reading up to 100 volts, in the neighbourhood of 100 on the
scale. We should select those terminals of the volt-box which
give us a ratio of 99 : 1 in the whole resistance. Wires
would then be taken from the smaller section r x r 2 of the
resistance to a potentiometer. We then know that, what-
ever may be the value of the fall of potential down the
small section r x r 2 of the resistance as measured by the poten-
tiometer, the total fall of potential down the whole wire r^
and therefore the actual true voltage applied to the voltmeter
terminals, is 100 times as great. In Fig. 9 is shown a
diagram of the connections to be made.
By varying the number of secondary cells in this battery
B attached to the terminals of the voltmeter V, we can make
various known or measured potential differences on these
terminals, and compare these values with the scale reading of
the voltmeter. A table can be drawn up of the true poten-
tial differences which correspond to various scale readings.
We then proceed, as in the case of an ammeter, to make a
curve of errors.
Take a straight horizontal line on a sheet of paper and
divide it into equal parts, representing the scale readings of
the voltmeter (see Fig. 10). At each point set up a perpen-
dicular the length of which is made proportional on same
scale to the difference between the scale reading of the volt-
meter and the true value found for the potential difference
making that reading. Let this perpendicular be drawn
upwards when the error of the voltmeter is positive and
downwards when the error of the voltmeter is negative.
Hence, if, corresponding to a scale reading of 100, the true
potential difference is 101*2, then the error is positive
that is, we have to add 1*2 volts to the scale reading to
arrive at the true voltage corresponding to the scale reading
MEASUREMENT OF ELECTROMOTIVE FORCE.
445
100. In this manner the voltmeter can be calibrated
throughout the scale and a curve of errors found for it.
If the voltmeter is one constructed on an electromagnetic
principle, then it is necessary to take a series of ascending
and descending scale readings to ascertain if there is sensible
hysteresis error. Also tests should be made with the volt-
meter in various positions, or with magnets near it, to discover
how far it is affected by position or the presence of other
magnetic fields.
In the case of an electrostatic voltmeter it is necessary to
be on our guard against errors introduced by contact difference
FIG. 10. Error Curve of a Voltmeter.
of potential. Take the case of a Kelvin electrostatic volt-
meter. In this instrument the " needle," or movable portion
of the instrument, is of aluminium, and the fixed quadrants
are made of brass ; hence, when a secondary cell battery is
joined in between the terminals of the instrument, the scale
reading will be determined by the voltage of this battery plus
or minus the Volta contact potential difference of an
aluminium-brass couple. This latter amounts to about 0'3 of
a volt. Hence we find that an electrostatic voltmeter gives
scale readings slightly different when the " needle " is positive
from that which it does when the " needle " is made negative
446 MEASUREMENT OF ELECTROMOTIVE FORCE.
by reversing the connections of the working battery. Hence,
in checking the voltmeter, note must be made of the mode in
which the working battery is connected.
6. Calibration of a High-Tension Voltmeter. Supposing
we have calibrated in the manner described in the previous
section an electrostatic voltmeter reading up to 100 volts.
We may then employ this voltmeter as an intermediate
standard instrument to check a high-tension voltmeter
reading, say, up to 2,000 volts. For this purpose we require
a divided resistance which can be safely placed across a
2,000-volt alternating-current circuit. This can be made as
follows :
Provide 100 coils of double silk-covered platinoid wire
No. 36, each wire 100ft. in length, coiled up into a coil of
FIG. 11.
6in. in diameter, leaving both ends out. Squeeze up each
coil into a sort of hank (see Fig. 11) and bind it in the middle
with tape. Boil each coil or hank well in melted paraffin
wax. The resistance of each hank of wire will be about
400 ohms. Make a wooden frame so that 25 of these hanks
can be spaced lin. apart and be held by silk string, as shown
in Fig. 12. Join up the wires of the hanks in series. Connect
four such frames of wood with cross bars and join up all coils
in series. Bring the ends of the whole series and of each hank
to well-insulated terminals on the outside of the wooden
MEASUREMENT OF ELECTROMOTIVE FORCE.
447
frame. The whole wire will then form a resistance of 40,000
ohms in 100 sections, and each section will be perfectly
insulated from its neighbour. The wire will bear placing
across a 2,000-volt circuit for any length of time without over-
heating or risk of failure of the insulation.
This divided resistance can then be placed across the
terminals of the high-tension electrostatic voltmeter, and a
calibrated low-tension electrostatic voltmeter joined across
the terminals of one section, say ^Vth of the whole wire.
Hence, when the high-tension voltmeter is connected to a
O
FIG. 12. Inductionless Safety Resistance.
2,000-volt alternator or transformer, the reading of the low
tension voltmeter will give the true volt fall down ^ih of
the resistance, and therefore the true voltage at the terminals
of the high-tension voltmeter.
It should be noticed, however, that there is a possible
source of error in the above process which arises from the
capacity of the low-tension voltmeter. This may be explained
as follows :
Let us suppose, in the first place, for the sake of avoiding mere mathematical
complexity, that the divided resistance is entirely non-inductive. Let R and Rj
be the resistances of the two sections of this resistance, and let the low-tension
electrostatic voltmeter be joined over the section of which the resistance
448
MEASUREMENT OF ELECTROMOTIVE FORCE.
is R (see Fig. 13). Let the capacity of the voltmeter be represented in the
figure (Fig. 13) by a condenser C. Then let the instantaneous values of the
currents through R, R, and C be i, i t and z 2 , and let the instantaneous values
of the potential fall down R, R, and R+Ri be v, Vi, and v'.
We have then the following equations :
}' fby the principle of continuity,
^ l ^=^c,)
Ohm's law,
dv
and ^ = dt ^ rom definition.
Also, let v' = V sin pt, the frequency being as usual p/Str.
v-'-
FIG. 13.
Obviously, then, we have the following equation :
dv v '
Differentiating with regard to t, we obtain, on re-arranging terms,
dv
and eliminating^ between (i) and (ii), and remembering that 0-^= - Cp^v,
if the variation of v is harmonic, we obtain finally the equation
In virtue of a well-known transformation (see "The Alternate^ Current Trans-
former," Fleming, Vol. L, p. 161) we can write the above equation in the form
Hence, if V is the maximum value of v, it follows that
V^R!
MEASUREMENT OF ELECTROMOTIVE FORCE. 449
or, if we write K a for 1/R, and K for 1/R, we have
V_ K,
V '
If, then, C = 0, or if the low-tension voltmeter has no sensible capacity, we
V R
have V^R-PR 5
in other words, the maximum or root mean-square value of the volt fall down
the section of the resistance R is to the fall down the whole resistance in the
ratio of those resistances. If, however, (J is not zero, or if p is large and if R
and Rj are large, then the root-mean-square values of the volt falls are no
longer in the exact ratio of the resistances.
There is no need to complicate the proof by considering the case when these
sections of the divided resistance have slight inductance. The same principle
holds good.
Hence, although the use of the divided resistance is
a convenient method of stepping from one voltmeter t:>
another, it is necessary to take the precaution to check
the high-tension voltmeter by the only unexceptionable
method viz., by connecting it to the terminals of a high
known resistance through which a known measured current
is passed.
7. Self-recording Voltmeters. In many cases it is
necessary to secure a continuous record of the difference in
potential between two points, and this can be accomplished
by the use of a self-recording voltmeter. These instruments
consist of two parts a voltmeter part and a paper-carrying
drum which is made to revolve by clockwork uniformly.
The voltmeter part carries a pen, which is displaced by the
voltage applied to the instrument. Hence, if the pen is at
rest and the drum revolves, the pen will* draw a line on the
paper which will be a straight line when the paper is removed
from the drum and spread out. If the pen is displaced by a
voltage applied to the instrument, then the line is a sinuous,
irregular line. If the displacements of the pen are exactly
proportional to the voltage, then the ordinaters of the curve
will measure this voltage. If not, then paper ruled up in
lines placed at intervals equal to 1 volt or 10 volts is 1
450 MEASUREMENT OF ELECTROMOTIVE FORCE.
employed, so that an inspection of the line drawn by the pen
suffices to determine the voltage. The voltmeter part may
be a hot-wire voltmeter, as in the Pitkin-Holden instrument
(see Fig. 14). In this case the expansion of the wire caused
by the current flowing through it is made to move the pen
arm by an amount increased by the use of a multiplying
gear.
In other cases the voltmeter mechanism is electro-
magnetic; as in the Kelvin recording voltmeter (see Fig. 15)
or Elliott instrument (see Figs. 16 and 17). In the Kelvin
instrument the control is by gravity, and the electro-
magnetic action of a solenoid or an iron core lifts or lowers
the pen.
In testing a self-recording voltmeter the clock mechanism
must first be examined, to see whether it keeps correct time.
Then the voltmeter part must be separately tested by the
potentiometer, to ascertain if this portion of the mechanism
works properly.
Self-recording voltmeters are employed to detect the
irregularities of pressure in connection with electric supply
stations, and to decide whether complaints as to abbreviated
lives of glow lamps are due to the qualities of the lamps or
to excessive variation of service pressure. A self-recording
voltmeter is useful in connection with tests of secondary
batteries to determine the exact time at which the voltage
per cell has fallen to 1*8 volts, below which voltage no current
readings are of any value. They are also necessary in con-
nection with life-tests of incandescent lamps.
8. Extra High-Pressure Yoltmeters. In connection with
cable and transformer testing it becomes necessary to employ
voltmeters for measuring extra high pressures and voltages
such as 20,000 to 60,000 volts. Instruments for this purpose
have been designed by Lord Kelvin depending on the
attraction exerted between a fixed disc and one suspended
over and parallel to it from the arm of a steelyard. The
MEASUREMENT OF ELECTROMOTIVE FORCE. 451
452 MEASUREMENT OF ELECTROMOTIVE FORCE.
MEASUREMENT OF ELECTROMOTIVE FORCE.
453
discs are included in a case which is well earthed (see
Fig. 18).
The movement of the suspended disc is limited by stops.
The control is a gravity control. The instrument is provided
with certain weights which, when hung on the beam, cause
the deflection of the scale beam under the electrostatic forces
to have a definite and indicated value in volts.
FIG. 18. Kelvin High-Tension Voltmeter.
Since the attractive force between two such parallel discs
varies as the square of the difference of potential, the
instrument is equally well adapted for use with continuous or
alternating-current voltages. A modification of this instru-
ment has been made by Messrs. Pirelli, of Milan (see Fig. 19),
for measuring voltages of 25,000 or so. A fixed plate, A,
exerts an attraction on a movable one, B. The two plates are
enclosed in a cylindrical copper case, M, and the whole is
placed in a glass cup filled with vaseline oil. C is a glass
454 MEASUREMENT OF ELECTROMOTIVE FORCE.
P'
Fio. 19. Pirelli & Co.'s Electrostatic Voltmeter. Scale : 2in. = lft.
MEASUREMENT OF ELECTROMOTIVE FORCE. 455
shade from the top of which the pole P' projects, this being
connected with the movable plate by a thin wire, D. The
apparatus rests on an ebonite stool, T, having ebonite legs.
Two weights are provided : with one weight one scale division
corresponds to 500 volts, and with the other a scale division
equals 1,000 volts. The instrument can thus read up to
60,000 volts.
Some instrument of the above type is indispensable in
testing cables or condensers with high voltage. The instru-
ment is best calibrated by the employment of a chain of
overlapping instruments, so that we can step up from an
electrostatic voltmeter capable of being calibrated directly by
FIG. 20. Kelvin Water Battery.
a Clark cell to one of the above type. Thus, if we have three
electrostatic voltmeters one reading from 500 to 2,000 volts,
one from 1,000 to 5,000, and one from 4,000 to 20,000, we
can reduce the readings to their equivalent in terms of the
international volt as denned by a Clark or Weston cell.
Without a chain of overlapping voltmeters there is some
difficulty in verifying the indications of an extra high-
tension voltmeter, because the construction of a resistance
capable of having these very high potentials put on its ends
is an expensive matter. One way in which it can be done
is by the use of a series of condensers charged by a bat-
tery of small cells. Lord Kelvin has designed a small
form of water battery consisting of small slips of copper
and zinc placed so close together (see Fig. 20) that, when
456 MEASUREMENT OP ELECTROMOTIVE FORCE.
dipped in water, a small drop is held up by capillary action
between the alternate plates. This arrangement may be made
to furnish E.M.F. up to 1,000 volts by having a sufficient
number of plates. The E.M.F. of the battery can be measured
by a standardised voltmeter of the electrostatic type. The
cells have, however, such high internal resistance that any
attempt to take from them a current, even though exceedingly
small, results in a great fall in terminal potential difference.
In addition to these cells we must be provided with a
number of condensers made with glass, paraffined paper or
mica as dielectric. These condensers must first be tested to
ascertain the rate at which the terminal potential difference of
the condenser falls off with lapse of time, after being charged,
due to internal or external leakage. If the condenser is
charged with the water battery and connected to an electro-
static voltmeter we can observe the rate at which the
voltmeter deflection decays. This is partly due to leakage in
the condenser, and partly to leakage in the voltmeter. The
voltmeter must be separately tested, and should have such
good insulation that, if charged and left to itself, the poten-
tial, as indicated by the needle, does not fall to half its value
in a quarter of an hour.
If the condensers are all found to be equally free from
leakage, then they may be arranged in series and all be highly
insulated. Each one is then separately charged in the
same direction, say to 1,000 volts, by the battery, and the
result is that the potential differences are added together, and
between the extreme terminals of the series of condensers we
have a potential difference represented by nV, where n is the
number of condensers and V is the E.M.F. of the batteries.
In this experiment both battery and operator must be very
highly insulated by being placed on blocks of paraffin wax
or sheets of ebonite.
It is easy to arrange a highly insulated commutator,
consisting of a block of paraffin wax having small holes
bored in it, to act as mercury cups, and, by means of wire
MEASUREMENT OF ELECTROMOTIVE FORCE. 457
forks attached to ebonite handles, to so connect up the
condensers that they can be charged in parallel and then
arranged in series.
Various forms of commutator have been devised to effect
such a change quickly. An arrangement was employed by
CT. Plante in his researches, and more recently by Prof.
Trowbridge. A more effective though expensive arrangement
is to employ small secondary cells. Series of 50 small litha-
node secondary cells may be arranged in trays so as to give
100 volts. These may be supported on shelves on blocks of
paraffin, and sets of these 50 cells may be joined up in series.
In this manner, high voltages may be created of known value.
These may be multiplied by the use of condensers charged
in parallel and then joined in series. In this way, by
employing series of cells and condensers charged in parallel
and then arranged in series, Prof. J. Trowbridge has built
up potential differences amounting to two or three million
volts, capable of giving electric sparks 7ft. in length. Under
these very high KM.F.s he finds the air at ordinary pressures
becomes conductive and behaves like the rarefied air in a
vacuum tube under lower electromotive force.
It is not beyond the bounds of possibility to provide in an
ordinary electrical testing laboratory a continuous voltage of
approximately 10,000 volts. This is best done by setting up
small secondary cells in sets of 40 cells. These can be put
up in stout glass test tubes, which are carried in holes bored
out in blocks of paraffin wax. These cells are joined up in
series, and each set can be charged off an ordinary 100- volt
circuit through a carbon filament lamp or high resistance.
The sets of 40 cells are joined in series, being arranged on
ebonite shelves in a sort of cabinet. One hundred arid
twenty-five of these sets can be arranged in the cabinet,
and give, when charged, an E.M.F. of 10,000 volts. The
test-tubes in which the cells are set up may be lin. in
diameter and 6in. high, and contain two small plates of
lithanode in each cell. Each shelf in the cabinet can be
458 MEASUREMENT OF ELECTROMOTIVE FORCE.
made to hold one dozen sets of 40 cells and on 10 or 11
shelves the sets requisite to give 10,000 volts can be arranged.
The cells can be used to charge mica or glass condensers,
and by means of 10 condensers, each having a capacity, say,
of O'l of a microfarad, charged in parallel and then arranged
in series, we have the means of building up a known potential
of 100,000 volts, and for calibrating an electrostatic voltmeter
for measuring extra high pressures.
9. Laboratory and Switchboard Voltmeters. A classi-
fication of voltmeters intended for laboratory and dynamo
room use, sufficient for present purposes, is as follows:
A. Classification by Type.
(I.) Continuous-current voltmeters.
(II.) Alternating-current voltmeters.
(III.) Universal voltmeters.
B. Classification by Principle.
(i.) Electrostatic voltmeters,
(ii.) Electromagnetic voltmeters,
(iii.) Electro- thermal voltmeters.
C. Classification by Range and Use.
(a) Laboratory or table voltmeters.
(b) Switchboard voltmeters.
(G) Extra high-tension or testing voltmeters.
It is impossible to describe here all the numerous forms of
voltmeter which have been devised. There are certain types
which have survived in the struggle for existence because
they have proved most convenient.
In laboratory work, for use with continuous currents only,
one of the best forms of table voltmeter is the Weston
voltmeter. This instrument is of the electromagnetic type,
and consists ot a well-aged magnet, which provides a
permanent field. In this field is supported on jewelled
centres an axis which carries a circular coil of wire. The
MEASUREMENT OF ELECTROMOTIVE FORCE. 459
coil carries an index needle. In series with the coil is a
high non-inductive resistance. The passage of a current
through the coil causes it to turn so as to place its magnetic
axis more or less in line with the field. This motion is
resisted by the torque of a steel spring like the hair spring of
a watch. The instruments are so made that the scale
division reading in volts or fractions of a volt are equal and
there is no dead or undivided portion of the scale. The
instruments are very dead-beat. One of the most useful
forms is the voltmeter reading from to 150 volts from
one pair of terminals, and by the use of another pair
reading from to 15 volts over the same range of scale,
These voltmeters have a very high resistance from 10,000
to 15,000 ohms. Hence the actual current taken is very
small. In the next place, for alternating -current laboratory
measurement the multicellular electrostatic voltmeter of
Lord Kelvin is very valuable. This instrument has already
been described in detail (see Chapter I, p. 132).
Other types of voltmeter available like the electrostatic
instruments both for alternating and continuous voltage are
the electro-thermal voltmeters represented by the Cardew and
Hartmann and Braun hot-wire voltmeters. The Cardew
voltmeter consists of a platinum-silver wire well aged by
being repeatedly heated and cooled. This is carried on a
support which in one form consists of a pair of compound
metal rods made of one-third of iron and two-thirds of brass.
The platinum-silver wire is fixed to one end of the support
and the other end of the wire is attached to a motion-
multiplying gear. The object of making the rods partly of
iron and partly of brass is to give them the same resultant
coefficient of expansion with heat as the platinum-silver wire,
so that no external changes of temperature cause any
difference of expansion in the wire arid rods ; but the
indicating mechanism is only caused to operate when the
wire expands more than the rods. The rods, wire and
mechanism are enclosed in a brass case.
460 MEASUREMENT OF ELECTROMOTIVE FORCE.
In another and better form of instrument the support
which carries the wire is not a pair of rods but a tube, partly
of brass and partly of iron, which is split longitudinally so
as to enable the wire to be easily inserted. This form is
called the tube instrument. The split tube is enclosed in
another outer casing tube. The resistance of the wire is
generally about 300 ohms. Hence, if its ends are attached to
a circuit of 100 volts, the wire passes about one-third of an
ampere. This causes it to be heated and to expand. The
heat radiated by the wire heats the rods or supporting tube
and causes it also to expand. After a short time a stationary
condition is reached, in which, whilst the wire and rods or
tube are both hot, the wire is hotter than the supports, and
hence the magnifying mechanism indicates on the dial by the
position of the needle a certain relative elongation. Corre-
sponding to each particular voltage on the wire there is a
position of the indicating needle on the dial. Hence the
instrument can be calibrated as a voltmeter.
In the rod instrument, if the current is switched off the
indicating needle goes back to zero and then passes back
beyond it. This is due to the fact that the thin wire cools
more quickly than the rods, and hence, for a short time, the
rods are expanded relatively to the wire. In the tube form
of instrument this effect is not so apparent. For the same
reason the reading of the instrument must not be taken until
the voltage has been kept on it for a few minutes. One
objection to the Cardew form of voltmeter is the large power
taken up by it. If the wire has a resistance of 300 ohms
when hot and with 100 volts on the terminals, then the
instrument is taking up about 33 watts, and if kept on the
circuit for three hours it uses nearly one-tenth of a Board of
Trade unit of electric energy. Hence, relatively to many
other electromagnetic instruments, and to electrostatic ones, it
is uneconomical for continued use. The Cardew voltmeter
should always be fixed with its tube horizontal, as in this
position the air convection currents in the tube are less
MEASUREMENT OF ELECTROMOTIVE FORCE. 461
FIG. 21. Hartmami and Brauu Hot- Wire Voltmeter.
FIG. 22. Kelvin Multicellular Vertical pattern Voltmeter.
462 MEASUREMENT OF ELECTROMOTIVE FORCE.
FIG. 23. Kelvin Edgewise Voltmeter.
MEASUREMENT OF ELECTROMOTIVE FORCE. 463
violent than when in a vertical position. If placed with the
tube upright, then the air convection currents cause small and
frequent changes in temperature in the wire which make the
indicating needle "breathe," or move slightly to and fro.
The instruments are usually calibrated for use between
40 and 150 volts, and hence are not suitable for measuring
very low voltages.
Another form of thermal voltmeter is that of Hartmann and
Braun (see Fig. 21). In this instrument the platinum-silver
wire is fixed at the ends, but when heated by a current
it " sags," and the sag is detected and measured by a delicate
multiplying mechanism. The needle is kept from vibration
by a damping copper disc attached to it which moves between
the poles of a permanent magnet.
These hot-wire voltmeters, like the electrostatic, are suit-
able for use with alternating currents of any frequency, not
very high, as well as with continuous currents, since their
indication depend upon the heating power of the current,
which is proportional to the square of the current, and there-
fore to the square of the potential difference of the terminals.
For switchboard purposes a voltmeter is preferred which
has a scale in a vertical plane If the voltmeter is to be
kept continuously in connection with a circuit, electrostatic
instruments have a great advantage over electromagnetic or
electrothermal, in that they take up no sensible amount of
power. Moreover, in contrast with electromagnetic instru-
ments, they can be employed for direct as well as alternating
currents, and in the latter case their indications are indepen-
dent of the frequency.
In the class of voltmeters suitable for switchboard work
we may especially include the vertical multicellular pattern
of Kelvin electrostatic voltmeter (see Fig. 22), which is made
for various ranges of voltage.
A type of voltmeter for switchboard work, called the Edge-
wise pattern (see Fig. 23), is often used on switchboards
because of the small space it takes up. This instrument,
464 MEASUREMENT OF ELECTROMOTIVE FORCE.
together with the Kelvin engine-room voltmeter, is of the
electromagnetic type, and depends for its action upon the
attraction of a small, carefully annealed rod of iron by a
solenoid.
In testing a voltmeter for station or workshop use it is
necessary to pay attention to the following points :
First, the accuracy of the scale readings must be checked
with the potentiometer if the voltmeter is for continuous
currents, or by reference to a carefully-calibrated electrostatic
voltmeter if the instrument is for alternating currents. In
so doing the voltmeter should be first tested with gradually
increasing voltage and then with gradually diminishing
voltage, to ascertain if there is any hysteresis error. This is
especially necessary in the case of electromagnetic instru-
ments containing iron in their construction.
In the next place, the voltmeter should be tested with the
voltage applied in both directions on the terminals, if the
instrument permits this being done. This is essential in
the case of electrostatic instruments to detect any contact,
potential or volta-effects due to contact of different metals.
In the case of alternating-current voltmeters the effect of
varying the frequency should be examined. In all cases the
disturbing effects of varying position, or of the proximity
of magnets or wires conveying continuous or alternating
currents, should be carefully employed. In the case of switch-
board instruments this is very necessary, as some types of
instrument indicate correctly when isolated but very incor-
rectly when in the neighbourhood of conductors conveying
strong currents.
In a vertical pattern electrostatic voltmeter, in which the
needle moves on pivots, it is essential that the needle axis
should be carried in jewels or on friction wheels. The
electrostatic forces brought into play are not large, and if
pivot friction exists the instrument will be sluggish and will
require a great deal of tapping to make the needle take up
its right position when the voltmeter is in the circuit.
MEASUREMENT OF ELECTROMOTIVE FORCE. 465
Another source of error in electrostatic voltmeters is that
due to the electrification of the glass front by friction.
Prof. Ayrton hsfe studied this question, and has devised
various transparent varnishes which are sufficiently con-
ducting when dry to prevent an electric charge being held
on them. The glass front of the voltmeter is covered with
a layer of this varnish, and it is impossible to disturb the
instrumental readings by electrifying the surface by touching
or rubbing. Two of Prof. Ayrton's formulae for a varnish
of the above kind are given below :
(i.) Dissolve |oz. of transparent gelatine in loz. of glacial acetic acid by
heating them at 100C. To this add half the volume of dilute
sulphuric acid (one part of strong acid to eight of water by
volume) and apply this whilst warm to the glass shade. When
this film has become hard, apply over it a coating of Griffiths'
anti- sulphuric enamel.
(ii.) Thin the gelatine solution prepared as above by the addition of
acetic acid (say, two volumes of acid to one of solution), and, after
drying the glass, float this solution over it. Drive off the excess
of acetic acid by warming. Allow the glass to cool, and repeat
the process. Thin anti-sulphuric enamel by the addition of
ether and float it over the gelatine layer. Expel the ether by
heating and apply a second layer of anti- sulphuric enamel.
A glass disc so coated is quite as transparent as one
not coated, but it cannot be electrified by touching or
rubbing it or holding near it an electrified body. The varnish
film acts as a metallic screen would do in preventing elec-
trification of the interior portions of the voltmeter.*
A good switchboard voltmeter should comply with the
following conditions :
(i.) It should not be affected by external magnetic fields,
such as exist in the neighbourhood of switch-
boards. It is quite common to find that the
stray fields on the front of a station switchboard
* See Ayrton and Mather "Transparent and Conducting Screens for
Electric and other Apparatus," Proc. Inst. Elec. Eng., April 12, 1894 ; also
The Electrician, Vol. XXXII., p. 693.
HH
466 MEASUREMENT OF ELECTROMOTIVE FORCE.
have a strength of 5 to 10 C.G.S. units that is,
25 to 50 times the earth's horizontal field.
(ii.) It should not be affected by outside electrostatic
fields, or by rubbing the dial glass.
(iii.) It should have no temperature error.
(iv.) It should have a high resistance, so as to measure
- equally accurately the pressure at the station
'bus bars or at the ends of long thin pilot wires.
(v.) It should have as large and open a scale as possible.
(vi.) It should be dead-beat if possible without the use
of dashpots.
(vii.) If employed with alternating voltages, its readings
should be independent of frequency.
(viii.) Its readings should not be affected by variations
in external temperature or by vibration, and it
should be easy to pack, transport and fix up on
a switchboard, and take up as little room as
possible.
Hardly any voltmeter complies perfectly with the whole of
these conditions. The electrostatic instruments comply well
with (i.), (iii.), (iv.) and (vii.), and the electrothermal with (iii.)
and (vi.). Many electromagnetic instruments of the movable
coil permanent magnet type are much affected by external
magnetic fields. Hence such switchboard voltmeters should
be calibrated in position and checked constantly against a
tested electrostatic instrument.
If a switchboard is equipped with electromagnetic volt-
meters it is well to have at least one electrostatic instrument
in connection with them.
In selecting these instruments, if not electrostatic, regard
should be taken of their resistance and of the amount of
power they take up and the energy absorption in watt-hours
per year of ordinary use. A voltmeter which has a resist-
ance of only 1,000 ohms takes up 10 watts when used on a
100-volt circuit, and absorbs therefore 1 B.T.U. in 100 hours
of use. Hence the switchboard absorption of power may
MEASUREMENT OF ELECTROMOTIVE FORCE. 467
amount to a not inconsiderable amount if voltmeters of low
resistance are largely employed.
Prof. Ayrton and Mr. Mather have devised an electro-
magnetic astatic voltmeter for switchboard purposes which
is, as far as possible, free from liability to disturbance by
external magnetic fields. For details of this instrument the
reader is referred to the Paper describing it in the Proceedings
of the Institution of Electrical Engineers, April 12, 1894, or
The Electrician, Vol. XXXII., p. 688, 1894.
HH2
468
MEASUREMENT OF ELECTROMOTIVE FORCE.
TABLE I.
Electromotive Force of the Clark Cell at Various Temperatures,
based on the Board of Trade Value at 15 C.
Temperature.
E.M.F.
Temperature.
E.M.F.
6C.
1-444
16C.
1-4331-4329
7C.
1-443
17C.
1-4321-4318
8C.
1-442
18C.
1-4311-4307
9C.
1-441
19C.
1.4301-4296
10C.
1-4401-4396
20C.
1-428 1-4285
ire.
1-488 1-4385
21C.
1-4271-4274
12C.
1.437_1 -4374
22C.
1-426
13C.
1-4361-4362
23C.
1-425
14C.
1-436 1-4851
24C.
1-424
15C.
1-4341-4340
25C.
1-423
The values from 10C. to 21C. are given to three and also to four places
of decimals.
CHAPTER V.
THE MEASUREMENT OF ELECTRIC POWER.
1. Electric Power: Mean Power and Power Factor.
When an electric current exists in a circuit there is an
absorption of power by the circuit due to its electrical resis-
tance, and this power is ultimately dissipated as heat. If the
circuit contains one or more sources of counter-electromotive
force against which a current is urged by the external impressed
electromotive force, additional work is done and power is
expended on the circuit. Considering, first, the case of
unvarying continuous or unidirectional electric currents, we
can estimate the power expended on the power-absorbing
circuit by measuring separately the current through the
circuit and the difference of potential of its ends.
If V be this difference of potential, then the work done
in raising a quantity of electricity, Q, through a difference
of potential V is QV, and if this work is uniformly per-
formed in a time T, then QV/T is the rate of doing work.
But Q/T=C, or is the measure of the current in the power-
absorbing circuit. Hence, the measure of the power being
taken up is the numerical value of the product CV.
Accordingly, in the case of unvarying unidirectional
currents the practical measurement of the power absorbed
electrically by any circuit consists in measuring the current
in the circuit and the fall in potential down it, and taking
the numerical product of these values. These two readings
may be taken by separate instruments, an ammeter and a
470
THE MEASUREMENT OF ELECTRIC POWER.
voltmeter, or the product may be directly obtained at one
reading by the use of a wattmeter, or electric power-
measuring instrument.
If the power taken up from instant to instant varies, the
mean value taken at equidistant intervals may be calculated
or obtained from a power curve. Thus, if the horizontal
distances in the diagram in Fig. 1 represent time and the
vertical distances power, then, if observations are taken at
certain times of the power being absorbed by a circuit, and
ordinates are drawn to scale to represent these values, the
curve obtained by joining their upper ends is a power curve.
The mean ordinate of this curve is the mean power, and the
product of the mean power and the whole time of observation
gives us the total energy absorbed by the circuit in that time.
If the current flowing in the power-absorbing circuit is an
alternating current, then we have two cases to consider:
first, when the circuit is non-inductive, and second, when
it is inductive. In the first case the mean power taken up
by the circuit is measured by the product of the root-mean-
square (K.M.S.) values of the current and the terminal
potential difference or voltage; in other words, by the
product of the ammeter and voltmeter readings, employing
proper instruments for recording these quantities. When
the circuit is inductive, the true mean power is measured by
the product of the root-mean-square values of the current
and terminal voltage and a factor called the power-factor. In
THE MEASUREMENT OF ELECTRIC POWER. 471
the case when the current and voltage vary periodically in
a simple harmonic manner the power-factor is the cosine of
the angle of phase-difference of the current and terminal
voltage.*
Hence, generally, we may say that in all cases the mean
power taken up in a circuit is measured by the product of
the three quantities the RM.S. value of the terminal
voltage, the R.M.S. value of the circuit current, and the
power-factor. If the circuit is non-inductive the power-
factor is unity, and if the current is continuous the RM.S-
value is the same as the unvarying value of this quantity.
If the current is alternating the product so obtained is the
mean power during this phase.
2. Measurement of Power in the case of Unvarying
Continuous or Direct Currents If a circuit is traversed
by a continuous or unvarying current, in order to measure
the power taken up we have to measure the current in
the circuit and the terminal voltage. The current can be
T
FIG. 2.
measured by a correct ammeter and the voltage by a volt-
meter. The voltmeter should preferably be of the electro-
static type. If, however, the voltmeter is electromagnetic, or
takes up a current, then a correction will be needed in the
ammeter reading.
The voltmeter and ammeter should be arranged as shown
in Fig. 2, where A is the ammeter, V the voltmeter and P
* The term power-factor, defined as above, was first suggested and so used
by the Author in a Paper entitled " Experimental Researches on Alternate
Current Transformers." See Proc. Inst. E.E ., 1892, Vol. XXII., p. 606.
472
THE MEASUREMENT OF ELECTRIC POWER.
the power-absorbing circuit. Then it is necessary to deter-
mine the current taken up by the voltmeter, and to deduct
this value from the ammeter reading to obtain the true
current taken by the power-absorbing circuit alone. This
correction is the more necessary in cases in which the current
taken by the power-absorbing circuit is small. It may, how-
ever, be neglected in many other cases in which the voltmeter
current is very small in comparison with the total current.
If the voltage or the current are either of them very small
it may be quite impossible to obtain really good power
measurements when using commercial ammeters and volt-
FIG. 3.
meters. This is the case in power measurements made on
small candle-power low- voltage incandescent lamps. Under
these conditions it is better to employ a potentiometer for
taking the current and voltage readings. The following
arrangement is a very effective one for obtaining quickly
good power readings in the case of incandescent lamps.
The lamp, or power-absorbing circuit P (see Fig. 3), has
placed in series with it a manganin resistance E of about
1 ohm, and across its terminals a manganin resistance r of, say,
10,000 ohms, divided into two sections, having resistances in
the ratio of 1 to 99. From the ends of the series resistance
THE MEASUREMENT OF ELECTRIC POWER. 473
and of the small section of the divided resistance, wires are
brought to a potentiometer, and the volt-fall down these
known resistances measured. If the series resistance is
exactly 1 ohm, these volt-falls give us at once the current
through the lamp in amperes and T ^th part of the terminal
voltage on the lamp. These voltage measurements are of
course referred to that of the Clark or Weston cell, Ck, used
to set the potentiometer.
It is necessary always to apply the above-mentioned cor-
rection, and to deduct from the current, through the series
resistance, the current passing through the divided resistance
attached to the terminals of the lamp. The measurements
can be depended upon to a fraction of 1 per cent., provided
that the standard cell and the resistances have been previously
carefully checked or standardised against correct standards.
The potentiometer measurements, and the setting of the
potentiometer, can be very quickly accomplished when using
a Crompton form of potentiometer.
The scheme of connections is shown in Fig. 3. The
resistance K in series with the power-absorbing circuit P
should, if possible, be a 1-ohm resistance, because then
calculations are simplified, and the volt-fall down this
resistance is the numerical value of the current through
the circuit. The divided shunt resistances may be either
divided in a 99:1 or 9:1 ratio. By the use of a double-
pole switch on the potentiometer, or parallel bars and plugs
pp, the readings of the volt-fall down the series and down
the decimal fraction of the divided resistance can be taken
successively with great expedition.
The same arrangement may be applied also in measuring
the power absorbed by a continuous-current motor, provided
that the load on it is steady.
3. Measurement of Continuous Current Power by the
Wattmeter. If it is desired to obtain the measurement of
the power absorbed in a circuit traversed by a direct or
474 THE MEASUREMENT OF ELECTRIC POWER.
unidirectional current by one observation, then a wattmeter
of the Siemens type may be used. This instrument has
already been described (see p. 181, Chap. I.). In using
it to measure continuous current power the fixed circuit
of the instrument is joined in series with the power-
absorbing circuit, and the movable or shunt coil of the
wattmeter is joined across the terminals of that circuit.
The fixed coil is then traversed by the current through
the power circuit, and the movable coil by a current
which is proporti&nal to the P.D. of the ends of this
circuit. The electromagnetic torque between the fixed
and movable circuits of the wattmeter has then to be
balanced by a mechanical torque produced by giving the
movable head of the wattmeter a twist. Let be this
FIG. 4.
twist in angular degrees or divisions of the wattmeter
circular scale. The electromagnetic torque between the
wattmeter coils is proportional to the numerical product
of the currents in these coils. Let C be the current in
the series coil, let c be the currents in the shunt coil, and
let K and r be the resistances of these circuits respectively.
Then let G be such a constant that G0 = Cc. G is called
the wattmeter constant. It can be determined by passing
known constant currents, or one and the same current,
through the wattmeter coils and observing the twist which
must be given to the wattmeter head to bring back the
movable coil to its normal position, with its axis at right
angles to that of the fixed coil.
There are two ways in which the movable or shunt coil
can be connected. First, it may be joined up as shown in
THE MEASUREMENT OF ELECTRIC POWER. 475
Fig. 4, where P is the power-absorbing circuit, S the series
coil of the wattmeter, and s the shunt coil. In this case
the power absorbed in P is equal to the product of the
current C and the potential difference of the ends of P,
which last is equal to cr - CE. Hence, if we call W the
power absorbed in P in watts, we have
but if G is the wattmeter constant, then G0=Cc, and hence
In other words, the twist which will have to be given to the
head of the wattmeter under the above conditions to bring
back the movable coil to its zero position is proportional to
the sum of the power absorbed in P and that in S the
series coil, and inversely as the resistance of the shunt coil.
r-A/WWW
v v v v y v v I
fWVWVWWWVW 1 ' ,'
FIG. 5.
If, on the other hand, the shunt coil of the wattmeter is
connected up as shown in Fig. 5, then we have, using the
same notation,
W=cr(C-c)=Ccr-c*r,
.'. W+cV=G0r,
and hence the twist is proportional to the sum of the
power absorbed in the circuits P and s, and inversely as the
resistance of s.
Accordingly, it will be seen that the scale reading of the
wattmeter is never proportional simply to the power
absorbed in the circuit under measurement, but it always
reckons in as well the power absorbed in one of its own
circuits.
476 THE MEASUREMENT OF ELECTRIC POWER.
This correction may be negligible, but it becomes of
importance in the case of circuits taking either very small
currents or very small voltages.
A precaution which must not be neglected in using the
dynamometer wattmeter in measuring continuous current
power is to set the instrument in such a position that the
horizontal magnetic field of the earth does not exercise any
action upon the movable coil when this last is traversed by a
current. For when a continuous current is passing through
the movable coil it becomes a magnet and is directed by the
magnetic field of the earth. This may be discovered and
neutralised in the following manner : Before beginning an
experiment pass a continuous current through the shunt
coil of the wattmeter only, and observe whether there is any
tendency in this coil to move one way or the other when
this current flows through it. If so, turn the wattmeter
bodily round into various positions. This may be easily
accomplished by placing it on a turntable. A position can
be found in which the movable coil of the wattmeter is not
changed in position by the passage through it of a current.
This will be the case when the magnetic axis of the movable
coil coincides with the direction of the earth's magnetic
field at that place. The wattmeter must then be used in
this position, and we shall know that the current through
the movable coil has no effect by itself and apart from the
action of that in the fixed coil in causing a displacement of
the suspended coil of the wattmeter.
The wattmeter can of course be calibrated or its constant
discovered by sending through its two circuits a current the
value of which in amperes is known. We may define the
wattmeter constant G, used in the equations above, as the
reciprocal of the numerical value of the twist which must be
given to the head of the wattmeter to bring the movable coil
back to its normal position when a current of 1 ampere flows
through both coils joined in series. For the wattmeter
constant G is defined by the equation
THE MEASUREMENT OF ELECTRIC POWEE. 477
where C is the current through one coil and c that through
the other. Hence, if C = c = 1, we have
G=l/ft
being the restoring twist which must be given to the
wattmeter head. Otherwise we may standardise the watt-
meter by observing the torsion necessary to be given to the
head when it is connected to a power-absorbing circuit
through which a known current is flowing and down which
there is a known volt-fall.
4. Measurement of Alternating-Current Power. In the
case of single-phase alternating-current power measurements,
when the current flows in a circuit having a power-factor
of unity, or one which is practically non-inductive, we can
measure the power taken up by the numerical product of the
root-mean-square (E.M.S.) value of the current and the
K.M.S. value of the voltage or fall of potential down it.
This can be done with any ammeter and voltmeter suitable
for measuring the alternating current and voltage in
question.
If, for instance, incandescent lamps are being operated by
means of a single-phase alternating current, the power taken
up in them, reckoned in watts, is obtained by taking the
product of the values of the terminal potential difference in
volts, as read by an electrostatic voltmeter, and the current
in amperes as given by a hot-wire or other suitable alternat-
ing-current ammeter ; or else a wattmeter can be used, with
certain precautions, named below, as to its construction, to
measure directly the same quantity. If, however, the circuit
is not non-inductive, but has a power factor sensibly less
than unity, then the product of the E.M.S. values of the '
current through it and the fall of potential down it does not
give the true power taken up in that circuit, but gives what'
is called the apparent power or, as it is also called, the volt-
amperes.
478 THE MEASUREMENT OF ELECTRIC POWER.
The true power taken up can be obtained by the employ-
ment of a properly constructed wattmeter.* In the con-
struction of a wattmeter for use with alternating currents it
is most important that there should be no metal near to the
fixed and movable coils. Instrument makers generally pay
no attention to this detail. They delight to devise wattmeters
in which the working parts are enclosed in brass cases or are
wholly made up of metal. When such an instrument is used
with alternating currents, eddy electric currents are set up in
the metal portions of the instrument near the coils, and these
react upon the movable coil when it is traversed by an
.alternating current and create additional and disturbing
mechanical forces which displace it. Hence the readings of
such a wattmeter may be, and generally are, quite erroneous
when it is used with alternating currents, and no reliance
can be placed upon them.
An alternating-current wattmeter must be constructed
entirely of non-conducting material, and no metal work
should exist in proximity to the coils of the instrument.!
We can show experimentally that this induction of eddy
currents in neighbouring conductors must be a source of
error in wattmeter readings when employing alternating
currents. Suspend a coil of insulated wire wound on a
rectangular or circular frame, and let an alternating current
flow through it. The coil may be suspended by a wire or by
& bifilar suspension. When traversed by the alternating
current, hold a sheet of copper near the coil It will be
found to be repelled. This repulsion arises from the reaction
of the eddy currents set up in the copper, and is an effect of
* For a full discussion of the formulae for obtaining the true power taken
up in an alternating-current inductive circuit the reader may consult the
Author's treatise on "The Alternate Current Transformer." See Vol. I.,
3rd Edition, pp. 147-157.
f For an illustration of the errors which may arise by neglecting the above
precautions, the reader is referred to a Paper by the Author entitled " Experi-
mental Researches on Alternating Current Transformers." See Proc. Inst.
E. E., London, Vol. XXI., 1892, p. 666.
THE MEASUREMENT OF ELECTRIC POWER. 479
the same character as that which gives rise to the phenomena
of electromagnetic repulsion*
It is evident, therefore, that, if mechanical forces are brought
to bear on the movable coil of an alternating-current watt-
meter due to any other cause than the mutual action between
it and the fixed coil, errors in its indications must ensue.
5. Measurement of the Power taken up in the case of
High Tension Alternating Current Circuits, When em-
ploying a wattmeter to measure the power taken up by an
inductive or non-inductive circuit, the voltage of supply
being high, as in the case of alternating-current transformers,
certain precautions are necessary for safety arid economy. It
is, of course, possible to place the series coil of the wattmeter
in series with the power-absorbing circuit and to join the
shunt coil of the wattmeter in series with a suitable induc-
tionless high resistance, and to place this last circuit as a shunt
in the ends of the power-absorbing circuit. If, however, the
volt-fall down the power-absorbing circuit is large, this will
in general necessitate a great expenditure of power in the
wattmeter shunt circuit and associated resistance. The
Author therefore devised, in 1892, the following method of
working, which has many advantages.* It depends upon the
well-known fact that, in the case of a good closed iron circuit
alternating-current transformer, not much loaded up on its
secondary side, the primary voltage is always exactly opposite
in phase to the secondary voltage and proportional to it.
Hence we may make use of such a transformer (called an
auxiliary transformer) to reduce voltage in a known ratio,
but still preserve its phase. The wattmeter is accordingly
arranged as follows :
The series coil of the wattmeter is joined in series with
the power-absorbing circuit (see Fig. 6). Across the circuit
terminals supplying the voltage is connected the primary coil
' For a full discussion and description of these effects, the reader is referred
to the Author's treatise on " The Alternate Current Transformer," Vol. I.,
3rd Edition, p. 307.
480
THE MEASUREMENT OF ELECTRIC POWER.
of the auxiliary transformer T, and its secondary circuit is
joined in series with the shunt coil s of the wattmeter and
with one or more incandescent lamps, L, of suitable voltage.
Under these conditions the series coil S of the wattmeter W
is traversed by the same current as that through the power-
absorbing circuit P, and the shunt coil of the wattmeter is
traversed by a current which is proportional to the difference
of potential of the ends of the power-absorbing circuit and
in step with it. Hence the torque, acting on the wattmeter
movable coil, will be proportional to the mean power taken
up in the power-absorbing circuit. It is desirable to annul
certain electrostatic eifects by connecting one end of the
FIG. 6.
series coil of the wattmeter with one end of the secondary
circuit of the auxiliary transformer nearest to it.
The wattmeter is then calibrated as follows : A circuit
must be provided, consisting of a practically inductionless
resistance, r, capable of being placed safely across the high-
tension circuit. An electrostatic voltmeter, V, and an
ammeter, A, must be provided suitable for measuring the
volt-fall down the resistance, called the standardising
resistance, and the current through it. We begin by con-
necting this inductionless, power-absorbing circuit to the
wattmeter, and observe the current through it and volt-fall
down it, whilst at the same time we take a wattmeter
reading. We then know that the true power taken up in
THE MEASUREMENT OF ELECTRIC POWER. 481
this inductionless resistance is given by the product of the
readings of the ammeter and voltmeter, and we can obtain
at once the wattmeter constant by comparing this product
with the wattmeter scale reading. We then substitute for
the inductionless circuit the inductive circuit P, and take a
second wattmeter reading.
A simple calculation then enables us to deduce the value
of the true power taken up in the inductive resistance, for
the wattmeter readings in the two cases are proportional
to the true power taken up respectively in these circuits ;
and in one of these viz., the non-inductive case the actual
power is independently obtained in watts as the product
of the numerical values of the current through it and its
terminal potential difference.
It is desirable that the wattmeter readings in the two
cases should not be very different, or, at any rate, that the
power taken up in the inductionless circuit used to stan-
dardise the wattmeter should not be less than that taken up
in the inductive power-absorbing circuit under investigation.
6. Power Measurements in the case of Circuits of
Small Power Factor. There are greater difficulties in
measuring accurately by a wattmeter the true mean power
taken up in a circuit of small power factor when supplied
with alternating current than in making the same measure-
ment when the power factor is large. This arises from the
fact that in all cases the small residual inductance of the
shunt circuit of the wattmeter causes the current in that
circuit to be not quite in step with its terminal potential
difference. If the power-absorbing circuit, being examined,
has a large power factor, or one approaching unity, then a
small shaft or lag in the phase of the shunt coil current
behind the phase of the potential difference between the
ends of the power-absorbing circuit does not affect the
reading of the wattmeter to the same percentage extent
as it does if the power factor is large.
ii
482 THE MEASUREMENT OF ELECTRIC POWER.
Consider the case of simple harmonic variation. Then,
if I is the RM.S. value of the current through the power-
absorbing circuit, and V that of the potential difference of
its ends, and if <p is the phase difference of these quantities,
then the true power, W, taken up on the circuit is IV cos <,
where cos <p is the power-factor. Hence,
W=IVcos0,
and cCW/d<j> = I V sin 0.
dW
Therefore -===- = tan <$>d$.
Accordingly, for a given variation, d<f> of the phase angle 0,
the error in the power measurement, which is measured by
dW/W, is greater in proportion as </> is greater.
If, therefore, we are employing a wattmeter of the dynamo-
meter type to measure the true power taken up in an open
iron-circuit transformer or in a condenser, great precautions
must be exercised or else the wattmeter readings will be
valueless. For, in the case of an open iron-circuit trans-
former or choking coil, the power factor is small, and the
current flowing into the circuit lags behind the impressed
electromotive force, whilst in the case of a condenser the
power factor is also small, but the current is in advance in
phase of the impressed electromotive force. If any eddy
currents are set up in metallic parts of the wattmeter by
the current in its movable or shunt coil, this will cause an
increase in the phase difference of the shunt coil current
and the current in the series coil, if the series coil current
normally lags behind the shunt coil current ; and, accordingly,
the reading of the wattmeter will be less than it ought to
be. This will be the case when the wattmeter is employed
to measure the power being taken up in a choking coil or
transformer of small power factor. The reverse is the case
with a condenser.
Then, since the series coil current is normally in advance
of the shunt coil current, any eddy currents established in
THE MEASUREMENT OF ELECTRIC POWER. 483
metal parts of the wattmeter by the shunt coil current will
tend to decrease the phase difference of the shunt and series
coil currents, and make the wattmeter readings larger than
they should be.
There is, therefore, always a tendency for the power
measurement made with the wattmeter on a choking coil or
transformer or inductive circuit of small power factor to be
too small, and for that made on a condenser or circuit of
small power factor having capacity to be too large.
In these cases wattmeter readings should always be care-
fully criticised and not too readily accepted as correct evalua-
tions of the true power absorption of the circuit.
One way in which this difficulty of making power measure-
ments on circuits of small power factor may be minimised is
by joining in parallel with the circuit under another inductive
circuit, or circuit having capacity, as the case may be. The
current-phase displacements in the case of the inductive
circuit and the permittive circuit (one having capacity) are
in opposite directions. Hence, if an inductive circuit in
which the current lags behind the impressed electromotive
force is joined in parallel with a permittive circuit or
condenser in which the current is in advance in phase of
the impressed electromotive force, the whole combination has
a larger power factor than either of them separately, and the
small power factor of one element annuls more or less that
of the other. Hence the difficulties which arise from the
small power factor in wattmeter measurement may be reduced
by taking two wattmeter measurements one on a combined
circuit and one on a single circuit.
Thus, if it is required to measure the power taken up
in a concentric cable or other condenser, due to dielectric
hysteresis or other causes, when it is subjected to an alter-
nating electromotive force, we may proceed as follows : An
inductive circuit must be provided, which should be one with-
out any iron core in fact, be simply a large coil of insulated
copper wire of many turns. The power factor of this inductive
n2
484 THE MEASUREMENT OF ELECTRIC POWER.
circuit will be small but positive that is, the current will lag
behind the impressed electromotive force. The true power
taken up in this inductive circuit must first of all be carefully
measured by the wattmeter, or its power factor determined,
as described in the following section. It is then joined in
parallel with the cable or condenser, and the true power
taken up in both together measured. The difference of the
two measurements then gives the true power taken up in the
condenser.
If the inductive circuit used is one with no iron core,
then the true mean power taken up in it is given at once
by taking the quotient of the mean-square value of the
impressed electromotive force by the ohmic resistance of the
circuit.
The advantage of combining the inductive circuit with the
cable or condenser is that in the latter case the capacity
current is in advance in phase of the impressed electromotive
force, whilst in the case of the inductive circuit it is in
arrear. Hence the opposite phase differences more or less
annul each other, and the combined circuit has a larger power
factor than either of them separately.
Instead of joining the ironless inductive circuit in parallel
with the cable or condenser, it may, as suggested by Mr.
Mather, be connected in series with it.* If the wire of
which the inductive circuit is formed is sufficiently stranded
to prevent eddy currents being set up in its mass, then the
actual power absorption in the circuit is sufficiently nearly
found by taking the product of its resistance and the mean-
square value of the currents through it.
It is obviously desirable that this ironless choker should
be wound in the form of a coil of maximum self-induciion, as
given by Maxwell.
* The method of employing a choking coil to increase the power factor of
a cable or condenser was suggested by Prof. Ayrton in a discussion on a Paper
by Mr. Mordey on " Capacity in Alternate Current Working." The plan of
using the choker in series is due to Mr. Mather. See The Electrician, Vol. XL VI.
1901, pp. 512, 518 and 667.
THE MEASUREMENT OF ELECTRIC POWER. 485
For a further discussion of the theory of the dynamometer
wattmeter the reader is referred to the Author's treatise on
"The Alternate Current Transformer," Vol. I., 3rd. Ed.,
Chap. III., p. 168. It is there shown that if the time
constant of the wattmeter shunt circuit is denoted by T, and
that of the circuit under test is denoted by T r , and p = 2?r
times the frequency, then, when simple harmonic currents
are being considered, a correcting factor F must be applied
to the wattmeter readings such that
Hence, if T r is greater than T,, F is a proper fraction, and
the wattmeter reading is too high and is corrected by
multiplying by F.
The practical utility of this formula is not, however, very
great, as the time-constants of most inductive circuits
cannot easily be measured, and if the circuit contains an
iron core, or is wound on an iron core, the time-constant or
ratio of inductance to resistance is not constant.
For a discussion of the practical precautions to be employed
in using the wattmeter the reader is referred to a Paper by
the Author read before the Institution of Electrical Engineers,
London, in 1892 (see Proc. Inst. E. E., Lond., Vol. XXL,
pp. 623-675).
Also a Paper may be consulted by Mr. C. V. Drysdale,
" On the Theory and Use of the Alternate Current Wattmeter "
(see The Electrician, 1901, Vol. XLVI, p. 774).
A useful discussion on power measurements in the case of
cable dielectrics took place after the reading of a Paper by
Mr. Mordey on "Capacity in Alternate Current "Working"
(see Proc. Inst. E. E., Lond., 1901, and The Electrician, Vol.
XLVL, p. 467, et seq.).
In this discussion the difficulties of such measurements and the precautions
which must be taken in dealing with wattmeter readings are well brought
out,
486 THE MEASUREMENT OF ELECTRIC POWER.
7. Power Measurements by Direct Measurement of
the Power Factor. It has been shown by Lord Kayleigh*
that we can use a shunt and series coil combined with a soft
iron indicating needle as a means of measuring either the
phase-difference of two currents or of the power factor of an
inductive circuit.
Let two circular coils of wire be placed with their axes in
one straight line and their planes parallel, and between them
let a soft iron needle be suspended by a glass fibre or torsion
wire, so that its centre is on the common axis of the coils and
its length at an angle of 45deg. to this line. If, then, a
current is passed through one of these coils it will create a
magnetic force proportional to the currents and a magnetisa-
tion in the iron nearly proportional to the magnetic force.
Hence the couple or torque tending to place the axis of the
soft iron needle in the direction of the coil axis is proportional
to the square of the current in the coil.
Suppose, in the first place, that the current i varies
harmonically and is expressed by the function ^=Isin^,
then the mean torque on the soft iron needle, and therefore
its angular displacement, if small, varies as the average value
throughout a complete period of Fsin 2 ^, or as JI 2 . Suppose,
then, that two separate simple periodic currents, differing in
phase, are passed through the two coils. Let these currents
be represented by the functions I 1 sin^ and I 2 sin(p 0).
The torques produced by these currents separately on the
soft iron needle will vary as JIi 2 and as JI 2 2 - Also the joint
effect, when both currents act together, is to produce a torque
on the needle proportional to the average value throughout a
complete period of the function
which varies as J
If, then, the first current is allowed to act alone on the
iron needle, it will produce a small displacement which may
* See The Electrician, Vol. XXXIX, p. 180, or Phil. Mag., May, 1897.
THE MEASUREMENT OF ELECTRIC POWER. 487
be represented by D x ; and, in the same way, the second
current acting alone will produce a displacement D 2 ; whilst
both acting together will produce an effect D 3 . We have
then the following equations
D^W, D 2 = C 2 2 I 2 2 ,
D 3 = (C^V + C 2 2 I 2 2 + 2C 1 C 2 I 1 I 2 cos 0),
where C x and C 2 are constants depending on the form of the
coils.
Therefore cos =
Accordingly, by observing the angular displacements of the
iron needle due to each coil acting separately and then that
due to the two acting together we can find the phase-difference
between the currents in the two coils.
The same formula holds good even when the currents are not simply
periodic, that is, have not a simple sine curve form, but we then derive from
the deflections the power factor and not merely the cosine of an angle of
phase-difference. For in this last case we have
D^htfitdt, and Da=t*fifdt,
where i\ and i% are the instantaneous values of the currents in the coils and p
and k are constants depending on the form of the coils, and the integrals are
taken throughout one complete period. Also we have
the + or - sign being used according as the coils act with or against each
other.
In the first case, then, we have
PS - D - D
The quantity on the right-hand side of the above equation is the expression
for the power factor of a circuit in which % is the current through that
circuit and z' 2 is the fall in voltage down a shunt across that circuit, or the
potential difference of the two ends of the circuit.
The above method gives us, therefore, a means of directly
determining the power factor of an inductive circuit for any
particular form of single-phase periodic electromotive force.
We have to introduce in series with that circuit a coil which
will carry the current flowing through the inductive circuit,
and we have to place as a shunt across the circuit another
488 THE MEASUREMENT OP ELECTRIC POWER.
nearly induetionless high-resistance coil, with its plane
parallel to that of the series coil and its axis coincident.
A short, soft iron needle is then to be suspended by a
fibre of glass or quartz, or by a metallic torsion wire of
phosphor bronze, in the axial line of the coils. The needle
may have a mirror attached to it, so that its small deflec-
tions may be read on a scale in the usual way. The coils
should be so arranged that the axis of the needle is at
45deg. to the line joining the centres of the coils drawn
perpendicular to their planes. The series coil should be
capable of being short-circuited at pleasure and the shunt
coil disconnected.
We can then observe the small deflections produced on
the soft iron needle by the separate actions of the series
and shunt-coil currents, and also their joint effect. These
deflections give us the quantities called D I} D 2 and D 3 in
the formula above. Then - / 2 * is the power factor
of the power-absorbing circuit connected to the coils.
The coils should be capable of being moved parallel to
themselves independently, so as to make the deflections of
the soft iron needle small and the deflections due to the
series and shunt currents separately approximately equal to
each other.
8. Three- Voltmeter Method of Measuring Alternating
Current Power. The following method of measuring the
alternating current power absorption of a circuit was first
given by Prof. Ayrton and Dr. Sumpner in 1891 : *
Let AB (see Fig. 7) be an inductive circuit traversed by an
alternating current. The first step is to join in series with
it another nearly induetionless resistance BC, and to pass
a current through both. In many cases, such as in the
* Sec " The Measurement of the Power given by any Electric Current to any
Circuit." By Prof. Ayrton and Dr. Sumpner. Proc. Roy. Soc., Vol. XLIX.,
1891, p. 424.
THE MEASUREMENT OF ELECTRIC POWER. 489
measurement of the power absorption of transformers, this
necessitates the possession of means for increasing the
circuit pressure, so as to enable this additional resistance
to be added to the circuit under test. Three measurements
of potential difference are then taken, either simultaneously
with three voltmeters or, better still, successively with one
and the same voltmeter suitable for alternating current
measurement. The voltage is measured across AB (call
it Vi), down BC (call it V 2 ), and over AC (call it V 3 ).
Then let v^ v 2) v 3 be the instantaneous values of these
voltages at any moment, and let i be the instantaneous
value of the current and U the resistance of the inductionless
-V 3 --
FIQ. 7.
part of the circuit. Then, at any moment we have the
equality
therefore vf = v-f + #2
But v 2 =:~R,i ;
hence 2R^ ~ v * ~ v ^ = v &
Multiplying all through by dt, and integrating throughout
a complete period T, or from to T, and then multiplying
by 1/T to obtain the mean-square values, we have
2R
where W is the mean power taken up in the inductive part,
AB, of the circuit.
490 THE MEASUREMENT OF ELECTRIC POWER.
The objection to this method is that great accuracy in
the voltmeter readings must be attained if the resulting
power value is to be correct to a small percentage. Since
the formula involves the difference of squares of voltages,
a small error in the measurement of the voltages themselves
will make a much larger percentage error in the calculated
value of the power.
If we take the equation given above for the power, viz.,
^(
and differentiate it, we have
dW= (
where dVi, dTV 2 , dV 3 are the errors made in the estimation of the three
potential differences, or rather in their R.M.S. values.
Let dV 3 =eV s , dV 2 =eV 2 , dV l =eV
where e is a small fraction. The most probable value of (dW) 2 is then
Let the resistance B have such a value that
V 2 =sV, .......... (2)
We proceed to find what value x should have that dW/W may be a minimum.
Since v 3 =vz+v v we have
V 8 2 =V 2 2 +V 1 2 +2V 1 V 2 cos0 ........ (3)
Hence, eliminating V,, V 2 and V 3 from the equations (1), (2) and (3), we
have
dWV (l+a-.aco8) g +l + g 4 ...
~~
Now cos H independent of x. Hence, if we differentiate the numerator
of (4) and equate to zero, we have the value of x which will make dW/W a
minimum. We find x=l satisfies this condition ; hence the arrangement
which will give the maximum sensibility is when R has such a value that
Vg = Vi.
In (4) put g = l. Then
COS0
i /7 wr
But - -=- is the ratio between the percentage error made in determining W
and that made in determining the potential differences.
Suppose, then, that the inductive circuit is an ordinary closed iron circuit
transformer on open secondary circuit. In this case cos0=0'75 nearly.
THE MEASUREMENT OF ELECTRIC POWER.
491
Accordingly, - -=5. Therefore, an error of 1 per cent, made in deter-
c w
mining the potential differences by the readings of one common voltmeter
would involve an error of 5 per cent, in the estimation of the power taken
up by the circuit. It is difficult to obtain commercial voltmeters reading to
less than quarter per cent., and therefore the limitation of accuracy in the
estimation of power by the three-voltmeter method is rather over 1 per cent.
In employing the three-voltmeter method to measure the
power taken up in an alternating current transformer we
proceed as follows : Suppose the transformer under test to
take a current at 2,000 volts on its primary circuit, and that
we have available the current from an alternator or circuit
having a pressure, say, of 100 volts. It is then necessary to
FIG. 8.
connect two step-up transformers, T v T 2 (see Fig. 8) with low-
tension sides in parallel and high-tension sides in series,
so as to create a voltage of 4,000 volts. Across the
terminals of this 4,000 volt circuit we join in series an
inductionless resistance, E, and the primary circuit of the
transformer to be tested. It is convenient to bring potential
wires or leads from the ends of the circuits AB, BC and AC
to mercury cups, mm, well insulated. A carefully standardised
electrostatic voltmeter then has potential wires attached to its
terminals, and these wires may be connected to two brass
pins carried on an insulating handle, by means of which the
492 THE MEASUREMENT OP ELECTRIC POWER.
voltmeter can be connected in between any two mercury
cups. The voltmeter reading of the required voltages can
then be quickly taken.
If the voltmeter range is only up to about 2,000 volts, then
the voltage AC must be measured in two parts by measuring
the PD of the terminals of each of the supply transformers
separately and adding these voltages together. Hence, if V
and V are these last readings and V x and V 2 , as before, the
volt-fall down the inductive circuit under test and the induc-
tionless resistance E, then the power W taken up in AB is
given by
The previous discussions of the theory of this method
shows, however, that it is not well adapted for accurate power
measurements in those cases in which the power factor of the
tested circuit is small. A modification of the three-voltmeter
method which does not necessitate the use of such a large
auxiliary resistance has been described by Mr. A. Campbell.*
9. The Three- Ammeter Method. In cases in which it is
not possible to obtain the augmented voltage required by the
three-voltmeter method, a variation of it, called the three-
ammeter method, proposed by the author in 1891, may be
used.f
In this case the circuit under test, the inductionless resist-
ance E, and three ammeters are arranged as in Fig. 9. The
first ammeter, AI, measures the current before division, the
second, A 2 , the current flowing through the inductionless
resistance, and the third, A 3 , the currents through the circuit
under test.
By a similar process of reasoning to that employed in the
case of the three-voltmeter method it can be shown that, if
* See Proc. Phys. Soc., London, 1901, or The Electrician, Vol. XLVL, p. 13,
" On a Method of Measuring Power in Alternating Current Circuits,"
t See The Electrician, May 8, 1891.
THE MEASUREMENT OF ELECTRIC POWER.
493
W is the power taken up in the tested inductive circuit and
E is the inductionless resistance, then
where Ii, I 2 , and I 3 are the readings of the three ammeters
AI, A? and A 3 respectively.
For if iiy i^ i s are the instantaneous values of these currents, we have
always *
therefore i
But Z2=v/R, where v is the potential difference of the ends of the inductive
circuit. Hence
Multiplying all through by dt, and integrating over a period, and then dividing
by T, so as to obtain the mean values of each term, we arrive at the formula
given above.
FIG. 9.
The three-ammeter method labours under the same diffi-
culty as the three-voltmeter method. Very small errors
in the absolute determination of the three currents make
a very much larger percentage error in the result. It is not
adapted for power tests on circuits of small power factor.
10. Dynamometer Methods of Measuring Power.
Mr. Blakesley gave, in 1891,* a method of measuring alter-
nating current power which is independent of the frequency
or wave-form and can be employed on any inductive circuit.
It involves the use of a split dynamometer or wattmeter, in
which the two circuits are traversed by two different currents.
* See Phil. Mag., April, 1891 p, 346.
494
THE MEASUREMENT OF ELECTRIC POWER.
Let P, Fig. 10, be the inductive circuit under test, let R be
an inductionless resistance joined in parallel with it, and let
an ammeter, A, be employed to measure the current flowing
through the inductive circuit. Then a dynamometer, D, of
the Siemens type has its two circuits joined as shown in the
diagram.
Let i be the current at any instant in the inductive circuit,
ii the current in the inductionless resistance, and 4 the
current flowing to both. Then at any instant
or
Therefore
FIG. 10.
Let v be the potential fall down the inductionless resist-
ance, R ; this is also the potential difference of the ends of the
inductive circuit, hence v = R* r Accordingly, from the two
last equations we have
Multiplying all through by dt and integrating throughout
the period, or from =0 to t=T, and dividing by T, we
obtain the mean value throughout a period of each of the
quantities in the above equation. Hence
i f T R r T . . R r T
or W=RD-RF,
where W is the mean power taken up in the inductive
circuit in watts, I the R.M.S. value in amperes of the current
THE MEASUREMENT OF ELECTRIC POWER. 495
through it, D the dynamometer value or mean value of the
product of the currents in the two coils throughout a period,
and E the ohmic resistance of the non-inductive shunt
employed.
If G- is the dynamometer constant and is the twist which
must be given to the torsion head to bring back the movable
coil to its zero position when steady currents C and c flow
through the coils, then
GO=Cc = D.
Accordingly, in the equation for W we can write EG0 for
ED, and we have
W = EG0-EF.
If we employ a hot-wire ammeter or another dynamometer
to measure the current, I, the method is perfectly general
and independent either of the frequency or wave-form of the
alternating current employed.
11. Power Measurement in the case of Polyphase
Circuits. In the majority of cases the practical measurement
of the mean electric power taken up in polyphase circuits
offers no greater difficulties than in the case of single-phase
alternating-current circuits, although it may involve a
multiplication of instrumental readings. The theoretical
treatment of the problem is rather more complicated, how-
ever, in the case of polyphase circuits, by reason of
the phase relations of the various currents involved. In
the very simple case of two-phase alternating currents the
power taken up in the inductive or inductionless circuit
supplied can be estimated by the employment of two watt-
meters, one placed in each circuit. Thus, for instance, whether
the outgoing line consists of three or four conductors, we can
measure the power supplied to a two-phase transformer in
motor by the employment of two wattmeters connected into
the circuits, as shown in Fig. 11.
Let Mj, M and M 2 be the two-phase leads and ABC the
power-absorbing circuit, whether motor or transformer. Then,
496
THE MEASUREMENT OF ELECTRIC POWER.
if two wattmeters, constructed with all the precautions already
described for use with alternating currents, are inserted in
the two sides of the two-phase circuit, the sum of their
readings will be the total power given to the circuit ABC.
M
M
M,
/-s 1 --
r rvvvvv
' WVWWVWv*
v.._SJ] t _..'
<=>
=5
^rWWNAA^
Wo
Fio. 11.
A similar arrangement can be applied in the case of three-
phase circuits when connected on the star pattern with a
common return.
For if OA, OB, 00, Fig. 12, are the three-phase power-
absorbing circuits and M I} M 2 , M 3 the leads, and M the
common return, then three wattmeters W lt W a , W 3 may be
employed to measure simultaneously the power given to the
circuits OA, OB, 00. The sum of these wattmeter readings
is the power taken up by the three-phase circuit.
The case of a three-phase circuit arranged on the delta
pattern is, however, of particular interest, because then two
THE MEASUREMENT OF ELEVTUW
497
wattmeters arranged as in Fig. 11 will give the power
absorption, whether the circuit be inductive or induction-
less. The problem may, however, be considered on first
principles.
Let ABC (Fig. 13) be a three-phase circuit arranged delta
fashion, and let M^M^Ma be the leads through which current
M 2
M,
M 3
FIG. 13.
is supplied to it. We may consider, then, in the first place,
the following problem : Given the ammeter values of the
currents in M x> M 2 and M 3 and the potential differences of
the ends of AB, BC, CA find the currents in the delta
branches and the mean electrical power taken up in the
circuit ABC.
FIG. 14.
Let us consider the general relation between the currents
in M p M 2 , M 3 , AB, BC, and CA. Eepresent the three-phase
system by a network of conductors arranged as in Fig. 14.
Let the instantaneous current values in the lines MI, M 2 , M 8
be represented by a, 6, c, and those in AB, BC, CA by x, y
KK
498 THE MEASUREMENT OF ELECTRIC POWER.
and z\ and let the outer circle represent the armature
circuit of the three-phase dynamo or other source of electro-
motive force. Then we may represent the relations between
the instantaneous values of the currents by the equations
x-y=a, ...... (i.)
y-s=&, ...... (ii.)
zxc ....... (iii.)
Hence, if we take large letters to represent the maximum
values of these currents, and assume a simple periodic mode
of variation, it is clear that, on a vector diagram of currents,
the line currents A, B, C will be represented by the sides of a
triangle, and the delta currents X, Y and Z by lines drawn to
the angular points of this triangle from some point in the
interior.
To find the currents X, Y and Z in terms of the line
currents A, B and C we may proceed algebraically as
follows : Square each of the equations (i.), (ii.) and (iii.)
above, multiply each by dt t integrate throughout a complete
period, and divide by T the periodic time. Thus
In other words, equate the mean-square values.
In the next place, make certain assumptions for the sake
of dealing with the simpler .problem first, and therefore
elucidating more difficult ones later on. Let us assume the
circuits AB, BC, CA are inductionless, and that the currents
and electromotive forces vary in a simple harmonic manner.
Then the currents x, y and % may be expressed thus
x = Xsinpt, ..... (v.)
2/ = Y sin 0^-120), . . (vi.)
z = Z sin ($t- 240), . (vii.)
when p=z2irn as usual, n being the frequency.
THE MEASUREMENT OF ELECTRIC POWER. 499
If we substitute the values for x, y and z given in the last
equation in (iv.) we arrive at equations of the form
X 2 +XY+Y 2 =A 2 , (viii.)
Z 2 =B 2 , (ix.)
C 2 (x.)
If these equations are solved for X, Y and Z in terms of
A, B and C, they will give us the expression for the R.M.S.
values of the currents in the delta circuits, which for shortness
we will call the delta-currents, in terms of the line currents.
Now, unfortunately, the above equations are very intractable.
They can be solved algebraically, and those who are fond of
algebra can amuse themselves by finding the solutions, which
are not very simple. But where algebra fails common sense
steps in, and a graphical solution sufficient for practical
purposes can easily be obtained.
It is clear, from an inspection of the equations (viii.), (ix.)
and (x.), that they are equivalent to the following geometrical
problem: Given a triangle whose sides are A, B, C in
length, find a point, P, within that triangle, such that lines
drawn from P to the angular points of the triangle are all at
120deg. angular distance from each other, and determine the
lengths X, Y and Z of these lines in terms of the sides of the
triangle.
It may be possible to solve this geometrical problem by
purely Euclidean methods, but it is a waste of labour to
attempt it.
From an electrical engineering point of view the following
graphical method gives a solution quite accurate enough for
all practical purposes : Procure a celluloid circular protractor
and cut out a sector subtending an angle of 120deg. Make
a scratch on the protractor forming an angle of 120deg. with
both the edges of the sector. The protractor will then look as
in Fig. 15. Observe with an ammeter, or with three ammeters,
the currents in the main leads M x , M 2 , M 3 . These are the
currents A, B, C. On paper set off to scale a triangle whose
KK2
500
THE MEASUREMENT OF ELECT RIG POWER.
sides represent these currents. Put two pins 'at two of the
corners of this triangle, I and m (Fig. 16). Then "apply the
protractor with the sector edges to these pins and move it
about until the scratch lies over the other corner of the
triangle nJ Then measure off the lengths, P/, Pra, Prc, where
P is the centre of the protractor. These lengths will be the
delta currents, X, Y and Z, on the same scale on which the
sides of the triangle are the line currents A, B, C.
FIG. 15.
Otherwise, in default of a protractor, we may draw on
paper three lines making angles of 120deg., and draw on
tracing paper the triangle of line currents A, B, C. Place this
tracing paper over the other, and trace off the lengths of the
FIG. 16.
lines from the centre, P, where the three radial lines inter-
sect, to the angular points of the triangle viz., measure the
lengths P/, Pm, Pn (see Fig. 17).
By this simple, graphical construction we can find the
ammeter or E.M.S. values of the currents in the delta branches
when we are given those in the lines. Hence, multiplying
the ampere value of these delta currents by the observed
potential differences of the delta corners, and adding the
THE MEASUREMENT OF ELECTRIC POWER. 501
three products, we have the total power in watts taken up
in the inductionless delta circuit.
It is obvious, if the resistances of the delta branches are
all non-inductive and equal, that the three line currents
(K.M.S. value) are equal, and also the three delta currents.
Also, each delta current is equal to the quotient of each
line current by \/3. Accordingly, in the very simple case of
a symmetrical inductionless delta circuit, the power taken
up in the whole delta is equal to the product of \/3 times
either line current and the potential difference of the ends
of either delta branch.
FIG. 17.
We have next to consider the case when the delta
branches are not inductionless, which is an important case,
as it involves the testing of three-phase motors and trans-
formers worked or constructed on the delta pattern. Let us
consider, first, the limited case when the three branches of the
delta circuit have equal inductance and resistance. This is
always the case with three-phase motors or transformers. A
little consideration will, then, show that the same rule given
above for finding the currents in the inductionless delta
circuits will give also, in the case of equi-inductive delta
circuits, the . value of the delta currents. On the other
hand, when the delta branches are inductive the current in
each branch lags in phase behind the potential difference
of the ends or delta corners. Hence we cannot find the
502
THE MEASUREMENT OF ELECTRIC POWER.
power taken up in the whole delta circuit until we have
discovered the value of this phase difference.
This may be achieved in the following manner :
Draw, as before, the triangle representing the line currents and
the radial lines P/, Pm, Pra at angles of 120deg., representing
the delta currents. Let the dotted lines on the diagram
(see Fig. 18) Pe, P/, P# represent the phase positions of the
potential differences of the ends of the delta circuits that is,
let the line ~Pe represent the potential difference of the ends
of the delta branch in which the current PZ exists. Then the
angle is the angle of lag of the current PZ behind the
impressed electromotive force Pe acting on that circuit.
FIQ. 18.
The angle is equal to the angle 0, minus the angle a.
(See Fig. 18.)
Now the angle is the phase difference between the
line current represented by the side ml and the potential
difference between the adjacent corners of the delta circuit.
The angle a can be measured by a protractor on the triangle of
currents.
Accordingly, we may find all that we require in the
following manner : Introduce into one of the lines a series
coil, and put across the terminals of one of the delta-branches
another high resistance shunt coil. Employ these two coils
in conjunction with a soft iron needle to determine, as already
described, the phase difference between any one of the line
THE MEASUREMENT OF ELECTRIC POWER. 503
currents and the potential difference between any two line
circuits. This phase difference is the angle <f>. Find from the
triangle of currents the angle a, and then the required phase
difference 6 = a.
Hence we can find, assuming sinoidal currents and electro-
motive forces, the phase difference between any delta current
and the potential difference creating it. The power taken
up in the whole delta is then easily found, for it is three
times that in any one branch of the delta, and this last
is XV cos 0, where X is any delta current (E.M.S. value) and
V the potential difference of the ends of that delta branch.
In place of a soft iron needle and series and shunt coil, a
phasemeter of the type devised by Dolivo von Dobrowolsky
may be employed. If the delta branches have unequal
inductance and resistance, then the above measurements must
be repeated on each line, and for the complete calculation
of the power taken up in the delta we require, then, to know
the value of each line current, the potential difference
between each corner of the delta, and the phase difference of
the above currents and potential differences.
The cases of most practical interest are, however, those in
which each delta branch has the same inductance and resist-
ance, as this involves the testing of three-phase transformers
and motors ; and the case when each branch is inductionless
but not of equal resistance, as with this we are concerned
in a three-phase distribution of current for lighting purposes
when unequal numbers of lamps are on each phase.
But now it is interesting to notice that, although it is
difficult to obtain an algebraical expression for the mean
power taken up in an inductive delta three-phase circuit,
given the line currents and line potential differences only and
such phase angles as can easily be measured, yet it is quite
easy to determine the power absorption practically by means
of two wattmeters or even one instrument properly arranged.
Consider again the state of the three-phase delta circuit at
any instant. Let c } , c z , c 3 be the line currents at any instant,
504
THE MEASUREMENT OF ELECTRIC POWER.
let i v i * 3 be the delta branch currents, and let v 1} v 2 , v 3
be the line potential differences or delta corner potential
C 2
FIG. 19.
differences respectively (see Fig. 19). Then it is clear that
Let w be the power absorption in the whole delta at any
instant, then
Fia. 20. Connections for Wattmeter Measurement of Power in Three-Phase
Circuit.
If therefore we arrange two wattmeters as in Fig. 20, one of
them will give a reading proportional to the average value of
THE MEASUREMENT OF ELECTRIC POWER. 505
CjV^ and the other will give a reading proportional to the
average value of c 3 v 2 , and accordingly the sum of the watt-
meter readings will be proportional to the total mean power
taken up in the whole delta circuit whether the branches be
inductive or not.
Hence we may arrange two suitable alternating current
wattmeters to give the required measurement, or we may
arrange one wattmeter and a series of switches which throws
over the wattmeter quickly from one side to the other of the
delta mains.*
Lord Kelvin has devised a form of duplex wattmeter
suitable for this purpose which is described in the next
section.
12. Practical Forms of Wattmeter The existing prac-
tical forms of wattmeter may be classified under two head-
ings : (i.) electrodynamic, (ii.) electrostatic instruments.
The electrodynamic instruments consist of two circuits or
coils of wire, one called the series coil and the other called
the shunt coil. One of these coils or circuits is fixed, and
the other is suspended and free to move over a small range
under the influence of the electrodynamic stress existing
between the coils when both are traversed by currem .
Generally speaking, the series coil is fixed, because it has to
carry the larger current, and the difficulty of getting this
current in and out of a movable coil is greater than in the
case of the smaller current used in the shunt circuit. The
movable coil must be restrained and brought back to a fixed
zero position by a couple or force due to gravity or a spring
control. In any case the conditions which must be complied
with are that a small displacement of the movable coil must
bring into existence an opposing mechanical force which
increases with the displacement. The electrodynamic stress
between the coils should be a maximum when the coils are
* See Science Abstract$, Vol. I., p. 554, M. Aliamet "On Three-phase Power
Measurement."
506
THE MEASUREMENT OF ELECTRIC POWER.
in their sighted or zero positions. For if the electrodynamic
force increases with the displacement, it may increase faster
than the opposing mechanical force, and then the equilibrium
will be unstable. It is also desirable, though not necessary,
that the mutual induction between the coils should be zero
when they are in the sighted or normal position.
In the case of wattmeters intended for use with alternating
currents, there must not be any metal enclosing case or metal
Fia. 21. Siemens Workshop Wattmeter.
work of any kind near the coils, and the coils themselves
must be wound on non-conducting formers or cores. If large-
sized wire has to be used for the series coil, it must be
stranded or formed of a cable of silk-covered wire twisted
together.
One of the simplest wattmeters for workshop use is the
Siemens wattmeter. It consists of a wooden base and
support which carries the fixed coil (see Fig. 21) and a
THE MEASUREMENT OF ELECTRIC POWER. 507
movable coil hung from a torsion head by means of a few
fibres of floss silk. In some instruments the ends of the
movable coil dip into mercury cups. In the one shown in
Fig. 21 the current is led into and out of the movable coil by
light flexible connections. The restoring couple is applied to
the movable coil by means of a spiral metal spring, one end
of which is attached to the movable coil, and the other to the
torsion head. In using the instrument the series coil is
joined in the circuit of the power-absorbing circuit, and the
movable coil is connected as a shunt across the ends of that
circuit and the series coil taken together. As already
explained, when so connected the reading of the wattmeter
is proportional to the power absorbed in the circuit under
test and that in the series coil of the wattmeter. If the
wattmeter is employed with continuous currents, care must
be taken to see that it is placed in such a position that the
magnetic field of the earth has no influence on the movable
coil when traversed by a current. When both coils have
currents through them, the movable coil is twisted round
through a small angle as far as a pair of stops will allow it
to move. The torsion head is then twisted round in the
opposite direction until the movable coil comes back to its
original position, and the angular displacement of the torsion
head noted. A table is furnished with each instrument,
which will then give the power being taken up in watts in
the circuit under test.
In the wattmeter designed by the Author for use with
alternating currents, special precautions are taken to obviate
sources of error. The wattmeter consists (see Fig. 22) of a
teak case about 15in. high and lOin. wide with glass
doors on each side. The case stands on levelling screws.
On the top surface is a celluloid divided scale. A
hollow axis through the centre of this scale carries on
its outside an adjustable index arm, and to a support
on the inside is suspended the movable coil. This is in a
rectangular form, and consists only of a few turns of
508
THE MEASUREMENT OF ELECTRIC POWER.
insulated wire kept in shape by shellac. This coil is hung
up to the torsion head by a few fibres of floss silk, and to it
is attached an index arm of aluminium wire. The torsion
spring is a spiral gilt steel chronometer spring, and this is
affixed by one end to the torsion head axes and by the other
FIG. 22. Fleming Alternating Current Wattmeter.
to the suspended coil. The ends of the coil dip into mercury
cups made of vulcanised fibre. The fixed coil is carried on
a wooden bar, and has its axis at right angles to the movable
coil. The wires bringing the currents to the coils are twisted
together. There are no metal parts or screws of any kind
THE MEASUREMENT OF ELECTRIC POWER. 509
near the coils. This wattmeter is used, as originally suggested
by the Author, in conjunction with an auxiliary transformer,
the secondary circuit of which is connected through two or
three incandescent lamps with the movable coil of the
wattmeter. The primary circuit of the transformer is
connected as a shunt across the ends of the power-absorbing
circuit and the series coil in series with that circuit. The
wattmeter is standardised, as already described, by the use of
an inductionless standardising resistance and an alternating
current ammeter and voltmeter.
Lord Kelvin's ampere balances are also constructed as
wattmeters by forming the fixed coils of thick copper strip,
and using them as the series coils, whilst the balanced or
movable coils are formed of thinner wire and constitute the
shunt coil (see Fig. 23). The shunt coil is made to have a
small resistance, and is joined up in series with a large
non-inductive resistance outside.
Lord Kelvin's form of alternating current wattmeter for
large powers is shown in Fig. 24. In this case the series coil
is a stranded cable bent in a U shape. The shunt coil
consists of a pair of balanced coils over it attached to the
scale beam arm. The electrodynamic action is the same as
in the other balances that is to say, the forces due to the
currents tend to raise one balance coil and depress the other.
The series coil in the instrument shown in the figure is
designed for carrying large currents. This conductor is
made up of ropes of insulated copper wire, twisted together
so as to form a cable with a hollow core. In order to correct
any effect due to the induction of one arm of the coil upon
the other the twisting is done in a very careful manner, so
that the strands of the cable which are inside on passing
the left-hand movable coil on one side are outside on passing
the right-hand movable coil on the same side, and are in the
reverse direction on the other arm of the U. The core of
the cable is hollow, and brass tubes are passed along each arm
of the U as far as the bend. The main object of these tubes
510
THE MEASUREMENT OF ELECTRIC POWER.
THE MEASUREMENT OF ELECTRIC POWER.
511
512 THE MEASUREMENT OF ELECTRIC POWER.
is to prevent any deformation in the cable, but they also
serve as a means of blowing air through to keep the con-
ductor cool, if it should ever be necessary to use it for
much heavier currents than those for which the instrument
is primarily intended.
Another form of dynamometer wattmeter is that devised
by the Author and Mr. Gimingham. In it there are two
helices of wire wound on non-conducting cores. These are
so wound as to have similar magnetic poles in the centre,
FIG. 25. Fleming and Gimingham's Voltmeter (lid removed).
and are placed parallel to each other. These coils form the
series coil of the wattmeter. They are embraced by two
circular coils attached to the ends of a bar suspended on a
needle point by means of a jewelled centre. These coils are
made with aluminium formers, and are wound with fine
wire. They constitute the shunt coils. The current is got
into and out of this movable coil by means of very fine
flexible leads, which do not prevent, the movable coil from
swinging freely within narrow limits. To the movable coil
THE MEASUREMENT OF ELECTRIC POWER. 513
is attached a spiral steel torsion spring, as in the Siemens
wattmeter, and its upper end is fixed to a torsion arm
moving over a divided scale. The scale can be divided to
read directly in watts. The operation of reading consists
in turning the torsion head until the movable coil is brought
back to its normal or zero position, as shown by a small
index needle attached to it. The external appearance of the
instrument is shown in Fig. 25. The figure, however, represents
the voltmeter designed by the same inventors,but the wattmeter
only differs from it in having four terminals instead of two, one
pair for the series circuit and one pair for the shunt circuit.
The above-described instruments are not direct reading.
The observer has to move or slide some part of the instru-
ment in the process of taking a reading. They are, therefore,
not adapted for switchboard purposes. In this latter case
an instrument must be employed which shows directly by
a needle upon a scale or dial the power passing through it. A
form of direct-reading wattmeter has been devised by Lord
Kelvin. It consists of a coil of one or two thick turns of
copper wire, and a spectacle-shaped fine wire coil in series,
with an external resistance. The instrument is adapted as a
central station wattmeter, giving indications of power passing
through it by means of the movement of a needle attached
to the fine wire coil over a scale. The interior is shown in
Fig. 26. It has a main circuit formed of a double rectangle
of copper rod having sufficient area to carry 200 amperes,
and a shunt circuit with two fine wire coils astatically
arranged. The main coil is mounted on a slate back so
that the rectangles are horizontal. The shunt coils are
mounted on a light but strong aluminium frame in the
manner shown in Fig. 27. One end of this frame has a
circular knife-edged hole fixed to it, and the other end has a
straight knife-edge. These two knife-edges rest on two
phosphor-bronze hooks attached by insulating supports to
the outside ends of the double rectangle. By this method
of suspension complete freedom from friction is obtained,
LL
514
MEASUREMENT Of ELECTRIC POWER.
FIG. 26. Kelvin Engine Room Wattmeter.
Removed
General View with Case
FIG. 27. View of Fine Wire Shunt Coils, showing details of Suspension
Springs removed.
THE MEASUREMENT OF ELECTRIC POWER.
515
while the movable system is kept in a definite position with-
out end guides.
Each fine wire coil has about 1,000 turns of insulated
wire, and its resistance is about 100 ohms. The current is
conducted in and out from the movable system by two
flat palladium spiral springs, which also supply the restoring
force for governing the sensibility of the instrument. Not
more than /^th of an ampere is allowed to pass through the
fine wire circuit, and in order to regulate this a large non-
inductive resistance is rolled on the case of the instrument,
which offers a large cooling surface. The scale has nearly
uniform divisions, and is graduated to read directly in watts
or kilowatts as required.
Main Coil
Main Coil
Fia. 28. Connections of Kelvin's Three-Phase Wattmeter.
Lord Kelvin has modified his single-phase balance watt-
meter to make it suitable for three-phase measurement.
It has two sets of fixed coils mounted on the opposite sides
of an ebonite or marble slab. Suspended inside these coils
are two sets of movable coils carried on the same spindle,
the pointer being also carried on the spindle. The only
opening in the ebonite slab is for the spindle. The fixed
coils are in the two arms of the main circuit, and the shunt
coils are connected across through non-induction resistances,
as shown in Fig. 28. With instruments for low pressures
the inductionless coils are in the case, and for high pressures
they are outside and separate.
LX.2
516 THE MEASUREMENT OF ELECTRIC POWER.
The use of the Kelvin quadrant electrometer, or some
modification of it, as a wattmeter was suggested almost
simultaneously by Profs. Ayrton, FitzGerald and Potier.
Maxwell showed that, in the case of the Kelvin electro-
meter, if A and B are the potentials of the quadrants and
C that of the needle, then the deflection of the needle should
vary as
It was shown, however, by Dr. J. Hopkinson, and also
by Profs. Ayrton and Perry, that the above law is not
fulfilled by every instrument of the quadrant type, but that
electrometers can be constructed which do obey it. A form
of Kelvin quadrant electrometer has been devised by
Messrs. Ayrton, Perry and Sumpner (see Fig. 29), which
strictly obeys the above law of deflection. Assuming that,
for any particular instrument, the law has been verified, we
may use it as a wattmeter as follows : Let AB be an induc-
tive circuit through which an alternating current can be set
flowing. It is desired to measure the power taken up in AB.
Join in series with AB an inductionless resistance BC, and
connect the quadrants of the electrometer to the terminals A
and B. Then take two readings, one with the needle joined
to B and one with it connected to C. Observe the deflections
in each case : call them 6 and 0'. Then we have
where K is an instrumental constant and V A , V B , V c signify
the potentials at the points A, B, C respectively. Subtract-
ing the equations, we have
Now (V^ - V B ) is the fall of potential down the inductive
THE MEASUREMENT OF ELECTRIC POWER.
517
circuit, and V B V c is the fall of potential down the non-
inductive circuit, and is proportional to the current through
FIG. 29.
the inductive circuit. The difference of the readings, viz.,
0', is proportional, therefore, to the mean value of this
518 THE MEASUREMENT OF ELECTRIC POWER.
product, assuming that the free periodic time of- the needle is
large compared with that of the alternating current.
It has been suggested by MM. Blondlot and Curie that
the power may be obtained by a single reading with a
double electrometer containing two needles and two pairs of
quadrants, the quadrants being connected to the terminals
A and B and one " needle " to B and the other needle to C.
A careful verification of the right to use the Kelvin quadrant
electrometer in the above manner as an alternating-current
wattmeter has been given by Prof. E. "Wilson (see Proc. Eoy.
Soc., London, Vol. LXIL, 1898, p. 356), but the experimentalist
employing any particular instrument should independently
verify for himself its obedience to the theoretical law.
Mr. G. L. Addenbrooke has devoted particular attention to
the improvement of the quadrant electrometer for alternating
current measurement, and has arranged a convenient form of
electrostatic wattmeter for this purposes. (See abstract of a
Paper read at the International Congress of Electricity in
Paris, 1900, The Electrician, Vol. XLV., p, 901.)
The various forms of continuously-recording wattmeters or
watt-hour-meters employed as house-meters will be considered
in the chapter on " Electric Quantity and Energy Measure-
ment."
13. Wattmeter Testing. Owing to the various disturb-
ing actions which tend to render wattmeter readings incorrect,
no prudent experimentalist will engage in a course of experi-
ments with any one particular instrument without previously
making a careful examination of its behaviour under various
conditions. Let us assume, in the first place, that the watt-
meter is of the dynamometer type and that it is to be
employed in measuring continuous-current power with the
series coil joined in series with the power-absorbing circuit
and the shunt coil joined across the ends of a circuit consist-
ing of the power-absorbing circuit and the series coil. The
wattmeter should be placed upon a turntable so as to move
THE MEASUREMENT OP ELECTRIC POWER. 519
it round in azimuth into different positions. The first experi-
ment which should be made is to pass the normal current
through the shunt coil, no current going through the series
coil ; and notice should be taken whether the interruption or
reversal of this current through the shunt affects its position
when freely suspended and movable. If this is the case, then
the wattmeter must be turned round its vertical axis and tests
made in different positions to discover if the displacement is
due to the earth's magnetic field. If so, an orientation can
be found in which the position of the shunt coil is not
disturbed by reversing the current through it. If no such
position of the wattmeter can be found, then the disturbance
may be due to currents flowing in neighbouring wires, and
these should be looked for and removed. The next step is
to measure the resistance of the series coil and calculate
the C 2 K loss in it when the current to be passed through
it is used.
As already explained, the torsion which has to be applied
to the wattmeter head to bring the movable shunt coil back
to its zero position is proportional to the power taken up in
the power-absorbing resistance, plus the power absorbed
in the series coil when the connections are made as above
described. It is necessary, therefore, to ascertain what pro-
portion the power absorbed in the series coil bears to that
taken up in the circuit under test, in order that the value
of the correction may be estimated. Again, it must not
be taken for granted without investigation that the twists
given to the wattmeter head as measured in angular dis-
placements of the head are proportional to the power taken
up in the power-absorbing circuit ; but special experiments
must be made with different power absorptions in a circuit
under test, and the quotient of true power taken up by the
wattmeter head displacement taken. This quotient, should
be constant throughout the range of currents within which the
wattmeter will be used. This test is best made by passing
currents through the wattmeter coils, the values of which are
520 THE MEASUREMENT OP ELECTRIC POWER.
Independently observed, and also the twist 6 given to the
wattmeter head to restore the movable coil to its zero
position. Then, if C and c are these currents, we have to
prove that, for the particular instrument in question, Cc/0=
a constant, in order that the wattmeter may be relied upon to
give consistent results when used to measure power.
In the case of a wattmeter to be used with alternating
currents, an additional examination has to be made into
its construction and behaviour before accepting its readings
as valid. Assuming it to be constructed in accordance with
the rules already laid down, we have to ascertain whether
its power readings when taken on a circuit of small power
factor are in agreement with those taken on circuits of large
power factor. For instance, let it be supposed that a watt-
meter is to be employed for measuring the power taken up in
concentric cables when employed with alternating currents.
In this case the power-absorbing circuit, which is the
dielectric of the cable, has a small power factor. "We have
to assure ourselves first that any wattmeter reading taken
on this circuit means the same in true power absorption
as when the same indication is found on a power-absorbing
circuit of high power factor. A cautious electrician will not
take this for granted, knowing, as he should do, that it is
quite possible for errors of 300 or 400 per cent, to be made
in evaluating by means of a dynamometer wattmeter the
power absorption in the case of a small power factor circuit,
In order to test the behaviour and trustworthiness of a
wattmeter when employed with alternating currents it is
essential, therefore, to possess a power-absorbing circuit of
known small power factor and known power absorption with
various voltages on its ends, and to compare the wattmeter
readings taken on this circuit with those taken on a prac-
tically inductionless power-absorbing circuit made as already
described.
The question arises, how is such an inductive circuit to be
made ? The following principles will guide the construction
THE MEASUREMENT OF ELECTRIC POWER. 521
of a useful form of inductive resistance for wattmeter testing.
It consists in making an ironless choking coil in the form of
a Gauss coil of maximum inductance. If a coil of insulated
wire is made on a former of circular shape, and if the shape
of the cross section of the coil is a square having a length of
side equal to a, then it was shown by Maxwell (see " Elec-
tricity arid Magnetism," Vol. II., p. 316) that the coil will
have a maximum inductance if the mean diameter of the
Let a core, therefore, be prepared formed by placing cheeks
on the sides of a circular disc of wood so as to form a square
channel in which insulated wire may be wound, and let the
square channel be fitted up with double silk or cotton-covered
copper wire well shellaced or paraffined. Let the diameter of
the circular former and the depth and breadth of the square
channel be such that the outside diameter of the circular coil
of wire formed in it is D and the inner diameter D I} and
these are so chosen that 37( Po ~ Dl )=( P
also let the width of the coil sideways or parallel to its
axis be equal to ~ *. The coil will then have the proper-
a
tions which will give it the maximum inductance for the
quantity of wire used according to the Gauss and Maxwell
rules.
The inductance of this coil may be calculated approximately
as follows : It is shown in the " Treatise on Electricity and
Magnetism " by Mascart and Joubert (see Atkinson's English
translation, Vol. II., pp. 152 and 153) that for a circular coil
of wire of N turns and mean radius a, having a rectangular
section of width 26 and depth (radial) 2c, the inductance L is
given by the following expression :
y?
where ^ and ^ are certain functions of the ratio T which are
tabulated by Mascart and Joubert,
522 TEE MEASUREMENT OF ELECTRIC POWER.
The deduction of the above formula from first principles
would occupy too much space to give it here in full, and the
reader must therefore be referred to the treatise of Mascart
and Joubert for details.
Suppose, now, that the axial width of the coil section is
equal to the radial depth, and that the proportions for
&
maximum inductance are fulfilled. That is, let b=:c=^~.
Corresponding to c/b=l, Mascart and Joubert give the
values ^=0-84834 and ^=0-8162.
Making, therefore, the above substitutions in the general
expression for L, we have
-3784 - 0-82501 = 4?raN 2 X 1*5525,
or =
where D = mean diameter of the coil and N = the total
number of turns of wire.
Now let the total length of wire on the coil = I, then
hence L =
Let d' be the diameter (over all) of the covered wire used
to make the coil ; then the length of the side of the square
section is equal to d' \/N. Accordingly, by the Gauss
relation,
and 7rDN=r/= total length of wire.
Substituting these in the above expression for L, viz.,
L = 31JN, we have, finally,
This last expression gives us, therefore, a very simple
formula for calculating the self-induction of a square-
sectioned circular coil made with the Gauss proportions
THE MEASUREMENT OF ELECTRIC POWER. 523
for maximum inductance, viz., 3'7 times side of section
= mean diameter of coil.
For example, let a coil of maximum inductance be made
with cotton-covered copper wire having an over- all diameter
of 2-omm. and, say, 1,600 turns. Calculate the inductance
and specify the form of the coil. Here
d'=0-2o cm.,
N=l,600,
.-. D = 3-7x0-25x40 = 37cm.,
and side of the section of the coil = 10cm.
Hence the coil must have an outer diameter of 47cm.,
an inner diameter of 27cm., a thickness (axially and
radially) of 10cm., and its inductance L is such that
L' = 36 XJX (1,600)2 X40
= 36 X 16 X 16 X 10 5 = 921,600,000cm.
= 0-9216 henry.
The resistance of the coil can easily be approximately
calculated as follows : Let p denote the specific resistance of
copper in C.G.S. units. At 0C for hard- drawn high conduc-
tivity copper p has a value near 1,600. The resistance K
of the coil of wire is equal to -~, where d is the diameter
ird"
of the copper wire and I is its length. But / = 7rDN, and
~D = 3'7d r Jy for the maximum inductance coil; hence,
R _ 6,400 DIST^ 23,680 flVyff
This value must, however, be increased by at least 15 per
cent, to allow for the temperature rise in the resistance.
The difference between d' and d is about O'Ol of an inch,
or 0*0254 of a centimetre, for double cotton-covered wire,
and 0-005 of an inch, or 0*0127 of a centimetre, for double
silk-covered wire. Accordingly, when we are given the
diameter, d', of the covered wire, its total resistance can
easily be calculated.
524 THE MEASUREMENT OP ELECTRIC POWER.
Having, then, the value of L and K for the coil, we can
calculate the impedance ( N/R 2 -}-^ 2 L 2 ) of the coil for simple
periodic alternating currents of a frequency n = 27r/p, and
find at once the current which will flow through the coil
under a given alternating voltage V (K.M.S. value). We
then obtain at once the true power W expended in the coil,
since it is equal to V 2 /K, and also the apparent power or
volt amperes, since this is equal to V 2 / \/R 2 +p' 2 L 2 and the
power factor E/ N/K 2 +jp 2 IA
We are thus able to design an inductance coil with any
desired power factor and power absorption and to use it to
check a wattmeter. The above formulae are, however, only to
be used to give an approximate notion of the power factor
and power absorption ; the true values for the coil in ques-
tion can best be obtained experimentally as described below.
One point of considerable importance to which attention
must be directed is the energy waste which arises from eddy
electric currents set up in solid copper wire when above a
certain diameter. If a coil of insulated wire is made, say, of
size as large as No. 14 S.W.G., and if this wire is' traversed
by an alternating current, the field of each turn embraces
and cuts that of other turns and sets up in the mass of the
copper eddy currents which dissipate energy. This is in
addition to the proper C 2 E loss due to the ohmic resistance of
the circuit. As this energy loss is not easily predicted and
taken into account, it is necessary to make the conductor of
such an ironless inductance coil of stranded wire. Generally
speaking, it will not be necessary to insulate each strand.
The film of dirt or grease on each constituent wire is usually
sufficient to stop the circulation of these eddy currents. If,
however, the wire is stranded, then its inductance per unit of
length is not quite the same as that of a round-sectioned
solid wire of the same cross-sectional area. Stranding the
wire reduces the inductance because it increases the average
distance of all the filamentary elements into which we may
conceive the currents divided.
THE MEASUREMENT OP ELECTRIC POWER. 525
Hence the calculations made by the above formulae for the
inductance and resistance of the copper circuit do not quite
exactly give the required quantities. If the wire is solid,
then the C 2 E waste in the coil with alternating currents will
be under-estimated; and if the wire is stranded, then the
inductance will be rather over-estimated when calculated by
the above-given rules.
As an illustration, however, of the use of the above formulae
let us for the moment neglect the copper eddy current loss,
and proceed to design an ironless choking coil having a power
absorption of J H.P., or 375 watts, when submitted to an
alternating electromotive force of 2,000 volts at a frequency
of 100, the power factor of the coil to be 2 per cent.
After a few trials we find the specification to be as
follows : Take No. 14 double cotton-covered copper wire, say
0'2cm. diameter, use 1,225 turns, and make it in the form of a
square-sectioned circular Gauss coil. Then
d = 0-2cm., N=l,225, x/N=35.
The inductance L = 36xO'2x35x(l,225) 2
= 378,157,500cm.
= 0-378 henry.
The resistance E in ohms at 0C
=23,680 X 1,225 X 35 X 5 x 10~ 9 =5-076 ohms,
or, say, 6 ohms when hot.
Then ^=2<7r^=200 x 3-1415=628-3,
the reactance =Lp=235'6 ohms at 0C,
the impedance= N/JR 2 +^ 2 L 2 ='V / 55,508-7 + 25*7=2357 ohms.
Hence, under an alternating electromotive force of 2,000
volts the current in the coil is 2,000/235'7=8*48 amperes.
The true power absorbed by the coil at 2,000 volts is
(8-48) 2 X 5-076=365-3 watts, if we neglect the increase in
resistance due to rise in temperature.
If the current is not kept on more than a few moments,
the true power absorption will not exceed 400 watts,
526 THE MEASUREMENT OP ELECTRIC POWER.
The volt-amperes, or apparent power, taken is equal to
2,000x848=16,960, and the power factor=400/16,960
=0-023.
The covered wire will have a diameter, d f , equal to 0*2 2 5cm.
Then as to the size of the coil. The mean diameter=D
=37 X 0-225 X 35 = 291cm., and the side of the square section
=a= 0'225 x 35 = 7*9cm. Hence the coil must have an inside
diameter of 21'2cm., an outside diameter of 37cm., and a
thickness of 7*9cm. It will contain 1,225 turns of No. 14
double cotton-covered copper wire. The length of the wire
will be 7 rDN = ^x291xl,225cm.=112,035crn.=l,250yd.
nearly. The weight will be about 801b. Hence 801b. of double
cotton-covered No. 14 wire will be required to make the coil.
As a matter of practical construction, it would not be
advisable to wind up this weight of cotton-covered wire in
one coil, and use it on a high-voltage circuit, because the
current would probably jump from layer to layer and destroy
the insulation. The coil should be wound like an ordinary
induction or spark-coil secondary circuit in a set of side-by-
side coils, or sections, insulated from each other by thin
ebonite or micanite discs. Before or during winding, the
covered wire should be well paraffined, and it is an advantage
to keep a coil of this description immersed in insulating
oil during experiments with high-tension currents.
Moreover, as above explained, in practice the wire of
which the coil is made should be stranded wire, using a
strand the constituent wires of which are not larger than
No. 30 S.W.G. Hence, instead of using solid No. 14 S.W.G.
copper wire, a stranded 36/30 should be employed.
Assuming the copper wire to be sufficiently stranded, the
actual power absorbed and the power factor at any voltage
can, however, best be determined experimentally as follows:
Provide a means for regulating the alternating voltage by
very small steps say, for instance, by introducing a variable
choking coil into the supply circuit, or by varying the
THE MEASUREMENT OF ELECTRIC POWER. 527
exciting current of the service alternator very gradually by
a carbon plate rheostat. Then provide also a supply of
continuous current from secondary batteries. Place in series
with the inductance coil under test a hot-wire ammeter
suitable for use with both continuous and alternating cur-
rents, and have at hand calibrated voltmeters for reading
accurately the alternating and continuous voltages. Then
begin by applying a measured continuous voltage to the
inductance coil sufficient to create in it a current equal to
that which it will take with the alternating voltage. In the
case of the above-described coil, since the resistance is about
5 ohms, a continuous voltage of 40 volts will create a
current of 8 amperes. Measure very carefully this voltage
and current. As soon as the currents become constant, or
very nearly so, switch off the continuous voltage and apply
an alternating voltage sufficient to maintain the same heating
current in the coil. In this case, since the impedance is
nearly 250 ohms, about 2,000 alternating volts (RM.S. value)
will be required. Measure this alternating voltage carefully.
Then, if the ventilation or cooling of the coil is rapid enough
to enable these voltages to be measured when the current is
practically the same in the two cases, we have at once the
power factor and the true power absorbed in the coil. For,
if Vc is the continuous voltage required to maintain a cur-
rent, A, through the coil, and V A is the equivalent alternating
voltage, then V C /V A is the power factor of the coil, and AV C
is the true power absorbed by the coil under an alternating
voltage V A and an apparent power absorption AV A .
The inductance coil so made, then, becomes a means of
checking a wattmeter. For this purpose we must provide
in addition a nearly inductionless resistance, taking up at
the 2,000 volts a true power equal, or nearly equal, to that
taken up by the inductance coil. For the above case, if
we make a resistance coil by winding on a wooden frame
non-inductively a length of 1,000 yards of No. 36 S.W.G.
cotton-covered platinoid wire, we shall have a resistance
528 THE MEASUREMENT OF ELECTRIC POWER.
of about 12,000 ohms, which, if properly ventilated, will
carry without sensible heating one-sixth of an ampere, or
the current it will take under an alternating voltage of
2,000 volts. The power absorbed will then be about 333
watts.
We have, then, two resistances, one, the above platinoid
resistance, taking up 333 watts or so at 2,000 volts, and
having a power factor nearly unity, and the previously-
described inductance coil, taking up 360 watts or so, and
having a power factor about 0'02. Proceed then to calibrate
the wattmeter under test by means of the inductionless
platinoid resistance, measuring the pressure with an alter-
nating electrostatic high tension voltmeter, and the current
through it with a hot-wire ammeter or by a resistance and
associated electrostatic low-reading voltmeter ; in this way
obtain the constant of the wattmeter on the high power-
factor resistance. Then, employing the same instruments on
the inductance coil, measure the power taken up calculated
out by means of the wattmeter constant observed as above.
If this power reading does not agree with the true power
absorbed by the inductance coil at that voltage, as already
determined by the use of the continuous and alternating
currents, then something is wrong with the wattmeter, and
it cannot be trusted when used with small power factor
circuits.
An inductance coil made as described, and built up in
sections so that one or more sections can be used in series as
required, is a very useful implement in a laboratory in which
cable testing is being conducted. For, if it is desired to
measure the true power absorption in the dielectric of a
cable under alternating voltage, then, since the power factor
of the dielectric circuit of the cable is small, its measurement
directly by a wattmeter becomes a matter of difficulty. But
the difficulty is reduced if an inductance coil of suitable
power factor is joined, either in parallel or in series, with the
dielectric of the cable or condenser, as suggested by Prof.
THE MEASUREMENT OF ELECTRIC POWER. 529
Ayrton and Mr. Mather,* and the power factor of the two
together, cable and coil, becomes greater than either of them
separately by reason of the fact that the current leads on the
electromotive force in the case of capacity and lags on it in
the case of inductance. In order to know approximately
how much we may expect to improve the power factor, we
must, however, have a rough knowledge of the power factor
and current taken in each case separately. Thus, suppose
the above-described inductance coil, having a power factor of
O02, and taking a current of 8*5 amperes at 2,000 volts, is
joined in parallel with a length of 5 miles of a cable
having a dielectric power factor of 0*02 and a capacity of 0'3
microfarads per mile. Then, under simple periodic currents,
the capacity current of the cable (I) would be equal to
CpV/10 6 , where C is the total capacity in microfarads, p = 2-n-
times the frequency, and V is the voltage. The reader
should note that this formula cannot be used to calculate
the condenser current when the capacity, inductance and
frequency have such values as to create electric resonance
in the circuit/)- If, however, resonance is absent, then, since
n = 100 and V = 2,000, we have
T _5x3x 2,000x628-3
10^
=r885 amperes.
Hence, to obtain the best result in augmenting the power
factor it would be desirable to couple the dielectric of this
cable in parallel with an inductance coil having a larger
number of turns (about twice as many) than the one above
specified, in order that the coil current under 2,000 volts
should be about equal in magnitude and opposite in phase,
as regards the electromotive force, to the capacity current
of the cable. With the assistance of the previously-
* See Prof. Ayrton's remarks in The Electrician, January 18, 1901,
Vol. XLVL, p. 476 ; also January 25, Vol. XL VI., p. 512 ; and Mr. Mather,
The Electrician, February 22, Vol. XLVL, p. 667.
t See Mr. T. Mather, Electrical Review, May 31, 1901 ; also Vol. II. of this
Handbook, in the chapter on "Measurement of Capacity."
MM
530 THE MEASUREMENT OF ELECTRIC POWER.
explained principles, the reader will have no difficulty in
doing this for himself.
If an ironless inductance coil is joined in parallel with
a condenser, and the two are supplied with alternating
current from an alternator at constant potential, there is
a certain value of the inductance which will, when asso-
ciated with a given condenser, make the current coming
out of the alternator a minimum. This value may be
ascertained as follows : Let i be the instantaneous value
of the current coming out of the alternator, i z that of
the current into the condenser, and i : that through the
inductance. Let C be the capacity of the condenser and
L and E the inductance and resistance of the coil. Then,
if v is the instantaneous value of the alternator voltage, we
have as fundamental equations
i 2 =i-i v
dv.
Hence, assuming a simple periodic variation of i, we have
Then, if i = I sin.pt, we shall have * 1 = I 1 sin (pt0\ because
there will be a difference of phase between \ and i. Accord-
ingly, we obtain, by substitution,
(1 - VLf)\ sin (pt-Q) H-CRpIiCOS (pt - 0)=I smpt,
and hence, by a well-known transformation,
But I 1= V/\/K 2 -t-/ 2 L 2 ;
therefore I
We have, then, to find what value of L will make I a
minimum. Differentiate therefore the last expression with
THE MEASUREMENT OP ELECTRIC POWER. 531
respect to L and equate to zero, and after some simple
reductions we have as a result the equation
C(CLp 2 - 1)(K 2 +^ 2 L 2 )=L{ (1 - C
1 R 2
which reduces to L 2 ,-!,= ; -
Cp 2 p 2
Hence the solution of the above quadratic equation gives us
the value of L which makes I a minimum. It is
or T _1 Vl-4C 2 Ry
In this last form the solution of the problem was given by
Prof. Ayrton in a discussion at the Institution of Electrical
Engineers in 1901. Given a condenser or cable of capacity
C farads subjected to an alternating current of frequency
n=p/27r, the condenser being shunted by an inductance L of
resistance R ; the value of L, calculated from the above
equation, is that which will make the total current taken by
coil and condenser a minimum.
END OF VOLUME I.
INDEX.
Absolute Galvanometer, 352
Absolute Resistance, Jones-Lorenz Appa-
ratus for Determining, 314
Accumulator Room, 12
Accumulators for Laboratory Purposes, 12
Addenbrooke Electrostatic Voltmeter. 394,
518
Alloys, Resistivity of, 263, 326
Alloys used for Making Resistances, 38
Alternating Current Curve Tracing,
Reference to Papers on, 407
Alternating Current Measurement, 388
Alternating Current Measurement, Use of
Transformers in, 409
Alternating Current Power, Measurement
of, 477, 479
Alternating Current Power, Measurement
of, by Three Ammeters, 492
Alternating Current Power, Measurement
of, by Three Voltmeters, 488
Alternating Currents, Delineation of Wave
Form of, 395
Alternating Currents, Generating, 2
Alternating Currents, Resistance of Con-
ductors to, 317
Alternators, Combined, 6
Ammeter, Calibration of, 372
Ammeter, Error Curve of, 374
Ammeter, Hartmann and Braun, 369
Ammeter, Hot Wire, 390
Ammeter, Kelvin Switchboard Form, 372
Ammeter, Weston Form, 368
Ammeters, Movable Coil, 142
Ampere, Board of Trade Specification for
the Recovery of the, 57 >
Ampere, The International, 341
Ampere Balance, 60
Ampere Balance, Board of Trade, 71
Ampere Balance, Pellat's Form, 366
Ampere Balance, Use of the, 65
Amperemeters, 367
Amperemeters, Classification of, 120
Ampere Standard, Board of Trade, 30
Arrangement of Dynamo Room, 2
Atomic Weights, Table of, 320
Ayrton Electrostatic Voltmeter, 516
Ayrton and Mather Method of Measuring
Power in Circuits of Small Power Factor,
529
Ayrton-Mather Galvanometer, 123
Ayrton's N on -Insulating Varnish, 464
Balance, Standard, 25
Ballistic Galvanometer, 128, 173
Bar Pattern Wheatstone's Bridge, 164
Berlin Reichsanstalt Standard Ohm, 42
Bidwell Rheostat, 82
Blakesley's Method of Measuring Alter-
nating Current Power, 493
Board of Trade Ampere Standard, 30
Board of Trade Electrical Laboratory, 186
Board of Trade Ohm Standard, 30
Board of Trade Specification for Clark Cell,
92
Board of Trade Specification for Unit Cur-
rent, 57
Board of Trade Standard Ampere Balance,
71
Board of Trade Standard Voltmeter. 113,
U7
534
INDEX.
Board of Trade Volt Standard, 31
Bridge, Dial Pattern, Arrangement of Coils,
in, 163
Bridge, Kelvin, Double Form, 278
Bridge, Plug Form of, 162
Bridge, Wheatstone's, 144
Bridge for Liquid Resistance Measurement,
307
Cadmium Standard Cell, Reichsanstalt
Form of, 102
Cadmium Standard Cell Weston Form of,
101
Calibration of Ammeter, 372
Calibration of a Slide Wire, 240
Callendar Clark Cell, 99
Callendar and Griffith Resistance Bridge,
221
Calomel Cell, 104
Carbon Plate Rheostat, 81
Cardew Voltmeter, 459
Cardew's Method for Measuring High
Resistance, 300
Carey Foster Bridge, 149, 238
Carhart- Clark Cell, 91
Circular Conductor, Magnet Field of, 350
Clark Cell, Board of Trade Specification
for, 92
Clark Cell, Determination of Electromotive
Force of, 423
Clark Cell, Original Form of, 87
Clark Cell, References to Various Papers
on, 108
Clark Cell, Various Forms of, 87
Coil of Maximum Inductance, 521
Combined Resistance Balance and Poten-
tiometer, 432
Conductivity Box, 215
Conductivity of Metals, 325
Conductors, Classification of, 292
Conductors, Networks of, 194
Construction of Current-Carrying Resist-
ances, 53
Continuous Current Power Measurement,
471
Copper, Conductivity of, 258
Copper, Temperature Co-efficient of, 261
Copper Wire, Resistivity of Various
Sizes of, 333
Crompton Galvanometer, 124
Crompton Potentiometer, 136
Crompton Water-tube Resistance, 51
Current Balance, 365
Current- Carry ing Capacity of Wires, 377
Current-Carrying Resistance?, 49
Current Measurement by Electrolysis of
Copper Sulphate, 342
Current Measurement by Electrolysis of
Silver Nitrate, 347
Current Measurement by Potentiometer,
376
Current Measuring Instruments, 119
Current Measuring Instruments, 349
Current, Regulation of, 79
Curve Tracer, Rosa's Form, 401
Daniell Cell, 104
Density of Metals, 320
Determination of Mean Temperature Co-
efficient of a Wire, 245
Dial Pattern Wheatstone's Bridge, 163
Dielectrics, Resistance of, Under Various
Electromotive Forces, 294
Dielectric Resistance, Measurement of, 297
Dielectrics, Resistivity of, 330
Differential Bridge, 149
Differential Bridge, Method of Using, 151
Dolivo-Dobrowolsky Phasemeters, 416
Duddell Oscillograph, 405
Dynamo Room, Arrangement of, 2
Dynamometer Method of Measuring Power,
493
Electric Current, Methods of Measuring,
341
Electric Current, Provision for Obtaining, 2
Electric Current, Root Mean Square Value
of, 340
Electric Current, Unit of, 29
Electric Currents, Classification of, 339
Electric Power, Measurement of, 469
Electrical Instruments, Foundations for, 9
Electrical' Laboratory, Arrangement of an, 8
Electrical Laboratory, Board of Trade, 186
Electrical Laboratory, Outfit of, 119
Electrical Laboratory, University College,
London, 4
Electrical Resistance, Board of Trade
Standard of, 30
Electrical Resistance, Practical Standard
of, 31
Electrical Resistance, Unit of, 29
Electrical Resistances, Measurement of, 191
Electrical Resistivity of Various Materials,
337
Electrical Units, 28
Electrochemical Equivalent of Silver, 58
Electrochemical Equivalents, 420
Electrodynamometer, 360
E lee trodynamo meter, Siemens, 130
Electrodynamometer, Theory of, 361
Electrolytes, Measurement of Resistivity
of, 311
Electromotive Force, Determination of, 427
INDEX.
535
Electromotive Force, Measurement of, 421
Electromotive Force, Potentiometer
Measurement of, 429
Electromotive Force, Practical Standard
of, 86
Electromotive Force, Unit of, 29
Electromotive Force of Clark Cell, Deter-
mination of, 423
Electromotive Force of Clark Cell, Table
of, 467
Electrostatic Voltmeter, Ayrton, 516
Elliott Potentiometer, 434
Elliott Recording Voltmeter, 452
Equipment of Test Room, 1
Equivalents, Electrochemical, Table of, 420
Error Curve of Voltmeter, 445
Eureka Alloy, 40
Evershed's Ohmmeter, 303
Fleming and Gimingham Wattmeter, 512
Fleming Circular Slide-Wire Bridge, 150
Fleming Inductionless Resistances, 80
Fleming Potentiometer, 441
Fleming Standard Daniell Cell, 105
Fleming Standard Ohm, 44
Fleming Wattmeter, 508
Foundations for Electrical Instruments, 9
Frequency Tellers, 411
Frequency of Alternating Current, Mea-
surement of, 411
Fundamental Standards, 22
Fuse Wire Currents, Table of, 419
Fusing Currents of Wires, 382
Galvanometer Absolute, 352
Galvonometer, Ayrton-Mather, 123
Galvanometer, Ballistic, 128, 173
Galvanometer, Ballistic, Theory of, 173
Galvanometer Calibration by Poten-
tiometer, 383
Galvanometer, Crompton, 124
Galvanometer, Deflectional Constant, 353
Galvanometer, Holden-Pitkin Form, 122
Galvanometer Lamps, 11
Galvanometer Shunt, 385
Galvanometers, Classification of, 120, 126
German Silver Alloy, 39
Glass, Resistivity of, 293
Guard Wire, 289
Hamilton Dickson Formula for Tempera-
ture Variation of Resistance of Platinum,
250
Hartmann and Braun Ammeter, 369
Hartmann and Braun Hot Wire Ammeter,
391
Heating Effects of Currents, References to
Papers on, 383
Helmholtz Calomel Cell, 104
High Resistance, Measurement of, 293
High-Tension Electrostatic Voltmeter, 133
High Tension Voltmeter, Kelvin, 453
High Tension Voltmeter, Pirelli, 454
Holden-Pitkin Galvanometer, 122
Holden-Pitkin Hot Wire Ammeter, 390
Housman Bridge, 279
Hydraulic Speed Indicator, 27
Indicator, Speed, 27
Inductance, Rules for Making Coil of
Maximum, 521
Insulation of Cables, Measurement of, 290
Insulation Resistance, 288
Insulation Resistance, Measurement of, 304
Insulation, Rules for, 305
Insulation Tests, Certificate of, 296
Inductionless Resistances, 80
International Kilogramme, 23
International Metre, 22
International Volt, 421
International Units, 29
Iron, Temperature Co-efficient of, 248
Kelvin Ammeter, 372
Kelvin Ampere Balance, 60
Kelvin Ampere Balance, Various Types, 67
Kelvin Double Bridge. 270
Kelvin Double Bridge, Practical Forms of,
275
Kelvin Double Bridge, Theory of, 275
Kelvin Edgewise Voltmeter, 463
Kelvin Electrostatic High-Tension Volt-
meter, 133
Kelvin Engine Room Wattmeter, 514
Kelvin High Tension Voltmeter, 453
Kelvin Multicellular Electrostatic Volt-
meter, 132
Kelvin Multicellular Vertical Pattern Volt-
meter, 462
Kelvin Multicellular Voltmeter, 118
Kelvin Recording Voltmeter, 451
Kelvin Standard One Ampere Balance, 77
Kelvin-Varley Slide, 273
Kelvin Water Battery, 456
Kelvin Wattmeter, 509
Kelvin Wire Rheostat, 82
Key for Wheatstone's Bridge, 220
Kilo-ampere Balance, 68
Kohlrausch Resistance Bridge, 307
Laboratory, Electrical, 1
Laboratory., Plan for, 14
Laboratory Tables, 10
536
INDEX.
Length, Unit of, 22
Lithanode Cells, 12 ITTa.
Lorenz Apparatus for Absolute Resistance
Low Resistances, Determination of, 265
Lyon Liquid Rheostat, 85
Magnetic Field Due to Currents of Various
Forms, 349
Manganin Alloy, 39
Manganin Wire, Ageing of, 41
Manganin Wire, Resistance of Various
Sizes of, 332
Mass and Volume Resistivity, Relation of.
253
Mass Resistivity, Definition of, 253
Mass, Unit of, 23
Matthiessen and Hockin Bridge, 235
Matthiessen's Standard for Conductivity
of Copper, 258
Mean Power, 470
Mean Solar Second, 23
Measurement of Alternating Current
Power, 477
Measurement of Electromotive Force, 421
Megohm, 56
Mercury Ohm, Secondary Standard, 36
Mercury, Resistance Standard, 33, 34
Mercury, Specific Resistance of, 31, 32
Mercury Standard Cell, Literature of, 107
Mercury, Temperature Co-efficient of, 37
Mecury, Temperature Resistance Curve
of, 251
Metal Strip Resistances, 50
Metals, Conductivity of, 325
Metals, Density of, 320
Metals, Mass Resistivity of, 321
Metals, Volume Resistivity of, 322, 323, 324
Motor Alternator Plant, 5
Muirhead-Clark Cell, 88
Multicellular Electrostatic Voltmeter, 132
Multicellular Voltmeter, Lord Kelvin, 118
Nalder Differential Bridge, 166
Nalder Potentiometer, 138
Networks of Conductors, 194
Non-Inductive Resistance, Construction of,
428
Non-Insulating Varnish, 464
Ohm, Absolute Dimension of, 48
Ohm Standard, Board of Trade, 30
Ohm's Law, 192
Ohmmeter, 301
Ohmmeter, Evershed's, 303
Ohmmeter, Theory of, 302
One Ampere Kelvin Balance, Standard
Form, 77
Oscillograph, 402
Oscillograph, Duddell, Description of, 402
Outfit of Testing Laboratory, 185
Paul's Carbon Plate Rheostat, 81
Pender Electrical Engineering Laboratory,
14
Phase Difference of Currents, Measurement
of, 413
Phasemeters, 413
Phasemeter, Dolivo-Dobrowolsky Form of,
416
Phasemeters, References to Papers on,
418
Pirelli High Tension Voltmeter, 454
Platinum Silver Alloy, 39
Platinum Silver Resistance Coils, 47
Platinum, Variation of Resistance with
Temperature, 250
Platinoid Alloy, 40
Platinoid Wire, Resistance of Various
Sizes of, 331
Plug Bridge, 162
Plug Pattern Resistance Bridge, 213
Polyphase Circuit Power Measurement, 495
Potential Differences, Measurement of
Small, 431
Potentiometer, 134
Potentiometer and Bridge Combined, 432
Potentiometer, Crompton, 136
Potentiometer, Elliott, 434
Potentiometer, Fleming, 441
Potentiometer Measurement of Current,
376
Potentiometer, Nalder, 138
Potentiometer, Use of, for Determining
Electromotive Forces, 429
Power Factor, 470
Power Measurement by the Wattmeter, 473
Power Measurement by Soft Iron Needle
Wattmeter, 486
Power Measurement by Three Voltmeters,
Theory of, 489
Power Measurement in Ca^e of Circuits of
Small Power-Factor, 481
Power Measurement in case of Continuous
Currents, 4-71
Power Measurement in Case of High-
Tension Alternating Current Circuits,
479
Power Measurement in Case of Polyphase
Circuits, 495
Power Measurement in Circuits of Small
Power Factor, Ayrton and Mather
Method of, 529
Power Measurement, Lord Rayleigh's
Method of, 486
INDEX.
537
Power Measurement, Three-Pbase Circuits,
497
Power Measurement, Use of Potentio-
meter for, 472
Preece's Table of Fuse Wire Currents,
419
Prices' Guard Wire, 289
Rayleigh-Clark Cell, 89
Rayleigh, Lord, Determination of the
Absolute Electromotive Force of Clark
Cells, 423
Rayleigh, Lord, Value of Electromotive
Force of Clark Cell, Found by, 426
Regulation of Current, 79
Resistance of Conductors to Alternating
Currents, 317
Resistance of Liquids, 306
Resistance for Carrying High-Tension
Currents, 447
Resistance, Absolute Measurement of, 312
Measurement, 314
Resistance Alloys, 38, 39
Resistance Balance. Nalder, 166
Resistance Bridge for Liquid Resistance
Measurement, Stroud and Henderson's
Form, 310
Resistance Bridge for Low Resistance
Measurement, Reeves Form, 276
Resistance Bridge, Plug Pattern, 213
Resistance Bridge, Slide Wire, 147
Resistance Coil, Determination of Tempera-
ture Co-Efficient, 243
Resistance Coil Wound with Bare Wire, 225
Resistance Coils for Carrying Large Cur-
rents, 49
Resistance Coils of Platinum Silver, 47
Resistance, Insulation, 288
Resistance Measuring Instruments, 144
Resistance, Measurement of by Fall of
Potential, 297
Resistance Measurement by Galvonometer
Deflection, 283
Resistance of Networks of Conductors, 194
Resistance of Networks of Conductors,
Calculation of, 194
Resistance Standards, Permanency of
Wire for, 38
Reichsanstalt Cadmium Cell, 102
Resistances, Determination of Low, 265
Resistances, Laboratory Outfit of, 56
Reichsanstalt Clark Cell, 95
Reicheanstalt Specification for Clark Cell,
95
Rheostat, Kelvin Form, 82
Rheostat, Lyon, 85
Rheostat, Shelford Bidwell's, 82
Rheostats in University College, London,
Dynamo Room, 84
Rheostats, Power-Absorbing, 86
Resistivity of Alloys, 263, 326
Resistivity of Copper, 258
Resistivity of Dielectrics, 330
Resistivity of Hard-Drawn and Annealed
Copper, 260
Resistivity of Liquids, 327, 328, 329
Re-istiyity of Liquids, Measurement of, 309
Resistivity of Pure Metals, 263
Resistivity, Reference to Papers on, 264
Sag of Wire, Calculation of, 370
Secondary Batteries, 12
Secondary Standard Mercury Ohm, 36
Series Plug Pattern of Wheatstone's Bridge
216
Siemens Electrodynamometer, 130
Siemens Wattmeter, 182, 506
Silver, Electrochemical Equivalent of, 58
Slide Wire Bridge, Double Gap, 148
Slide-Wire Bridge, Fleming Form, 150
Slide Wire, Calibration of, 240
Slide Wire Resistance Bridge, 147, 209
Specific Resistance of Mercury, 31, 32
Specific Resistance of Metal or Alloy,
Determination of, 252
Speed Counter, 27
Standard Balance, 25
Standard Cell, Determination of Electro-
motive Force of, 422
Standard Daniell Cell, Fleming Form of,
105
Standard Megohm, 56
Standard Mercury Ohm, 34
Standard Ohm, Berlin Reichsanstalt, 42
Standard Ohm, Fleming's, 44
Standard Potential Difference, Recovery of,
427
Standard Voltmeters, 112
Standard Voltmeter, Board of Trade, 113
Standards of Length, Mass and Time, 22
Standards, Mechanical, of Electromotive
Force, 112
Tangent Galvanometer,}Helmholtz Form,
357
Tangent Galvanometer, Theory of, 354
Temperature Co-efficient, Determination
of, 243
Temperature Co-efficient of Iron, 248
Temperature Co-efficient of Mercury, 37
Terrestial Magnetic Field, Determination
of, 359
Testing Laboratory, Hints on Outfit of, 185
Testing of Wattmeters, 518
538
INDEX.
Test Room Equipment, 1
The Electrolytic Measurement of Current.
342
Three-Phase Power Measurement, 497
Time, Unit of, 23
Trotter Resistance Bridge, 229
Trowbridge Researches on High Tension
Discharges, 457
Unit Electric Current, Recovery of, 57
Unit of Electric Current, 29
Unit of Electrical Resistance, 29
Unit of Electromotive Force, 29
Unit of Length, 22
Unit of Mass, 23
Unit of Time, 23
Units, Electrical, 28
Units, International, 29
Universal Shunt Box, Ayrton-Mather
Form, 386
University College, London, Electrical
Laboratory, 14
University College, London, Dynamo Rheo-
stats, 84
University College, London, Dynamo Room,
6
Vibration Effects, Overcoming, 9
Volt, International, 421
Volt Standard, Board of Trade, 31
Voltmeter, Addenbrooke Electrostatic, 518
Voltmeter, Calibration of a High Tension,
446
Voltmeter, Calibration of Low Tension. 443
Voltmeter, Cardew, 459
Voltmeter, Effect of Capacity of, 447
Voltmeter, Electrostatic, Addenbrooke
Form, 394
Voltmeter, Elliott Recording, 452
Voltmeter, Error Curve of, 445
Voltmeter, Hartmann and Braun Hot
Wire, 461
Voltmeter, Kelvin Edgewise, 463
Voltmeter, Kelvin Multicellular Vertical
Pattern, 462
Voltmeter, Kelvin Recording, 451
Voltmeter, Pitkin-Holden Hot- Wire, 450
Voltmeter, Practical Forms of, 505
Voltmeter, Self-Recording, 449
Voltmeter, Standard, 112
Volmeter Switchboard, Requirements iu a,
465
Voltmeters, Classification of, 458
Voltmeters, High Tension, 453
Volume and Mass Resistivity, Determina-
tion of for Metals, 257
Volume Restivity, Definition of, 252
Water Battery, 456
Water- tube Resistance, 51
Wattmeter, Fleming, 508
Wattmeter, Fleming and Gimingham, 512
Wattmeter, Kelvin, 509
Wattmeter, Kelvin Engine Room, 514
Wattmeter, Power Measurement by, 474,
475
Wattmeter, Siemens, 182, 506
Wattmeter Testing, 518
Wattmeter, Theory of, 485
Wattmeter for Alternating Current
Measurement, Construction of, 478
Wattmeters, 181
Wave Form of Current, Measurement of,
395
Weston Ammeter, 368
Weston Cadmium Cell, 101
Wheats tone Bridge, Housman Form, 279
Wheatstone Bridge, Kohlrausch's Form of,
307
Wheatstone's Bridge, 144
Wheatstone's Bridge, Bar Pattern, 164
Wheatstone's Bridge Battery Key, 220
Wheatstone Bridge, Best Arrangement of
Conductors for, 235
Wheatstone's Bridge, Callendar and
Griffith Form, 221
Wheatstone's Bridge, Dial Pattern of, 163
Wheatstone's Bridge, Fleming Form, 150
Wheatstone's Bridge, Fleming Workshop
Pattern, 168
Wheatstone's Bridge, Foster's Method of
Using, 149
Wheatstone Bridge, Matthiessen and Hockin
Form, 235
Wheatstone's Bridge, Method of Using, 145
Wheatstone's Bridge, Nalder Form, 166
Wheatstone's Bridge, Plug Pattern, 216
Wheatstone Bridge, Portable Forms of, 228
Wheatstone's Bridge, Practical Forms of,
146
Wheatstone Bridge, Theory of, 232
Wheatstone Bridge, Trotter Form of, 229
Wheatstone's Bridge, Workshop Form, 168
Wheatstone-Kirchoff Bridge, 209
Wire Resistance Standards, Permanence
of, 38
Wire Standard of Electrical Resistance, 42
Wires, Current- Carry ing Capacity of, 377
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the lives of well-known men in the Electrical World, with many excellent Portraits.
Following are some of the Permanent Features of this indispensable
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Whitaker of the Electrical Trades " :
A DlKECTORY OF THE PROFESSIONS AND TRADES CONNECTED WITH ELECTRICITY AND ITS APPLICATIONS :
BRITISH DIVISION.
COLONIAL DIVISION.
CONTINENTAL DIVISION.
ASIATIC & AFRICAN DIVISION.
Alphabetically Arranged and Classified Into
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CENTRAL & S. AMERICAN DIVISION.
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Summary of Electrical Events for the preceding year. Obituary Notices for the preceding year.
PATENTS, DESIGNS, AND TRADE MARKS.-( Specially written.)
Principal British Electrical Patents expiring in the near future. [<fec., &c. (Special.)
DIGEST OF THE LAW OF ELECTRIC LIGHTING, of ELECTRIC TRACTION, TELEGRAPHS TELEPHONES,
Latest Revised Board of Trade Regulations Concerning the Supply of Electricity.
German High-Pressure Regulations.
Board of Trade Regulations as to Railways in Metal-Lined Tunnels.
London County Council Regulations as to Theatre Lighting, Overhead Wires, Electric \leter Testing, &c.
Rules and Regulations for the Prevention of Fire Risks arising from Electric Lighting : British and Foreign
Lloyd's Suggestions for the Use of Electric Light on Board Vessels. [( Special.)
Electric Lighting and Electric Traction Notices for the year.
Provisional Orders and Licenses granted by the Board of Trade in the preceding year.
Light (Electric) Railway applications granted in the preceding year.
New Companies Registered and Companies Wound Up in the preceding year.
CENTRAL LIGHTING STATIONS OF THE UNITED KINGDOM. (Specially-Compiled Folding Sheets.)
COLOURED SKETCH MAP OF ELECTRIC TRAMWAYS AND RAILWAYS OF THE KINGDOM, and Systems
of Operation. (Special.)
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Colonial and Foreign Import Duties on Electrical Machinery and Apparatus. (Specially prepared.)
Table of Systems of Charging for Electric Current, "Easy " Wiring, " Free " Lamps, Motors, <fec.
tflre Gauge Tables. Resistance and Weight Tables. Comparative Price of Electricity and Gas.
Cables relating to Water Power, Hydraulic Heads, Rope Gearing, &c. Sinking Fund Tables.
Slectric Traction Tables and Data. Carrying Capacity of Resistance Materials.
Notes on Illumination. Table and Curve of Hours of Lighting. Post Office Regulations. Electric Heating Table.
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Local Authorities and Chief Officers in London and Provinces, with Chairmen of Lighting and
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Post Office Telegraphs : Chief Officials. Institution of Electrical Engineers : Officers, Rules, &c.
List of Universities, Colleges, Schools, &c. (with Professors).
[nstitution of Electrical Engineers : Its Constitution and Working. The Institution Benevolent Fund.
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iChe BIOGRAPHICAL SECTION contains sketches of the careers of about 300 of the leading men in the Electrical
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" THLE ELECTRICIAN " SERIES.
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Vol II. 568 pages, price IZs. 6d., post free; abroad, 13s.
ELECTROMAGNETIC THEORY.
BY OLIVER HEAVISIDE.
EXTRACT FROM PREFACE TO VOL. I.
This work is something approaching a connected treatise on electrical theory, though without
the strict formality usually associated with a treatise. The following are some of the leading
points in this volume. The first chapter is introductory. The second consists of an outline scheme of
the fundamentals of electromagnetic theory from the Faraday -Max well point of view, with some
email modifications and extensions upon Maxwell's equations. The third chapter is devoted to
vector algebra and analysis, in the form used by me in former papers. The fourth chapter is
devoted to the theory of plane electromagnetic waves, and, being mainly descriptive, may perhaps be
read with profit by many who are unable to tackle the mathematical theory comprehensively.
I have included in the present volume the application of the theory (in duplex form) to straight
wires, and also an account of the effects of self-induction and leakage, which are of some
significance in present practice as well as in possible future developments.
EXTRACT FROM PREFACE TO VOL. II.
From one point of view this volume consists essentially of a detailed development of the
mathematical theory of the propagation of plane electromagnetic waves in conducting dielectrics,
according to Maxwell's theory, somewhat extended. From another point of view, it is th-
development of the theory of the propagation of waves along wires. But on account of the
important applications, ranging from Atlantic telegraphy, through ordinary telegraphy and
telephony, to Hertzian waves along wires, the author has usually preferred to express results in
terms of the concrete voltage and current, rather than the specific electric and magnetic forces
belonging to a single tube of flux of energy. . . . The theory of the latest kind of so called
wireless telegraphy (Lodge. Marconi, &c.) has been somewhat anticipated, since the waves sent up
the vertical wire are hemispherical, with their equatorial bases on the ground or sea, which they
run along in expanding. (See 60, Vol. I. ; also 393 in this volume.) The author's old predictions
relating to skin conduction, and to the possibilities of long-distance telephony have been abundantly
verified in advancing practice : and his old predictions relating to the behaviour of approximately
distortionless circuits have also received fair support in the quantitative observation of Hertzian
waves along wires.
NOW READY. 382 pages, 173 Illustrations. Price 10s. 6d. f nett. THIRD EDITION.
MAGNETIC INDUCTION IN IRON AND OTHER METALS.
BY PBOF. J. A. EWINQ, M.A., B.So., F.B.S.,
Professor of Mechanism and Applied Mechanics in the University of Cambridge.
SYNOPSIS OF CONTENTS.
After an introductory chapter, which attempts to explain the fundamental ideas and the
terminology, an account is given of the methods which are usually employed to measure the
magnetic quality of metals. Examples are then quoted, showing the results of such measurements)
for various specimens of iron, steel, nickel and cobalt. A chapter on Magnetic Hysteresis folk
and then the distinctive features of induction by very weak and by very strong magnetic foi
are separately described, with further description of experimental methods, and with additional)
numerical results. The influence of Temperature and the influence of Stress are next discussed.
The conception of the Magnetic Circuit is then explained, and some account is given of experi-
ments which are best elucidated by making use of this essentially modern method of treatn
The book contains a chapter on the Molecular Theory of Magnetic Induction, and the opporti
is taken to refer to a number of miscellaneous experimental facts on which the moleci
theory has an evident bearing. The concluding chapter deals with the important subject
Practical Magnetic Testing. In this Edition a number of references are given to advances whi(
the subject has made since the book was originally published, and a chapter dealing with A1
important subject of Practical Magnetic Testing has been added. _
Strongly bound in Cloth, price 4s., post free.
COMPREHENSIVE INTERNATIONAL WIRE TABLE:
ELECTRIC CO3STIDTJCTORS.
BY W. S. BOULT.
Giving very Full Particulars of Wires and Gables ranging from 2-2 6 in. to 'OOlin- diameter,
Including Board of Trade, Standard, Birmingham, Brown and Sharpe, and Metric Gauges to the number of
arranged in consecutive order according to cross-section, so that when any conductor is sought the nearest size
in the other gauges can at once be found. Any No. of any one of the gauges named, Single Wire or Cable, cai
be readily ascertained. Full particulars are given of Cross-section, Gauge, Weight and Resistance in English
American and Continental Units, one Table supplying the place of the various independent Tables whicl
have hitherto been published. Great pains have been taken throughout these Tables to ensure accuracy.
"The Electrician" Printing and Publishing Co., JLtd. 5
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ELECTRIC LAMPS AND ELECTRIC LIGHTING.
By PROF. J. A. FLEMING, M.A., D.Sc., F.R.S., M.R.I.,
Professor of Electrical Engineering in University College, London.
SYNOPSIS OF CONTENTS.
I. A Retrospect over 25 Years Present Condition of Electric Lighting Chief Properties of an Electric
Current Names of Electrical Units Chemical Power of an Electric Current Hydraulic Analogies Electric
Pressure Fall of Electric Pressure Down a Conductor Ohm's Law Joule's Law Units of Work and Power
The Watt as a Unit of Power Incandescence of a Platinum Wi?e Spectroscopic Examination of a Heated
Wire Visible and Invisible Radiation Luminous Efficiency Radiation from Bodies at Various Temperature;
-Efficiency of Various Sources of Light The Glow Lamp and Arc Lamp as Illuminants Colours and Wave-
^engths of Rays of Light Similar and Dissimilar Sources of Light Colour-Distinguishing Power Causes o
Colour Comparison of Brightness and Colour Principles of Photometry Limitations Due to the Eye
Luminosity and Candle Power Standards of Light Standards of Illumination The Candle Foot Comparison
of Sunlight and Moonlight Comparison of Lights Ritchie's Wedsje Rumf ord and Bunsen Photometers
Comparison of Lights of Different Colours Spe'ctro- Photometers Results of Investigations.
II. The Evolution of the Incandescent Lamp The Nature of the Problem Necessary Conditions
Allotropic Forms of Carbon The Modern Glow Lamp Processes for the Manufacture of the Filament Edison-
Swan Lamps The Expansion of Carbon when Heated Various Forms of Glow Lamps Velocity of Molecules of
Gases Kinetic Theory of Gases Processes for the Production of High Vacua Necessity for a Vacuum Mean
Free Path of Gaseous Molecules -Voltage, Current and Candle Power of Lamps Watts per Candle Power-
Characteristic Curves of L imps Life of Glow Lamps Molecular Shadows Blackening of Glow Lamps Salf-
Recording Voltmeters Necessity for Constant Pressure of Supply Changes Produced in Lamps by Age-
Smashing Point Efficiency of Glow Lamps Statistics of Age Variation of Candle Power with Varying Voltage
Cost of Incandescent Lighting Useful Life of Lamps Importance of Careful " Wiring "Average Energy
Consumption of Lamps in Various Places Load Factors Methods of Glow Lamp Illumination for Production
of Best Effects Artistic Electric Lighting Molecular Physics of the Glow Lamp-High Voltage Lamps-
Varieties of Carbon Densities and Resistances Deterioration of Carbon Lamps High Efficiency Lamps
Hecently Suggested Improvements.
III. Forms of Electric Discharge Vacuum Tubes Sparking Distance The Electric Arc The Optical
Projection of the Arc The Arc a Flexible Conductor The High Temperature of the Arc Non- Arcing Metals-
Lightning Protectors The Distribution of Light from the Arc Continuous and Alternating Current Arcs
VoUage Required to Produce an Arc The Physical Actions in the Arc The Changes in the Carbons The
Distribution of a Potential in the Arc The Unilateral Conductivity of the Arc The Temperature of the Crater
Comparison with Solar Temperature The "Watte per Candle" of the Sun Intrinsic Brightness and Dissi-
patiye Power of Heated Surfaces Comparison of Glow Lamp, Arc Lamp and Sun in Respect of Brightness and
Radiation Arc Lamp Mechanism Arc Lamp Carbons The Hissing of Arc Lamps The Applications of Arc
Lamps Inverted Arcs Series and Parallel Arc Lighting The Enclosed Arc Lamp.
IV. The Generation and Distribution of Electric Current The Magnetic Action of an Electric Current
The Magnetic Field of a Spiral Current The Induction of Electric Currents The Peculiar Magnetic Property
of Iron Iron and Air Magnetic Circuits The Typical Cases of an Iron Conduit With and Without Air Gaps
The Prototypical Forms of Dynamo and Transformer The Transformation of Electrical Energy Hydraulic
Illustrations The Mechanical Analogue of a Transformer The Mode of Construction of an Alternate Current
Transformer The Fundamental Principle of all Dynamo Electric Machines Alternating and Direct Current
Dynamos Alternating Current Systems of Electrical Distribution Description of the Electric Lighting Station
in Rome The Tivoli-Rome Electric Transmission Views of the Tivoli Station Continuous Current Systems
The Three- Wire System Description of St. Pancras Vestry Electric Lighting Station Liverpool, Glasgow and
Brussels Electric Lighting Stations Direct Driven Dynamos Alternating and Continuous Current Systems
Contrasted Secondary Batteries House and Maximum Demand Meters.
NEW EDITION NOW READY.
800 pages, specially bound bookwise to lie open, ?S. 6d. nett, post free, at home or abroad, 7s. 9d.
A. POCKET - BOOK OF
ELECTRICAL ENGINEERING FORMULA. &c.
BY W. GEIPEL AND H. KILGOUR.
With the extension of all branches of Electrical Engineering (and particularly the heavier
branches), the need of a publication of the Pocket-Book style dealing practically therewith
increases ; for while there are many such books referring to Mechanical Engineering, and several
dealing almost exclusively with the lighter branches of electrical work, none of these suffice for the
purposes of the numerous body of Electrical Engineers engaged in the application of electricity to
Lighting, ^ Traction, Transmission of Power, Metallurgy, and Chemical Manufacturing. It is to
supply this real want that this most comprehensive book has been prepared.
Compiled to some extent on the lines of other pocket-books, the rules and formulae in general
use among Electricians and Electrical Engineers all over the world have been supplemented by
brief and, it is hoped, clear descriptions of the various subjects treated, as well as by concise
articles and hints on the construction and management of various plant and machinery.
No paing have been spared in compiling the various sections to bring the book thoroughly up
to date ; and while much original matter is given, that which is not original has been carefully
selected, and, where necessary, corrected. Where authorities differ, as far as practicable a mean has
been taken, the differing formulae being quoted for guidance.
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THE ALTERNATE CURRENT TRANSFORMER
IN THEORY AND PRACTICE.
By J. A. FLEMING, M.A., D.Sc., F.K.S., M.R.I., &c.,
Professor of Electrical Engineering at University College, London.
Since the first edition of this Treatise was published, the study of the properties and applications of
alternating electric currents has made enormous progress. . . . The author has, accordingly, rewritten the
greater part of the chapters, and availed himself of various criticisms, with the desire of removing mistakes and
remedying defects of treatment. In the hope that this will be found to render the book still useful to the increas-
ing numbers of those who are practically engaged in alternating- current work, he has sought, as far as possible,
to avoid academic methods and keep in touch with the necessities of the student who has to deal with the
subject not as a basis for mathematical gymnastics but with Hie object of acquiring practically useful knowledge.
SYNOPSIS OF CONTENTS OF VOL. I.
CHAPTER I. Introductory. Faraday's Electrical Researches Faraday's Theories Magneto-Electric
Induction Views of Maxwell, Helmholtz and Kelvin Action at a Distance The Electro-Magnetic Medium
J*%eph Henry'* investigations.
CHAPTER II. Electro-Magnetic Induction. Magnetic Force and Magnetic Fields MagnetitfForce
t'M Conductors Typical Cases Magneto-Motive Force and Magnetic Induction Flux of Force Magnetic
I ermeability Lines of Induction -Faraday's Law of Induction Electromotive Force One to the Change of Induc-
tion The Magnetic Circuit Magnetic Resistance Lines of Induction of Closed and Open Magnetic Circuits
Fundamental Delations Between Magnetic Force and Magnetic Induction Intensity of Magnetisa' ion Magnetic
Moment Lines and Tubes of Magnetic Induction Curves of Magnetisation Permeability Curves Determina-
tion of Permeability Magnetic Hysteresis Hysteresis Curves H.B. Diagram Effect of Temperature on Hyster-
esis Electromotive Force of Induction Graphical Representations Electromotive Force of Self-Induction.
a CHAPTER III. The Theory of Simple Periodic Currents. Variable and Steady Flow Current
and Electromotive Force Curves Fourier's Theorem Mechanical Harmonographs Mathematical Sketch of
Fourier's Theorem Practical Application of Fourier's Theorem to the Harmonic Analysis of a Periodic Curve
Simple Periodic Currents and Electromotive Forces Description of a Simple Periodic Curve The Mean Value
of the Ordinate of a Sine Curve The Square Root of the Mean of the Squares of the Ordinates of a Simple
Periodic Curve Derived Curves Inductance and Inductive Circuits; Inductance, Resistance and Capacity of
Circuits ; Inductive and Non-inductive Circuits Faraday's and Henry's Experiments on Self-induction - Edlund's
and Maxwells Arrangement for Exhibiting Inductance of Circuits -Electro-Magnetic Momentum Electrot-nic
State and Electromagnetic Energy Co-efficient of Mutual Induction; Energy of Two Circuits The Unit of
Inductance Value of the Self-Induction in Henry's for Various Instruments Current Growth in Inductive
Circuits Analogy of Current and Velocity Change ; Fundamental Equations for Current Growth in Inductive
Circuits Equation for the Establishment of a Steady Current in Inductive Circuits Time Constant of an
Inductive Circuit- Logarithmic Curves Instantaneous Value of Simple Periodic Current Solution of Current
Equation -Impedance of Inductive Circuit Relations of Impressed Electromotive Force, Current and Im-
pedance- Geomet ical Illustrations Impressed and Effecive Electromotive Forces clock Diagram of Electro-
motive Forces in Inductive Circuit Triangle Representing Resistance, Impedance and Reactance of Circuit
The Mean Value of the Power of a Periodic Current Geometrical Theorem Power Curves for Inductive and
B on-Inductive Circuits Experimental Measurement of Periodic Currents and Electromotive Forces Mean
Square Value Method of Measuring the True Mean Power Given to an Inductive Circuit Theory of the
Wattmeter Divided Circuits Important Trigonometrical Lemma Impedance of Branched Circuits Watt-
meter Measurement of Periodic Power Mutual Induction of Two Circuits of Constant Induct mce The
low of Simple Periodic Currents into a Condenser Time Constant of a Condenser Charging a Condenser
through a Resistance-Condenser equation Annulment of Inductance by Capacity Representation of Periodic
Currents by Polar Diagrams -Initial Conditions on Starting Current Flow in Inductive Circuits Complex
Periodic Pun ctions Apparent and True Power given to Inductive Circuits Power Factor.
, CHAPTER IV. -Mutual and Self-Induction. The Researches of Joseph Henry Experiments with
toils ai d Bobbins ; Discovery of Self-induction Mutual Induction Induction at a Distance Induction between
Telephone Circuits-Induction over Great Distances Induced Currents of Higher Orders Inductive Effects by
Qsient Electric Currents Magnetic Screening -Direction of Induced Currents Various Qualities of au
Induced Current Elementary Theory of Mutual Induction of Two Circuits Theory of Induction Coil with Non-
Magnetic Core Comparison of Theory and Experiment Duration of Induced Currents Magnetic Screening
Action of Good-Conducting Masses Faraday's and Henry's Experiments Willoughby Smith's Investigations on
Magnetic Screening -Doves Experiments and Henry's Views on same The Reaction of the Secondary Currents
on the Primary Circuit in the Case of an Induction Coil Induction Balance and Sonometer Transmission of
Alternating Currents through Conductors Prof. Hughes' Experiments Lord Rayleigh's Researches Flow of
uum through Conductor- Surface Flow of Alternating Currents Increased Resistance of Conductors for
natmg Currents of High Frequency Limiting Size of Conductors for Conveyance of Alternating Currents
btep^ans Analogies Electro-Magnetic Repulsion Elihu Thomson's Experiments Electro-Magnetic Rotations.
CHAPTER V, Dynamical Theory of Induction. Electro-Magnetic Theory Faraday's Concep-
>r an Electro-Magneto Medium Maxwell's Suggestion The Lumini erous Ether Maxwells Theory of
Jtnc Displacement Electric Elasticity of the Medium-Displacetient and Conduction Currents Electro-
motive Intensity-Displacement Currents and Displacement Waves-Theory of Molecular Vortices Mechanical
Analogy comparison of Theory and Experiment Maxwell's Law Connecting Dielectric Constant and Refrac-
wvity or a Dielectric Tables of Comparison Velocity of Propagation of Electro-Magnetic Disturbances
rtftvfn j v "~ Vector Potential Electrical Oscillation Charge and Discharge of Leyden Jar The Function
01 in- condenser in an Induction Coil Impulsive Discharges and Relation of Inductance Thereto Impulsive
impettunce Ifertz's Researches Experimental Determination of the Velocity of Electro- Magnetic Waves.
th T F VI.- The Induction Coil and Transformer. Gem ral Description of the Action of
rvT v sformer or Induction Coil The Delineation ol Periodic Curves of Current and Electromotive Force
s iracers Transformer Diagrams -Curves of Electromotive Force- Cuircnt and Induction in Cases of
various .transformers Taken off Various Alternators Open-Circuit Cuirtnt of Transformers Symmetry of
rs, >rme c . u r v es Harmonic Analysis of Transformer Curves Power and Hysteresis Curves Hysteresis
uurve f \anous Transformers Efficiency of Transformers Efficiency Curves of Transformers Tables of
ri pH n p- eS ~? U -!r rent Dia 8 rams of a Transformer Tables of Complete Tests-The Power Factor-Open and
ivSS ^ ir ? ult Transformers- Magnetic Leakage ami Secondary Drop Various Causes of Secondary Drop
ijeiermination of Magetic Leakage Investigations of the Author and Dr. Roessler Form Factor and Amplitude
ctor of a Periodic Curve-General Analytical Theory of the Trausfc rmer and Induction Coil.
"The Electrician" Printing and Publishing Co., Ltd.
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THIRD ISSUE. More than 600 pages and over SOO illustrations. Price 12s. 6d., post free;
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THE ALTERNATE CURRENT TRANSFORMER
IN THEORY AND PRACTICE.
By J. A. FLEMING, M.A., D.Sa, F.R.S., M.E.I., &c.,
Professor of Electrical Engineering in University College London,
SYNOPSIS OF CONTENTS OF VOL. 2.
CHAP. I. Historical Development of Induction Coil and Transformer.
The Evolution of the Induction Coil Page's Researches Callan's Induction Apparatus-
Sturgeon's Induction Coil Bachhoffner's Researches Callan's Further Researches Callan'g
Great Induction Coil Page's Induction Coil Abbot's Coil Automatic Contact Breakers
Ruhmkorff's Coils Poggendorff's Experiments Stohrer's, Hoarder's, Ritchie's Induction
Apparatus Grove's Experiments Apps' Large Induction Coils Jablochkoff's Patent Fuller's
Transformer Early Pioneers Gaulard and Gibbs Zipernowsky's Transformers Improvements
of Rankin Kennedy, Hopkinson, Ferranti, and others The Modern Transformer since 1885.
CHAP. II. Distribution of Electrical Energy by Transformers.
Detailed Descriptions of Large Alternate-Current Electric Stations using Transformers in
Italy, England, and United States Descriptions of the Systems of Zipernowsky-D6ri-Blathy,
Westinghouse, Thomson-Houston, Mordey, Lowrie-Hall, Ferranti, and others Plans, Sections,
and Details of Central Stations using Transformers Illustrations of Alternators and Transformers
in Practical Use in all the chief British, Continental, and American Transformer Stations.
CHAP. III. Alternate-Current Electric Stations.
General Design of Alternating-Current Stations, Engines, Dynamos, Boilers Proper Choice
of Units Water Power Parallel Working of Alternators Underground Conductors Various
Systems Concentric Cables Capacity Effects dependent on Use of Concentric Cables Phenomena
of Ferranti Tubular Mains Safety Devices Regulation of Pressure Choice of Frequency
Methods of Transformer Distribution Sub-Stations Automatic Switches.
CHAP. IV. The Construction and Action of Transformers.
Transformer Indicator Diagrams Ryan's Curves Curves of Current Electromotive Force
and InductionrAnalysis of Transformer Diagrams Predetermination of Eddy Current and
Hysteresis Loss in Iron Cores Calculation and Design of Transformers Practical Predetermina-
tion of Constants Practical Construction of Transformers Experimental Tests of Transformers
Measurement of Efficiency of Transformers Calometric Dynamometer and Wattmeter Methods
Reduction of Results.
CHAP. V. Further Practical Application of Transformers.
Electrical Welding and Heating Transformers for producing Large Currents of Low Electro-
motive Force Theory of Electric Welding Other Practical Applications Conclusion.
NEW EDITION. Fully Illustrated. Price 6s. nett, post free; abroad 6s. 3d.
STUIXEJMTS' GTJXOE TO
SUBMARINE CABLE TESTING.
By H. K. C. FISHER and J. C. H. DARBY.
The authors of this book have, for some years past, been engaged in the practical work of Submarine Cable
Testing in the Eastern Extension Telegraph Company's service, and have embodied their experience in a Guide
for the use of those in the Telegraph Service who desire to qualify themselves for the examinations which the
Cable Companies have recently instituted. To those desirous of entering the Cable Service, Messrs. Fisher and
Darby's book is indispensable, as it is now necessary for probationers to pass these examinations as part of the
qualification for service.
1, 2 and 3, Salisbury Court, Fleet Street London, E.G.
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Volumell. PRACTICE.
Primer
No.
21. The Electric Telegraph.
22. Automatic and Duplex
Telegraphy.
23. The Laying and Repair of
Submarine Cables.
24. Testing Submarine Cables.
25. The Telephone.
26. Dynamos.
27. Motors.
28. Transformers.
29. The Arc Lamp.
30. The Incandescent Lamp.
31. Underground Mains.
32. Electric Meters.
33. Electric Light Safety De-
vices.
34. Systems of Electric Distri-
bution.
35. Electric Transmission ol
Energy.
36. Electric Traction.
37. Electro-Deposition.
_ 38. Electric Welding.
A DIGEST OF THE
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AND OTHEE SUBJECTS.
By A. C. CUKTIS-HAYWAKD, B.A., M.I.E.E. Price 3s., post free.
Being a full critical abstract of the Electric Lighting Acts, 1882 and 1889, of the Tramways Act, 1870, and ol
Volume I. THEORY.
Primer
Mo.
1. The Effects of an Electric
Current.
2. Conductors and Insulators.
8. Ohm's Law.
4. Primary Batteries.
0. Arrangement of Batteries.
6. Electrolysis.
7. Secondary Batteries.
8. Lines of Force.
9. Magnets.
10. Electrical Units.
11. The Galvanometer.
12. Electrical Measuring In-
struments.
13. The Wheatstone Bridge.
14. The Electrometer.
15. The Induction CoiL
16. Alternating Currents.
17. The Leyden Jar.
18. Influence Machines.
19. Lightning Protectors.
80. Thermopiles.
The object of "The Electrician '
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state of electrical knowledge. Each
Primer is short and completein itself,
and is devoted to the elucidation of
some special point or the description
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stated and made clear by reference
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put. Both volumes are suited to
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Supply Undertakings. The Digest treats first of the manner in which person* desirous of supplying electricity
must set to work, and then of their rights and obligations after obtaining Parliamentary powers ; and gives in a
succinct form information of great value to Local Authorities, Electric Light Contractors, &c., up to date. The
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was regarded as subservient to the question of lighting. The Author has felt the want of such a book in dealing
with his clients and others, and in " ELECTRIC MOTIVE POWER " has endeavoured to supply it.
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tinuous and alternate currents are fully enlarged upon, and much practical informatio gathered from actual
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HISTORICAL SKETCH.
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THEORETICAL DIVISION.
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Induction, Quantity, Capacity, Potential Electromotive Force Electric Current Conduction
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posability of Electrolytes Electro-Chemical Equivalents of Substances Consumption of Electrifl
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Section F. : The Generation of Electric Currents by Dynamo Machines. Definition of a
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PRACTICAL DIVISION.
Section G. Establishing and Working an Electrolytic Copper Refinery. Planning a Refinery
Kinds of Dynamos Employed Choice and Care of Dynamo The Depositing Room The Vats
The Electrodes The Main Conductors Expenditure of Mechanical Power and Electric
Energy Cost of Electrolytic Refining.
Section H. : Other Applications of Electrolysis in Separating and Refining Metals. Elec-
trolytic Refining of Copper by other Methods Extraction of Copper from Minerals and Mineral
Waters Electrolytic Refining of Silver Bullion and of Lead Separation of Antimony, of Tin, of
Aluminium, of Zinc, of Magnesium, of Sodium and Potassium, of Gold Electrolytic Refining of
Nickel Electric Smelting.
Appendix. Useful Tables and Data.
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PRACTICAL NOTES FOR ELECTRICAL STUDENTS.
LAWS, UNITS, AND SIMPLE MEASURING INSTRUMENTS.
By A. E. KENNELLY and H. D. WILKINSON, M.I.E.E.
Chapter I. Introductory.
II. Batteries.
,, III. Electromotive Force and Potential.
IV. Resistance.
.. V. Current.
CONTENTS.
Chapter VI. Current Indicators.
VII. Simple Tests with Indicators.
VIII. Calibration of Current Indicators.
IX. Magnetic Fields and their Measure-
ment.
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Electrical Laboratory Notes & Forms.
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These " Laboratory Notes and Forms " have been prepared to assist Teachers, Demonstrators
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SERIES.
1. The Exploration of Magnetic Fields.
2. The Magnetic Field of a Circular Current.
3. The Standardisation of a Tangent Galvanometer by the Water Voltameter
4. The Measurement of Electrical Resistance by the Divided Wire Bridge.
5. The Calibration of the Ballistic Galvanometer.
6. The Determination of Magnetic Field Strength.
7. Experiments with Standard Magnetic Fields
8. The Determination of the Magnetic Field in Air Gap of an Eleccro-magnet.
9. The Determinaticn of Resistance with the Post Office Pattern Wheatstone Bridge.
10. The Determination of Potential Difference by the Potentiometer.
11. The Measurement of a Current by the Potentiometer.
12. A Complete Report on a Primary Battery.
18. The Standardisation of a Voltmeter by the Potentiometer.
14. The Photometric Examination of an Incandescent Lamp.
15. The Determination of the Absorptive Powers of Semi-Transparent Screens.
16. The Determination of the Reflective Power of Various Surfaces.
17. The Determination of the Electrical Efficiency of an Electromotor by the Cradle Method.
18. The Determination of the Efficiency of an Electromotor by the Brake Method.
19. The Efficiency Test of a Combined Motor-Generator Plant.
20. Efficiency Test of a Gas Engine and Dynamo Plant.
ADVANCED SERIES.
2L The Determination of the Electrical Resistivity of a Sample of Metallic Wire.
22. The Measurement of Low Resistances by the Potentiometer.
23. The Measurement of Armature Resistances.
24. The Standardisation of an Ammeter by Copper Deposit.
25. The Standardisation of a Voltmeter by the Potentiometer.
26. The Standardisation of an Ammeter by the Potentiometer.
27. The Determination of the Magnetic Permeability of a Sample of Ironi
28. The Standardisation of a High Tension Voltmeter.
29. The Examination of an Alternate-Current Ammeter.
80. The Delineation of Alternating Current Curves.
81. The Efficiency Test of a Transformer.
82. The Efficiency Test of an Alternator.
83. The Photometric Examination of an Arc Lamp.
84. The Measurement of Insulation and High Resistance
35. The Complete Efficiency Test of a Secondary Battery.
36. The Calibration of Electric Meters.
37. The Delineation of Hysteresis Curves of Iron.
88 The Examination of a Sample of Iron for Magnetic Hysteresis Loss
39. fhe Determination of the Capacity of a Concentric Cable
40. The Hopkinson Test of a Pair of Dynamos
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This Handbook has been written especially to meet the requirements of Electrical Engineers in
Supply Stations, Electrical Factories and Testing Rooms. The Book consists of a series of Chapters
each describing the most approved and practical methods of conducting some one class of Electrical
Measurements, such as those of Resistance, Electromotive Force, Current, Power, &c., &c. It does
not contain merely an indiscriminate collection of Physical Laboratory processes without regard to
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Electrical Testing for Telegraph Engineers.
By J. ELTON YOUNG.
This book embodies up-to-date theory and practice in all that concerns everyday w irk of the Telegraph Engineer.
CONTENTS.
Chapter VII. Measurement of Inductive Capacity.
Chapter I. Remarks on Testing Apparatus.
,, II. Measurements of Current, Potential,
and
Battery Resistance.
III. Natural and Fault Current.
IV. Measurement of Conductor Resistance.
V. Measurement of Insulation Resistance.
VI. Corrections for Conduction and Insulation
Tests.
VIII. Localisation of Disconnections.
IX. Localisation of Earth and Contacts.
X. Corrections of Localisation Tests.
XI. Submarine Cable Testing during Manu-
facture, Laying and Working.
XII. Submarine Cable Testing during Localis-
ation and Repairs.
In the Appendices numerous tables and curves of interest to telegraph engineers are given.
CENTENARY OF m ELECTRIC C
By Prof. J. A. FLEMIiNG, F.R.S. 1799-1899.
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interesting Lecture delivered by the Author before the Royat Institution in June, 1894, form the first chapter of
the book. The second chapter is devoted to the Application of Hertz Waves and Coherer Signalling to
Telegraphy, while Chapter 3 gives Details of other Telegraphic Developments. In Chapter 4 a history of the
Coherer Principle is given, including Professor Hughes' Early Observations before Hertz or Branly, and the
work of M Branly. Chapters are also devoted to " Communications with respect to Coherer Phenomena on a
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CARBON MAKING FOR ALL ELECTRICAL PURPOSES.
By FRANCIS JBHL.
This work gives a concise account of the process of making High Grade and other Carbon for Electric
Lighting, Electrolytic, and all other electrical purposes.
CONTENTS.
Chapter I. Physical Properties of Carbon.
II. Historical Notes.
III. Facts concerning Carbon.
IV. The Modern Process of Manufacturing
Chapter IX. The Estimation of High Temperatures.
X. Gas Analysis.
XI. On the Capital necessary for starting a
Carbon Works and the Profits in
Carbons. i Carbon Manufacturing.
V. Hints to Carbon Manufacturers and ! XII. The Manufacture of Electrodes on
Electric Light Engineers. Small Scale.
VI. A " N ew " Raw Material. XIII. Building a Carbon Factory.
VII. Gas Generators,
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XIV. Soot or Lamp Black.
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