THE ELEMENTS OF
LIEUTENANT-COLONEL, UNITED STATES ARMY, PROFESSOR
OF CHEMISTRY, ETC., UNITED STATES
JOHN WILEY & SONS, INC.
LONDON: CHAPMAN & HALL, LIMITED
F. H.GILSON COMPANY
The following text book on electricity has been prepared for
use of the Cadets of the United States Military Academy.
The course being required of all members of the third year
class, explanations have been given in more detail than would be
necessary were it elective. Recitations on the text proper are
accompanied by the solution of numerous problems and class room
instruction is supplemented by from eight to ten lectures and
twenty laboratory periods.
WEST POINT, NEW YORK.
December 18, 1913.
TABLE OF CONTENTS.
Need of Units Fundamental Units Standard of Length Metric System
Units of Mass and Time C. G. S. System Absolute Units 1
Origin of Name Divisions of Subject 6
Electric Attraction and Repulsion.
Electric Attraction Electric Charge Conductors and Non-Conductors
All Bodies Susceptible of Electrification Electric Repulsion Two
Kinds of Electrification Simultaneous Production of Equal Amounts
Electroscopes Theories of Electricity 9
Electrification by Influence Distribution of Induced Charge Attraction
and Repulsion Explained Amount of Induced Charge Separation
of Induced Charges Free and Bound Charges Gold Leaf Electro-
scope Electrophorus 17
Distribution of Charge.
Charge on Non-Conductor On Conductor Confined to Surface Biot's
Experiment Distribution of Charge Surface Density Effect of
Points Franklin's Experiment Other Experiments Division of
vi TABLE OF CONTENTS.
Kinds Frictional Machines Cylinder Machine Toepler's Machine
Holtz's Machine Electrical Diagrams 30
Laws of Electric Attraction "and Repulsion.
Coulomb's Torsion Balance Law of Inverse Squares Variation of Force
with Charges with Intervening Medium Unit Quantity of Elec-
Electric IJield Intensity Direction Lines of Force Graphic Represen-
tation of Field Tubes of Force Lines from Unit Charge Gauss'
Theorem Field about Uniformly-Charged Sphere near Uniformly-
Charged Plane Force Exerted upon Internal Point by Uniformly-
Charged Sphere Charge Resides on Surface 43
Cause of Movement of Electric Charges Physical Analogues of Electric
Potential Mechanical Potential Electric Potential Zero Potential
Potential at Point Due to a Charge Expression for Electric Force
Electromotive Force Practical Unit of E. M. F. Summary 51
Electrostatic Capacity Capacity of Sphere Case of Two United Spheres
of Two Coalescing Spheres Condensers Invention of Leyden Jar
Explanation of Leyden Jar Location of Charge of Condenser
Capacity of Spherical Condenser of Plate Condenser Dielectric
Capacity Determination Dielectric Capacity of Various Sub-
stances Dielectric Strength Commercial Condensers Practical
Unit of Capacity Work Expended in Charging a Condenser Energy
of a Condenser 59
Electrostatic Measurements Unit Jars Principle of Electrometers
Attracted Disc Electrometer Quadrant Electrometer 77
TABLE OF CONTENTS. vii
Natural Magnets Lodestones Fables of Ancients Doctor Gilbert
Artificial Magnets Magnetic Poles Poles Inseparable Magnetic
Attraction Mutual Action of Magnets Why Needle Points North
and South Poles Misnamed Magnetization by Induction Induc-
tion Induction Takes Place through Space Magnetic Attraction
Explained Other Magnetic Substances Diamagnetism 85
Measurement of Magnetic Forces.
Coulomb's First Law Lifting Power of Magnets Strength of Magnets
Magnetic Pole Defined Measurement of Magnetic Forces Cou-
lomb's Second Law Method by Oscillations Magnetic Moment
Experimental Proof of Law of Inverse Squares Unit Magnetic Pole . 93
The Magnetic Field.
Magnetic Field Direction Intensity Magnetic Lines of Force Map-
ping Lines of Force Permanent Record of Magnetic Figures Com-
pounding Magnetic Fields Properties of Magnetic Lines of Force
Magnetic Lines Pass Preferably through Magnetic Substances Law
of Maximum Flux Graphic Representation of Intensity of Magnetic
Field Comparison of Magnetic Fields Tangent Law Sine Law
Determination of Strength of Magnetic Field Turning Moment of
Theory of Magnetism.
Magnetism Molecular Magnetism Ewing's Theory Magnetization Ac-
companied by Molecular Movement Effect of Vibration Effect of
vHeat Effect of Solution 118
Manufacture of Magnets.
Most Suitable Metal Principle of Manufacture Method by Single
Touch Divided Touch Magnetization by Electric Current Con-
sequent Poles Magnetization Confined to Outer Layers Aging of
Vlll TABLE OF CONTENTS.
Location of Earth's Magnetic Poles Magnetic Declination Isogonic
Chart Magnetic Dip Dipping Needle Isoclinic Chart Magnetic
Intensity Magnetic Elements Variations Secular Change in Dec-
lination and Dip Diurnal Change in Declination Annual Change
in Declination Magnetic Storms Theories of Earth's Magnetism
Mariner's Compass Adjustments 127
Discoveries of Gaivani and Yolta.
Galvani's Discovery Volta's Investigations Volta's Contact Series
Contact Theory Later Theory Voltaic Pile Circlet of Cups
Source of Electrical Energy 145
The Simple Cell.
Simple Voltaic Cell Material Used for Elements Chemical Action
Local Action Remedy Polarization Depolarizers Requirements
of a Voltaic Cell 154
Kinds of Cells.
Great Variety of Cells Classification Grove Bunsen Bichromate
Daniell Gravity Edison-Lalande Leclanche Dry Cells Need of
Standard Cells Clark's Cell Weston's Standard Cell Conven-
tional Sign for Cell 160
The Electric Current and Its Chemical Action.
Electric Current No Current unless Circuit Complete Direction of
Flow Decomposition of Water Electrolysis of Water Faraday's
Terminology Substances Subject to Electrolysis Electrolysis of
Fused Compound of a Base of a Metallic Salt Electro-Chemical
Classification of Elements Faraday's First Law Voltameter The
Coulomb and Ampere Equality of Current at Every Cross-Section
Corollary Faraday's Second Law Electro-Chemical Equivalent
Definition of Ampere in Terms of Silver Applications of Electrolysis
Refining of Copper Electroplating Electrotyping 170
TABLE OF CONTENTS. ix
The Storage Battery.
Reversibility of Cells Storage Battery Elements of a Secondary Cell
Preparation of Plates Plante Cell Chloride Accumulator Shape
and Size of Plates Grouping of Plates Reactions Charging
Indications of Charge Troubles of Lead Batteries Care Objections
Edison Storage Battery Reactions Charging Advantages and
Disadvantages Use of Storage Batteries 182
Theory of Electrolytic Dissociation.
Interdependence of Physical Sciences Laws of Variation of Gaseous
Pressure Decomposition and Dissociation Example of Dissociation
by Heat Osmosis and Osmotic Pressure Demonstration Measure-
ment of Osmotic Pressure Observations of Pfeffer Osmotic Pressure
Follows Laws of Gaseous Pressure Van't Hoff's Generalization
Exceptions Dissociation Theory of Arrhenius Why lonization
Takes Place in Solutions How lonization Takes Place lonization
Incomplete Demonstration of Free Ions Ions not from Same Mole-
cule Grotthus' Theory Electrolytes and Non-Electrolytes Elec-
trolytic Properties Depend upon lonization Vapor Tension Solution
Tension Theory Applied to Simple Cell Atomic Character of Elec-
tricity Scope of Theory 198
Resistance Example of Effect Practical Unit The Ohm Laws of
Resistance Variation with Length with Cross-Section Specific
Resistance Variation with Temperature Platinum Thermometer
Ohm Denned in Terms of Column of Mercury Resistance and Con-
ductance Resistance of Conductors in Parallel Internal Resistance
of Cells Wire Tables Circular Measure of Wires. . . 213
Ohm's Law Drop of Potential Law Applies to Any Portion of Circuit
Division of Current in Divided Circuit Shunts Rheostats Kir-
choff's Laws Lost and Useful Volts Short Circuit Definitions
Based on Ohm's Law. . . 223
X TABLE OF CONTENTS.
Measurement of Resistance.
Measurement of Resistance Drop of Potential Proportional to Resistance
Measurement by Drop of Potential Resistance Coils Drop in
Divided Circuit Principle of Wheatstone Bridge Arrangement of
Resistances Evolution in Form Operation of Measurement
Bracketing Order of Closing Keys Ratio to Use Bridge with Re-
versible Ratios Dial Bridge Resistances that may be Measured
Slide Wire Bridge Measurement of High Resistance Resistance of
Electrolytes Internal Resistance of Cells 233
Measurement of E. M. F. of Cells Preliminary Arrangement of Poten-
tiometer Calibration Measurement 248
Grouping of Cells in Batteries.
Grouping of Cells in Series in Parallel Comparison of Two Groupings
Analogy between Cells and Pumps Multiple Grouping Maximum
Current Diagrams Cost of Power from Primary Cells < 251
Magnetic Field About a Wire Carrying a Current.
Oerstedt's Discovery Right Hand Rule for Deflection of Needle Mag-
netic Field about Wire Direction Clock Rule Wire Carrying a
Current is not a Magnet Rotation of Magnetic Pole by Current of
Current by Pole Left Hand Rule for Direction of Motion Intensity
of Field about Straight Conductor Field on Axis of Circular Coil
Absolute Unit of Current Force Exerted by Magnetic Field upon
Conductor Carrying a Current Work Done in Moving across a Field
a Conductor Carrying a Current Energy Expended on an Electro-
Magnetic Field Force between Parallel Conductors Carrying Cur-
Galvanoscopes and Galvanometers.
Galvanoscopes Increase of Sensitiveness Schweigger's Multiplier
Methods of Weakening Controlling Force Haiiy's Method Astatic
Combinations Magnetic Shells De La Rive's Battery Maxwell's
TABLE OF CONTENTS. xi
Law Galvanometers Tangent Galvanometer Measurement of
Current by Tangent Galvanometer Sine Galvanometer Mirror
Galvanometer Suspended Coil Galvanometer Damping Galvan-
ometer Shunts Universal Shunt Weber's Electro-Dynamometer
Siemen's Electro-Dynamometer Ballistic Galvanometer 274
Electric Magnetization of Iron and Steel.
Solenoid Equivalent to Bar Magnet Intensity of Field on Axis Am-
pere Turns Variation of Field with Current Effect of Material of
Core on Field Permeability Magnetic Saturation Curves of Mag-
netization Ewing's Theory of Molecular Magnetism Hysteresis
Cycle of Magnetization Energy Loss due to Hysteresis Law of
Magnetic Circuit Calculation of Flux Diamagnetism 295
Electro-Magnets Rules for Polarity Value of Electro-Magnets Trac-
tive Power Shape Use Lifting Weights Electric Bells Tele-
graph Morse Telegraph American System Overload Switch
Underload Switch 310
Faraday's Discovery of Induction Faraday's Second Discovery Inertia
of Electro-Magnetic Fields Explanation Applied to Magnet and "
Coil to Two Coils Rule for Direction of Induced E. M. F. Right
Hand Rule Mechanical Production of Electric Current Cutting of
Lines of Force Relation between Rate of Cutting and Resulting E.
M. F. Absolute Electro-Magnetic Unit of E. M. F. Practical Unit
of E. M. F., the Volt Eddy Currents Foucault's Experiments
Lenz's Law Transformers Self-Induction Measure Inductance
Expression for Inductance of Coil Helmholtz's Equation Induced
E. M. F. at Make and Break Induction Coil Use of Condenser
Bell Telephone Transmitter Operation of Telephone 321
Ammeters and Voltmeters.
Electrical Quantities to be Measured Effects Used in Measurements
Effect Best Adapted for Measurement Electro-Chemical Effect Se-
lected Why Silver Selected Reason for Weight Electro-Chemical
Effect Unsuitable for Industrial Needs Electro-Magnetic Effect
Xll TABLE OF CONTENTS.
best for Practical Measurements Calibration of Galvanometer
Difference between Ammeters and Voltmeters Ammeters Voltmeter
between Two Points of a Circuit E. M. F. of a Cell or Battery
Classification of Ammeters and Voltmeters Hot Wire Instruments
Moving Iron Instruments Switchboard Shunts Weston D. C. Am-
meter Weston D. C. Voltmeter Multipliers Weston D. C. A. C.
Voltmeter Thomson Inclined Coil Instruments Use of Transform-
ers with A. C. Instruments Milli voltmeters Millivoltmeters as
Ammeters Millivoltmeter Shunt 349
Heating Effect of Electric Current.
Work done by Electric Current Determination of Laws of Heating Effect
The Joule Theoretical Deduction of Joule's Law Electric Heating
of Wires Calculation of Temperature Localizing the Heating Effect
Electric Fuzes Electric Welding Electric Arc Electric Furnace
Moissan's Furnace Manufacture of Carborundum Manufacture
of Aluminum Electric Iron Furnaces The Induction Furnace 376
Power Defined Horse Power Expression for Electric Power Develop-
ment of Power in a Battery Units of Electric Power Measurement
of Power by Electro-Dynamometer Indicating Wattmeter Integrat-
ing Wattmeter Electrical Transmission of Power Considerations
Affecting Electrical Transmission of Power 387
The Electric Light Incandescent Lamp Carbon Filament Manufacture
of the Lamp Recent Incandescent Lamps Nernst Lamp Candle
Power Photometry Life of Incandescent Lamp Efficiency Con-
trol of Light Grouping of Incandescent Lamps Arc Light Car-
bons Requirements of Arc Light Mechanism Clutch Constant
Potential Arc Lamp Constant Current Arc Lamp Enclosed Arc
Flaming Arc Magnetite Arc Lamp Efficiency of Arc Lights
Luminous Vapor Lamps The Moore Light Cooper-Hewitt Mercury
Vapor Lamp 397
T her mo-Electrics.
Seebeck's Discoveries Thermo-Electric Inversion The Peltier Effect-
Thomson Effect Thermopile Radiometer Radio-Micrometer. . .416
TABLE OF CONTENTS. xiii
Remarks on Certain Electric Units.
Two Systems of Electric Units Units of Current and Quantity Units of
Electro-Motive Force Primary Electro-Magnetic Units Dimen-
sional Formulae Dimensional Formula of Electro-Magnetic Resist-
ance Resistance Expressed as Velocity Absolute Measurement of
Resistance The Ohm The Ampere The Volt Resume Compari-
son of the dimensional Formulae in the Two Systems Explanation
of Lack of Agreement 423
Direct Current Generators.
Electro-Mechanics Classes of Electrical Machines Coil Rotating in a
Magnetic Field Calculation of E. M. F. of Rotating Coil Produc-
tion of Current by Rotating Coil Alternating Current Graphic
Representation of Alternating E. M. F. and Current Rectification of
Alternating Current Increase in Number of Turns of Coil Increase
in number of Coils Open and Closed Coils Essential parts of D. C.
Generator The Field Excitation of Field Magnets Methods of
Self-Excitation Control of Field Armature Core Classes of Arma-
tures The Commutator Brushes Ring- Wound Generator Arma-
ture Reaction Commutation Sparking Multipolar Generators
Advantages of Multipolar Generators Drum Windings Plane De-
velopment of Drum- Winding Star Development of Drum- Winding
Calculation of E. M. F. of Generator Switchboards Example of
Switchboard Coupling of Generators; Three- Wire System 433
Adaptation of Generator to Work Required Characteristics Magneti-
zation Characteristic Characteristic of Series Generator Critical
Resistance Characteristic of Shunt Generator Compound Gener-
ator Over-Compounding 466
Direct Current Motors.
The Motor and the Generator Identical Explanation of Motion Power
Developed by a Motor Counter Electro-Motive Force Relation Be-
tween Counter E. M. F. and Power Developed Reading of Voltmeter
Across Seat of Counter E. M. F. Efficiency of Motors Maximum
Xiv TABLE OF CONTENTS.
Output of Power Classes of D. C. Motors The Shunt Motor
Control of Speed of Shunt Motors Starting Box for Shunt Motors
Series Motors Speed of Series Motors Change of Direction of
Rotation Motor-Generators 474
Alternating E. M. F. and Current Why Considered Separately Cycle,
Period and Frequency Phase Vector Diagrams Composition of
Alternating E. M. F.s Value of an Alternating Current Self Induc-
tion Inductance Inductance and Resistance Alternating E. M. F.
in a Circuit having Resistance and Inductance Graphic Construction
of E. M. F. and Current Curves Inductive Reactance Impedance
Choke Coils Explanation of Operation of Choke Coils Inductance
and Resistance in Series Inductance and Resistance in Parallel
Capacity Condenser in an Alternating Current Circuit E. M. F.
and Current Curves in Case of Capacity Capacity Reactance
Alternating E. M. F. in Circuit containing Resistance, Inductance
and Capacity Electric Resonance Resonance with Inductance and
Capacity in Series Resonance with Inductance and Capacity in
Parallel Power in an Alternating Current Circuit Power Factor . . 488
Alternating Current Generators.
Alternators Field Excitation of Alternators Compound Alternators
Alternators Usually Multipolar Classes of Alternators Alternators
with Revolving Armatures Alternators with Revolving Field The
Inductor Alternator Polyphase Alternators Tri-Phase Alternators
Tri-Phase Delta-Connection Tri-Phase Y-connection Trans-
formation of Direct and of Alternating Currents Transformers
Operation of Transformer Connection of Transformers Auto-Trans-
formers Rectification of Alternating Current The Mercury Arc
Rectifier Rectification of Single-Phase Current Comparison of
Alternating and Direct Currents . 515
Alternating Current Motors.
Alternating Current Motors Classes of A. C. Motors Series Motors
Synchronous Motors Operation of Synchronous Motors The Re-
pulsion Motor Principle of Induction Motor Production of Rotat-
ing Field The Induction Motor .533
TABLE OF CONTENTS. XV
Discharge of Electricity Through Gases.
High Potential Conductivity of Gases Discharge Through Moderate
Vacua Effect of Magnetic Field on Positive Column Discharge
Through High Vacua Cathode Rays Nature of Cathode Rays
Effect of Magnetic Field on Cathode Rays Effect of Electric Field
upon Cathode Rays Nature of Charge Carried by Corpuscles
Positive Rays Lenard Rays X-Rays Becquerel Rays Increase
of Conductivity of Gases lonization of Gases Investigation of
Corpuscles Velocity of Corpuscles Mass of Corpuscle Nature of
Henry's Theory of Oscillatory Discharge of Leyden Jar Thomson's Math-
ematical Proof of Oscillation Feddersen's Experiment with Revolving
Mirror Explanation of Oscillation Maxwell's Electro-Magnetic
Theory Electric Elasticity Electric Density Velocity of Propaga-
tion of Electric Wave Hertz's Confirmation of Maxwell's Theory
Further Experiments by Hertz Length of Electro-Magnetic Waves
Tuning of the Resonator Principle of Wireless Telegraphy The
Aerial The Transmitter Coupled Circuits Tuning of Coupled Cir-
cuits Branley's Coherer Operation of Receiving Circuit Use of
Telephone and Detectors Tuning of Receiving Circuits Distance
Attained by Wireless Telegraphy 556
1. Need of Units. In the orderly study of any concrete
science we early encounter the necessity for dealing with quanti-
ties. Quantities may be specified and an accurate conception of
them conveyed to others only by stating how many times greater
or less they are than some like quantity of which there is common
knowledge. Those quantities employed as bases of comparison
are called units.
2. Electrical Units to be Defined Later. In beginning a study
it might seem logical that we should first define the units to be
used, but in electricity the number of units is perhaps greater than
in any other one branch of science and a preliminary definition
of them would from their mere number tend to confusion rather
than to clearness; moreover, an accurate conception of some of
them requires more or less knowledge of certain electrical principles
and relations, therefore, it is found best to reserve these definitions
until, in the development of the subject, the necessity for their
3. Fundamental Units. There are, however, certain units of
general application in all sciences and of these it is well to have
from the beginning a definite conception. Such are the so-called
"fundamental" units of length, mass and time and some others
derived from these.
We may, in a sense, regard the unit of length alone as the fun-
damental unit for it is possible to define all the others more or less
directly by reference to length. Thus, the unit of mass may be
defined as the mass of water under certain conditions contained
in a cube of certain dimensions, the unit of time in terms of the
period of oscillation at a certain locality of a pendulum of a cer-
tain length, the unit of heat in terms of the linear expansion of
2 ELEMENTS : OF ELECTRICITY.
The term "fundamental" is however applied to the units of
length, mass and time because in addition to the simpler derived
units of area, volume and weight, it is possible, as will be shown
below, to express all such dynamical quantities as velocity, force,
work, etc., in terms of these units. This does not mean that there
is one universal fundamental unit of length or of mass or of time.
The units are chosen arbitrarily, but once having been selected
the system of derived units follows.
4. Standard of Length. The desirability of having a single
unvarying standard of length, one that could be reproduced should
existing standards be destroyed, has long been evident. It has
been proposed to take as such standard the length of the simple
seconds pendulum at the sea level at some definite locality. This
is about 39.14 inches.
The French government caused to be made most accurate meas-
urements of several meridian arcs of the earth's surface whence
was calculated the length of the meridian quadrant through Paris
and one ten-millionth part of this quadrant (about 40 inches)
was adopted as the measure of length and hence called the meter.
A standard meter of platinum was made and is preserved in
France. It is now known that an error was made in the deter-
mination of the length of the quadrant and that it is some 880
meters longer, so that practically the meter is the length of the
platinum bar, the "metre des archives" of France. Its length is
5. Need of Multiples and Submultiples. Although it would
seem that there should be but one unit for any one kind of quan-
tity, as a matter of fact this is not the case. The need of more
than one arises mainly from the fact that the average human
mind can not form a direct concrete conception of a quantity
expressed by more than three figures. For example, should a
person say that he had walked 63,360 inches we have no precise
image of the actual distance, and even when expressed as 5280
feet we involuntarily translate into the next higher unit; but when
he says that he has walked one mile we get a definite idea. In the
other direction, to speak of an object as one 63,360th of a mile thick
is almost meaningless but one inch conveys the exact impression.
Therefore in practical affairs we require large units to measure
large quantities and small units to measure small quantities.
6. The Metric System. It is not necessary to explain here
the advantages of the metric or decimal system. The following
table of English measures of length
3 barleycorns make an inch
12 inches make a foot
3 feet make a yard
1760 yards make a mile
and the fact that besides these we have the line, the hand, the
ell, the fathom, the rod, perch or pole, the chain, the furlong, the
geographical mile, the nautical mile, the knot, the league, etc.,