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» i O 3 ° 































TEXT-BOOKS OF SCIENCE 


ADAPTED FOR THE USE OF 


ARTISANS AND STUDENTS IN PUBLIC AND OTHER SCHOOLS. 


ELECTRICITY AND MAGNETISM. 



LONDON : PRINTED BY 
SPOTTISWOODE AND CO., NEW-STREET 
AND PARLIAMENT STREET 


SQUARE 


p f r ...|\ 

ELECTRICITY and MAGNETISM. 



« 



FLEEMING JENKIN, F.R.SS. L. & E., M.I.C.E. 
m 

PROFESSOR OF ENGINEERING 


IN 

THE UNIVERSITY OF EDINBURGH. 


SECOND EDITION. 


LONDON: 

LONGMANS, GREEN, AND CO. 

1874. 


All rights reserved. 










« 








7W 

BO 1910 























4 













INTRODUCTION. 


WHEN the author was asked to write the following 
little treatise he acceded to the request with much 
pleasure, because he had long known that an ele¬ 
mentary treatise on Electricity and Magnetism of a 
somewhat novel character was much needed. In 
England at the present time it may almost be said 
that there are two sciences of Electricity—one that 
is taught in ordinary text-books, and the other a 
sort of floating science known more or less perfectly 
to practical electricians, and expressed in a fragmentary 
manner in papers by Faraday, Thomson, Maxwell, 
Joule, Siemens, Matthiessen, Clark, Varley, Culley, 
and others. The science of the schools is so dis¬ 
similar from that of the practical electrician that it 
has been quite impossible to give students any 
sufficient, or even approximately sufficient, text-book. 
It has been necessary to refer them to disjointed 
treatises in the Reports of the British Association, in the 
‘Cambridge Mathematical Journal,’ the ‘Phil. Trans.’ 
and the ‘Phil. Magazine.’ A student might have 
mastered Delarive’s large and valuable treatise and 


VI 


Introduction. 


yet feel as if in an unknown country and listening to 
an unknown tongue in the company of practical men. 
It is also not a little curious that the science known 
to the practical men was, so to speak, far more scientific 
than the science of the text-books. These latter 
contain an apparently incoherent series of facts, and 
it is only by some considerable mental labour that, 
after reading the long roll of disjointed experiments, 
the student can even approximately understand any 
one experiment in its entirety; the explanation of 
part of the very first phenomenon described cannot 
be given until one of the very last experiments has 
been mastered. 

The author has found it quite impossible, for this 
very reason, to write his treatise on the ordinary plan 
of beginning with simple experiments and gradually 
building up a science by the description of a series of 
more and more complex phenomena. Not a single 
electrical fact can be correctly understood or even 
explained until a general view of the science has 
been taken and the terms employed defined. The 
terms which are employed imply no hypothesis, and 
yet the very explanation of them builds up what may 
be called a theory. The terms cannot be explained 
by mere definitions, because they refer to phenomena 
with which the reader is unacquainted. The mere 
explanation of the terms, therefore, requires some 
rapid description of facts, the truth of which the 
reader must at first take for granted. Many of the 


Introduction. 


vii 


assertions cannot be proved to be true except by 
complex apparatus, and the action of this complex 
apparatus cannot be explained until the general 
theory has been mastered. 

The plan followed in the book is therefore as 
follows:—First, a general synthetical view of the 
science has been given, in which the main phenomena 
are described and the terms employed explained. This 
general view of the science cannot be made very easy 
reading, although it will probably be found easier by 
those who have no preconceived notions about tension, 
intensity, and so forth, than by students of old text¬ 
books. If this portion of the work can be mastered, 
the student will then be readily able to understand 
what follows, viz., the description of the apparatus 
used to measure electrical magnitudes and to produce 
electricity under various conditions. The difference 
between the Electricity of schools and of the testing 
office has been mainly brought about by the absolute 
necessity in practice for definite measurement. The 
lecturer is content to say, under such and such cir¬ 
cumstances, a current flows or a resistance is increased. 
The practical electrician must know how much current 
and how much resistance, or he knows nothing; the 
difference is analogous to that between quantitative 
and qualitative analysis. This measurement of elec¬ 
trical magnitudes absolutely requires the use of the 
word and idea potential, and of various units each 
with an appropriate name, in terms of which each 


vili 


Introduction. 


electrical magnitude can be expressed. On a proper 
choice of units depends the simplicity of the ex¬ 
pression for the laws which connect electrical phe¬ 
nomena. After describing these laws and measure¬ 
ments, the author has given their chief practical 
application to telegraphy and a few examples of the 
construction of telegraphic apparatus. These fluctuate 
in form from year to year, and the special forms now 
in use will soon become antiquated; but the general 
theory of Electricity on which the construction and 
use of these depends is permanent, depending on no 
hypothesis, and it has been the author’s aim to state 
this general theory in a connected manner and in 
such a simple form that it might be readily under¬ 
stood by practical men. 


The above introduction is allowed to stand un¬ 
altered because it correctly describes what the author 
aimed at. He feels that the actual book falls very 
far short of the ideal he had conceived ; he perceives 
only too well that the arrangement might be very 
greatly improved, and the statements made in much 
clearer language. The book has been unfortunately 
written in intervals snatched from professional en¬ 
gagements at irregular periods, but the author would 
rather claim indulgence on the score that the effort 
made has at least been in the right direction, although 
far from fully successful. 



Iiitroductio7i. 


IX 


He has to acknowledge having received very kind 
assistance from his friends Sir W. Thomson, Professor 
J. C. Maxwell, Mr. Culley, and Mr. C. F. Varley; as 
well as from three of his assistants, Mr. W. Bottomley, 
Mr. W. E. Ayrton, and Mr. W. F. King, who kindly 
examined the proofs. 

Mr. Latimer Clark and Mr. Culley have allowed 
free use to be made of extracts from their valuable 
handbooks. 











































































































CONTENTS 


CHAPTER I. 


ELECTRIC QUANTITY. 


PAGE 

§ I. Definition of Electricity, and how it is produced by Friction ; i 
Conductors, Insulators. § 2. Resinous and Vitreous Electricity ; 
Attractions and Repulsions ; meaning of a Charge. § 3. 
Quantity of Electricity ; depends on the measurement of Force. 

§ 4. Experiments illustrating the foregoing ; Electroscope. § 5. 
Electricity at rest resides on the Surface of Conductors. § 6. 
Justification of the names positive and negative Electricity. 

§ 7. Attraction and Repulsion between Bodies positively and 
negatively electrified. § 8. When Electricity is produced, equal 
quantities of positive and negative Electricity are produced. § 9. 
Electric Series or List determining the sign of the Electricity pro¬ 
duced by Friction. § 10. Preliminary Explanation of the word 
Potential. §11. Statical Induction. § 12. The existence of 
any Charge implies an equal and opposite induced Charge. 

§ 13. Induction implies two Conductors at different Potentials 
separated by Insulators. § 14. Attractions and Repulsions con¬ 
sidered as due to Induction. § 15. Distribution of Electricity 
examined by Proof plane. § 16. Electrification does not imply 
Charge at all points of Surface; Leyden Jar or Condenser. 

§ 17. Meaning of the measurement of a quantity of Electricity. 

§ 18. Absolute Electrometer measures Quantity. § 19. Pro¬ 
duction of Electricity by other means than Friction; galvanic 
Cell. § 20. Identity of Electricity, however produced. § 21. 
Electricity produced by contact of Insulators. § 22. Electricity 
produced by unequal distribution of Heat. § 23. Effect of a 
Metal Screen between two electrified Bodies . . . .26 



Contents. 


Xll 


CHAPTER II. 
potential. 

p 

§ i. Definition of Difference of Potentials. § 2. Work done in 
moving Electricity from one Point to another is not affected by 
Path followed. § 3. Constant Potential. § 4. The Potential 
of a Body is the difference of its Potential from that of the 
Earth. §5. On what electric Potential depends. §6. Mean¬ 
ing of higher and lower Potential. § 7. Illustration of 
foregoing ; Surface and Interior of electrified Conductor. § 8. 
Space round charged Conductor. § 9. Illustration by Leyden 
Jar. § 10. More complex Illustration. §11. Effect of Changes 
of electrification of Leyden Jar on Potentials of the several parts. 
Effect of connecting two Jars. § 13. Relation between Charge 
and Potential. § 14. Immaterial which coating of Leyden Jar 
is to Earth. § 15. Theory of Electroscopes. § 16. Flow of 
Electricity determined by difference of Potential. § 17. Effect 
of joining a Conductor by a Wire with a Point of no Capacity 
but of different Potential. § 18. Electricity in motion always 
does work. § 19. Difference of Potential produced by Induction. 

§ 20. Difference of Potential produced by Friction. § 21. Dif¬ 
ference of Potential produced by Contact; Electric-contact Series 
or List of Conductors. § 22. Analogies and differences in the re¬ 
sult of contact in the cases of Solids and Liquids ; Galvanic-cell; 
Electrolytes ; Electrolysis. § 23. Electromotive Force, E. M. F. 

§ 24. It is affected by Temperature. § 25. Currents of Elec¬ 
tricity and Magnetism can produce E. M. F. § 26. Unit of 
E. M. F. or difference of Potential. 


CHAPTER III. 

CURRENT. 

§ i Definition of voltaic or galvanic Current. § 2. Transient and 
permanent Currents. § 3. Currents involve the performance of 
work. § 4. Is the Current due to contact or chemical action ? 
§ 5. Why no arrangement of Metals without Electrolytes can 
give a Current. § 6. Attractions and Repulsions between Cur¬ 
rents. § 7. Verification of Statements by Experiments ; rectangle 
and straight Wire. § 8. One Rectangle inside another. § 9. 


Contents. 


PAGE 

Multiplication of effect by multiplying the number of turns made 
by the Wires ; Electro-dynamometer. § io. Solenoids and fla 
Coils. § II. Analogy between Magnets and Solenoids; Galvano¬ 
meters and Galvanoscopes. §12. Simplest form of Mirror Gal¬ 
vanometer. §13. Magnetization of Iron by Currents. §14. A 
Current heats the conducting Wire ; amount of Heat. § 15. 
Electrolysis described; Ions, Anode Kathode ; electrolysis of 
Water. § 16. Effect produced by Currents traversing bad Con¬ 
ductors. § 17. Analogy between effect of Current on Magnet 
and effect of Current of Water in Pipe on a Piston. § 18. One 
Current can induce another; this is explained by the above analogy. 

§ 19. Direction of the induced Current under various Circum¬ 
stances ; distinction between electromagnetic and electrostatic 
Induction. § 20. Induction due to the increase or decrease of 
a Current. § 21. Reaction of the induced on the inducing Cur¬ 
rent. § 22. Induction in a Circuit which is not closed. § 23. 

Case where the closed Circuit is long and of sensible Capacity. 

§ 24. Strength of constant Current equal in all parts of Circuit. 

§ 25. Currents are not constant in all parts of Circuit when they 
start and cease. § 26. Thermo-electric Currents. § 27. ResumS 
of the several Causes which produce Currents . . . .80 

CHAPTER IV. 

RESISTANCE. 

§ 1. Meaning of Resistance. § 2. Definition of Resistance; 81 
Ohm’s Law. § 3. Relations between Resistance and Dimen¬ 
sions of Conductor; comparison of Resistance by differential 
Galvanometer. § 4. Relation between Resistance and Weight 
per Unit of length of Conductor. § 5. Effect of Temperature 
on Resistance. § 6. Object of determining Resistance. § 7. 
Effect of Changing Resistance of Parts of a Voltaic Circuit; 
Cells joined in Series and Multiple Arc. § 8. Effect of Resist¬ 
ance of Galvanometer. § 9. Apparent Resistances which are 
not really Resistances. §10. Polarisation of Insulators. §11. 
Resistance of Air to Sparks or Brushes not subject to Ohm’s 
Law. § 12. Resistance of Rarefied Gases . . . *93 


XIV 


Contents . 


CHAPTER V. 

ELECTRO-STATIC MEASUREMENT. 

PAGE 

I. Fundamental Units. § 2. Definition of Unit Quantity, Unit 94 
Difference of Potentials and Unit Resistance. § 3. Relation 
between Force of Attraction or Repulsion and Quantity of 
Electricity. § 4. Definition of Capacity ; Expression for Capa¬ 
city of simple geometrical Forms. § 5. Capacity of Conduc¬ 
tors ; specific inductive Capacity of Materials ; Table. § 6. 
Effect of polarisation or absorption on Capacity of Condensers. 

§ 7. Experimental Measurement of Difference of Potential be¬ 
tween two opposed Plane Surfaces by Thomson’s guard ring 
Electrometer. § 8. Electromotive Force of Daniell’s Voltaic 
Cell. § 9. Capacity of long cylindrical Conductor ; Subma¬ 
rine Cable. § 10. Electric Density; electrostatic Force. § 11. 
Diminution of air pressure in consequence of Electricity on 
Surface of Conductor ; Table giving Relation between Electro¬ 
static Force and Sparks from convex Plates. § 12. Effects of 
silent Discharge or Brush and Sparks from Points. § 13. 
General Ideas on distribution of Electricity. § 14. Material 
representation of electrostatic Units. § 15. Equations ex¬ 
pressing Relations between electrostatic Units. Unit of Cur¬ 
rent in electrostatic Measure ....... 109 


CHAPTER VI. 

MAGNETISM. 

§ i. Description of a Magnet. § 2. Definition of north and 109 
south Poles; the Earth a Magnet. § 3. Definition of the 
strength of a Pole and of Unit Pole. § 4. Magnetic Field; 
intensity of Field; lines of Force. § 5. Lines of Force from 
Single Pole and in uniform Field. § 6. Couple acting on 
Magnet in uniform Field; Magnetic Moment; Intensity of 
Magnetisation. § 7. Magnetism produced by magnetic In¬ 
duction ; paramagnetic and diamagnetic Bodies. § 8. Effect 
of laying bar Magnets side by side. § 9. Residual Magnetism 
and coercive Force. § 10. Magnetic Potential; equipotential 
Surfaces. §11. Faraday’s Lines of Force completely map out 


Contents. 


xv 


PAGE 

magnetic Field. § 12. Magnetic Fields due to single Pole 
and to single long straight Current. § 13. Importance of a 
Knowledge of magnetic Fields in practical Telegraphy. § 14. 
Position of Poles in bar Magnets ; the fragments of a Magnet 
are Magnets ; a Magnet induces Poles in all Bodies which it 
attracts. § 15. How Magnets are made. § 16. Electro-mag¬ 
nets ; ring Magnets produce no magnetic Field. § 17. Mag¬ 
netic Moment of a long thin Bar and of a Sphere in Terms of 
Intensity of magnetic Field. § 18. Coefficient of magnetic In¬ 
duction for Iron. § 19. Coefficient of magnetic Induction for 
other Materials. § 20. Coefficient of Magnetic Induction for 
paramagnetic Bodies. § 21. Attraction between a Magnet and 
Armature. .125 


CHAPTER VII. 

MAGNETIC MEASUREMENTS. 

I. Introduction to Measurement of magnetic Phenomena in ab- 126 
solute Measure. § 2. Magnetic Meridian; magnetic Declina¬ 
tion ; magnetic Inclination; Dip. § 3. Periodic Changes in 
Earth’s Magnetism ; isoclinic Lines. § 4. Horizontal Compo¬ 
nent of Earth’s Magnetism. § 5. Determination of magnetic 
Moment of a Magnet and of horizontal Component H of Earth’s 
Magnetism. § 6. Single Experiment will determine mag¬ 
netic Moment of Bar in terms of H. § 7. Units to be employed 
in above Measurements. § 8. How to find Moment of Inertia 
of a given Weight; Comparison of magnetic Moments. § 9. 
Difference between real Magnet and hypothetical Magnet . 133 


CHAPTER VIII. 

ELECTRO-MAGNETIC MEASUREMENT. 

§ I. Electro-magnetic System of Units based on action of Currents 133 
on Magnets; Definition of unit Current. § 2. Ratio between 
electrostatic and electro-magnetic Series. § 3. Tangent Galva¬ 
nometer used to measure Current in electro-magnetic Measure. 

§ 4. Ampere’s Theory of the action of Currents on Currents. 

§ 5. Weber’s Electrodynamometer. § 6. Kohlrausch’s Method 


XVI 


Contents . 


PAGE 

of measuring Current. § 7. Action between Rings conveying 
Currents in parallel Planes. § 8. Magnetic Field produced by 
Current in a long Helix. § 9. Theory of the Solenoid. § 10. 
Sucking action of Solenoid on Bar of Iron partially covered by 
it. § 11. Difference between hollow Magnet and Solenoid. 

§ 12. Effect of introducing soft iron Wire into a Solenoid . 146 


CHAPTER IX. 

MEASUREMENT OF ELECTRO-MAGNETIC INDUCTION. 

§ I. Electro-magnetic Force experienced by a Wire moving in a 147 
magnetic Field. § 2. Electromotive Force produced in a Wire 
so moving. § 3. Illustration of the foregoing. § 4. Rotation 
of a Coil in a magnetic Field. § 5. Determination of the Re¬ 
sistance of a Conductor in electro-magnetic Measure by the ro¬ 
tation of a Coil in a magnetic Field. § 6. Second Method 
adopted by electrical Standards Committee of British Associ¬ 
ation for Advancement of Science. § 7. Electromotive Force 
produced in a Wire by the increase or decrease of Current in a 
neighbouring Wire. § 8. Mathematical Expression for this 
E. M. F. § 9. Measurement of electric Quantity in electro¬ 
magnetic Measure. § 10. General Deductions applicable to 
Practice ...... .... 157 


CHAPTER X. 

UNITS ADOPTED IN PRACTICE. 

§ I. British Association Standard of Resistance. § 2. Practical 158 
Units of electromotive force and Capacity. § 3. Practical Units 
are all intended to be Multiples of absolute electro-magnetic 
Units. § 4. Units of Current and. Quantity; Ohm, Volt, 
and Farad; Farad per Second. § 5. Multiples and Sub¬ 
multiples; Dimensions of Units; Table of Units compared 
with absolute Measure ; Table of Dimensions of Units ; useful 
Constants for the conversion of Measurements expressed in 
Terms of one Series of fundamental Units into Measurements 
based on another fundamental Series . . . . 16c 


Contents. 


xvii 


CHAPTER XL 

CHEMICAL THEORY OF ELECTROMOTIVE FORCE. 

PAGE 

§ i. Electrolysis. § 2. Electro-positive and electro-negative Ions. 166 
§ 3. Electrolysis of Salts. § 4. Electro-chemical Series; 
Table. § 5. Electro-chemical Equivalents; Table. § 6. 
Relation between Work done by the Current and Electro¬ 
lysis. § 7. Measurement of chemical Affinity by electro¬ 
motive Force required for Electrolysis. § 8. Calculation of 
electromotive Force produced by a Combination, in Terms of 
the heat of Combination. § 9. Electromotive Force of Daniell’s 
Cell calculated from chemical Action. § 10. Practical Appli¬ 
cations of Electrolysis. §11. Mode of Transfer of Ions through 
the Electrolyte.174 


CHAPTER XII. 

THERMO-ELECTRICITY. 

§ 1. Definition of Thermo-electric Power of a Circuit of two 174 
Metals. § 2. Thermo-electric Series ; Table. § 3. Electromo¬ 
tive Force of a thermo-electric Pair producing a Current in a 
complex Circuit. § 4. Variations in thermo-electric Series due 
to change of Temperature; Diagram. § 5. Calculation of 
E.M.F. of a thermo-electric Pair from their thermo-electric 
Powers at different Temperatures. § 6. Neutral Points. § 7.. 
Professor Tait’s Law ; Calculation of E.M.F. of a thermo-electric 
Pair from Diagram and from Table. § 8. Addition of Electro¬ 
motive Forces of Pairs arranged in Series. § 9. Thermo electric 
Action of non-metallic Substances. § 10. Measurement of 
Temperature by Thermo-electric Batteries. §11. Peltier’s Law 
of absorption and evolution of Heat at the Junctions. §12. 

Sir William .Thomson’s Law; absorption and evolution of Heat 
at other parts of the Circuit.187 

CHAPTER XIII. 

GALVANOMETERS. 

§ 1. General Description and Classification. § 2. Galvanoscopes 187 
with vertical weighted Needles. § 3. Relation between the 
Circuit and Class of Galvanometer to be employed ; long Coils 

a 



xviii Contents. 

PAGB 

and short Coils; Intensity and Quantity. § 4. Equal Deflec¬ 
tions on any constant Galvanometer indicate equal Currents. 

§ 5. How to measure and regulate the sensibility of Galvano¬ 
meters. § 6. Astatic Galvanometers. § 7. Tangent Galvano¬ 
meters. § 3. Sine Galvanometers. § 9. Best form of Coil for 
mirror Galvanometers. § 10. Graded Galvanometers. § 11. 

Dead beat Galvanometers. § 12. Marine Galvanometers. §13. 
Differential Galvanometers. § 14. Shunts used to vary Sensi¬ 
bility. § 15. General Remarks on constructive Details . . 203 

CHAPTER XIV. 

ELECTROMETERS. 

§ I. General Description ; Canton’s, Bennet’s, Peltier’s, Bohnen- 203 
berger’s, heterostatic Electrometers. § 2. Sir William 
Thomson’s quadrant Electrometer. § 3. Sir W. Thomson’s 
portable Electrometer. §4. Absolute Electrometers . .211 

CHAPTER XV. 

GALVANIC BATTERIES. 

§ I. Single fluid Cell; common zinc and copper Cell; sand 211 
Battery; Smee’s and Walker’s. § 2. Points of Merit in a gal¬ 
vanic Cell. § 3. Polarisation by deposition of Gas on Plates 
of Cells. § 7. Local action causing waste of Zinc ; amalga¬ 
mation of Zinc. § 8. Inconstancy of Solution in single fluid 
Cell. § 9. Daniell’s Cell; Double Fluid. § 10. Theory of 
Daniell’s Cell. §11. Practical management of Daniell’s Cell. 

§ 12. Large Forms of Daniell’s Cell; sawdust Cells. § 13. 

Sir William Thomson’s or Menotti’s sawdust Cell; gravitation 
Cell. § 14. Marie Davy’s, Grove’s, Bunsen’s, Faure’s Cells ; 
Chromate of Potassium Element; Leclanche’s Cell; L. Clark’s 
Cell. § 1 5 * Practical Management of a galvanic Battery . . 22S 

CHAPTER XVI. 

MEASUREMENT OF RESISTANCE. 

§ I. Arrangement and construction of Boxes of resistance Coils. 229 
§ 2. Alternative Arrangements and practical Details. § 3. Use 
of Shunts. § 4. Definition of Conductivity ; addition of Con- 


Contents. 


xix 


PAGE 

ductivities. § 5. Comparison of Resistances b„y Comparison of 
Deflections on Galvanometers. § 6. Extension of this Method 
by the use of Shunts ; Tests of Insulation of Core of Submarine 
Cables. § 7. Four Methods of determining the Resistance of 
a Battery. § 8. Comparison of Resistances by shunted diffe¬ 
rential Galvanometer. § 9. Potential at different Points of a 
Conductor through which a permanent Current is flowing. 

§ 10. No Current flows through a Wire conecting two Points 
of two Circuits if these Points are at one Potential; this 
Law allows us to divide two Conductors of different resist¬ 
ances in one and the same ratio. § 11. Measurement of 
Resistance by Wheatstone’s Balance or Bridge. § 12. Kirch- 
hoff’s Laws. § 13. Theory of Bridge deduced from Kirch- 
hoff’s Laws. § 14. Specific resistance of Materials ; Defini¬ 
tion ; Table for Metals. § 15. Specific Conductivity. § 16. 
Effect of Temperature on specific resistance of Metals. § 17. 
Specific resistance of Insulators, Gutta-percha, India-rubber; 
Electrification. § 18. Measurement of resistance of Insulators 
by loss of Charge. § 19. Effect of Temperature on specific 
resistance of Insulators. § 20. Specific resistance of Miscel¬ 
laneous Insulators. § 21. Graphite, gas Coke, Tellurium Phos¬ 
phorus. § 22. Specific resistance of liquid Electrolytes. § 23. 
Precautions to be observed when measuring high Resistances . 261 


CHAPTER XVII. 

COMPARISON OF CAPACITIES, POTENTIALS, AND QUANTITIES. 

§ I. Comparison of Capacities by relative Throws of Galvano- 261 
meter ; ballistic pendulum Formula. § 2. Effect of shunting 
Galvanometer. § 3. Differential Methods with Galvanometer 
and resistance Slides. § 4. Comparison by Platymeter. § 5. 
Absolute Capacity from ballistic Formula. § 6. Comparison 
of Potentials. § 7. Comparison of Quantities .... 268 

CHAPTER XVIII. 

FRICTIONAL ELECTRICAL MACHINES. 

§ 2. Electrophorus. § 2. Common frictional Machine. § 3. Con- 268 
ductors or Condensers used with frictional Machines. § 4. Sir 
William Armstrong’s Machine producing Electricity by Steam 
issuing in a Jet. 2 73 


XX 


Contents . 


CHAPTER XIX. 

ELECTRO-STATIC INDUCTIVE MACHINES. 

§ I. C. F. Varley’s Arrangement; Sir William Thomson’s replen- 273 
isher and Mouse Mill. § 2. Holtz electrical Machine . . 279 

CHAPTER XX. 

MAGNETO-ELECTRICAL APPARATUS. 

§ i. Definitions. § 2. Pixii or Clarke’s Apparatus. § 3. Rise 279 
and Fall of induced Current. § 4. Mr. T. Holmes’ Apparatus. 

§ 5. Limit of Current. § 6. Mr. Wild’s and Mr. Judd’s 
Apparatus. §.7. Siemens’ Arrangement. § 8. Magneto signal¬ 
ling Keys. § 9. Inductorium, or Ruhmkorffs Coil. § 10. Siemens’ 
large Inductorium ; Discharges through Geissler Tubes . .291 


CHAPTER XXI. 

ELECTRO-MAGNETIC ENGINES. 

§ 1. Elementary Combinations in which action between Currents 291 
produces Rotation. § 2. Rotation of Magnet caused by action 
of Current. § 3. Electromotors ; Froment’s Engine ; beam 
Engine. § 4. Relative Economy of heat Engines and Electro¬ 
motors . .296 


CHAPTER XXII. 

TELEGRAPHIC APPARATUS. 

§ 1. Classification of Instruments, Class I. and Class II. § 2. De- 296 
scription of telegraphic Circuit. § 3. Elements of which tele¬ 
graphic Alphabets are compounded; Class I. § 4. Morse 
Alphabet. § 5. Morse Apparatus; Ink-writer ; Bain’s System, 
or electro-chemical Morse. § 6. Single Needle ; Bell. § 7. 
Relays. § 8. Double-current System. § 9. Return Currents ; 
Discharging Keys. § 10. General Remarks on Design of 
Telegraphic Apparatus. §11. Magneto Senders. §12. Rate 


Con ten ts. 


xxi 


PAGE 

of working; Wheatstone’s automatic Transmitter. § 13. 

Class II.; Step by step dial Instruments; Siemens’ and 
Wheatstone’s. § 14. Step by step Printers. § 15. Hughes’ 

printing Instrument. § 16. Bakewell’s and Caselli’s. § 17. 
Duplex System; Steam’s, Siemens’, Frischen’s. § 18. Bells . 327 

CHAPTER XXIII. 

SPEED OF SIGNALLING. 

§ i. Velocity of Electricity; Retardation ; Law of Variation in 327 
the incipient Current; arrival Curve ; Result of successive 
Signals. § 2. Effect of rapidly alternating Currents. § 3. 
Retardation on land Lines. § 4. Retardation on Sub-marine 
Cables ; use of mirror Galvanometer as receiving Instrument. 

§ 5. Sir William Thomson’s siphon Recorder. §" 6. Valley’s 
System of signalling by Condensers ; recorder Alphabet. § 7. 
Speed of working with various Instruments and Lines . . 338 

CHAPTER XXIV. 

TELEGRAPHIC LINES. 

§ 1. General Description. § 2. Sizes of iron Wire used for land 338 
Lines; Poles. § 5. Insulation of land Lines ; Designs for 
Insulators ; Objects aimed at in Design. § 4. Danger of Con¬ 
tact between adjacent Wires. § 5. Effect of uniform Leakage 
on received Current; allowable Leakage. § 6. Description of 
submarine insulated Conductor; Resistance per Knot of Con¬ 
ductor ; Insulation Resistance of insulating Sheath ; Constants 
for Gutta-percha and Hooper’s - Material. § 7. Capacity per 

Knot of submarine Cables. § 8. Anglo-American Type of 
Cable ; other Types of Cable. 349 

CHAPTER XXV. 

FAULTS IN TELEGRAPHIC LINES. 

§ 1. Classification of Faults. § 2. How to find Position of a Fault 349 
causing a Leak to Earth. § 3. Second Method. § 4. Third 
Method by Wheatstone Bridge when there is a return Wire. 


XXII 


Contents. 


PAGE 

§ 5. Determination of Position of a small Fault by simultaneous 
Tests at both Ends of Line. § 6. Effect of Faults. § 7. Fault 
involving loss of Continuity. § 8. Fault produced by Contact 
between adjacent Conductors . . . . . * 35 ^ 


CHAPTER XXVI. 

USEFUL APPLICATIONS OF ELECTRICITY OTHER THAN 
TELEGRAPHIC. 

§ i. Classification. § 2. Electro-metallurgy; Electro-plating. 357 
§ 3. Reproduction of Objects. § 4. Reduction of Minerals; 
Electrolysis. § 5. Electric Light; Holmes’ Lamp ; Waring’s 
Light. § 6. Firing of Mines ; Fuses. § 7. Medical Applica¬ 
tions. § 8. Clocks, Governors, and Chronoscopes . . . 364 


CHAPTER XXVII. 

ATMOSPHERIC AND TERRESTRIAL ELECTRICITY. 

§ 1. Distribution of Electricity on Surface of Earth. § 2. Earth 365 
Currents. § 3. Examination of Potential of the Atmosphere by 
Flame-bearing or Water-dropping Apparatus. § 4. Connexion 
between earth Currents and Magnetism. .... 367 


CHAPTER XXVIII. 
mariner’s COMPASS. 


§ 1. General Description. § 2. Deviation from Magnetic Meri- 367 
dian j Methods of Correction.368 


LIST OF TABLES 


Insulators relatively electro-positive and electro-negative 
Metals, potential or contact series ...... 

Specific inductive capacity of insulators . 

Sparks, length of, with given electro-motive force 
Magnetic induction, coefficient of, in various solids 
Magnetic induction, coefficient of, in various liquids . . 

Force attracting magnet introduced into coil conveying current 
Units, relative values of ....... 

Dimensions of units ......... 

British into metrical units, table for conversion of 
Metrical into British units, table for conversion of 

Electro-chemical series (ions) . .. 

Electro-chemical equivalents ....... 

Thermo-electric series .. 

Thermo-electric table giving E. M. F. in microvolts . 
Potential-series of metals in various solutions . 

Specific resistance of metals and alloys . ... . 

Metals, coefficient for calculating change of resistance with tem¬ 
perature ......... 

Electrification, change in apparent resistance of insulators due to . 
Insulators, change in resistance due to temperature of . 

Specific resistance of bad conductors ...... 

Specific resistance of electrolytes ...... 

Morse Alphabet. 

Arrival curve, table of ordinates ....... 

Amplitude of dots at various speeds ...... 

Wire iron—sizes, weights, and strengths . . . . . 

Insulation resistances of cables per knot ..... 


PAGE 

9 

43 

97 

104 

124 

124 

145 

162 

163 

164 
164 

168 

169 
176 
182 
216 
249 

251 

255 

256 

258 

259 
299 

330 

331 
340 
346 














































































j 

_ 







* 

. 








Errata 


Page 122, line 4, for 32-9 x io~ c read 32-9 x io - -* 
» >» >> 5, j; ‘000266 ,, -0000517 

ATT.’ ATT; 

i 154, 


A L K ,ALKH 
21, ,,-r<?a<7- 


,, 240, for equation 9 0 and preceding proportion read 
G 

R-t--I.*-+G=i:« or x = u R . . . . Q° 

u y 

,, 274, line 3 from bottom, for negative read positive 
,, 327, ,, 2, for while read bell 

| 345> 3> „ z = 2-7183// readz = 2-7183 ^ i 

,, 346, in heading of table, at bottom of page, for 

R v K 

, read « 

megohms. megohms. 

,, ,, line 2 of table, under R s , for Ox io 6 read 10 x 10 s 


A ddition 

A paper on the ‘Electrical Conductivity of certain Saline Solutions,’ 
by T. A. Ewing and T. G. MacGregor, B.A., published in vol. xxvii. 
of the Transactions of the Royal Society of Edinburgh , gives tables 
and results which are much more trustworthy than those quoted in 
Chap. XVI. § 22. 

^ 5 k<,. 

^ it.- Vrcv a. ^ l" 1 ’" 

LV- V v^CY'.vwAulvva i. 

.» — ^ «.«/ Hum wiictiever; out m this treatise 

the names employed will be chiefly those which have been 
suggested to men of science by thinking of electrical pheno¬ 
mena as due to the presence or absence of a single fluid. 

The stick of resin or glass, while retaining the properties 

! - B 






2 Electricity and Magnetism . [Chap. I. 

described above, is said to be electrified or charged with 
electricity; it carries electricity with it if moved from 
place to place. If these electrified bodies are wiped with 
a wet cloth, a damp hand, or with metal foil, they cease to 
be electrified. The electricity is then said to have been 
conducted away and the bodies which allow it to run off the 
glass or resin are called conductors of electricity. Metals, 
water, the human body, damp wood, and many other bodies 
are conductors. 

The air must be a non-conductor, or it would have re¬ 
moved the electricity as well as the wet cloth. 

Similarly, the resin and glass themselves are non-con¬ 
ductors, for when the electrified pieces are simply laid on 
a conductor they do not lose all their electricity, but remain 
electrified for some time in those portions which are not in 
the immediate neighbourhood of the conductor. 

Non-conductors are also called insulators. Glass, gutta 
percha, india-rubber, air, are examples of insulators. 

§ 2 . If a small piece of metal, supported by an insulating 
rod, be allowed to touch the electrified piece of glass or 
resin, it will be found to be in an electrical condition, 
similar to that of the glass or resin which it has touched. 

The insulated conductor which has touched the resin 
repels the resin itself or any other insulated conductor which 
may have touched the electrified resin : it may be said to 
be electrified as the resin was, or charged with resinous 
electricity ; it attracts the electrified glass, or any insulated 
conductor electrified by the glass or charged with what is 
sometimes called vitreous electricity. 

It follows from these experiments that part of the elec¬ 
tricity on the resin or glass is communicated to any conductor 
which touches either of the bodies. The electrical pro¬ 
perties gained by the insulated conductor electrified by 
contact with the electrified resin have been gained at the 
expense of those possessed by the resin—the resin or glass 
loses what the metal gains ; similarly, the electrified con- 


Chap. I.] 


3 


Electric Quantity. 

ductor can impart a portion of its properties to another 
conductor, losing that which it gives. We may, then, so far 
as can be yet seen, with propriety speak of a conductor as 
carrying a certain quantity of electricity, or as being charged 
with that quantity. 

The insulated conductor has acquired the special pro¬ 
perties in virtue of which the resin or glass was said to be 
electrified, or charged with electricity; but the insulated 
and electrified conductor has some peculiarities which dis¬ 
tinguish it from a similar piece of an electrified insulator. 
For instance, if the conductor be touched by the hand, or 
by the point of a wire held in the hand of a man not him¬ 
self insulated, it will lose all its electricity in a time so short 
as to appear inappreciable; whereas the insulator can only 
lose its electricity gradually, when every part of its surface 
has been successively touched. 

We may also expect that if from any cause the distribu¬ 
tion of electricity in a body can be varied, even without its 
total amount being changed, this redistribution will take 
place almost instantaneously in the electrified conductor, 
and much more slowly in the electrified insulator. 

§ 3 . The force exerted (other things being equal) by the 
electrified body on another similar body in its neighbour¬ 
hood, is found to depend on the quantity of electricity. If 
I halve the quantity, distributing that electricity over two 
equal balls, which was previously contained on one, the 
force exerted by the electricity on each ball will, under any 
given circumstances, be halved. It is in virtue of this force 
only, that we have known the ball to be electrified, and we 
may therefore, with propriety, speak of the quantity of 
electricity on each ball after the redistribution, as half that 
on the first ball originally. 

Resin and glass have been chosen as two typical materials, 
but any two different insulators rubbed together behave more 
or less as resin and glass do; thus relatively to a stick of 
shellac or resin, flannel behaves as a piece of glass would do. 


4 


Electricity and Magnetism . 


[Chap. I. 


Fig. i. 



§ 4 . The following experiments illustrate what precedes. 

Suspend a pith ball by 
a silk thread (Fig. i): 
pith, in order that the ball 
may be light; silk, in 
order that it may be in¬ 
sulated. 1 

1. A stick of shellac 
rubbed with flannel at¬ 
tracts the pith ball. 

2. After contact with 
the shellac, the pith ball 
will by conduction become 
negatively electrified as 
the shellac is, and will be 
repelled by it. 

3. Arrange the flannel, 
which is not a very good insulator, so that it may be insulated 
both while rubbing the shellac, and afterwards; this may be 
done by shaping it like a cup, and supporting it on a silk 
thread, or by gumming it on a metal disc fastened to a stick 
of vulcanite. Then the flannel, after rubbing the shellac, 
will be electrified with vitreous electricity, and will attract 
the pith ball electrified with resinous electricity. 

Converse effects will be produced by electrifying the pith 
ball by means of the flannel. The silk threads, shellac, and 
flannel must all be very dry, or the moisture will form a 
conductor along which the electricity will rapidly escape. 
Sometimes the pith ball is gilt, to make it a better conductor. 

Experiments, illustrating the proportion between the force 
observed and the charge of electricity, can be made by 
means of the pith ball. 

4. Two pith balls electrified with different electricities 
attract one another (Fig. 2). 

1 The parts of the drawings shown dark, but crossed by thiii white 
lines, are intended to represent insulators. 




Chap. I.] 


Electric Quantity. 


5 


5. Two similarly electrified pith balls hung side by side 
repel one another (Fig. 3). The same effect may be observed 
by means of two pieces of gold leaf insulated, and hanging 
side by side. When these apparatus are arranged (as in Fig. 4) 


Fig. 2. 


Fig. 3. 


Fig. 4. 



with glass cases and stands, and with means, such as the 
metal rod 0, of readily communicating an electrical charge 
from any body the condition of which is to be examined, 
they are called electroscopes. 1 They indicate the presence 
of electricity by showing the existence of a force. They 
do not, strictly speaking, measure either the force or the 
quantity of electricity, but only indicate the presence of some 
force and some quantity. The little electroscope in Fig. 4 is 
furnished with a metal cap d\ and two uninsulated strips of 
metal c c , the object of which is explained in § 14 and § 23. 

In testing the laws of electrical quantity, it is convenient 
to use a more complex arrangement for producing electricity 
than is afforded by the mere stick of shellac or glass. The 
common electrical machine may be used to produce the 
electricity. This machine consists of a plate or cylinder of 
glass rubbed by flannel or some other semi-insulator while 
being turned, and having conductors conveniently arranged 
so as to gather either the vitreous electricity produced on the 
surface of the glass or the resinous electricity produced on 
the flannel. The best construction of these instruments will 

1 The name electro meter is often improperly applied to what is above 
described as an electrof^te. Electrometers are described below, § 18. 
















6 Electricity and Magnetism . [Chap. I. 

be described when electrical laws have been more fully 
explained. The balls by which the foregoing laws are 
illustrated, may be held on glass or vulcanite stems, which 
must, however, be very dry and clean, or the electricity will 
only be retained for a very short time upon the balls. 

§ 5 . It is found that the distribution of electricity on 
the balls is unaffected by the mass of the ball, provided the 
surface remain constant. Balls made of wholly different 
materials but of the same size, if their surfaces be con¬ 
ductors, will behave in a precisely similar manner, so far as 
regards the quantity of electricity which each will abstract 
from any electrified body which it may touch : one ball may 
be wholly of brass, another a mere gilded pith ball, a 


Fig. 5. 



third a hollow iron ball; yet each will be found under 
similar circumstances to have what may be termed the same 
capacity for electricity. Moreover, let a ball (Fig. 5) be made 
of two hollow hemispheres, enclosing an independent con¬ 
ducting ball within them, and in contact with them, and let 
the system be electrified and the enclosing hemispheres 
removed by insulating handles. The internal ball will not 
be found electrified, and the two hemispheres, when placed 
in contact so as to form a complete ball, will, if the insulation 
has been perfect, be found to be as strongly electrified as at 
first. Electricity, while at rest, is therefore looked upon as 
residing in the surface only of the conductors. These state- 




Chap, I.] Electric Quantity. J 

ments may be verified with the assistance of the electro¬ 
scopes before described. 

Although electricity when at rest can only be detected on 
the surface of bodies, we shall presently see that, when in 
motion, it does not run over the surface only; it will pass 
more readily from one conductor to another along a solid 
rod than along a hollow rod of equal external dimensions 
and the same materials, vide § 3, Chapter IV. 

§ 6. Let one insulated conducting ball a be electrified by 
contact with rubbed resin, and another exactly similar ball b 
by contact with rubbed glass. If the two balls be now put in 
contact with one another, they will assume an electrical condi¬ 
tion which is the same in both. If the ball a had most electri¬ 
city at first, the whole system will be electrified as by rubbed 
resin; if b had most electricity at first, the whole system 
will be electrified as by rubbed glass; and in all cases the 
quantity of electricity on the two balls after contact will be 
equal to the difference of the charge on the two balls at first 
(it being remembered that the • quantity of electricity is 
assumed to be measured by the force, which, if contained 
on a given conductor, it would be capable of exerting). 

The distinction between the electricity due to rubbed 
glass and that due to rubbed resin is therefore analogous to 
that between positive and negative algebraic quantities, and 
justifies the use of the epithets positive and negative in place 
of vitreous and resinous. When positive and negative 
electricities are summed, the result is equal to the dif¬ 
ference between the arithmetical values of the quantities. 
If the two quantities of electricity of different kinds were 
equal on the two balls, the result of the contact would be 
wholly to put an end to all electrical charge. The two 
bodies would be discharged and would be unelectrified, 
which we shall find to mean no more than that they will be 
in the same condition as all surrounding uninsulated bodies. 

§ 7 . The electricity appearing on the rubbed glass is 
called positive, that appearing on the rubbed flannel or 


8 


Electricity and Magnetism. 


[Chap. I. 


gutta percha is called negative; and the algebraic signs 
+ and — are often used to denote the two different electrical 
conditions. 

+ positive, vitreous 1 are three synonymous modes of 

— negative, resinous J describing electrical conditions. 

The symbols + and — have already been used on the 
foregoing figures showing attractions and repulsions, + 
repels + ; — repels — ; + attracts —. 

§ 8. When electricity is produced, it is found invariably 
that equal quantities of positive jmc 1 negative electricity are 
produced. True, the glass when rubbed becomes positive 
only, but the material with which it is rubbed becomes 
negative, and the quantity on the glass is precisely equal 
and opposite to that upon the rubber. If the rubber be not 
insulated, the electricity upon it will be at once conducted 
to the earth, and will for the time being make the rest of 
the earth more negative than before ; but the earth, including 
the rubbed piece of glass, contains as a whole neither more 
nor less electricity than it did before ; the distribution only 
has been altered. 

When the whole surfaces of the two substances which 
have been rubbed together are thoroughly connected, either 
through the intervention of the mass of the earth or by 
any other conductor, the positive and negative electricities 
disappear, being neutralised as before. No substance is found 
to insulate so perfectly as to possess the power of keeping 
the two electricities asunder for more than a limited time. A 
perpetual leakage is always occurring from the one to the other 
through the mass of the insulator, until the combination or 
neutralisation is complete and all signs of electricity dis¬ 
appear. In elementary electrical experiments the one kind 
of electricity only is made manifest, because the one kind is 
concentrated in a small conductor and the other is probably 
diffused over the earth in the neighbourhood; the quantity 
at any one spot being too small to produce appreciable 
effects. Thus, when a stick of sealing-wax (being one kind 


Chap. I.] 


Electric Quantity. 


9 


of resin) is rubbed by a cloth, the sealing-wax alone appears 
electrified, simply because the positive electricity diffuses 
itself over the earth from the cloth, through the hand of 
the person holding it. 

§ 9. When one insulator is rubbed against another, one 
of them becomes charged with positive and the other with 
negative electricity; and with any given pair of materials, 
one invariably becomes positively and the other negatively 
electrified; but whereas glass rubbed with silk or flannel 
becomes positively electrified, when rubbed with a cat’s skin 
it becomes negatively electrified. It follows from this that 
the positive or negative electrification of the material does 
not depend absolutely on the substance of that material, 
but depends on some peculiar relation between the two 
substances in contact. It is proved by experiments that all 
insulators can be arranged as in the following list, which is 
such that those first on the list invariably become positive 
when rubbed by any of the substances taking rank after 
them, but negative when rubbed by a substance preceding 
them. This list is given on the authority of M. Ganot. 


Cat’s skin. 
Glass. 

Ivory. 

Silk. 

Rock crystal. 
The hand. 
Wood. 
Sulphur. 


Flannel. 

Cotton. 

Shellac. 

Caoutchouc. 

Resin. 

Gutta percha. 
Metals. 

Gun cotton. 


Those bodies which stand far apart on the list are dis¬ 
tinctly and decidedly positive or negative relatively to one 
another, but those bodies which appear near together on the 
list may possibly be misplaced. A very trifling difference in 
the composition of the body, or even in the state of its surface 
or of the colouring matter employed, will raise or lower the 
place of the body in the list. A rise in temperature lowers the 
body in the list, i.e. a hot body rubbed by a cold one identical 


io Electricity and Magnetism. [Chap. I. 

with it in chemical composition becomes negatively elec¬ 
trified. Generally it may be said that no difference between 
two insulators can be so trifling as not to necessitate the 
production of electricity when they are rubbed together. 
The relative position of two bodies on the scale can be 
readily tested by rubbing two insulated discs together and 
observing their action on a pith ball charged with electricity 
of a known character or sign. 

§ 10 . The word potential will now be substituted for the 
general and vague term electrical condition. When a body 
charged with positive electricity is connected with the earth 
electricity is transferred from the charged body to the earth ; 
and, similarly, when a body charged with negative elec¬ 
tricity is connected with the earth electricity is transferred 
from the earth to the body. Generally, whenever two 
conductors in different electrical conditions are put in con¬ 
tact electricity will flow from one to the other. That which 
detennines the direction of the transfer is the relative 
potential of the two conductors. Electricity always flows 
from a body at higher potential to one at lower potential 
when the two are in contact or connected by a conductor. 
When no transfer of electricity takes place under these con¬ 
ditions the bodies are said to be at the same potential, which 
may be either high or low. The potential of the earth is 
assumed as zero. The potential of a body is the difference 
of its potential from that of the earth. Potential admits of 
being measured and this measurement is fully described with 
the conditions tending to produce a given potential in 
Chapter II. Difference of potential for electricity is ana¬ 
logous to difference of level for water. From the above 
definition it follows, that all parts internal and external of 
any conductor in or on which electricity is at rest must be at 
one potential. 

A body is said to be uninsulated when connected by a 
conductor with the earth. The potential of any uninsulated 
body is neither negative nor positive. There is in this 



Chap. L] Electric Quantity. 11 

view nothing to prevent our regarding the earth as an electri¬ 
fied body; indeed, we know that any one part of the earth 
is seldom or never in exactly the same electrical condition 
as any other partin the neighbourhood. We simply assume 
as our zero the condition of the earth in our neighbourhood 
for the time being; just as we may assume, in measuring 
heights, any arbitrary level, such as Trinity high-water mark: 
a point above this is a positive height, a depth below it may 
be written or regarded as a negative height. 

§ 11 . It is frequently said that positive electricity attracts 
negative electricity, but that positive repels positive and 
negative repels negative. We have stated that electrified 
bodies do present attractions and repulsions of this kind, 
and by a slight extension of language the electricity itself 
may be spoken of as attracting or repelling; but there is a 
further phenomenon called statical induction , which does 
appear more distinctly to represent an attraction or repulsion 
of electricity, besides the attraction and repulsion of the 
bodies charged with electricity. A body a brought into 
the neighbourhood of a body b at a different potential 
immediately produces a distribution of electricity over the 
surface of b, such as would be produced by the system of 
attractions and repulsions enumerated in § 7. If a be 
charged positively it attracts negative electricity to that end 
of the body b which is near it, and repels positive electricity 
to the remoter portions of b. If the body b be insulated, 
it neither loses nor gains electricity, but its ends are com¬ 
petent to produce electrical phenomena of opposite kinds. 
Separating the two ends we may retain each charged with 
its positive and negative electricity. Or if we connect the 
further end of b with the earth even for a moment, the 
positive electricity will be driven off to the earth, and a 
permanent negative charge will then be retained on b. 
Otherwise when a is removed the + and — electricities on 
b recombine and exactly neutralise one another. By in¬ 
duction, as in the case of electricity obtained by friction, 


1 2 Electricity and Magnetism. [Chap. i. 

precisely equal quantities of positive and negative elec¬ 
tricities are simultaneously produced. It will be convenient 
to represent the distribution of electricity on the surface 
of bodies by dotted lines, the distances of which from 
the surface are proportional to the quantity of electricity 
per square inch at that point; then, if the electricity be 
positive the dotted line will be shown outside the body; 
if negative, the dotted'line will appear inside the body. 
Along one line separating the positively charged portion 
from the negatively charged portion there will be absolutely 
no charge. The annexed Figure (6) represents an original 
and an induced charge represented to the eye according to 
this plan. The dotted line on a shows the original charge 


Fig. 6 . 

4 - 4 - 



when a was at a great distance from b. When brought into 
the position Aj near b the original distribution is disturbed, 
and at the same time positive and negative electricities are 
induced at the two ends of b ; at the point e there is no 
charge. 

§ 12 . This induction of electricity must take place in the 
space surrounding every electrified body. In a room con¬ 
taining a ball electrified positively, the surface of the walls, the 
furniture, the experimenter himself must necessarily all De 
charged negatively in virtue of this induction. Where does 
this negative electricity come from ? If the electrified body 
has been charged positively by rubbing, and the negative 
electricity has been allowed free access to the earth, it may 

















Chap. I.] 


Electric Quantity . 


13 


be said that this negative electricity has been attracted to 
the surface of the walls, furniture, &c., distributing itself 
according to definite laws which must be separately studied. 
If both rubber and glass have been insulated, then each 
induces on all surrounding surfaces positive and negative 
electricities equal each to each, but these induced quantities 
are now not necessarily equal to the amount on the glass 
or on the rubber, unless these be removed very far apart 
from one another. If the two oppositely electrified bodies 
are kept close together, their inductive actions are spent 
almost entirely on each other and their action on the 
surrounding walls of the room is almost nothing, for 
where the one tends to induce a positive, the other tends 
to induce a negative charge; as the insulated electrified 
bodies are removed farther apart each produces its in¬ 
dependent effect more completely. It will be found im¬ 
possible rightly to understand electrical phenomena without 
always recognising the presence of this induced charge of 
electricity opposite in character to the first or original charge. 
The very existence of the original charge implies the induced 
charge. 

§ 13 . Induction always takes place between two con¬ 
ductors at different potentials separated by an insulator. If 
the conductors are at the same potential, whether this be 
high or low, there is no induction. 

If the wall of the room and an insulated body inside 
the room are at the same potential, the insulated body 
will be found to produce no electrical effects. The walls 
of the room and the insulated body might both be insu¬ 
lated from the earth and at a high potential, but none of 
the electrical effects hitherto described could be produced 
by an experimenter in the room. The insulated body would 
not attract light bodies; it would induce no charge or redis¬ 
tribution of electricity on a conductor held in its neigh¬ 
bourhood, and would not itself be charged with electricity 
or electrified. To produce all these phenomena we require 


Electricity and Magnetism. [Chap. i. 


not only that the insulated body in the room be at a high 
potential, but that the surrounding walls be at a different ! 
potential. If the insulated body at a high potential were : 
connected with the earth electricity would run from it to the I 
earth, and then a negative charge would appear on the 
surface of the body and a positive charge on the inside of 
the room. The body would then become electrified. 

§ 14 . Viewed in the light given by these facts the attrac¬ 
tion which an electrified body a exerts on uncharged bodies 
in the neighbourhood is simply due to the induced elec¬ 
trification which it produces in those bodies. The light 
uninsulated body b (Fig. 7) is attracted to the negatively 


Fig. 8 . 


Fig. 7. 



electrified body a in virtue of the positive charge on b ; this 
positive charge is also repelled by the walls of the room 
which will be positively electrified by induction from a. 
The light insulated body b (Fig. 8) is attracted because its 
charge at the near side is attracted. The charge on the 
far side of b is repelled, on the contrary, by the body a, 
but less repelled than the near side is attracted, because it 
is more distant. The charge on the near side of b is again 
repelled from the walls of the room towards the body a ; 
the charge on the far side is attracted towards the walls 
and from a, but less than the near side is attracted, because 
the far side is nearer the walls. It is not until all these 





Chap. I.] Electric Quantity . 15 

actions are taken into account that the forces set in action 
can be fully calculated; moreover, unless b be very small, 
it disturbs the distribution of electricity on a very sensibly. 

In the electroscope shown in Fig. 4, § 3, the metal strips cc 
are inductively electrified by any charge on the gold leaves 
bb. They attract the gold leaves and increase their diver¬ 
gence. They also make the action of the instrument more 
regular than it could be if glass were opposite b b, for 
the glass would always be liable to have an electrical charge 
of its own, independently of any charge on b b. 

A similar complicated series of actions occur when a 
positively electrified ball is brought into the neighbourhood 
of another positively electrified ball : each ball repels its 
neighbour and is attracted by the negative induced electri¬ 
city on the surrounding walls. If the walls were positive 
also they would repel the balls back to one another, and if all 
were at the same potential the two positive balls would be in 
equilibrium and would not be electrified. 

The phenomenon of induction allows us to examine the 
electrical condition of any body without abstracting elec¬ 
tricity from it. If I hold a positively electrified body over 
the knob on the electroscope (Fig. 4), the knob will be 
negatively charged and the gold leaves positively charged 
by induction ; the gold leaves will therefore be deflected. 
On the removal of the inducing body, the electricities re¬ 
combine and the deflection ceases. It is easy, however, by 
touching the under side of the knob or plate used for this 
purpose with an uninsulated conductor such as the hand, to 
allow the one electricity to run to earth, and then we have 
the electroscope permanently charged with electricity of 
the opposite kind to that contained on the inducing body. 

§ 15 . The distribution of electricity can be examined in 
two ways, the first of which is the following. We may 
touch the surface of the body which we believe to be 
electrified with a small insulated disc called a proof plane , 
and then remove this conductor, and observe whether it is 


16 


Electricity and Magnetism . 


[Chap. I. 


competent to produce any of the electrical attractions and 
repulsions or inductions. If the conductor be small, and 
if it be held on a long insulating stem of small size also, 
it will not much disturb the distribution of the electricity 
over the surface to be tested though some disturbance will 
always be produced by induction. While touching the 
body, it will sensibly form part of the surface of that body, 
and will be charged as the body is charged at that point, or 
nearly so. When removed, it will therefore retain a charge 
nearly proportional to what is termed 
the density of the electricity at that 
i—-\ point, and this density may therefore 

be tested by observing the attracting or 
'■ ' repelling force which the proof plane 

is in each case capable of exerting 
directly or by induction on some body 
assumed to be at a constant electrical 
potential — for instance, on the pith 
ball electroscope. By experiments of 
this nature, the distribution of electri¬ 
city has been studied, and it is found 
that no electricity can be detected inside 
a hollow and empty conductor. A proof 
plane introduced (as in Fig. 9) into the 
interior of a highly electrified ball with¬ 
draws no sensible charge of electricity 
unless by accident it touches the edge of the aperture while 
being withdrawn. This distribution is a necessary conse¬ 
quence of the law that each elementary portion of a charge 
of electricity repels every other similar portion with a force 
inversely proportional to the square of the distance separat¬ 
ing them. We shall study hereafter a few of the laws of 
distribution of electricity on the surface of conductors of 
regular form, on the assumption that they are so far from 
all neighbouring conductors, that the distribution depends 
only on the form of the electrified surface. These laws 





Chap. I.] Electric Quantity. 17 

will show that electricity tends to accumulate on all pro¬ 
jections, and that the density at points is necessarily very 
large. Next we must study the distribution of electricity 
over two conducting surfaces opposite each other. The 
distribution in this case depends not only on the form of 
each surface, but on their proximity. For instance, the 
inside of a hollow conductor will be inductively charged 
by any electrified and insulated body placed there, and the 
charge on the internal surface will be greater the closer the 
two surfaces are placed. The charge is also affected by 
the-insulator separating the conductor. 

A second mode of testing the distribution of electri¬ 
city is to remove the portion of the body the electricity of 
which is to be tested from the system of which it forms part, 
by insulating it from that system ; its electricity may then 
be tested by the proof plane or by its direct effects. 

§ 16 . It follows from what has already been stated (§ n) 
that an electrified conductor may at certain portions of its 
surface have little or no charge. If those parts are touched 
by the proof plane no electricity will be removed by it. 
Thus, if a cylinder be electrified by induction, so that one 
end is positive, the other end negative, as shown on the 
body b, Fig. 6, some point near the middle at e will not be 
charged. It will not electrify the proof plane or any other 
small conductor, and even if a portion of the cylinder itself 
be removed it will give no signs of electricity. If it be 
touched by a large conductor, the whole distribution of 
electricity will be changed by induction before the contact 
takes place. Thus, if I connect the point e, Fig. 6, with- 
the earth the whole distribution of electricity on b will be 
changed, for although e is no more charged with electricity 
than the earth itself the potential of the whole body b has 
been raised by induction from a on b ; the approach of 
the connecting wire alters the distribution of electricity, 
positive electricity accumulates opposite the wire even be¬ 
fore the contact is made, and the result of connecting e with 

c 





18 Electricity and Magnetism. [Chap. I. 

the earth would be to leave the body b charged with negative 
electricity only and at the potential of the earth. 

There are distributions of electricity such that the electri¬ 
fied conductor may actually be in contact with the largest 
conductor or with the earth without losing its electricity or 
the distribution being in any way changed, the conductor 
being at the potential of the earth; for instance, consider the 
positively electrified conductor a, Fig. io, insulated and 
separated from the conductor b by a thin dielectric c. Let 
there be a negative charge on the conductor b equal to the 
positive charge on a, then no sensible charge will be found 
upon the external surface of either a or b, supposing them 
held far away from other conductors. I can produce this 
distribution by electrifying a while b is in contact with the 
earth. The positive charge on a will induce a negative 
charge on b, as shown by the dotted lines. The charge 
on a will be on the surface opposite b : 'the charge 
on b will be on the surface opposite a. I may then 
allow either a or b to be in connection with the earth 
without sensibly disturbing the charge on a or b. If I 
allow both to be in connection with the earth or with one 
another, the electricities will combine and neutralise one 
another. The dielectric need not be solid, as in Fig. io, 
but may consist of air only, as in Fig. n. The distri¬ 
bution of electricity described is that which occurs in 
a charged Leyden jar (Fig. 12). The outside coating a has 
a large charge of electricity almost equal to the charge of 
the internal coating b ; nevertheless none cf the electricity 
runs from the outer coating to the earth. The potential 
of the outer coating is zero. It is often said that electricity 
in this case is latent or fixed—in truth it. is no more latent 
or fixed than any other charge of electricity. The distribu¬ 
tion in this case is such that no sensible charge is on the 
outside of the outside coating, the whole quantity being on 
the inside of the outside coating. 

If we were to form a Leyden jar with an opening ad- 


Chap. I.] 


Electric Quantity . 


19 


mitting the introduction of a proof plane between the inner 
and outer coatings, we might take off from either coating a 
quantity proportional to the charge at each place. This, in 
fact, is what we do when by the proof plane we remove a 
portion of the charge from a conductor inside a room, or 
from the walls of a room inside which an electrified body is 


Fig. 10. 


Fig. 12. 


Fig. 11. 





placed. There is no difference in theory between the inner 
and outer coatings of the Leyden jar; the outside of the 
inner coating, the inside of the outer coating are charged. 
From these electricity can be withdrawn by the proof 
plane; from the other faces of either coating none can be 
taken. 

Whenever a conductor is charged a kind of Leyden jar is 
necessarily formed. The conductor is the inner coating, 
the air the dielectric, and the nearest surrounding conductors, 
such as the wall of the room or the person of the operator, 
form the outer coating; but the name of ‘Leyden jar' is 
reserved for those cases in which the two opposed con¬ 
ductors are brought very close together purposely. The 

















20 


Electricity and Magnetism. 


[Chap. I. 


arrangement is also called a condenser or accumulator. The 
difference of potential between the two coatings of the 
Leyden jar remains constant whichever coating is in connec¬ 
tion with the earth. If the original charge on the inside be 
positive, the outer insulated coating will be at a negative 
potential when the inner coating is put to earth. 

§ 17. The quantity of electricity on a given conductor 
may be measured. The existence of the quantity of elec¬ 
tricity is proved merely by the force which it exerts on other 
quantities of electricity. In order to measure quantities of 
electricity we must therefore measure the relative forces 
which different quantities exert under the same circum¬ 
stances : if a quantity a of electricity exerts twice the force 
that quantity b exerts under precisely similar circumstances y 
we may properly say that quantity a is double the quantity 
B. In order to measure anything a unit must be adopted. 

The unit quantity of electricity may conveniently be 
called that quantity which, concentrated at one point, 
would exert the unit force upon a similar and equal quantity 
concentrated at a point distant by one unit of length. There 
are many different units of length and force which might be 
adopted. The units chosen by the author in the present 
work are the centimetre for the measure of length ; and 
the force capable of giving in one second a velocity of 
one centimetre per second to a gramme mass for the unit 
of force. The unit quantity of electricity upon this system, 
known as the electro-static system, is that which if concen¬ 
trated at one point would repel an equal quantity at a point 
one centimetre distant with such a force as would, after 
acting for one second, cause a gramme to move with a 
velocity of one centimetre per second. Another unit of 
electricity might be defined as that which would repel a 
similar unit with the force of one grain at a distance of one 
foot. The idea at the root of both definitions would be 
identical, but the apparently more complex definition leads 
to greater simplicity in calculations. 


Chap. I.] Electric Quantity. 21 

§ 18. The practical measurement of quantities of electri¬ 
city can in many cases be made by directly measuring the 
electrical forces in action; the apparatus in which these 
forces are weighed is called an absolute electrometer. Any 
apparatus in which the forces produced by different quantities 
under the same circumstances are numerically compared but 
not actually measured in units of force is termed an electro¬ 
meter. Indirect methods of measuring quantity are often 
more convenient for practical purposes, but these measure¬ 
ments can and ought to be all made in units of the kind 
described. In studying the distribution of electricity under 
various conditions, we must not be satisfied with merely 
knowing generally that at certain points there will be more, 
at others less, electricity; we must not even be satisfied 
with knowing the relative amounts on various points of a 
given conductor; we must aim at knowing exactly the 
quantity of electricity per square unit of surface, which is 
termed the density of the electrical charge. The electro¬ 
meters employed in comparing quantities of electricity on 
different portions of any surface or surfaces must give us 
the relative amounts on various points, or they will not be 
measuring instruments. An absolute electrometer does more, 
it gives not only the relative but the absolute amounts. 

§ 19. Hitherto electricity has been spoken of as pro¬ 
duced directly by friction and indirectly by statical induc¬ 
tion only; there are several other modes by which elec¬ 
tricity is produced :— 1 . The simple contact of two in¬ 
sulated pieces of dissimilar metals results in charging one 
metal with positive, the other with negative electricity in 
precisely-equal amounts; or it may be more correct to say 
that after contact the metals are found to be thus dissimilarly 
charged. The charges so produced or observed are very 
small. 2 . If a metal be dipped in a liquid a similar 
effect occurs, the liquid and the metal being electrified in 
opposite ways. A difference of potentials is produced by 
the contact. The amount of electrification differs with 


22 Electricity and Magnetism. [Chap. I. 

% 

different metals and different liquids, but is always very 
small compared with that which might be produced by 
friction. 3 . When two dissimilar metals are plunged side 
by side into a liquid, such as water or a weak solution of 
sulphuric acid, they do not exhibit any signs of electrification. 
The three materials remain at one potential or nearly so . 1 
A further description of this curious fact is given Chapter II. 
§ 22 . 4 . If while the two dissimilar metals are in the 

liquid they are joined by metallic contact to terminal pieces 
of one and the same metal, these terminal pieces will be 
brought to the same difference of potentials as that which 
would be produced by direct contact between the dissimilar 
metals. Thus, though zinc, water, and copper in an insulated 


Fig. 13. 



jar are all at one potential, if I join a copper terminal to the 
zinc, then this copper tenninal will become positive rela¬ 
tively to the zinc, water, and second copper, which all remain 
at one potential. 

The name of galvanic cell is given to an insulating jar con¬ 
taining two dissimilar metals plunged in a liquid composed 
of two or more chemical elements, one of which at least 
tends to combine with one or other of the two metals, or 

1 The Voltaic theory of the galvanic cell is adopted in this treatise. 
The above statement is in direct contradiction with many treatises on 
electricity, which generally state that the metals become one positive 
and the other negative. Vide Chapter II. § 23. 

































Chap. I.] 


Electric Quantity. 


23 


both in different degrees. But whereas in the single cell no 
charge of electricity is given to either metal, if we insulate 
successive jars of the liquid one from another, and plunge 
successive pairs of metals, c and z, joined as in Fig. 13 , 
into these jars, very considerable charges of electricity will 
be communicated to conductors in contact with the final 
plates of metal; thus, if coppers and zincs be used, the 
liquid being water or a weak solution of sulphuric acid, the 
last copper plate will charge a conductor positively, the 
last zinc plate an equal conductor negatively. Sulphate 
of zinc will be formed during the process, and this chemical 
action is found to be essential to the production of any 
considerable quantity of electricity in this manner, which is 
therefore often said to be due to chemical action as dis¬ 
tinguished from friction. The charge of electricity obtained 
in this way may be looked upon as wholly due to the 
chemical action; but, on the other hand, it may be looked 
upon as due to the successive junctions between the zincs 
and coppers, and it is found that the amount of charge 
obtained in this manner on a given conductor is simply 
proportional to the number of these junctions, and that it 
depends on the metals in contact, not upon the liquids. 
In other words, the difference of potentials produced is 
proportional to the number of junctions. These two views 
are called respectively the chemical theory and the contact 
theory of the galvanic cell, and have been supposed to be 
incompatible. They are both true. 

§ 20. There is no difference whatever in kind between 
the electricity produced by friction and that produced by 
chemical reaction. It is worthy of remark that, in each 
case, the electricity requires for its production the contact of 
dissimilar materials. This contact requires to be supple¬ 
mented by friction in the case of insulators, by chemical 
reaction in the case of conductors. The friction between 
two dissimilar insulators invariably produces electricity. The 
difference of the chemical action of any conducting liquid 


24 Electricity and Magnetism. [Chap. I. 

compound on two dissimilar metals produces electricity. 
The analogy between friction and chemical action is not 
known. Electricity in each case is produced so that equal 
quantities of positive and negative electricity are simulta¬ 
neously produced. This is sometimes expressed by saying 
that all bodies are always electrified, and that the contact 
and friction, or contact and chemical action, produce 
merely a redistribution of electricity. 

§ 21. Electricity may also be produced by the simple 
pressure, or indeed contact, of two dissimilar insulators. 
The electricity will be retained by the insulators after their 
separation. This is precisely analogous to the production 
of electricity by the contact of two conductors. 

§ 22. Certain minerals when warmed acquire an electric 
charge, differing in sign at different parts of the mineral; 
thus, one end of a heated crystal of tourmaline will be 
positively electrified, while the other is negatively electrified. 
This electricity is sometimes called pyro-electricity. The 
phenomenon has not been much studied; the electrical 
charge is probably due to a polarity in the structure of the 
tourmaline at different parts, which virtually makes in one 
crystal a system like that of a magnet having opposite pro¬ 
perties at opposite ends. The electrical phenomena pro¬ 
duced by the contact of dissimilar metals are produced 
even when the dissimilarity consists merely in the difference 
of temper in one and the same piece of metal. A soft and 
a hard piece of brass wire behave as dissimilar metals, 
although their chemical composition may be identical. If 
this view be correct, we may say that, wherever electricity 
is directly produced, it requires the contact of two dissimilar 
materials. 

§ 23. The attractions and repulsions produced by elec¬ 
tricity have hitherto been spoken of as absolute, or as being 
produced under all circumstances; but if an uninsulated metal 
plate d (Fig. 14 ) be interposed between an electrified body a 
and the insulated suspended pith ball b all attraction or repul- 


Chap. I.] 


Electric Quantity. 


2 5 


sion will cease, just as if the metal plate were opaque to the 
electric influence. If, however, the metal plate or screen 
be insulated (as in Fig. 15 ) it will increase the attraction or 
repulsion instead of destroying them. These two apparently 
different effects are due to the different distributions of elec¬ 
tricity produced in the two cases. 

Let a be electrified positively, and the plate d be uninsu¬ 
lated, then on the side next a a negative charge will be 
induced, diffused over a considerable surface ; the effect 
of this diffused negative charge is very nearly to neutralise 
all attractions or repulsions due to a, on the farther side of 
the screen. The metal cap of the electroscope (Fig. 4 ) is in¬ 
tended to screen the gold leaves from inductive effects, and 
should not be insulated. The whole glass case should be 
coated with an open wire case for the same reason. 

When, however, the metal plate d is insulated the farther 


Fig. 14. 


Fig. 15. 





o 


side of d becomes positively electrified as a was, the charge 
on the side n near to a and the charge on a nearly neutralise 
one another as before; but the positive charge on the far 
side / of d is thus left free to attract or repel, and the result 
is the same as if the body a had been advanced in the direc¬ 
tion of the screen by an amount equal to the thickness of the 
screen. 

We can now understand the reason why a Leyden jar con- 













2 6 


Electricity and Magnetism. [Chap. II. 

taining a very large quantity of electricity neither attracts 
nor repels light bodies in its neighbourhood. The effect of 
the more concentrated inner charge and more diffused outer 
charge is such that one precisely neutralises the other. This 
statement is here made as of a fact ascertained by experi¬ 
ment. It can also be theoretically demonstrated. 


CHAPTER II. 

POTENTIAL. 

§ 1. The word Potential , introduced by Green, has only 
lately been generally adopted by electricians, and is still 
often misunderstood ; it expresses a very simple idea, and one 
quite distinct from the meaning of any other term relating 
to electricity. 

As already explained in Chapter I. § 7 difference of 
potential is that difference of electrical condition which de¬ 
termines the direction of the transfer of electricity from one 
point to another; but electricity cannot be so transferred 
without doing work or requiring work to be done, hence 
the following definition. Difference of potentials is a differ¬ 
ence of electrical condition in virtue of which work is done by 
positive electricity in moving from the point at a higher potential 
to that at a lower potential and it is measured by the amount 
of work done by the unit quantity of positive electricity when 
thus transferred. The idea of potential essentially involves 
a relative condition of two points, so that no one point or 
body can be said simply to have an absolute potential but 
for the sake of brevity. 

The potential of a body or point is used to denote the differ¬ 
ence between the potential of the body or point a?id the potential 
of the earth. 

These definitions require considerable illustration before 
they can be fully understood. 




Chap. II.] 


Potential. 


27 


Electrified bodies repel and attract one another, and by 
a slight extension of language we say that a quantity of 
positive electricity attracts a quantity of negative, but repels 
a quantity of positive electricity. If, therefore, we move a 
quantity of positive electricity towards another similar 
quantity we meet with a resistance capable of measure¬ 
ment, equal, for example, to the weight of so many grains. In 
overcoming this resistance work must be done, precisely as 
work must be done to lift a pound or. a grain. The work 
done in moving a body from a to b is measured by the 
product of the distance multiplied into the force overcome; 
if the weight of a grain be the unit of force and the foot the 
unit of distance, the unit of work will be the foot grain. If, 
then, in moving a certain quantity of electricity from a to b 
we overcome a resistance of ten grains through a space of 
five feet we do work equal to fifty foot grains during the 
operation. On the other hand, the repulsion or attraction 
of electrified bodies tends to perform work; for the body just 
brought to B may be driven back to a by the force of 
electricity alone. In the one case, work is said to be 
done upon the electrified body in consequence of its electri¬ 
fication; in the other case it is done by the electrified body 
in virtue of its electrification ; less accurately we might 
say the work was done by the electricity, or performed upon 
the electricity; the measure of the work is the same in the 
two cases, which are analogous to letting a body fall from 
the level a to the level b, and raising it up again from b 

to A. 

§ 2. An electrified body moving from one point to another 
may at one time require work done upon it in order to 
overcome the resistance; at another part of the journey it 
may pull in the direction it is going and then work is done 
by it. I speak here only of the work done or required in 
consequence of the electrical condition of the body. 

The whole work which has been required in consequence 
of electrical attractions or repulsions to move it from any 




28 


Electricity and Magnetism. 


[Chap. II. 


point a to any point b will be the algebraic sum of the work 
done by and done upon the electrified body, the first being 
called positive and the second negative work. 

Thus, if in moving the electrified body from a to b, we first 
have to overcome a resistance, and do work upon it equal to 
io foot grains, whereas afterwards it pulls towards b, doing 
work equal to 30 foot grains, then in the whole passage 
from the point a to the point b the work done by the body 
may be said to be 20 foot grains; it is true that during one 
part of the passage it did more than this, but only after 
having required aid previously. 

The path followed in going from a to b will be a matter of j 
indifference so far as this total work done by or upon the body 
is concerned. We have a precisely analogous case in gravi¬ 
tation: a body of a pound weight in falling from a height of 40 
feet to a height of 20 feet above the sea, will do necessarily 20 
foot-pounds of work in virtue of that fall, no matter what path 
it follows. We may lift it above a and do work upon it by lifting 
it before letting it fall, still the whole work done by the body 
in its passage from a to b and in virtue of that fall will be 20 
foot-pounds; it may fall by the most roundabout or the most 
direct road, the work done will be the same; it may fall 
below the level of a, and bound up to a: the whole sum 
of the work will be unchanged, depending merely on the 
difference of level between the first and second spot. This 
work may indeed be represented in various ways: thus, if the 
body fall direct through a vacuum the work appears in the 
form of what is called actual or kinetic energy; that is to say, 
it is wholly represented by the motion of the mass. If, on 
the other hand, the body falls slowly, lifting another weight, 
the work will be represented partly by the weight lifted, 
partly by the heat due to the friction of the mechanism; but 
the work done by a body due to its fall from one level to 
another is constant in amount however various in form. 
The work done in overcoming electrical force or done by 
electrical force is subject to the same law, 



Chap. II.] 


Potential. 


2 9 


§ 3 . In moving a weight from a point a to a point b on 
the same level no work on the whole is either done upon or 
by the body in respect of its weight; and similarly in moving 
a small electrified body from a point a to some other point b, 
it may happen that the point b is so situated that on the 
whole no work is either done upon or by the body in re¬ 
spect of the electrical forces in action on the body. In that 
case the two points might be at the same electrical level 
or height, but the recognised term in respect of electrical 
forces is potential; the points a and b are at the same 
potential. If our small electrified body, for instance, be 
moved round another large electrified body, neither ap 
proaching nearer nor receding farther from it, and so far 
from all other conductors as not to be sensibly attracted or 
repelled by them, it will pass along a path every point of 
which is at the same electric potential. 

In moving any actual body from spot to spot some work 
must always be performed to overcome friction, but as in 
moving a heavy body from one point to another, at the same 
gravitation potential or level, no work is required in respect 
of its gravitating properties, so in moving an electrified body 
from one point to another at the same electrical potential no 
work is required in respect of its electrical properties, 
although of course work will certainly be required to over¬ 
come friction and may be required in respect of gravitation 
if the body be raised or in respect of inertia if we accelerate 
the motion of the mass. 

§ 4 . The potential of a body is the excess or defect of its 
potential above or below that of the earth in the neighbour¬ 
hood—the potential of the earth at that point being arbitrarily 
assumed as nil. 

The potential increases in proportion to the increase of 
work done by any given quantity of electricity in moving 
from the point to the earth; and since the potential is pro¬ 
portional to the work and to the quantity of electricity 
transferred, and to no other quantity, the potential of a point 





30 Electricity and Magnetism. [Chap. II. 

is measured by the work which a positive unit of electricity 
does in passing from that point to the earth. The unit 
quantity of electricity might, so far as this definition is 
concerned, be chosen arbitrarily, but there is a certain 
convenience for many calculations in choosing the unit as 
defined in Chapter I. § 17. Every point everywhere may be 
said to be at a certain electric potential, just as every point 
everywhere may be said to be at a certain level above or 
below a datum line arbitrarily chosen, such as the Trinity 
high-water mark. In speaking of the potential at a point 
it is as unnecessary to conceive of the presence of any 
electricity at that point as it is to think of the presence of a 
heavy body at a point when we speak of its height above 
the sea. 

§ 5 . The electric potential at the point depends on the 
electrical condition of all bodies in the neighbourhood; that 
is to say, sufficiently near to exercise any sensible force on 
a small electrified body at the point. Moreover, in testing 
the equality of the potential at two points by the work 
done upon or by an electrified body in its motion from one 
point to the other we must remember to choose a body con- > 
taining only a very small charge of electricity, which we 
will call the test charge; otherwise, the mere presence of 
this test body or test charge of electricity would sensibly 
change the potential at the point at which it was at the 
time of the experiment; increasing or decreasing for the 
time being the work which must be done in order to 
bring any other small quantity of electricity to that point. 
At first it might appear as if the analogy of gravitation 
deserted us here, but that is not so; for if I say that 
two points a and b shall, relatively to the earth, be at 
the same level when no work is done upon or by a 
heavy body in passing from one to the other, I must 
remember that in placing a heavy body at the point a, I do 
change for the time the gravitation level of that point if the 
body be of sensible size compared with the earth; for its 


‘Chap. II.] 


Potential. 


31 


presence at a has increased the attraction of all other heavy- 
bodies to a, so that for the time being a small weight 
passing from a to b would do work; the position of the 
centre of gravity of the earth having been changed. 

§ 6. The differejice of potential between two points a and b, 
being the difference of condition in virtue of which elec¬ 
tricity does work in moving from one to the other, is measured 
by the work required to move a unit of electricity against 
electric repulsion from a to b, or, what is the same thing, 
it is measured by the work which a unit of electricity would 
do while being impelled from b to a. 

The point a is said to have a higher potential than 
b if a unit of positive electricity in passing from a to b 
performs work. It is assumed that the unit of electricity 
does not disturb the distribution of electricity in the neigh¬ 
bourhood. 

The conception of the work which must be done upon or 
by electricity in passing from one point to another must 
be grasped as the only idea which can explain difference 
of potential. When bodies are spoken of as being in the 
same electrical condition we mean that they are at the same 
potential. Difference of potential can therefore be expressed 
in foot grains or any other recognised unit of work. 

In this paragraph the work is spoken of as being done by ' 
the unit of electricity simply to avoid the awkward periphrasis 
‘ done by a small electrified body charged with one unit of 
electricity ’ and ( done in consequence of the electric charge 
only.’ That is to say, it is the extra work which must be 
done in moving the body from the one place to the other in 
consequence of its being electrified. 

§ 7 . Let us apply our definition to special cases. First, 
take an electrified conductor on which electricity is at rest, 
having assumed that distribution which is determined by 
its own shape and the shape and position of neighbouring 
conductors. All points on the surface of such a conductor 
are at the same potential If any one point a were at a 


32 


Electricity and Magnetism. 


[Chap. II. 


higher potential than another b, the electricity at a would 
as surely run to b as a weight would fall from a higher level 
to a lower unless resisted by some force; whereas, on the 
conductor there is no impediment to the free motion of 
electrieity. One end of the conductor may be positively 
electrified, the other end negatively electrified ; the centre 
may have no sensible charge as in the body b, Fig. 6 ; never¬ 
theless all points of the surface are at the same potential, for 
I might move any little electrified body all over the surface 
without its being retarded or impelled in any direction by 
electrical forces. All points in the interior of the conductor 
are also at the same potential as the surface, although no 
charge of electricity is ever found at any internal point. 

The little test charge of electricity, when introduced into 
any cavity in the interior of a body, would be equally ready 
to move in all directions, and would be in perfect equili¬ 
brium. At first it might seem that inside or outside the 

body a unit of positive elec¬ 
tricity a (Fig. 16) would be 
attracted by that end n of the 
conductor n p which was ne¬ 
gatively charged, and would 
be repelled by the other end p; 
but in thinking thus we forget the influence of the external 
neighbouring conductor m, which has already produced 
the arrangement of the charge upon n p. The test charge, 
wherever applied, will not tend to move in one direction 
more than another, but to subdivide itself over the large 
conductor n p, in the same manner as the original charge 
is distributed. 

§ 8. Let us next consider the space round a charged con¬ 
ductor, this space being necessarily filled with air or some 
other insulator. First, conceive the conductor to be uni¬ 
formly charged with one kind of electricity, as a sphere might 
be in the centre of a spherical room (Fig. 17). Then the 
space close to the sphere would be very nearly at the same 


Fig. 16. 




Chap. II.] 


Potential. 


33 


potential as the sphere, for our test charge of electricity 
would do very little work in moving up to the sphere if 
attracted to it, and would require little work to be done 
upon it to move it up to the sphere against the repelling 
force. Let us conceive the potential of the sphere to be 
positive and the test charge positive also. Then the 
potential of the space round the sphere falls, or becomes 
less positive as we recede from the sphere. The work 
required to bring the test charge to the 
ball increases as it is removed farther 
and farther from the ball, although the 
force with which it is repelled dimi¬ 
nishes. Again, the case is analogous 
to that of gravitation. The work, which 
a body will do falling to the earth in¬ 
creases as the height increases from 
which it falls, although the attraction 
between the earth and the body diminishes as it recedes 
from the earth. 

§ 9 . As the test charge approaches the wall of the room 
surrounding our positively charged sphere, it approaches a 
negative charge of electricity, and is more and more attracted 
by it; this attraction further increases the work required to 
bring the test charge back to the electrified sphere, and the 
potential falls faster and faster. The fall continues until the 
test charge touches the wall of the room, which is thus shown 
to be necessarily at a lower potential than the charged 
sphere. Had we begun with a negative charge on the 
internal sphere, we should have found that the wall of the 
room would have been at a higher potential than the sphere. 
Thus we find that there is a necessary difference of potential 
between the inner and outer coating of a Leyden jar, or 
generally that any two conductors between which induction 
is taking place must be at different potentials. 

The potential diminishes gradually from the internal sphere 
to the surrounding conductor, and all concentric spherical 


Fig. 17. 






34 


Electricity and Magnetism. 


[Chap. II. 


surfaces will be at one potential, i.e. we might, so far as 
electrical forces are concerned, without doing or receiving '< 
any work, move the test charge all over any concentric 
spherical surface, indicated by the lines/i, /2,/3, in Fig. 17. 
Whatever be the shape of the internal electrified body, I 
may conceive in the dielectric surrounding it equipotential 
surfaces of this kind, the form of which will depend on the 
form of the internal and external conductors. 

We may further conceive successive equipotential surfaces 
separated by such distances that the same amount of work 
would be done by the test charge in moving from any one to 
the next. An equal amount of work would be required to 
move the test charge back from any one of these surfaces to 
that adjacent to it and at a higher potential. 

§ 10 . Consider the more complex case of a body charged 
partly with positive and partly with negative electricity but 
all at one potential. This in¬ 
volves a complicated distribution 
of electricity in neighbouring 
conductors, such, for instance, 
as is shown in the annexed dia¬ 
gram (Fig. 18). 

Very near the surface of the 
conductor a, the potential of the 
dielectric will be sensibly the same as that of a, and there 


Fig. 18. 



is nothing here to indicate whether the potential of a is 
positive or negative relatively to the general enveloping 
conductor b ; but receding from a towards c the potential 
of the space falls, whereas, as we pass from a towards d, it 
rises; again, receding from d towards the envelope b, the 
potential falls, but as we pass from c to the envelope the 
potential rises, so that close to b the potential is the same 
at all points, but whether higher or lower as a whole, there 
is nothing in the diagram to tell us. All these conclusions 
are deduced from the simple conception of the work required 
to move our imaginary test charge from place to place. Nor 








Chap. II.] 


Potential. 


35 


can any simpler conception be suggested. We see from the 
above diagram, that a body charged with negative electricity 
might have a positive potential relatively to a point charged 
with positive electricity, and vice versa. For the body a 
may all be at a positive potential relatively to the body b, 
notwithstanding the fact that the part a of this conductor 
is negatively charged while some point of b, such as b , is 
positively charged. 

§ 11 . The charge induced between two opposed con¬ 
ductors separated by a dielectric, implies a difference of 
potential between the conductors as shown above. More¬ 
over, as the difference of potentials increases, so must the 
induced charges increase, for in order to make it more and 
more difficult to move the test charge from one surface to 
the other, the repulsion from one side and attraction to the 
other must increase, and this additional attraction and 
repulsion can only be increased by increasing the quantities 
of electricity. On the other hand, so long as the difference 
of potentials between the surfaces remains constant the 
charge on the opposing surfaces must remain constant; both 
potentials may rise and fall together, but the constant 
difference of potential implies a constant internal charge. 
An example will make the meaning of this statement clear. 
Suppose an ordinary Leyden jar to be charged with negative 
electricity and to have its outer coating in connection with 
earth. The potential of the inner coating will be negative, 
relatively to the earth; and calling the potential of the earth 
zero, as is usually done for brevity, we may, as stated in 
§ 4, simply say that the potential of the inner coating of our 
jar is negative. There will be a positive charge of electri¬ 
city on the inside of the outer coating of the jar equal to the 
negative charge within. 

Insulate the outer coating, and electrify it with a positive 
charge. Its potential will be raised, but the potential of the 
inner coating will be raised by a like amount. The negative 
charge will remain inside the jar undisturbed in amount ■ 


36 Electricity and Magnetism. [Chap. II. 

opposite to it will remain the positive charge on the inner 
side of the outer coating, the only change being that on the 
outer side of the outer coating we have now a positive 
charge. The effect of this additional positive charge will be 
to increase the work required to bring our test charge from 
a distance up to the jar, or to any point inside the jar, i.e. 
the potential both of inside and outside and of all adjacent 
points has been raised. 

§ 12 . Next, suppose that two jars (Fig. 19), having their inner 
coatings in electrical connection, are 
f,g - t 9* charged with negative electricity, the 

outer coatings being uninsulated, i.e. 
at the potential of the earth. The 
potential of the inner coatings will 
be negative, and if the two jars are 
equal in all respects, the negative 
charge in each will be equal. In¬ 
sulate jar a, and increase the poten¬ 
tial of its outer coating by electrifying it positively. The 
negative charge will now redistribute itself between the two 
jars. 

The potential of the outer coating of b remains constant. 
The potential of the inner coatings of a and b must be 
uniform throughout, since they are in metallic connection. 
Their potential as a whole will be somewhat raised, but 
not so much as that of the outer coating of a ; hence the 
difference of potentials between the coatings of a, will have 
been increased, and its internal charge will have increased, 
and this will have occurred at the expense of B, where the 
difference of potentials between the inner and outer coatings 
will have diminished. 

§ 13 . If one coating of any Leyden jar be kept at a 
constant potential, such as that of the earth at the spot is 
generally assumed to be, the quantity of electricity which 
the other coating contains is simply proportional to its poten¬ 
tial, a fact determined by experiment. Thus, if I have the 































Chap. II.] 


Potential. 


37 


means of producing a constant potential, or rather a constant 
difference of potential, from that of the earth, I shall also 
have the means of collecting a constant quantity of electri¬ 
city. The charge assumed by any insulated conductor inside 
a conducting envelope, however far remote, is simply propor¬ 
tional to the difference of potentials between the envelope 
and insulated conductor; and as a limit we may say that 
the charge on any insulated conductor, when there are no 
electrified bodies in the neighbourhood, is simply propor¬ 
tional to the potential of the conductor ; that is to say, 
the difference of its potential from that of the earth. The 
force it exerts is proportional to the quantity, and the work 
required to overcome that force is proportional to the 
force. 

§ 14 . In a Leyden jar it is immaterial which of the 
coatings is in connection with the 
earth, or whether either of them be 
so. Connection with the earth is 
merely a device for keeping the po¬ 
tential of that particular coating con¬ 
stant, or nearly so, by maintaining it 
in connection with a very large con¬ 
ductor. Thus, the inner coating of a 
jar when in connection with the earth, 
will take a negative charge if the outer 
coating be positively electrified, and, 
the difference of potentials being the 
same, this charge will be precisely the 
same in amount as if the outer coating had been in con¬ 
nection with the earth, and the inner coating had been 
directly electrified by negative electricity. 

§ 15 . Let us consider the construction of electroscopes 
by the light of the knowledge we have now acquired; for 
instance, the gold leaf electroscope, Fig. 20. 

The repulsion between the two gold leaves a and b de¬ 
pends on the quantity of electricity with which they are 


Fig. 20. 













38 Electricity and Magnetism. [Chap. II. 

charged. But upon what does this quantity itself depend ? 
Merely on the difference of potential between the gold leaf 
and the conductors c and d immediately surrounding it. 
When the gold leaves a and b are connected with the 
electrified body a to be examined, a b and a assume 
the same potential; then the quantity of electricity ac¬ 
cumulated on the gold leaf depends on the difference 
of that potential from the neighbouring conductors c 
and d: let c and d be insulated, and at the same poten¬ 
tial as a, then, no matter how much electricity there 
may be on a, none will come to a and b , and no diver¬ 
gence will occur in the leaves. In the ordinary construc¬ 
tion of electroscopes, some parts of the surrounding con¬ 
ductors c and d are glass, and their potential depends on 
conditions over which we have no control; c and d should 
be in a metal case with openings, to allow a and b to be seen; 
for instance, a wire cage round glass, the meshes of which 
approach sufficiently near to keep the whole surface of the 
glass at one potential; then, if c and d be in connection with 
the earth, a and b will be charged with electricity whenever 
there is a difference of potential between 
Fig. 21. a and the earth. Exactly similar reason¬ 
ing applies to the Peltier electroscope, 
Fig. 2 j . In this instrument instead of 
the gold leaf we have a rod a b , free to 
move on a vertical axis v, and repelled at 
each end by a fixed conductor c d in 
electrical connection with it, but placed 
on an insulating support d; the rod is 
directed by a small magnet m n; the in¬ 
strument is so placed that when c d has 
no charge of electricity, the magnet places 
the rod just clear of these fixed conductors 
c and d ; then when b with a b are all charged with electricity, 
the rod a b is repelled until the force of electric repulsion is 
just balanced by the directing force of the magnet. The 




Chap. II.] 


Pote7itial. 


39 


force depends on the quantity of electricity on the rod and 
balls, but this quantity is proportional to the difference of 
potential between the system Bed, &c., and the enveloping 
conductor a, which is not shown in the drawing but which 
encloses the whole insulated system Bed. This electroscope, 
therefore, like the preceding one, and like all others, indi¬ 
cates difference of potential by means of the quantity 
which that difference causes to accumulate on an insulated 
conductor. 

In the instruments usually made there is a divided ring to 
show how far the rod a b is deflected. The instrument 
indicates more conveniently than the gold leaf electroscope 
whether a given potential be higher or lower than another; 
but inasmuch as the deflections are not proportional to the 
difference of potential between a b and the case a, and are 
not even connected by any simple law with this difference 
of potential, the Peltier electroscope cannot be used to 
measure difference of potentials, i.e. to compare two poten¬ 
tials or differences of potentials accurately, so as to allow us 
to say that one is distinctly two, three, or four times as great 
as another. For this purpose we require much more com¬ 
plex arrangements, electrometers or instruments in which 
the attractions and repulsions produced by given differences 
of potential between the parts can be calculated definitely. 

All electrometers measure directly differences of potentials, 
and measure quantities only indirectly. 

§ 16 . If two electrified conductors a and b, which are 
at the same potential, be joined by a wire, no disturbance 
in the electric distribution on the system will take place, 
unless indeed the wire be of sensible size relatively to the 
other conductors, and at a different potential; but, assum¬ 
ing the wire to be small, or at the same potential as a and 
B, the electricity on the bodies after being joined will be in 
equilibrium as before, the necessary condition of equality 
of potential throughout being satisfied. If, on the other 
hand, a be at a higher potential than b, positive electricity 





40 Electricity and Magnetism. [Chap. II. 

must, when the connection is made, flow from a to 6, to 
re-establish electric equilibrium. The amount of the elec¬ 
tricity thus transferred must be such as will restore the 
equilibrium; it will be great when the difference of poten¬ 
tial is great and when the size of the bodies is large, and 
small under the opposite conditions. The existence or 
continuance of the flow of electricity from one point to 
another depends solely on the difference of potential 
between the points. The magnitude of the conductors has 
only one influence in the result, by requiring that a larger 
quantity of electricity shall flow to re-establish equilibrium. 
We may illustrate this by an experiment with water. If we 
join two reservoirs of water, big or little, by a pipe, no 
flow takes place from one to the other if the surfaces of 
the water in both are at the same level. If they be not, 
the flow will take place from the higher to the lower; the 
quantity of fluid transferred depends on the capacity of the 
reservoirs and original difference of level: it continues 
until the level is the same in both. Substitute potential for 
level, electricity for water, conductor for reservoir, and the 
above statements are all true for electricity. 

§ 17 . If I put one end of a wire in connection with the 
earth and the other at a point x in the air (which may 
be at a very high potential) no electricity flows through 
my wire from the point to the earth, simply because at 
the point in question there was no electricity to flow, its 
capacity and charge being zero ; but the potential of the 
point will :have been changed by the mere presence of the 
wire to that of the earth. For this purpose, while the 
wire was approaching the point, a redistribution of electri¬ 
city on its surface has been going on under the influence of 
the induction to which the potential of point x was due. 

If the wire has a sharp point so that a very small quantify' 
of electricity will produce a great density, electricity will 
actually flow from the air to the earth; successive particles of 
air negatively charged will fly from the point, and be replaced 


Chap. II.] 


Potential ’ 


41 


by particles of air positively charged, each of which will be 
discharged through the wire. If the potential of the point 
be sufficiently high the phenomenon is accompanied by noise 
and a brush of light. A lighted match on the end of the 
wire also allows the transfer of electricity to take place; the 
burnt particles fly off with the charge of one sign and the air 
about to be burnt brings electricity of the other sign to the 
wire. 

§ 18 . By definition the difference of potential was de¬ 
clared to depend on the work done by or upon electricity 
in moving from one point to another. The nature of the 
work done by or to a quantity of electricity moved on a 
conductor by or against a force of attraction or repulsion is 
clear enough—a tangible force is used or overcome ; a solid 
body is either put in motion, or its motion is resisted; but 
when electricity moves along a wire from a body at one po¬ 
tential to a body at another, no solid body is moved at all, 
and no equivalent work appears at first sight to have been 
done. The equivalent is found, however, in heat generated 
in the wire by the passage of the electricity. It is well 
known from the research of Joule that 772 foot-pounds of 
work are equivalent to the quantity of heat which raises 1 lb. 
of water i° Fahr., and although no visible mechanical work is 
done, where a quantity q of electricity passes along a wire from 
a to b, heat is generated precisely equivalent in amount to 
the work which the attractions and repulsions of the elec¬ 
trified bodies a and b would have done when acting upon 
the same amount of electricity Q, conveyed on a small 
moving conductor from the body a to the body b. We 
shall find that electricity in motion is capable of doing 
work in other ways, but in whatever way work or its equiva¬ 
lent is produced by electricity moving from a to b, the amount 
will always be equal to the quantity of electricity transferred 
multiplied into the excess of potential of a over b. 

§ 19 . Difference of potential may be produced by mere 
induction. A small insulated conductor placed at any point 


42 


Electricity and Magnetism. 


[Chap. II. 


in space where, owing to the neighbourhood of electrified 
bodies, the potential was x, will itself assume the potential x , 
without losing or gaining any electricity. Then if this body 
be connected with the earth, electricity will flow from the 
body to or from the earth sufficient in amount to bring 
the body to the potential of the earth ; if x be positive, the 
current will be to the earth ; if x be negative, the current 
will be from the earth to the body. 

§ 20 . Difference of potential is produced by friction 
between insulators followed by separation. Two insulators 
rubbed against each other become oppositely charged, 
and there is a difference of potential between them. It 
is probable that for each pair of substances rubbed to¬ 
gether there is a certain maximum difference of potential 
which cannot be exceeded. The list already given, Chapter 
I. § 9, showing the order in which some materials stand, so 
that each becomes positive when rubbed by any of the sub¬ 
stances placed after it, necessarily shows also the order in 
which materials must be classed, so that when one is touched 
or rubbed by another following it in the list, the potential of 
the former may become positive relatively to that of the 
latter. Moreover, a greater difference of potential is pro¬ 
duced by friction between substances far apart on the list 
than between substances close together on the list. It is 
possible that the law which will in the next paragraph be 
enunciated for conductors may also hold good for insu¬ 
lators. 

§ 21 . When two dissimilar conductors touch one another, 
a difference of potential is produced between the conductors 
charging them, as mentioned Chapter I. § 19. The dif¬ 
ference of potential is constant with constant materials, i.e. 
copper and zinc at a given temperature touching one another 
are invariably at potentials differing by a constant measurable 
amount. The same may be said of any two metals. Moreover, 
all metallic conductors may be ranged in a list, such that any 
one of them in contact with any of the conductors later in the 


Chap. II.] 


Potential. 


43 


Fig. 22. 


| Gold | Cojpper | Zinc | 

A B 


list will have a potential positive relatively to that conductor. 
Moreover, calling these bodies abcd, &c., the difference 
of potential between a and c is equal to the difference 
of potential between a and b added to the difference of 
potential between b and c, or generally if these bodies were 
all in contact one with another in the order abcd...n, 
&c., and if we call abed . . . n, &c., the potentials of 
these bodies, a — n — (a — b) + (b — c) -f- (e — d) 
... + (m — n). Thus if three 
bodies be in contact, as in Fig. 22, 
the difference of potential between 
the ends a and b may be calcu¬ 
lated from the two end metals 
only ; in the example given, it does not matter what the 
difference of potentials between gold and copper alone 
would be, for call that a , and call the difference between 
gold and zinc c, and that between copper and zinc b , then 
{a — b) + (b — c) — a — c, as if gold and zinc had been 
directly in contact. It may be stated quite generally that in 
any series of metallic conductors thus placed in contact, the 
difference of potentials between the ends depends on the 
extreme conductors of the series. The following is a list of 
conductors, ranged in such an order that each becomes 
positive when touched by those which follow. Zinc, lead, 
tin, iron, antimony, bismuth, copper, silver, gold. The 
earlier metals on the list are called electropositive to those 
which follow. The exact relative differences of potential 
have as yet been experimentally ascertained only in a few 


cases. 

§ 22 . It is believed that all compound solid bodies which 
are conductors behave in the same way as simple metallic 
conductors so far as the production of a difference of poten¬ 
tial due to mere contact is concerned, and this is certainly 
the case in many instances. Liquid conductors also appear 
relatively to one another to form a series of the same kind. 
But compound liquids and solids do not admit of being 




44 


Electricity and Magnetism. [Chap. II. 

arranged relatively to one another in the simple order 
described as applicable to metals. 

This difference between the compound liquid and the 
simple metallic conductor, appears to be intimately con¬ 
nected with the fact, that electricity in passing through these 
compounds decomposes them, a phenomenon to be more 
especially described hereafter. The compounds which are 
thus decomposed are called electrolytes . The following 
series of phenomena occur when metals and electrolytes are 
placed in contact:— 

Fra. 23. Fig. 23*. 




1. When a single metal is placed in contact with an elec¬ 
trolyte, a definite difference of potentials is produced between 
the liquid and the metal. If zinc be plunged in water, 
the zinc becomes negative, the water positive, as in Fig. 23. 
Copper plunged in water also becomes negative but much 
less so than zinc. 

2. If two metals be plunged in water (as copper and zinc, 
in Fig. 23), the copper, the zinc, and the water forming a 
galvanic cell, all remain at one potential and no charge of 
electricity is observed on any part of the system. (It may be 
proper to remark that this statement is in direct contradic¬ 
tion to the popular impression.) If the copper and zinc had 
been joined by a metal they would have assumed the same 
difference of potential as if in direct contact. If a piece 
of copper be now joined to the zinc (as in Fig. 23J c will 


































Chap. II.] 


Potential. 


45 


become positive and c' negative, the difference of potentials 
being that due to the direct contact between c' and z only, 
the water having the effect of simply conducting the charge 
from z to c, and of maintaining c and z at one potential. 

3. If a series of galvanic cells be joined (as in Fig. 13), 
there will be a difference of potentials between the first 
copper and the last zinc equal to the sum of the differences 
produced by the two joints between zinc and copper; or, 
taking the difference of potential which a single junction can 
produce as one unit, the arrangement in Fig. 13 would give 
a difference of potential = 2 ; but if we join another piece 
of copper to the last zinc, this extra piece of copper will 
differ in potential from the copper at the other end by the 
amount 3. This is Volta’s theory of the galvanic battery. 
The difference of potential produced by these arrangements 
is so small that its direct observation presents considerable 
difficulty until a large number of galvanic cells be joined in 
series, when they will be found to be capable of producing 
a difference of potentials, which can be indicated by electro¬ 
scopes. It will be observed that the electrolyte is an 
essential element of the series, for we cannot accumulate 
differences of potential by simply joining metals in series, 
the difference which any series produces being simply the 
same as if the first and last metals were in contact. The 
electrolyte behaves as if it tended to produce no diffe¬ 
rence of potentials when in contact with metals, and Volta 
believed that it did not. We know that it does; but its 
apparent passivity when two metals are plunged into it in¬ 
stead of one is proved by the following experiments. 

Place a metal disc b (Fig. 24) under a light suspended 
flat strip of metal or needle a, maintained at a high positive 
potential by connection with a highly charged Leyden 
jar d. When the disc is of uniform metal the needle a is 
not deflected to right or left by the presence of b. A charge 
accumulates on a and b when they are brought close, but 
the charges are symmetrically distributed relatively to a, so 


46 Electricity and Magnetism. [Chap II. 

that a is simply attracted to b and does not tend to turn 
round on the axis or suspending wire e. But if the disc b 
be made of two metals, such as zinc and copper, with their 

Fig. 24. 



junction placed under the needle a, this needle no longer 
remains in equilibrium, but deflects towards the side on 
which the copper is placed, showing that now the charge on 
b is not symmetrically distributed but that there is a greater 


Fig. 25. 



induced charge on the copper than on the zinc. This 
can only be due to the fact that there is a greater 
difference of potential between the needle and the copper 
than between the needle and the zinc ; in other words, there 
is a difference of potential due to contact between the zinc 
and copper, the zinc being positive relatively to the copper. 
If the potential of a be negative instead of positive the 




















Chap. II.] 


Potential. 


47 


deflection will be in the opposite direction. The two half 
discs may be separated from one another by a narrow open¬ 
ing as in Fig. 25. The needle will not deflect if the two 
halves are of the same metal. It will deflect to a definite 
amount if the discs are of different metals but in metallic 
connection by a wire, and the deflection d will, when a is 
positive, be as before from the zinc to the copper, if these 
are the metals employed for b and b v In making this 
experiment care must be taken to ensure that the half discs 
are symmetrically placed on the two sides of a, otherwise 
deflections occur due to charges induced on the two sides 
of a even when b and B t are at one potential. If when the 
potential of a is reversed being made alternately-}- and — to 
equal amounts, we obtain equal deflections in opposite direc¬ 
tions, we may be certain that this symmetry is attained. 
Let two such half discs of copper be carefully adjusted 
under a ; when these are joined by metallic contact there 
should be no deflection however high the potential of a may 
be. Then connect the side b with the copper pole of a gal¬ 
vanic cell, and the side Bj with the zinc pole (Fig. 25); the 
needle a will deflect towards the side Bj which is in connec¬ 
tion with the zinc pole, and the amount of the deflection will 
correspond to the same difference of potential as that 
already observed as due to the simple contact of zinc and 
copper. Remark that, whereas in Fig. 24 a was attracted to 
the copper half disc it is in Fig. 25 attracted to the half 
disc in connection with the zinc. We know from the first 
experiment that the junction m has made the zinc in the 
water positive and the copper above m with the half disc Bi 
negative. We find that the copper c and the half disc b are 
positive to just the same extent as z must be, and therefore 
conclude that the water has simply brought the copper strip 
and disc b to the potential of the zinc. The experiment is 
a delicate one, and it can hardly be said to be proved that 
the difference of potentials between b and B t is exactly 
equal to that produced by the simple metallic contact of 


48 Electricity and Magnetism. [Chap. II. 

zinc and copper ; there may be a slight difference due to the 
liquid, and different liquids may possibly augment or decrease 
this small difference. Another experiment, hitherto un¬ 
published, still more strikingly proves the Voltaic theory. 
When the two half discs of copper and zinc (Fig. -24) are con¬ 
nected by a metallic wire, it is impossible to find any position 
of a such that a reversal of its potential does not cause a de¬ 
flection, and if a is in a symmetrical position relatively to those 
discs a reversal of the potential of a will always give equal 
deflections to right or left. When this symmetrical position 
has been found connect the zinc and copper by a drop of 
water instead of by the metallic wire. The needle a will 
remain undeflected in its central position whether its poten¬ 
tial be high or low, positive or negative. The two half discs 
of different metals behave as if they were of one and the 
same metal in metallic connection. This experiment, which 
has been carefully made by Sir William Thomson, appears to 
be absolutely conclusive. The surface of the metals should 
be polished and clean, for the experiment will not succeed 
if they are tarnished. Oxides on the surface of the metals 
•introduce complex actions. 

The reason why the erroneous statement has so long 
remained unchallenged undoubtedly is because whenever 
the two poles of a galvanic cell are connected with electrodes 
or wires of one metal, as in at least nine hundred and 
ninety-nine cases out of a thousand they are, the difference 
between the two electrodes or wires really is what it has 
always been supposed to be. Thus the difference of poten¬ 
tial between the two copper wires attached to the zinc and 
copper of a Daniell’s cell is that which has hitherto been 
generally attributed to the zinc and copper plates of the 
cell. 

§ 23 . The property of producing a difference of potential 
may be said to be due to a peculiar force, to which force 
the name of electromotive- force is given. "When we say 
that zinc and water produce a definite electromotive force, 


Chap. II.] 


Potential. 


49 


we mean that by their contact a certain definite difference 
of potentials is produced. A series of the galvanic batteries 
or cells (Chapter I. § 16) produces a definite electromotive 
force between the terminal metals plunged in the solution 
which, if the law above stated held good, would depend on 
the metals only and not on the solution employed. This, as 
stated in the last section, is approximately at least found to 
be true. The electromotive force of a cell or the difference 
of potentials between the metal poles or electrodes, as they 
are often called, is constant so long as constant metals and 
a constant solution are used. The words electromotive force 
and difference of potential are used frequently one for the 
other, but they are not strictly speaking identical. It must 
be remembered that electromotive force is not a mechanical 
force tending to set a mass in motion, but a name given to 
the supposed force which causes or tends, to cause a transfer 
of electricity. Wherever difference of potential is found 
there must therefore be an electromotive force ; but we shall 
find (Chapter III. § 22) that there are cases in which electri¬ 
city is set in motion, from one point to another, between 
which that difference of condition does not exist which we 
have defined as difference of potential. Electromotive force 
is therefore the more general term of the two, and includes 
difference of potential as one of its forms. 

§ 24 . The electromotive force exerted between two dis¬ 
similar metals is altered by every change in their temperatures, 
but the connection between the change of temperatures and 
the change of electromotive force has not been thoroughly 
investigated. Two parts of one and the same body at 
different temperatures are probably always at different 
potentials. This has been verified only in certain cases, as 
in the crystals of tourmaline. 

§ 25 . Electromotive force may also be produced by 
electricity in motion, and by magnetism in ways which we 
cannot even describe, until the simpler phenomena of 
electricity in motion and of magnetism have been described; 

E 


50 


Electricity and Magnetism. [Chap. II. 

but it may be said generally that all causes which have the 
power of altering the distribution of electricity can produce 
electromotive force or difference of potential. Every source 
of electricity must as such be able to produce a difference of 
potential; since no charge of electricity whatever can be 
made sensible without some difference of potentials between 
the charged body and the earth or neighbouring con¬ 
ductors. Friction between insulators is found to produce 
a great electromotive force, producing a large charge on 
even a small conductor, whereas the galvanic cell or the 
contact of conductors produces a very small electromotive ' 
force, giving a small charge only if the conductor be small. 
On the other hand, when the conductor is large the gal¬ 
vanic cell will almost instantaneously charge the whole to the 
maximum potential it can produce, developing by chemical 
reaction an immense quantity of electricity; whereas the 
quantity developed by friction from the contact of insulators 
is so small that if it be allowed to diffuse itself over a large 
conductor the potential of the conductor will be very little 
raised. For instance, if we connect a brass ball of a few 
inches diameter with the conductor of a frictional machine, 
a few turns of the machine raise its potential so much that 
its mere approach to the knob of an electroscope will cause 
the gold leaves to diverge. If we touch the same ball with 
one electrode of a galvanic cell, the other being connected 
with earth, the brass ball will indeed receive a charge, but its 
quantity will be so small and its potential so low that instru¬ 
ments to detect it must be perhaps a thousand times more sen-' 
sitive than any I have yet described. But if we connect the 
conductor of a very large condenser or Leyden jar with the 
galvanic cell, we shall communicate to it such a charge that 
although its potential would be insensible on the electro¬ 
scopes hitherto described, its quantity is such that it would 
sensibly heat a wire in its escape to earth, and would produce 
many other effects which could not be obtained without 
the greatest difficulty from the same Leyden jar charged by 


Chap. II.] 


Potential. 


51 


a frictional machine. A frictional machine charges a small 
Leyden jar with a much greater charge than could be obtained 
in the same jar even from 1000 galvanic cells ranged in series 
as in § 16. 

§ 26 . Difference of potential or electromotive force must 
be measured in terms of some unit adapted to measure 
work. Every unit of work must be represented by the 
operation of a force overcoming a resistance so as to move it 
through a distance; or, what is the same, it may be repre¬ 
sented by the resistance overcome and moved through a dis¬ 
tance. In other words, the unit of force exerted through the 
unit of space is the unit of work. The most common unit 
of work is the foot-pound, being the weight of a pound over¬ 
come so as to be lifted through the distance of a foot, but 
the so-called absolute unit of work is that which leads to 
greatest simplicity in electrical calculations. This unit is the 
absolute unit of force (Chapter I. § 17) overcoming a resist¬ 
ance through the unit distance, say one centimetre. The 
absolute unit of work (centimetre, gramme, second) is equal 
to the foot-pound divided by 13,825 g , where^is the velocity 
acquired at the end of one second by a body falling in vacuo : 
taking this as 981 centimetres per second the absolute unit 
of work is equal to the foot-pound divided by 13,562,325. 
The unit difference of potential or electromotive force in 
electrostatic measure exists between two points when the 
unit quantity of electricity in passing from one to the other 
will do the unit amount of work. 

The practical measurement of the difference of potentials 
between two points can in certain cases be made by observing 
the work done by definite quantities of electricity in passing 
from one point to the other; thus we may observe the total 
amount of heat generated in a wire by a given quantity of 
electricity passing between two points kept at a constant 
difference of potentials. From the heat we may calculate 
the work, and from the heat and quantity we may calculate 
the difference of potentials. [Similarly, if we wished to 


52 


Electricity and Magnetism . [Chap. III. 

ascertain the difference of level between two points we might 
let a weight (a standard quantity of matter) fall from one to 
the other, measure the total heat generated by the concus¬ 
sion which brought the weight to rest, from the heat deduce 
the amount of work done, and from this work and the known 
quantity of matter, deduce the difference of level or of 
gravitation potential. Fortunately there are more direct 
methods available or engineers would have some difficulty in 
levelling.] 

Difference of electric potentials is more generally ascer^ 
tained indirectly by a knowledge of the laws connecting 
potential with other electrical magnitudes. Thus we know thai 
the quantity of electricity with which two opposing surfaces 
of conductors are charged is simply proportional to the 
difference of potential between them, assuming the distance 
and dielectric to remain constant. Electrometers afford us 
the means of comparing such quantities as these, and there¬ 
fore electrometers (as shown in § 16) afford us the means 
of comparing differences of potential. The measurement 
of currents and of resistances to be described in the follow¬ 
ing chapters give other means of comparing differences of 
potential. 


CHAPTER III. 

CURRENT. 

§ 1 . Electricity has already been frequently spoken of as re¬ 
distributing itself over a given conductor, or moving from one 
conductor to another along a wire, and we may with propriety 
speak of the current of electricity by which the redistribution 
is effected. Bodies along which electricity moves acquire, 
so long as the motion lasts, very singular properties, and in 
order to avoid cumbrous phraseology the properties which 
are actually observed as belonging to the bodies through 
which a current of electricity flows, are spoken of as the 
attributes of the current of electricity itself. Some of the 



Chap. III.] 


Current, 


53 


properties of electric currents are most conveniently observed 
in long uniform conductors, such as wires, along which the 
flow takes place in one simple direction. Currents in wires 
will chiefly be spoken of in the first instance, although 
identical properties are possessed by currents moving in any 
manner through bodies of any form. The direction of a 
current is assumed as the direction from the place of high 
potential to the place of low potential; in other words, it is 
the direction in which positive electricity flows. Thus, 
to recur to our earliest definition of positive and negative 
electricity, if one conductor a be electrified by contact 
with a stick of glass which has been rubbed with a resinous 
material, and another conductor b be electrified by contact 
with the resin used to rub the glass, then upon joining a 
and b, a current of positive or vitreous electricity will flow 
from a to b until they are brought to the same potential. 
By using two large conductors a and b, or two Leyden jars 
of large capacity, and electrifying them with a frictional 
electrical machine of considerable size to a high potential, a 
considerable quantity of electricity may be accumulated on 
a and b, and a considerable current will flow from a to b, 
when they are joined. 

§ 2 . A current of electricity thus produced will be transient, 
and even while it lasts it will not remain con¬ 
stant, for during its continuance the difference 
of potentials producing it will continually 
diminish ; indeed, if the above were the only 
manner of producing an electric current, we 
might stilt be ignorant of its peculiar proper¬ 
ties. When plates of zinc and copper not 
touching one another are plunged in water 
and the copper is then joined to the zinc by 
a wire outside the water, a current flows from the copper to 
the zinc along the wire, and from the zinc to the copper 
through the water. According to the theory of the cell 
explained in the last chapter, the zinc when it touched 
the copper became positive and die copper negative, the 










54 Electricity and Magnetism . [Chap. III. 

electricities being separated at the metallic junction, but 
there being no opposition to their recombining through the 
water, the current flows in the direction shown. The exis¬ 
tence of the current is shown by the fact that if a and b 
be joined by a long copper wire, this wire acquires the same 
properties as if it joined two large conductors charged with 
opposite kinds of electricity. These properties are described 
in § 6 and the rest of this chapter. 

§ 3 . The transfer of electricity from a to b involves the 
performance of work or its equivalent, and to perform work 
implies a source of power, or in other language an expenditure 
of energy. The mere contact of two dissimilar substances 
cannot be a source of power. It is found that while the 
current flows the water is decomposed, and oxide of zinc 
formed. This chemical reaction is a true source of power ; 
the oxygen leaves the hydrogen of the water to join with 
the zinc, for which it has a greater affinity. The zinc is 
consumed in the process, as coal is consumed when it burns 
while combining with the oxygen of the air. The source 
of power is accurately described by saying : the intrinsic 
energy of a given weight of zinc and water is greater than 
that of the hydrogen gas and oxide of zinc produced by the 
combination, the difference is equal to the work done by 
the current of electricity produced. The work done by the 
current is therefore proportional to the amount of zinc con¬ 
sumed. The electromotive force of the cell is constant, 
depending on the metals in contact; the performance of 
a given amount of work by the transfer of electricity from 
one point to another, between which there is a* constant 
difference of potentials or electromotiv e force, requires the 
transfer of a definite amount of electricity, hence the quan¬ 
tity of electricity produced by the galvanic cell is propor¬ 
tional to the zinc consumed. The effect described as oc¬ 
curring in the simple form of the galvanic cell is produced 
whenever we join two solid conductors a and b plunged 
in a compound liquid, one element of which tends to 


Current. 


Chaf, III.] 


55 


combine more strongly with a than with b, or with b than 
with a. 

If we consider the liquid alone we find that positive elec¬ 
tricity is produced apparently at the surface of contact 
between the liquid and one conductor, and is taken away 
as fast as it is produced to neutralise the negative electricity 
produced apparently at the surface, where the other conductor 
touches the liquid. 

§ 4 . A bitter war raged for a long time between the electri¬ 
cians who maintained that in this case the electricity was 
due to contact, and those who maintained that it was due 
to chemical action ; like many other disputes, it turns much 
upon the use of words. 1 Both contact between dissimilar 
substances and chemical action are necessary to produce 
the effect; the laws regulating the potential and those re¬ 
gulating the current are intimately connected with the 
nature of the substances in contact, and with the amount of 
chemical action. Perhaps it is strictly accurate to say that 
difference of potential is produced by contact, and that 
the current which is maintained by it is produced by chemi¬ 
cal action. As we shall see hereafter, the difference of 
potentials can be accurately determined from a considera¬ 
tion of the chemical action, but then this chemical action 
depends probably on the very properties which cause a 
difference of potential to be produced by contact. In 
cases where no known chemical action occurs, as where 
copper and zinc touch one another, the difference of po¬ 
tential is produced, and since this involves a redistribution 
of electricity, a small but definite consumption of energy 
must then occur; the source of this power cannot yet be 
said to be known. 

§ 5 . The law described in Chapter II. § 21, by giving a con¬ 
tact potential series, or electromotive series, for metals, shows 

1 The opponents of contact electricity denied and falsely -explained 
things now known to be true, and the original supporters of the contact 
theory were ignorant of dynamics. 


56 


Electricity a 7 id Magnetism . [Chap. III. 


Fig. 27. 
c 


why we have no hope ever to obtain a permanent current by 
any arrangement of metals, each at one temperature. The 
electromotive force at the joint c (Fig. 27) is necessarily 
equal to that at joint d, and opposed 
to it, i.e. the e. m. f. (as electromotive 
force may for brevity be written) at c 
tends to send the electricity round in 
the direction opposed to the hands of 
a watch, while the e. m. f. at d tends 
D to send electricity round in the opposite 

direction, and the two forces being equal, electricity moves 
neither way. 

When instead of bringing the zinc and copper into contact 
at d they are plunged into water, the e. m. f. at the junction 
remains as before; but owing apparently to the electrolysis 
or decomposition of the water, little or no electromotive 
force is at first manifested at the surface where the water 
touches the metals, and the current can therefore flow as 
described in § 2. The arrangement of potentials in the cell, 
in the plates, and in the wire joining the plates, cannot be 
explained until after Chapter IV., and indeed has never been 
very fully or clearly established. What chiefly concerns us 
is that galvanic cells can be arranged so as to produce a 
permanent current conveying considerable quantities of 
electricity ; the strength of the current is simply proportional 
to the quantity conveyed in a given time. 

§ 6. The properties of electric currents are very impor¬ 
tant. Two parallel wires in which electric currents flow in 
the same direction, attract one another It is simpler to 
state this fact by saying that parallel currents in the same 
direction attract one another. Parallel currents in opposite 
directions repel one another. 

When the wires conveying the currents are straight but not 
parallel, they attract one another if both currents flow to or 
from the apex of the acute angle which the wires make with 
one another. 






Chap. III.] 


Current . 


57 


The wires or currents repel one another if one current 
approaches and the other recedes from the apex of the angle. 

§ 7 . Consider a rectangle of wire efgh (Fig. 28) held over 
a straight wire A b, each having currents circulating in them, 
as shown by the arrows, and let the rectangle be capable of 
turning on a vertical axis x ; it is found by experiment that 
e G is attracted towards a;fh, on the contrary, towards B ; 
both therefore tend to turn the rectangle in the same direction 
round its axis; that portion of h g which is behind a b 
is attracted towards b, and repelled from a by § 6. On 
the contrary, the portion of h g which is in front of a b 
is repelled from b and attracted towards a ; all these forces 
act therefore in one direction, and tend to place efgh in 


Fig. 28. 


Fig. 25. 


o 


Of— 


a plane parallel to a b. The forces in e f are acting in the 
opposite direction, but e f being farther from a b than the 
other portions of the current, the forces due to it are weaker 
and are overpowered. These attractions and repulsions are 
easily verified with a rectangle of copper wire made as in 
Fig. 29, and supported by two pivots a and b resting in two 
mercury cups, which are connected by thick wires with a 
Grove’s cell. 

§ 8. If we conceive one rectangle abcd (Fig. 30) inside 
another efgh, all the actions described in the last will be 
strengthened, and the two rectangles will tend to place 
themselves in parallel planes, and moreover in such a posi¬ 
tion that the current is going in the same direction in both 











58 


Electricity and Magnetism. 


[Chap. III. 


Fig. 3a 



rectangles. The truth of this proposition is evidently not 
limited to rectangular systems, and generally any two 
closed wire circuits in which currents are 
flowing tend to arrange themselves in 
this manner. When the two are in the 
same plane they may be so arranged, a? 
for instance where they are concentric 
circles, that the one does not attract the 
other at all but merely directs it, as de¬ 
scribed above. If the one circuit were not 
in the same plane as the other they would 
attract one another even after they had placed themselves 
in parallel planes, and if forced to remain in such a position 
t-hat the currents were flowing in opposite directions in the 
two circuits, they would repel one another. If the two 
circuits were in one plane, but not concentric, there might 
be a resultant force tending to cause relative movement in 
that plane, due to the greater proximity of the wires at 
certain parts. All these attractions and repulsions. are 
wholly distinct from the attractions and repulsions between 
charges of electricity at rest. They were discovered by 
Ampere. 

§ 9 . All the actions of currents one upon another may 
obviously be multiplied by using, instead of a single wire, a 
coil of wires, through each winding or turn of which the same 
current is flowing. Thus, a circuit composed of twenty turns 
of wire on a reel would be acted upon with twenty times the 
force that a single turn would experience with the same current 
flowing through it; and again, if the second circuit be also 
composed of twenty wires, each with a current equal to the 
original one, the forces in action will be again multiplied 
twentyfold. So that a circular coil a (Fig. 31) of twenty turns 
of wire hung up by a fibre inside a fixed coil b of twenty 
turns of wire, will experience a directing force 400 times 
greater for any given current circulating in both than would 
be experienced by a coil with a single turn hung inside a 






Chap. III.] 


Current. 


59 


coil with only one turn. This fact allows the construction 
of instruments called electro-dynamometers, adapted to show 
the presence of electric currents. A coil a of 
perhaps several thousand turns may be hung 
up inside a coil b, also consisting of a large 
number of turns, each turn being insulated 
from its neighbours by silk, a and b are, 
when no current is passing, maintained in 
planes at right angles to one another by a 
small directing force, such as the torsion of 
a wire. When a current is passed through both, the inner 
coil is turned in such a direction as to place it more parallel 
to b than before, and with the currents running in the same 
direction. The instrument may be modified, so that a 
known current is passing through a, and the one to be 
examined passed through b only. The direction of the 
unknown current is indicated by the direction in which a 
turns, and its magnitude or strength by the angle through 
which it is turned. 

§ 10 . Other arrangements of a similar kind will suggest 
themselves to the reader. If the centre coil a, instead of 
resembling a ring, were a coil of small diameter as in Fig. 32, 
forming a cylinder of considerable length, 
so arranged that the current flowed in the 
same direction round all parts of the cylin- a 11 y 
der, the deflection of the internal cylinder (jTOTOO 
would be more immediately visible, and 
the ends a and b might be considered as two poles, having 
a tendency to place themselves at right angles to the plane 
of the directing coil. When such a cylinder as this is placed 
wholly inside another, having similar coils parallel to it, 
it will be in stable or unstable equilibrium, as the currents 
flow in the same or in opposite directions. 

If the pole a were introduced inside the coil b a, as 
shown in Fig. 33, the coil a would be sucked in by the action 
of one current on the other. If. on the other hand, the 




6 o 


Electricity and Magnetism. [Chap. III. 

currents flowed in such a direction that the pole b were placed 
inside or near the similar pole b, as in Fig. 34, the inner coil 
would be expelled or repelled from b. These actions are 
apparent whatever be the diameter of the coils. Conceive 
next that two flat spiral coils (Fig. 35) are placed face to 
face : if the currents flow in the same direction, they will 
attract one another ; if in opposite directions, they will repel 
one another. 

Any of these arrangements may be made use of to show 


Fig. 33. 



the presence, direction, and magnitude of a current in a 
wire. By using a large number of turns of fine copper wire 
insulated with silk, and suspended so as to turn with very 
small frictional or torsional resistance, it is easy to construct 
apparatus showing all the phenomena described in § 9 and 
§10. The long cylindrical coil described in this section is 
sometimes called a solenoid. 

§ 11 . Magnets are found to be influenced by electric 
currents almost exactly as solenoids are. In the presence 
ot a current, they are directed so that if free to move, 
they stand across the current. This fact was first observed 
by Oersted. The end of the magnet which points to the 








Chap. III.] 


Current. 


6 1 


south, when freely suspended, is similar to that pole of the 
solenoid in which the current is moving in the direction 
of the hands of a watch, holding the watch with its back 
to the coil; or, in other words, if the solenoid be like a 
right-handed corkscrew and the current enters at the point, 
the point will behave like the end of a magnet which points 
south. The solenoid and magnet have many properties in 
common. The solenoid may be directed by a single rec¬ 
tilinear current, and so may the magnet; but just as the 
directive action on the solenoid is increased by wrapping 
the directing coil all round it, by bringing the coils into 
close proximity, and by increasing the magnitude of the 
current flowing through the directing coil, so the directing 
force or couple acting on a magnet is greatly increased 
by sending the current m the directing coil round it many 
times, by bringing that coil very close to the magnet, and by 
using a powerful current. This property of the magnet 
allows us to construct instruments called galvanoscopes 
and galvanometers for the detection and measurement of 
currents without using a double coil of insulated wire. In 
galvanoscopes a magnet hangs inside a directing coil, each 
turn of which is placed north and south. The magnet hangs 
with its poles north and south 
so long as no current passes 
through the coil, but when a 
current passes, it is deflected 
more or less towards one side 
or the other, until the couple 
due to the directing action of 
the current is balanced by the 
couple due to the directing 
action of the earth. When 
the current in the directing 
coil (Fig. 36) flows from south 
to north in the top of the coil, 
the end of the magnet which pointed south, and wl 


Fig. 36. 









62 Electricity and Magnetism. [Chap. III. 

hereafter be called the south pole of the magnet, turns 
towards the east. 

The direction in which a magnet tends to turn across a 
current may also be described as follows. Imagine a man 
lying on the wire which conveys the current, in such a direc¬ 
tion that the current was from his feet towards his head, his 
face being turned towards the magnet; then, under the in¬ 
fluence of the current, the pole of the magnet which, when 
free, turns to the south, will turn towards the right hand of 
the man. Or let a current be flowing through a copper cork¬ 
screw, and let the magnet take up its natural position inside 
the coils of wire : then if the corkscrew be turned the way of 
the current it will screw from south to north, through the 
compass needle considered as a cork. 

The following is a third description of the direction in 
which a current deflects a magnet. Imagine a watch strung on 

the ware conveying a 
current so that this 
current goes in at the 
back of the watch 
and comes out at the 
face through the cen¬ 
tral pivots; then the 
south pole of the magnet is impelled by the current in the 
direction of the hands of the watch (Fig. 37). 

§ 12 . Thegalvanoscope and galvanometer are instruments 
of such importance that they will be described at length in 
Chapter X.; but since we shall have occasion in future con¬ 
tinually to speak of electric currents and their properties, it 
is desirable to state how a galvanometer may be easily con¬ 
structed capable of indicating the presence of a current and 
of comparing the relative strengths of various currents. Wind 
copper wire insulated with silk on a hollow brass cylindrical 
bobbin a (Fig. 38) with deep flanges BB b which may have feet 
at c by which the bobbin is supported on wood or vulcanite. 
Inside a fit a small brass plug d, having at one end a hollow 


Fig. 37. 



Chap. III.] 


Current . 


63 

chamber, closed by the lens e, with a focal distance of 
about 120 centimetres. In the little chamber suspend a 
mirror and magnet by a 
single silk fibre, such as 
may be drawn out of a 
cheap silk ribbon. This 
fibre must be so thin as to 
be nearly invisible. The 
mirror should be formed of 
microscope glass as truly 
plane and as thin as possi¬ 
ble. The magnet may be 
attached to the back by a 
little shellac dissolved in 
spirits of wine. Care must 
be taken that the mirror 
is not drawn out of shape 
by the magnet. The silk 
fibre must also be attached with shellac varnish. It ma\ 
then be threaded through a hole in the chamber by 
means of a needle of sealing wax or shellac, and secured 
with a little mastic or other varnish. The plug d can then be 
introduced or withdrawn from a at pleasure. 

If currents are to be observed which are passing through 
circuits of great length or containing bad conductors the wire 
should be thin, say No. 40, and many thousand turns may 
be employed : the diameter of the chamber inside the plug d 
maybe 1*5 centimetre, the length from b to Bj 3*5 centi¬ 
metres, and the outside diameter of the flanges bBj 6 or 7 
centimetres. This size will contain many thousand turns 
of fine wire. 

If currents are to be observed which are passing in 
short lengths of wire or other good conductors the space 
inside the flanges bBj may be filled with two or three dozen 
turns of stout copper wire, say No. 16 or No. 20. The two 
ends of this coil tt, may conveniently be connected to two 


Fig. 38. 
























































Chap. III.] 


Current . 


65 


brass pieces (Fig. 39) well insulated by vulcanite and having 
screws by which other wires can be joined to the same ter¬ 
minals as they are called. The instrument is completed by a 
paraffin lamp l, placed behind a screen having a slit m in 
it about 60 centimetres in front of the coil and horizontal 
white scale n about 45 centimetres long. 

When placed as in Fig. 39 the light from the lamp passes 
through the slit in the screen, through the lens e on to the 
mirror f, by which it is reflected back on to the scale. 
An image of the flame is seen on the scale. When the 
light falls perpendicularly on the mirror this image appears 
on the scale immediately above the slit in the screen. If 
by the passage of a current through the coil the magnet is 
deflected to the right or left, the image moves to the right 
or left along the scale, the angle formed by the reflected 
rays being twice the angle through which the magnet and 
mirror are deflected. A very small angle produces a great 
displacement of the image. With the dimensions named 
the horizontal displacement of the image is nearly propor¬ 
tional to the strength of the current. If the scale be bent 
so as to form part of a cylindrical surface having the axis of 
suspension of the mirror as its central axis, the reflected 
spot of light is more clearly seen through the whole range. 
This instrument is Sir William Thomson’s mirror galvano¬ 
meter. With its assistance the presence, increase, or 
decrease of a current can be observed. It is convenient 
to place a bar magnet s in the magnetic meridian imme¬ 
diately above the coil; by raising or lowering this magnet, 
the directive force of the earth may be increased or weak¬ 
ened. If the south pole of s is placed to the south the 
magnet may by trial be put at such a distance from the 
suspended mirror and magnet as almost exactly to counter¬ 
balance the effect of the earth’s magnetism. The instru¬ 
ment will then be very sensitive, but the spot of light will never 
remain quite stationary. A second magnet t, placed per¬ 
pendicular to the magnetic meridian, may be used to adjust 

F 


66 Electricity and Magnetism . [Chap. IIL 

the zero of the instrument, i.e. to bring back the spot of 
light to a fiducial mark at the centre of the scale when no 
current is passing. The direction of the magnetic meridian 
is that in which a free magnet naturally points. 

§ 13 . A current not only acts on a piece of steel or 
iron which is already a magnet, but it converts any piece 
of non-magnetised steel or iron in its neighbourhood into 

a magnet having its poles so 
situated that they lie in the 
line along which a free magnet 
would place itself under the 
action of the current. This 
magnetising action is more 
powerful as the iron is placed nearer the current, as the 
current is more powerful, and as a greater length of the 
current acts in the same sense on the iron. Thus, a piece 
of iron placed inside a helix or bobbin (Fig. 40) of many 
coils is strongly magnetised by the current and has its north 
and south poles placed as shown in Fig. 40. 

The magnetisation produced by the current is only tem¬ 
porary if the iron be soft or annealed, but a portion of the 
magnetisation produced in hard iron is retained long after 
the current has ceased to flow, and in a hard steel bar some 
portion of it is permanently retained. Work is done, and 
energy expended, in producing this magnetisation. 

§ 14 . The current in the wire implies a transfer of elec¬ 
tricity under the action of electromotive force ; and by the 
very definition of electromotive force work in some form 
must be done during the transfer. 

When a current flows through a simple wire and does 
not magnetise iron or set any mass in motion, the energy 
expended in producing the current is wholly employed 
in heating the conducting wire, the heat developed in any 
part of the wire being precisely equivalent to the work 
which would be done in bringing the same quantity of 
electricity from the one end of the wire to the other on a 



Chap. III.] 


Current. 


6 ; 


little conductor against the statical repulsion described in § i, 
Chapter II. If any portion of the energy is employed in other 
ways, as described above, so much less heat is developed in 
the wire. The rise of temperature in the wire depends on the 
specific heat of the metal of which it is composed. 

§ 15 . When the current traverses a compound liquid 
conductor instead of a solid simple metal wire, the liquid is 
in many cases decomposed, one element or group of ele¬ 
ments moves to the spot at which the current enters the 
fluid, and the other to the spot at which the current leaves 
the fluid. Faraday called the metal surface at which the 
positive current entered the fluid the anode, and the 
other surface the kathode. The compound decomposed 
by the electricity is called an electrolyte, the process of 
decomposition electrolysis and the products of electrolysis 
ions. Thus when two glass tubes (Fig. 41) c and d, filled 
with water, are inverted over a vessel of water, and the two 
platinum wires a b introduced into the vessel, then upon 
connecting a and b with a suffici¬ 
ently powerful galvanic battery so 
that a current may pass from a to b, 
the water is electrolysed; oxygen is 
found in c and hydrogen in d, in 
the proportions forming water. 

Energy is expended in decom¬ 
posing any compound, just as 
energy is evolved in the combina¬ 
tion of elements which have a 
chemical affinity one for another. 

The energy expended in the de¬ 
composition of an electrolyte is not 
available to produce motion or heat 
in the circuit. 

§ 16 . Currents traverse even very 
bad conductors, but the current is 
small, i.e. comparatively little electricity passes in a given 






68 Electricity and Magnetism. [Chap. III. 

time with a given e. m. f. Bad conductors are generally 
compound bodies. The resins, may be taken as examples. 
Feeble currents also traverse electrolytes without producing 
any sensible amount of electrolysis. It is certain that work 
of some kind is done by the current as it passes through 
these bodies; but it is not yet known by what action the 
work is represented, that is to say, it is not known whether 
the bad conductor is heated, or decomposed, or whether 
some other form of work represents the energy expended. 

§ 17 . If a current be allowed to set a magnet in motion, 
for instance, to expel one pole of a magnet previously intro¬ 
duced into a helix, the current experiences a real resistance, 
and its flow is checked by the effort. The mere presence 
of the magnet if it is at rest does not check the current; a 
certain statical force exists between the current and the 
magnet, but so long as no motion occurs in consequence of 
this force or against this force no work is done, and the 
current flows as if the magnet were not there. A rough 
analogy to this might be found in the following arrangement. 
Let water be flowing through a pipe at one side of which 
there is a piston a (Fig. 42) held 
in position by a spring at B. The 
water as it flows through the pipe 
will press on the piston a, and by 
means of a piston-rod may exert a 
force at b. When this force just 
balances the force of the spring, the 
water in flowing past the piston does no work by means of it 
or on it, and the current proceeds as if no piston were there; 
out if the spring be then weakened or let go so as to be forced 
back by the piston, the lateral pressure of the water in 
forcing back the piston overcomes a resistance through 
a certain space and does work as the current of electricity 
does in moving the magnet. Moreover, the flow of water 
will be checked or diminished while the work of pushing 
back the spring is being done. When the spring has been 













Chap. III.] 


Currejit . 


69 

pushed back so far that its elastic force balances the pressure 
in the pipe, the current in the main pipe will flow on as 
before, unaffected by the presence of the spring b. In 
like manner the electric current which was checked in its 
flow while deflecting the magnet flows on as before after the 
magnet has come to rest. The analogy is imperfect, inasmuch 
as the diminution of the water current is accompanied by a 
change of capacity for the water, whereas the diminution of 
the electric current is unaccompanied by any increase of 
capacity. The water is only diverted, whereas the elec¬ 
tricity is really retarded. This diminution of the current 
while it is doing work occurs not only when the work con¬ 
sists in moving a magnet, but also when the work consists 
in moving a wire or wires conveying currents, as in the 
electro-dynamometer, or in magnetising soft iron. 

§ 18 . If the piston a in Fig. 42 be forced back towards 
the pipe containing water, it will produce a current, the 
effect being reciprocal to that which was produced when the 
current was diminished by forcing forward the piston; work 
is done by the piston as it is forced forward, and this work 
is expended in producing an extra current of water. 

Similarly, if the magnet which has been deflected be 
forcibly moved back, energy is required to force it back 
against the resistance due to the electrical repulsion of the 
current, and this energy performs work represented by an 
increase in the current exactly corresponding to the diminu¬ 
tion experienced when the current was expending energy 
in forcing back the magnet. The current is said to be 
induced in the wire by the motion of the magnet relatively 
to the wire. The case is one of energy stored and restored. 
When the current forced back the magnet the energy of the 
current was expended in such a manner as to be stored up 
in the system. When the magnet returns to its original 
position the energy is restored to the current. The exam¬ 
ple already given of water in a pipe forcing back water 
against a spring affords one instance of energy stored and 


7 o 


Electricity and Magnetism . [Chap. III. 


restored; another is afforded by the common pendulum. 
The energy of the pendulum exists alternately in a latent 
or potential fonn due to the attraction of gravitation, 
and as actual energy due to motion. As the bob rises 
the actual energy is gradually transformed into potential 
energy, being thus stored up. As the bob falls the 
potential energy is reconverted into actual energy, being 
thus restored. Just so, if a current deflects a magnet and 
causes it to swing backwards and forwards, the energy 
alternately exists in the form of electric repulsion and 
actual energy of motion; but there is this difference between 
electric and gravitation examples : the force of gravitation 
is neither increased nor diminished by the motion of the 
pendulum, whereas when the magnet swings in obedience 
to the impulse given by the current, the current diminishes, 
and when the magnet swings back against the impulse of 
the current, the current is increased. 

§ 19. Motion of the piston in Fig. 42 would produce a 
current in the pipe, whether one existed before or not; 
if the piston were drawn back from the pipe it would suck 
water in at the mouth, if moved forward it would drive 
water out; quite similarly, the motion of a magnet in the 
neighbourhood of a conductor, the motion of a wire contain¬ 
ing an electric current, or the increase or decrease of 
magnetism in a magnet near a conductor, will each of them 
cause currents to flow in that conductor; the direction of 
the current in the conductor or wire will be such that it resists 
the motion of the magnet or of the current , or the change in the 
current , or the change of magnetisation. 

The following are examples of the application of this 
general principle, first enunciated by Lenz. Let there be 
a metallic ring a b (Fig. 43), a second ring c D, in which a 
current flows in the direction of the arrows, and a magnet 
n s ; then, while the relative position of c d, a b, and n s 
do not vary, and while the current in c D and the mag¬ 
netism in n s remain constant, neither increasing nor 
diminishing, no current whatever will flow in the ring a b. 


Current. 


Chap. III.] 


7 1 


but any change in any one of these conditions will produce 
a current in a b; thus : 

1. If the ring c d moves 
nearer a b a current will be 
induced in a b in the direc¬ 
tion of the inside arrows, and 
during this action the current 
in c d will be diminished. 

2. If the ring c d be re¬ 
moved farther from a b a 
current will be induced in a b 
in the direction of the outside 
arrows, and during the induction the current in c D will be 
diminished. 

3. If the pole n of the magnet ns be pushed into the 
ring or nearer to it, a current will be induced in a b in the 
direction of the inside arrow, and the motion is resisted. 

4. If the pole n of the magnet be withdrawn to the right 
hand, out of or away from the ring, a current will be induced 
in a b in the direction of the outside arrows, and the motion 
is resisted. 

5. If the magnetism of the magnet be increased, a current 
will be induced in a b in the direction of the inside arrows, 
and the increase of magnetism is thereby resisted. 

6. If the magnetism of the magnet be diminished, a 
current will be induced in a b in the direction of the outside 
arrows, and the diminution of magnetism is thereby resisted- 

If instead of simple rings we have long thick coils of many 
turns, the effects will be much more sensible. The effects 
of induction between straight wires and magnets can with 
ease be deduced from the general principle enunciated 
above. Induction is the name given to this phenomenon, 
which, however, has nothing in common with the induction 
described in Chapter I. To distinguish between these phe¬ 
nomena, that described in Chapter I. must be designated 
electrostatic induction, and the induction of currents, electm- 


Fig. 43. 


c A 







72 Electricity und Magnetism . [Chap. Ill, 

magnetic induction. Electrostatic induction is called * in¬ 
fluence ’ in French and German. 

Owing to electro-magnetic induction magnets and wires 
conveying electric currents are not as free to move as other 
bodies. They may when at rest be in perfect equilibrium, and 
apparently free to move in all directions, but when we move 
them they induce currents in neighbouring conductors, and 
these currents are in such a direction as to produce a force 
opposing the motion of the first magnet or current. It is, 
indeed, impossible to conceive that by moving they should 
produce a force helping their own proper motion as in 
that case perpetual motion, or rather a perpetually increasing 
source of energy, would be the result. 

§ 20 . A current which commences in a given circuit may 
be likened, so far as its effects on a neighbouring conductor 
are concerned, to a permanent current brought suddenly 
from an infinite distance to the spot where it stands. We 
know that by bringing a current c d (Fig. 43) from a distance 
to a position alongside a wire forming part of a distinct 
circuit a b, we should cause the induction of a current in 
a b opposite in direction to that flowing in the parallel 
wire C d. The beginning of a current in CD has exactly the 
same effect and induces a current in the opposite direction 
in a b ; again, an increase of current in c d acts in the same 
manner as bringing c d nearer to a b. It induces a current 
in the opposite direction to that in c d. These induced 
currents cease as soon as the inducing current c d ceases to 
increase, just as the induced current in a b would cease as 
soon as c d, while conveying a permanent current, ceased 
to approach a b. 

The diminution of a current in c d produces the same 
effect as removing c d from the neighbourhood of a b, i.e. it 
induces a current in a b in the same direction as that in c d. 
The total cessation of the current c d acts like the infinitely 
distant removal of c d with its current, and of course induces 
a current in a b in the same direction as that which flowed 



Current. 


Chap. III.] 


73 


through cd. We may therefore add to the examples given 
in § 19 two more. 

7. If the current in c d ceases or is diminished, a current 
will be induced in a b in the direction of the outside arrows, 
and the diminution of the current in c d is thereby delayed. 

8. If the current in c d commences or is increased, a 
current will be induced in a b, in the direction of the inside 
arrows, and the increase of the current in c d is thereby 
delayed. 

§ 21 . Induction is the unfailing accompaniment of the be¬ 
ginning or increase and termination or decrease of a current, 
for there are always conductors somewhere near in which the 
induced currents flow. The induced currents diminish for 
the time being the strength of the inducing current, and 
thus we see that neighbouring bodies change the rate at which 
a beginning or ceasing current comes to its permanent con¬ 
dition. If the whole or a large part of a circuit of small 
resistance is very near the inducing current, and so disposed 
that the induction tends to occur throughout in one direction, 
the induced current will be considerable, and its reaction on 
the inducing current will also be great, shortening the time 
it requires to reach the permanent condition. If the circuit 
in which the induced current flows is, on the contrary, far 
removed from the inducing current, or only exposed to in¬ 
duction for a small part of its length, or so placed that the 
current tends to flow in opposite directions at different parts 
of the circuit, or has a great resistance, then the induced 
current will be small and its reaction on the inducing 
current will also be small. The inducing current produces 
an electromotive force in the circuit conveying the induced 
current, and we may say that the induced current is due 
to the induced electromotive force. If the inducing current 
a be near a number of conductors bcd, the induced current 
in b tends to weaken that in c and d, inasmuch as a current 
beginning in b would induce currents in c and d in the 
direction of the original current a. Thus the induced 


74 Electricity and Magnetism . [Chap. III. 

current in b is less than it would have been if c and d had 
not been there, and the inducing current in a is less 
checked than it would have been if c and d had not been 
there. 

An increasing or diminishing current not only induces an 


Fig. 44. 

■<- mr 



< -«Kr 


Fig. 45 . 


e. m. f in neighbouring conductors but also exercises an in¬ 
ductive action on the current in which it flows. Thus let 
us consider a circuit coiled back as in 
the annexed figure. An increasing current 
between a and b, flowing as shown by the 
arrow, tends to induce a current between 
c and d in the opposite direction. The 
e. m. f thus induced between c and d op¬ 
poses the original current, and delays its 
increase. If the current between a and b 
is diminishing, it tends to induce a current 
between c and d in the same direction as it is flowing, and 
the result is to delay the decrease. Thus the action in both 
cases is to delay change. Even when the wire is straight a 
similar but much weaker effect occurs. A current flowing 



Fig. 46. 

B C 


(Fig. 46) from a to b repels one flowing from c to d ; if then a 
current increases in a b, it induces a current in front of itself 
in the direction in which it is flowing, and is checked in so 
doing. The effect is to diminish the abruptness of the 
increase. 

§ 22 . The conductor in which the current is induced 











Chap. III.] 


Current. 


75 


need not form what is called a closed circuit, i.e. such 
a conductor as is formed by a ring of wire round which 
the current can continue to flow permanently if a per¬ 
manent e. m. f. be kept up round it, as distinguished from a 
broken circuit, such as would be formed by a ring of wire 
incomplete at one or more points, where the presence of air 
or other non-conductors would stop any permanent current; 
but although the induced current will be very different in 
the two cases of a closed and open circuit it will be pro¬ 
duced in both. In the closed circuit we may have a current 
induced without difference of potentials between the parts. 
We cannot have difference of potential between two parts 
of a conductor without a current ensuing, but we may have 
a current due to e. m. f. without any difference of poten¬ 
tial. The analogy of water in a pipe will make this clear. 
If there be difference of level between two reservoirs in 
connection with one another, as in Fig. 47, the water will 
flow from the higher level to the 
lower. But even if the two reser- FlG ' 47 * 

voirs be at the same level, when pipl 

a rope is rapidly drawn through __ 

the pipe from a to b, water will 

by friction be dragged along the pipe, and water will flow from 
a to b, causing b to rise in level or gravitation potential. 
Here the current cannot be said to be due to a difference of 
potential, and the difference of potential which finally results 
from the action is opposed to that which would have pro¬ 
duced the current. 

Again, if the water be enclosed in a circular pipe (Fig. 48), 
and an internal wire a a a be caused to rotate inside this pipe 
about the axis of the ring, it will set all the water m the 
pipe in motion, without causing any difference of pressure 
between two parts of the pipe; in this case there is no 
difference of gravitation or pressure potential causing the 
motion, nor is any difference of potential necessarily caused 
by the motion. The two cases of a closed and broken 










76 Electricity and Magnetism . [Chap. III. 

circuit are analogous to this. In the closed circuit the 
current may continue indefinitely so long as the motion of 
the inducing magnet continues, but no 
difference of potential need be produced 
between any parts of the circuit. In 
the broken circuit, on the contrary, the 
current is not produced by a difference 
of potential between different parts, but 
the e. m. f. drives positive electricity to 
one end of the wire, and negative electri¬ 
city to the other, producing a difference of 
potentials which will send back a reverse current so soon as 
the inducing action of the magnet is over; the first cuirent 
may be exceedingly small, even in cases where if the circuit 
were closed the current would be great, for a small quantity 
will in bodies of small capacity be quite enough to produce 
a difference of potential balancing the inductive action of 
the magnet. Just as in Fig. 47, if the reservoirs a and b 
are small, a very little water dragged from a to B by friction 
will establish such a difference of potentials as will stop all 
further current though the friction might be sufficient to 
cause a great current in the closed circuit (Fig. 48). As 
soon as the difference of potentials between a and b in the 
broken circuit is sufficient to cause a reverse current equal 
to that which the magnet moving as it does can induce, no 
further current will be induced in the broken circuit, pre¬ 
cisely as under similar circumstances the friction of the rod 
would cease to produce a current of water; but no motion 
of the magnet or other inducing system can be so small as 
to fail to produce a continued current in the closed circuit, 
for no difference of potentials is necessarily created tending 
to reverse the action. 

§ 23 . A complex case arises when the closed circuit is 
long and of sensible capacity while the inducing action takes 
place on one part only. This case is analogous to a long 
elastic pipe (as in Fig. 49), inside which a short rod is 


Fig. 48. 



Chap. III.] 


Current. 


77 


moving, producing a current by friction; here there may 
be accumulation of water in front of the rod and a deficiency 
behind. There may be, there¬ 
fore, an increase of pressure in 
front of the rod and a defect 
behind, tending to reverse the 
current produced by the fric¬ 
tion of the rod. Just so with 
the electric current, there may be at parts of the long circuit 
differences of potential produced tending to reverse the 
direction of the induced current; the potential being raised 
at the parts into which the positive current is flowing, and 
depressed at those parts from which it is flowing. This 
implies unequal currents in different parts of the circuit. 
Examples of this kind of action occur in submarine cables. 

§ 24 . The strength of a constant current in any circuit is 
equal in all parts of the circuit. In this case, although one 
part of the circuit may be a thick wire and another part a 
thin one, a third part an electrolyte, &c., the quantity of 
electricity conveyed past each section is the same in the 
same time, i.e. the strength of the current is the same at 
each part. Equal lengths of current, whether conveyed 
in a thick or thin wire, will produce precisely the same 
effect in directing magnets and in producing magnetism, &c. 
This equal current in all parts of the circuit is independent 
of the capacity of each part, as it is independent of the dif¬ 
ference of materials. There are not two kinds or qualities of 
current; a current has but the one quality of magnitude, 
meaning that it conveys a certain definite quantity of electri¬ 
city past a given point in a given time. When the epithets 
great, strong, intense, are applied to currents they all mean 
the same thing, and mean that a large quantity of electricity 
is conveyed by them. The uniform current of electricity is 
analogous to the uniform current of water. If water be 
flowing from one reservoir to another through a succession 
of pipes of different diameters all full, the water will flow in 


Fig. 49. 





78 


Electricity and Magnetism. 


[Chap. III. 


a uniform current as defined above through all of them; that 
is to say, the same quantity of water per second passes 
through every pipe; the velocity of the water is different 
wherever the diameters of the pipes differ; but the current 
is constant in the sense that it is a current of so many 
gallons per second. When a good form of voltaic battery is 
used to produce the difference of potentials, and the current 
is allowed to flow through a metallic conductor, kept at rest 
at the same temperature and away from the neighbourhood 
of moving magnets or other moving currents, we obtain this 
simple uniform current in all parts of the circuit 

§ 25 . It will be obvious that this simplicity must be 
widely departed from, when even this uniform current is first 
started and when it ends, and that simplicity is still farther 
removed from the case in which currents are induced by 
moving magnets, &c.; these currents must vary at every 
moment in any one place, and differ at all parts of the circuit. 
To take the simplest case first: when the poles of the galvanic 
cell z c are first joined at n and m to the wires abcd 
electricity will rush from the cell into the wires; this elec¬ 
tricity has to charge each portion of 
the wires statically: the current begins 
close to the cell some time before 
it reaches the remoter portions of 
the wire; it flows at different rates 
through different sections of the wire, 
according to their size, capacity, and 
material; it induces currents in all conductors in the neigh¬ 
bourhood, and is checked while doing so, and not until all 
this is over shall we have that permanent condition in which 
a constant current flows through all parts of the circuit. 
The series of phenomena just described occurs whenever 
an electric signal is sent along a wire. The earth generally 
forms one part of the circuit used for this purpose, and the 
circuit is completed or closed by making contact at one 
place only, as at m , the wire at n being already joined to z; 




Chap. III.] 


Current . 


79 


the phenomena are not made at all simpler by these changes. 
The speed of electricity is often spoken of, but what has 
now been said shows that these words without qualification 
can have no meaning ; electricity starting from m does not 
reach a, b or c like a bullet, but in a gradually increasing 
wave, and the manner and rate of its arrival depend evi¬ 
dently on many circumstances, such as the size and material 
of the wire, its distance from 
surrounding conductors, &c. 

If the cell be connected with 
two long wires insulated at 
the further ends (as in Fig. 

51), or if one pole be connected with the earth and the 
other with a large insulated conductor or long wire, we 
shall have a series of precisely similar phenomena, except 
that the final condition of equilibrium will be that in which 
all parts of the conductors being duly charged to the 
potentials which the cell produces, no further current will 
flow at all. 

The laws according to which the varying induced currents 
flow in different parts of the circuit are subject to the still 
further complication, that the inducing system does not 
produce any constant difference of potential such as is pro¬ 
duced by the cell, and that even the current which it induces 
in any one part of the circuit varies as the magnet or 
inducing system varies in its position relatively to the 
circuit. 

§ 26 . When two dissimilar metals (Fig. 27) are joined so 
as to form a conducting circuit, and the junction c is at a 
different temperature from the junction d, an electric current 
is found to flow through the circuit, a difference of poten¬ 
tial or E. m. f. occurring at both junctions. In both cases, 
taking iron and copper below 300° C. as an example, we 
should have the tende$cy to send the current from the iron 
to the copper across the junction, but that tendency is 
greatest at the cold junction, and therefore the current flows 


Fig. 51. 











80 Electricity and Magnetism. [Chap. III. 

from the iron to the copper across the cold junction. The 
source of energy here is heat, which is absorbed at the hot 
junction, and given out at the cold junction; but less heat 
is given out at the cold than is absorbed at the hot junction 
by an amount equivalent to the work done by the electric 
current. This current is often called a thermo-electric cur¬ 
rent, but it differs in no quality from other currents. The 
E. M. f. produced is small. 

§ 27 . In conclusion, we have found that currents are 
produced by the friction of non-conductors, by chemical 
reactions, by heat; by the approach, commencement, or 
increase of a current in any neighbouring conductor; by the 
removal, cessation, or diminution of any neighbouring cur¬ 
rent ; by the motion of a neighbouring magnet relatively 
to a conductor and by the increase or decrease in the 
magnetism of this magnet. 

Lastly, any change in the distribution of the statical 
charge of electricity on the surface of bodies produces 
currents until the redistribution is completed and equili¬ 
brium is restored. We find no difference of kind between 
all these currents; they all have the same properties, but 
combined in very varying degrees. In studying the laws 
which connect currents with other electrical magnitudes, 
we find that we must distinguish the case of the constant 
current which is uniform in all parts of the circuit, and at 
rest relatively to all other conductors and magnets, from that 
of the more complex varying currents, and of those which 
move relatively to other currents, conductors, or magnets. 



Chap. IV.] 


Resistance . 


8i 


CHAPTER IY. 

RESISTANCE. 

§ 1. Bodies have already been described as being bad or 
good conductors, and an imperfect conductor may be said 
to oppose the passage of an electric current. All known 
conductors oppose a sensible resistance to the passage of a 
current, by which we mean that if two bodies of any sensible 
capacity and at different potentials be joined, the current 
produced occupies a sensible time in passing between them, 
whatever material be employed to join the bodies, and how¬ 
ever it may be shaped. 1 The strength of the current, or, in 
other words, the quantity of electricity passing per second 
from one point to another, when a constant difference of 
potentials is maintained between them, depends on the re¬ 
sistance of the wire or conductor joining those two points. 
K bad conductor does not let the electricity pass so rapidly 
as a good conductor, or, in other words, a bad conductor 
offers more resistance than a good one. When no electro¬ 
magnetic phenomena are produced, the current flowing 
from a point at potential a to a point at potential b depends 
simply on what is here called the resistance of the conductor 
separating them. 

§ 2 . With a given conductor joining two points, it is found 
by experiment that upon doubling the difference of potential 
between the points, twice as strong a current flows as 
before ; in other words, with a constant resistance, the 
current is simply proportional to the e. m. f. or difference of 
potentials between the points. Again, it is found that keep¬ 
ing the difference of potential constant, and keeping the 
section and material of the conducting wire constant but 
doubling its length, we halve the current which flows, and 

1 The self-induction of a current would cause a delay in its passage 
between two points even if the conductor had no resistance, but the 
delay due to resistance is easily separated from that due to self-induction. 

G 


82 


Electricity and Magnetism. [Chap. IV. 


generally that if the e. m. f. and section and material of the 
wire be kept constant, the current will be inversely pro¬ 
portional to the length of the conductor. Again, keeping 
the e. m. f., length, and material all constant the current is 
halved by halving the area of the cross section of the wire. 
Consequently, if^ we define resistance as proportional to the 
length of the wire of constant section, and as inversely pro¬ 
portional to the cross section where that varies, we shall be 
justified in saying that with a given difference of potentials 
or e. m. f. between two points, the current which flows will 
be inversely proportional to the resistance separating these 
points ; and, again, that with a constant resistance separating- 
two points, the current flowing will be simply proportional 
to the e. m. f. or difference of potential between the points. 
If, then, we call c the current, i the electromotive force, 
and r the resistance of the conductor, we find that c is 

proportional to the quotient -, and is affected by no other 

R 

circumstance, hence we have 


c = i, or r 



or i = c r. 


R 


This equation expresses Ohm’s law, which may be stated 
thus :— 

When a current is produced in a conductor by an e. m. f. the 
ratio of the e. m. f. to the current is independent of the strength 
of the current , and ifeal/ed the resistance of the conductor. 

This definition of resistance would not be" justified if 
we did not always obtain one and the same value for r 
in any one conductor, whatever electromotive force may be 
employed to force a current through it. The electrical 
resistance of a conductor is not analogous to mechanical 
resistance, such as the friction which water experiences in 
passing through a pipe, for this frictional resistance is not 
constant when different quantities of water are being forced 
through the pipe, whereas the magnitude called electrical 
resistance is quite constant whatever quantity of electricity 
be forced through the conductor. This fact leads to much 


Chap. IV.] 


Resistance. 


83 

greater simplicity in the calculations of the distribution of 
electrical currents than in calculations of the flow of water. 
The accuracy of Ohm’s law is most easily illustrated with 
a galvanometer having a short coil of thick wire. Take a 
Grove’s cell and make a circuit through the galvanometer, 
and such a length of fine wire as gives a convenient deflec¬ 
tion, it will be found that the deflection is nearly inversely 
proportional to the length of the fine wire ; when this length 
is doubled, the deflection is halved. This would be strictly 
true if the deflections of the galvanometer were proportional 
to the current, and if the resistance of the galvanometer and 
of the cell were nil. Taking these resistances into account, 
then, with any cell or battery of constant e. m. f. and with 
any galvanometer, we shall find the deflections inversely 
proportional to the total resistances of the circuit, 

§ 3 . Resistance in a wire of constant section and material 
is directly proportional to the length and inversely proportional 
to the area of the cross section. The form of the cross section 
is a matter of indifference, showing that the resistance is 
in no way affected by the extent of surface of the conducting 
wire or rod, and that although electricity at rest is found only 
on the surface, electricity when flowing as a current is pro¬ 
pagated along all parts of the conductor alike. 

The most easily explained manner of comparing two resist¬ 
ances is by means of the differential galvanometer. Let the 
coil of a galvanometer be formed of two insulated wires wound 
on side by side, so that each makes the same number of turns. 
Then if equal currents be sent round the two coils in oppo¬ 
site directions there will be no deflection; if the two currents 
be not equal, the stronger will produce a deflection. Let 
G! G represent the two coils in the annexed diagram, and 
let Rj R be two resistances which are to be compared ; join 
the two galvanometer coils at b and the two resistances at a 
connecting Rj with G! and r with G, as shown; complete 
the circuit by connecting b with a, through a battery c z. 
One portion of the current wall pass through g r, the other 
G 2 



84 Electricity and Magnetism. [Chap. IV. 

portion through g } Rj. The magnitude of the current through 
both these conductors depends on their resistance and on the 
difference of potential between a and 
b which is the same in both cases. 
Hence the current through G and r will 
be equal to the current through Gj and 
Rj if the resistances of the two branches 
are equal. It is easy to make the resist¬ 
ance of G t equal to the resistance of G, 
by adding a little piece of wire to the 
coil which has the smallest resistance if 
there be any difference between them. 
If therefore we find no deflection 
caused by completing the circuit as 
above we may conclude that r = r^ 
If r } be the greater, less current will 
pass through Gj than through g and a 
deflection in one direction will follow ; 
a deflection in the opposite direction 
would be produced if Ry were the smaller. It is easy by suc¬ 
cessive trials to find the relative lengths of two wires r and R! 
which balance one another when different materials or differ¬ 
ent forms are used. By this instrument the law stated at the 
beginning of the paragraph is easily proved. 

§ 4 . Since the resistance of a wire of any given material is 
inversely proportional to the cross section of the wire, it 
will also be inversely proportional to the weight per 
unit of length ; or, in other words, the resistance of a uniform 
wire of any material is inversely proportional to the weight 
per foot of the wire, i.e. a wire weighing twenty grains per 
foot has half the resistance of a wire weighing ten grains per 
foot. Inasmuch as all bodies have not the same specific 
gravity, the relative resistance of different materials will 
be different, according as we refer them to similar cross 
sections and lengths, or to similar weights and lengths. 
When treating of the measurement of resistance, a Table 


Fig. 52. 








Chap. IV.] 


Resistance. 


8; 


will be given in which the relative resistances of various 
materials are given, referred to both units; meanwhile, it 
may be sufficient to state that pure copper or pure silver 
have smaller resistances than any other known material; 
that alloys have a larger resistance than metals; electro¬ 
lytes a considerably greater resistance than most alloys; 
that some liquids, such as oil, have so great a resistance 
as to become insulators, but that all known insulators, 
except gases, do permit the passage of electricity in a way 
differing rather in degree than in kind from the way in 
which metals permit the passage of electricity. Thus bad 
conductors or insulators will hereafter be frequently spoken 
of as bodies of great resistance. The difference in this 
respect between an insulator and a good conductor is enor¬ 
mous. Taking the resistance of silver at o° C. as the unit, 
a wire of equal length and diameter of German silver would 
have a resistance of 12-82, and a rod of guttapercha of equal 
bulk and length about 850,000,000,000,000,000,000, or 
8*5 x io 20 ; nevertheless, Ohm’s law applies to the resist¬ 
ance of each material. 

§ 5 . The resistance of all materials alters with a change of 
temperature. With the metals and good conductors, the 
resistance becomes greater with a rise of temperature ; with 
electrolytes and bad conductors it diminishes. There is thus 
less difference between the resistances of these dissimilar 
bodies at high temperatures than at low. Inasmuch as the 
passage of a current through a wire heats it, the passage of a 
current tends continually to increase the resistance which it 
meets with. This can easily be seen with a differential gal¬ 
vanometer. After carefully balancing r and R b Fig. 52, alter 
the circuit so as to pass the current for some minutes through 
R! and Gy only. On reconnecting r and G a deflection will be 
observed, and R will have to be increased to balance r,, 
until the wires have been left to resume their former tempera¬ 
ture. Wires of graduated length and section, insulated by 
silk and wound on bobbins, are employed to represent certain 


86 


Electricity and Magnetism. [Chap. IV. 


definite resistances, and these bobbins of insulated wire are 
called resistance coils. It is essential that they should be 
made of a material, such as German silver, the resistance of 
which varies little with a change of temperature, and that in 
careful experiments the temperature of the resistance coil 
should be noted and allowed for. 

§ 6. A knowledge of the resistance of a conductor is 
essential to determine how much electricity will flow between 
two points in a given time when joined by that conductor; 
in other words, to determine the strength of a current which 
will under any given circumstances be produced; how 
much the current will be modified by a change in any given 
conductor; how a current will be subdivided and affected by 
having two or more paths open to it between the same 
points; to determine the effect of galvanic cells of different 
sizes and materials, since each kind of galvanic cell has an 
internal resistance depending on the size of the plates, on 
the distance between them, and on the solutions employed; 
to allow a comparison between the qualities of insulators; 
and to enable us to augment, diminish, and in all ways regu¬ 
late any current at will. 

§ 7 . The resistance of the materials of which any gal¬ 
vanic cell is made limits the current which it can produce. 
When the two metals are joined by the shortest and thickest 
wire practicable, the resistance of the circuit is practically 
the internal resistance of the battery, and in most forms this 
is very considerable. In a sawdust Daniell it is often more 
than the resistance of a mile of No. 8 iron wire, the size 
usually employed for land lines of telegraph : a quarter of 
a mile of such wire is a small resistance for a Daniell’s cell. 
The resistance of the Grove cell is much smaller. The 
resistance of a battery decreases as the size of the plates is 
increased, because this is equivalent to increasing the area 
of the cross section of the liquids, the resistance of which is 
from i to 20 million times as great as that of metals of the 
same size. 


Chap. IV.] Resistance. 87 

Take two cells of any battery, join them as in Fig. 53, 
the copper being connected to the copper and the zinc to 
the zinc. Cells thus joined are said to be joined in multiple 
arc. The two cells are exactly equivalent to a single cell of 
double the size. The e. m. f. produced is that of one cell; 
the resistance is half that of one cell. Complete a circuit by 
inserting a galvanometer with a short thick coil between c 
and z; the deflection obtained will be nearly double that 
which the one cell gives through the same galvanometer, 
because halving the resistance of the cell very nearly halves 
the resistance of the whole circuit. Next, make a circuit 


Fig. 53. Fig. 54. 



with one of the two cells and a galvanometer with a com¬ 
paratively long coil of fine wire, reducing the current so as 
to have a convenient deflection by adding a resistance r if 
necessary. Add the second cell in multiple arc; no visible 
change will be produced in the deflection, because the resist¬ 
ance of the circuit is now chiefly made up of that of the gal¬ 
vanometer and resistance R. Diminishing the resistance of 
the battery hardly alters the whole resistance and does not 
sensibly alter the current. Thirdly, join the two cells in the 
manner described in Chapter I. § 19, the zinc being joined to 
the copper as in Fig. 13 or Fig. 54. This manner of joining is 
described by the words ‘ in series.’ Now complete the circuit 
with the fine wire galvanometer and R, as in the second experi- 













88 Electricity and Magnetism. [Chap. IV. 

ment. The deflection will be nearly doubled. The resistance 
has been slightly increased by adding the second cell in series, 
but the resistance of the batteries is only an insignificant por¬ 
tion of the whole ; while therefore the resistance of the circuit 
has hardly been changed, the e. m. f. has been doubled by 
doubling the number of metallic junctions, and twice the 
e. m. f. with a constant resistance gives twice the current and 
twice the deflection. Fourthly, return to the thick wire gal¬ 
vanometer, complete the circuit through it with the two cells 
in series; the deflection will be almost exactly the same as 
when one cell only is used, and only half that obtained when 
the two cells are joined in multiple arc. When the two cells 
were joined in series the e. m. f. was doubled, but the resist¬ 
ance of the whole circuit was also nearly doubled and there¬ 
fore the current remained nearly the same as before. Thus 
we see that with a short circuit of small external resistance 
we can increase the current by increasing the size of cells, or, 
what is equivalent to this, by joining several cells in multiple 
arc. We can also increase the current by employing liquids 
of smaller specific resistance, but we cannot increase the 
current by adding cells in series. With a long circuit of 
great external resistance large cells, or many of them joined 
in multiple arc, will fail to give us strong currents, but we 
may increase the current by joining the same cells in series. 

When the resistance of the battery is neither excessively 
large nor excessively small in comparison with that of the 
rest of the circuit the current will be increased both by 
adding cells in series and by increasing their size or adding 
them in multiple arc. By the former process we increase 
the e. m. f. more than we increase the resistance. By the 
latter process we sensibly diminish the resistance of the 
circuit, leaving the e. m. f. unaltered. 

Cells joined in series are sometimes described as joined 
for intensity, and cells joined in multiple arc as joined for 
quantity. These terms are remnants of an erroneous 
theory. 


Chap. IV.] 


Resistance. 


89 


§ 8. The resistance of the galvanometer employed to 
indicate a current in a circuit is a very material element in 
the circuit. A. powerful current may be flowing from a 
large cell through a circuit of small resistance. If we intro¬ 
duce a galvanometer having a long coil of thin wire, we 
may by that very act diminish the current a thousand-fold. 
For circuits of small resistance galvanometers of small re¬ 
sistance must be used. For circuits of large resistance 
galvanometers of large resistance must also be used; not 
that their resistance is any advantage, but because we 
cannot have a galvanometer adapted to indicate very small 
currents without having a very large number of turns in the 
coil, and this involves necessarily a large resistance. 

§ 9 . There are several forms of apparent resistance which 
are not resistances. 

When a current passes to or from a metal to a liquid 
electrolyte, a great apparent resistance occurs, i.e. the 
current is diminished by the change of medium much more 
than by a considerable length of either material. This 
resistance is sometimes said to be due to the polarisation 
of the metals dipped into the solution. This word polarisa¬ 
tion is sometimes very vaguely employed, but apparently here 
it means that the plates become coated with the products of 
the decomposition of the electrolyte, and that this coating 
produces a diminution of current. This diminution, which of 
course affects the current throughout its entire length, does 
not, however, appear to be due to anything analogous to 
resistance. The effect in question is due to something in 
the nature of a reciprocating force by which energy is 
stored up, i.e. when the original current ceases, a current in 
the opposite direction is set up at these surfaces of passage 
from liquid to solid by a kind of rebound. It appears, there¬ 
fore, that the current has been diminished by the creation of 
an opposing electromotive force due to the arrangement of 
the elements into which the electrolyte itself has been 
decomposed. The term resistance is, however, continually 




9 ° Electricity and Magnetism. [Chap. IV. 

applied to this cause of the diminution of a current even by 
those who are convinced that the diminution is not due to a 
true resistance. This false resistance or polarisation is easily 
observed. Make a circuit of a galvanometer, a copper wire, 
two DanielFs cells, and a couple of plates of one metal sepa¬ 
rated by water or any electrolyte. The deflection of the 
galvanometer during the first few minutes will be found to 
decrease rapidly ; then if the cell be removed and the circuit 
closed, the two metal plates will send a current deflecting 
the galvanometer in the opposite direction ; this, current is 
strongest at first, and gradually ceases altogether. 

§ 10 . When a current begins to flow across a solid in¬ 
sulator, such as gutta percha, a very similar phenomenon 
occurs; the current gradually and rapidly diminishes, as if 
the resistance of the gutta percha increased under the 
influence of the current. This apparent extra resistance 
is, however, no true resistance; when the original current 
ceases, the gutta percha sends back a gradually decreasing 
current in the opposite direction, and this current is of 
such magnitude and lasts for such a time as precisely to 
send back all the electricity which had, at first, apparently 
flowed through the gutta percha in excess of the quantity 
which would have passed in the same time through a con¬ 
stant resistance equal to the final resistance. The final 
resistance of the gutta percha is looked upon by some elec¬ 
tricians as its true resistance, inasmuch as it is the only part 
of the apparent resistance which follows Ohm’s law ; the 
greater flow of current in the first instance is, according to 
this view, due not to a diminished resistance, but to an appa¬ 
rent absorption of electricity, as if by a number of condensers. 
Other electricians look upon this property of the solid 
insulator or electrolyte as quite analogous to the polarising 
property of the liquid electrolyte, and consider that the 
resistance of the material, as shown by the first current, is the 
true resistance and the subsequent diminution of current is 


Resistance. 


Chap. IV.] 


91 


Fig. ss. 


due to an opposing electromotive force. The former view 
appears to the writer to be the more tenable. 

This phenomenon is most easily observed with the aid of 
a considerable length of wire insulated with india-rubber or 
gutta percha. Take, say, a mile of such insulated copper wire 
as is used for submarine telegraph cables ; place it in a tub of 
water; insulate one end n of the wire and connect the other 
m through a galvanometer g with one pole of a galvanic 
battery c z of say 50 
cells. Connect the 
other pole of the 
battery with the wa¬ 
ter by a copper plate, 
as in Fig. 55. The 
galvanometer must 
have a coil with some thousands of turns of fine ware. 
All the connections must be carefully insulated. When 
all the other arrangements have been completed the cir¬ 
cuit may be completed by joining the wires at m ; this 
will be followed by a violent throw of the galvanometer 
needle, due to the rapid rush of the electricity to charge the 
wire. When the needle comes to rest a steady deflection in 
the same direction will be observed, due to a current flowing 
from c through g and across the gutta percha sheath to the 
water and thus to z. This deflection will gradually diminish, 
until after an hour it may be two-thirds or half the original 
deflection. Call this final deflection x and the deflections 
at each minute after the wires at m were joined 



x + a lt x + a 2 , x+a 3 . . . x + <z 60 . 

Now remove the cell c z and substitute for it a metallic con¬ 
nection, as shown by the dotted line. This may be done by 
means of prearranged stops or keys so as not to disturb the 
insulation of any part. Then the charge in the wire will 
rush out through g, causing a violent throw in the opposite 












92 Electricity and Magnetism. [Chap. IV. 

direction to that produced by the charge and equal in amount. 
After this discharge has taken place a steady deflection will 
be observed in the same direction as that due to the discharge, 
and this deflection at the end of each successive minute will 
be equal to a x a 2 a 3 . . . a 60 . It is assumed that a reflect¬ 
ing galvanometer is used, in which the deflections are pro¬ 
portional to the currents. The violence of the charge and 
discharge is such that in delicate experiments they are not 
allowed to flow through the galvanometer, but are conducted 
across between the terminals by what is termed a short 
circuit, being a connection of small resistance temporarily 
inserted. 

§ 11 . Electricity is not only conducted from one body to 
another, by flowing as a current along a conductor ; it may 
also be conveyed or carried in a solid conductor, through 
such an insulator as air, from one place to another. When 
two conductors charged to very different potentials are 
brought close together, the attraction of the electricity is 
such that it tears off the metal or material in fine powder, 
and this powder springs across the intervening space, 
carrying with it a charge of electricity. The air or gas 
itself is also electrified by contact with the conductor, 
and helps to convey the electricity. Light and heat are 
evolved in the process apparently much as light and heat 
are evolved when sparks are struck from steel. Electric 
sparks thus produced are said to overcome the resistance of 
the air, but this resistance has nothing in common with the 
resistance which is the subject of Ohm’s law. The laws 
according to which sparks pass, and brushes, as they are 
called, form on points electrically charged, must be sepa¬ 
rately studied. The brush discharges, whether luminous or 
otherwise, are due to the accumulation of electricity in 
large quantities at points. The electricity has such a re¬ 
pulsion for itself, that if it accumulates sufficiently, the force 
becomes great enough to break down the pressure of the 
air, and highly electrified particles of the conductor and of 


Chap. IV.j 


Resistance. 


93 


air fly off the point. Every electrical spark seen is an illus¬ 
tration of this convection. Lightning is one example; 
another is the luminous brush which in the dark may be 
observed discharging the conductors of an electrical fric¬ 
tional machine. The air or gas heated by the spark pro¬ 
bably conducts some electricity, so that only part of the 
electricity passing in the spark or brush is transferred by 
convection. 

§ 12 . Rarefied gases are found to be tolerably good 
conductors. The laws of their resistance to the passage of 
electricity have only lately been investigated, and are but 
partially understood. It is uncertain how far their resistance 
can properly be said to follow Ohm’s law. According to 
recent experiments by Mr. Varley, conduction in rarefied 
gases does follow Ohm’s law, but there is a very large 
resistance at the surface of contact between the attenuated 
gas and the metal conductor. This resistance is con¬ 
stant and prevents any current from passing until the e. m. f. 
employed exceeds a certain definite magnitude, which is con¬ 
stant for each material and degree of rarefaction. This is 
very analogous to what takes place in electrolytes, except that 
through these some current apparently always passes whatever 
e. m. f. be employed, although no complete decomposition oc¬ 
curs until a certain definite e. m. f., constant for each electro¬ 
lyte, has been reached. Experiments showing the action of a 
partial vacuum can be made with Geissler’s tubes, which can 
be bought at any respectable optician’s. These glass tubes 
contain highly rarefied gases, and electrodes leading through 
the glass are employed as part of the circuit. If a galvano¬ 
meter and an electric battery form part of the circuit no 
current will be observed until perhaps two hundred cells are 
employed. Then the current passes with brilliant optical 
effects in the tube and the galvanometer is deflected. Induc¬ 
tion apparatus producing high electromotive force, such as 
the well-known Ruhmkorff’s coil, may be employed instead 
of the galvanic battery. 


94 


Electricity and Magnetism . 


[Chap. V. 


CHAPTER V. 

ELECTRO-STATIC MEASUREMENT. 

§ 1. Our knowledge of electricity and magnetism is derived 
from observation of certain forces, and the comparison of 
currents, quantities, potentials, and resistances are all effected 
by a comparison of forces acting under various circum¬ 
stances. The measurement of forces requires fixed stand¬ 
ards of length, mass, and time, which will also serve as 
fundamental standards for all electrical measurements. The 
centimetre . . . gramme . . . second 

are the three units of length, mass, and time which will be 
adopted in the present treatise. 

As stated in Chapter I. § 17, the unit of Force adopted 
by us is the force which will produce a velocity of one centi¬ 
metre per second in a free mass of one gramme by acting 
on it for one second. 

This unit of force = *00101915 x weight of a gramme 
at Paris. The weight of the gramme itself wherever we 
happen to be is the more common unit of force, but we shall 
find the so-called absolute unit more convenient in calcula¬ 
tions, and any result can be readily reconverted into the 
more familiar measure by multiplying it into the above 
coefficient, or dividing it by the number 980*868. 

The unit of work is the work performed by the unit force 
moving over a distance of one centimetre; it is equal to 
•00101915 centimetre grammes; in other words, to lift 
the weight of one gramme through one centimetre at Paris 
requires an expenditure of work equal to 980*868 of the units 
of work. 

§ 2 . In what is termed electro-static measure the unit 
quantity of electricity is that which exerts the unit force on 
a quantity equal to itself at a distance of one centimetre 
across air. 


Chap. V.] Electrostatic Measurement. 95 

The unit difference of potential or unit electromotive 
force exists between two points when the unit of work is 
spent by a unit of electricity in moving from one to the 
other against the electric repulsion, described in Chapter I. 

The resistance of a conductor between two points is a 
unit if it allows only one unit of electricity per second to 
pass from one to the other when the unit of electromotive 
force is maintained between them. 

The system of electrical units as defined in this paragraph 
is called the electro-static absolute system, based on the cen¬ 
timetre, gramme, and second. No special names have yet 
been given to these units. They are the most convenient for 
use when dealing with the phenomena described in Chapter I. 
The equations expressing these definitions are given below 
in § 14. 

§ 3. It is found by experiment that the force f with 
which, at a given distance d, two small electrified bodies 
repel or attract one another, is proportional to the product 
of the charges, q and q u upon them ; and further, that when 
the distance varies this force f is inversely proportional to 
the square of the distance d between them; it follows, from 
the definition adopted of force and quantity, that 

/= q -jt « 

from which equation, if we observe the force, and make q 
either equal to y l5 or to bear any known relation to it, we can 
determine the quantity q in absolute measure; or vice versa , 
knowing q and q lt we can determine what force they will 
exert at a given distance, as, for instance, in moving the 
index of an electrometer. The application of this equa¬ 
tion is limited to small electrified bodies. In any body of 
sensible size the mutual induction between the two electri¬ 
fied bodies would disturb the distribution of electricity over 
the surface, and change that distribution at every distance. 

§ 4. The quantity of electricity with which a given con¬ 
ductor in a given place can be charged depends simply on 
the difference of potential between it and neighbouring con- 


9 6 


Electricity and Magnetism. [Chap. V. 


ductors, and if these neighbouring conductors are uninsu¬ 
lated we may say that the charge will be simply proportional 
to the potential of the body charged; we may therefore 
speak of the capacity jof a given conductor for electricity, 
meaning thereby the constant quotient of the quantity on 
the conductor divided by its potential; or calling the quantity 
q , as before, and the potential /, we have 

q = si (2) 

The capacity of a sphere at a distance from all conductors 
is equal to its radius; that is to say, a sphere one mhtre in 
diameter will, when charged to the potential 6, contain 
6 x 50, or 300 units of electricity. 

The capacity s x of a sphere of radius x, suspended in the 
centre of a hollow uninsulated sphere, radius y } is 

'* = j*~* . (3) 

The dielectric separating the two spheres is supposed to be 
air. The capacity of the internal conductor would change 
if any other dielectric were used. The capacity of a metal 
conductor is independent of the metal employed. The 
phenomenon is more complex when either solid or liquid 
electrolytes or insulators are used as the bodies to be charged. 

Equation (3) shows that when the distance between the 
two opposed conductors is diminished, so that^y — x becomes 
small, the capacity of the system is very much increased. 
This is equally obvious from the formula for the capacity of 
a large flat plate one side of which is near a similar un¬ 
insulated flat plate, and separated from it by air, while the 
other side is far removed from all conductors; in such a 
case, let a denote the distance between the metallic surfaces 
and let s be the capacity per unit of area y then 

* = — (4) 

47 r a 7 

(7r here and elsewhere always means the ratio of the circumference 
to the diameter of a circle = 3-1416. The surface of a sphere of 
radius unity is equal to 471-.) 



Chap. V.] 


Electrostatic Measurement. 


97 


and in order to find the total capacity of the plate we may 
multiply s into the area of the plate with sufficient accuracy 
for practical purposes, whenever a is small in comparison 
with this area; a must be measured in centimetres, and 
the surface in square centimetres. This method is not ab¬ 
solutely accurate, because at the edges of the plates the 
electricity will not be uniformly distributed, as it will in the 
middle of the plate. By increasing the surface and diminish¬ 
ing <z, we may increase indefinitely the quantity which the 
plate or conductor will contain when raised to a given 
potential. The quantity with which the plates will be 
charged with a given potential is q = s i as before. 

§ 5 . The arrangement of opposed conductors intended to 
give a large capacity with comparatively small surface is 
termed a condenser. The capacity of a condenser depends 
on the dielectric separating the conductors. If for air we 
substitute gutta percha, the capacity will be increased about 
four and a quarter times. The coefficient by which the 
capacity of an air condenser must be multiplied in order 
to give the capacity of the same condenser when another 
dielectric is substituted for air is constant for each substance, 
and is called the specific inductive capacity of the dielectric. 
It is a quantity of much importance in telegraphy, and will 
in this treatise be designated by the letter k. It has been 
approximately determined for a few substances. The fol¬ 
lowing table gives the numbers for these : 



Values of K. 

Air. . . 

= i 

India rubber . . . = 2*8 

Resin . . 

. . . = 177 

Hooper’s vulcanised in- 

Pitch . . 

. . . = i*8o 

dia rubber . . . = 3*1 

Beeswax . 

. . . = i-86 

W. Smith’s gutta percha = 3*59 

Glass . . 

. . . = i' 9 ° 

Gutta percha . . . = 4*2 

Sulphur . 

. • • - i ‘93 

Mica.=5 

Shellac 

. . . = i -95 

Paraffin.= i'98 2 


§ 6. The numbers are approximate values only, and, in- 
1 Gibson and Barclay. 

H 










9 8 


Electricity and Magnetism. [Chap. V. 



deed, extreme accuracy is unattainable on account of the 
following peculiarity observed in all solid dielectrics. When 
one plate A of the condenser is first raised to the desired 
potential by contact, say with one electrode c of a galvanic 

battery, the other elec- 
Fig - s 6 - trode z being in con¬ 

nection with the earth 
or second plate of the 
condenser as in Fig. 56, 
a charge rushes in with 
great rapidity, but the 
entrance of the elec¬ 
tricity does not instantly cease, as is the case with an air 
condenser; on the contrary, although it decreases very 
rapidly, the flow of electricity into the condenser does not 
cease for many hours. This phenomenon has already been 
described in Chapter IV. § 10 in its bearing on currents. 
Similarly, when the two plates are joined by a wire so as 
to be brought to one potential, the electricity is discharged 
very rapidly at first; but this discharge is so far from 
being completed immediately that electricity continues to 
flow out for precisely as long a time as it ran in, and 
with precisely the same rapidity after each interval of 
time; Le. if, upon maintaining a difference of potential 
x between the plates, coatings , or armatures (as they are 
often called) of the condenser, a quantity q per second 
is found flowing into the condenser at the expiration of 
thirty minutes, then thirty minutes after the two arma¬ 
tures have been joined, or, in ordinary language, after 
the condenser has been discharged, the same quantity 
q per second will be found flowing from one armature to 
the other. The effect produced is as though the dielectric 
were a kind of sponge absorbing electricity at a certain 
rate when subjected to a certain difference of potential, 
and yielding it all up again when the two plates were brought 
to one potential. A condenser with glass or paraffin be¬ 
tween the armatures has not, therefore, the same definite 








Chap. V.] Electrostatic Measurement . 99 

capacity as an air condenser; the capacity is generally 
understood to mean the capacity for receiving electricity from 
the first contact. When a condenser is discharged, if con¬ 
tact be not maintained between the armatures, the gradual 
restoration of this quasi absorbed charge raises the potential 
of the armature which had previously been highly charged, 
and accumulates upon it, so that on again making contact 
between the armatures a second considerable discharge is 
given, and a succession of discharges of this kind can be 
obtained from a large condenser for several hours. These 
are called residual discharges. The same law holds as to 
charges; after charging the armature to a given potential, 
and leaving it insulated, the potential gradually falls, owing 
to the absorption by the glass or gutta percha; then, on 
raising the potential of the armature afresh, by connecting 
it with the electrode cf a battery, a fresh charge can be 
poured into the condenser. This apparent absorption of the 
electricity by the dielectric is said by some writers to be due 
to polarisation caused by the continued electrification of the 
dielectric; the word polarisation, like induction, is applied 
to a great variety of phenomena having little in common. 

These phenomena are readily observed in a condenser 
consisting of a mile of telegraph wire insulated by gutta 
percha; the copper wire is the one armature ; if the gutta 
percha be covered with lead or tinfoil, as is sometimes 
done, this forms the other armature ; or, if the gutta percha 
covered wire be placed in a tub of water, that water will be 
the second armature. With a sensitive galvanometer and 
a battery of 50 cells, or even less, all the phenomena de¬ 
scribed are easily observed. Condensers of smaller bulk 
and equal capacity can be obtained from the makers of tele¬ 
graphic apparatus. When the condenser is like a common 
glass Leyden jar of small capacity, and insulated with a 
hard material, the residual discharges may be observed in 
the form of a succession of sparks after the jar has been 
charged to a high potential by a frictional machine. 

h 2 


IOO 


[Chap. V. 


Electricity and Magnetism . 


Fig. 57. 


§ 7 . Let a small flat movable plate / supported by the 
torsion of a wire m n in Fig. 57, be placed flush with a much 

larger flat fixed plate h h 
surrounding it on all 
sides, and let both plates 
be placed opposite and 
parallel to a third unin¬ 
sulated plate g , then if a 
permanent difference of 
potentials be established 
in any way between g 
and the plates f and h , 
the quantity of electricity 

per unit of area on the plate /will be —— , and the elec- 

47 r a 



tricity will be uniformly distributed over the plate /, and the 
electricity of the opposite sign will also be uniformly distri¬ 
buted over the opposing surface of the plate g. The total 
force with which the plate f is attracted by g will be 


2 2 M 
8 7r a 2 


(5) 


Where m is the surface of the plate in square centimetres. 1 
Apparatus can be constructed by which this force is actually 
measured, by weighing or otherwise, and this apparatus 
forms an absolute electrometer (Sir William Thomson’s guard 
ring electrometer) by which we can determine the difference 

of potential i between the plates: i — a / ^ * f . f must 

m 3 

of course be expressed in absolute measure, Chapter V. § 1. 

§ 8. Measured by apparatus of this kind, the ordinary 
Daniell’s cell (one form of galvanic battery) is found to 
produce a difference of potentials between its electrodes 
equal to *00374. Experiment showed the attraction to be 


1 Vide paper * On the Mathematical Theory of Electricity in Equili¬ 
brium, by Sir W. Thomson. Phil. Mag. 1854, second half-year, and 
republished in 1872 in a volume entitled Electrostatics and Magnetism. 







Chap. V.] Electrostatic Measurement, ioi' 

*°57 grammes per square centimetre between discs separated 
by -i centimetre, with a difference of potentials produced by 
1000 Daniell’s cells. 

Hence, in equation (5), if the weighings had taken place 
in Paris, we should have had f — 980 868 x *057 ; but in 
Glasgow the force with which a gramme mass weighs is less 
than in Paris, so that f — 981*4 x *057 = 55*94; a — *1, 
and M = 1 ; substituting these values in our equation, we 
obtain i = 3*74 for tooo Daniell’s cells. 

Using this value in equation 4, we find that an air con¬ 
denser, with a square metre surface and the plates one 
millimetre apart, electrified by a thousand cells, would take 

a charge of 10000 —— =2976 units. If the plates 

4 7 T x 0*1 

had been separated by gutta percha instead of by air, 
the charge on the plates would be 4*2 x 2976 = 12499, the 
coefficient 4*2 being the specific inductive capacity of the 
material taken from § 5. 

A ball, one centimetre in diameter, electrified by 1090 
Daniell’s cells, would take a charge of *5 x 3*74, or 1*87 
units of electricity. 

From a knowledge of this quantity we may calculate the 
force on a similar ball similarly electrified, but so far off 
that the electricity on each ball would remain almost 
uniformly distributed. Two such balls similarly electrified 
at a distance of one mbtre would repel one another with a 

force = 1 ^7 x 1 & 7 _ _ -ooo^ absolute units of force 
10000 

(equation 1) or *000000357 grammes weight. When the balls 
are brought closer, the calculation of attractions or repulsions 
between them become exceedingly complicated, owing to the 
redistribution of the electricity on their surface. 

§ 9 . The capacity of a long cylindrical conductor of the 
diameter d and length l enveloped by a concentric cylin¬ 
drical conductor of the diameter d, and separated from it 
by an insulator with the specific inductive capacity k is 




102 


Electricity and Magnetism. 


[Chap. V. 


K L 


K L 


( 6 ) 


2 l0g e 


d 4 ' 6 ° 52 Iog d 


(loge signifies that natural logarithms are to be employed instead of 
Napierian logarithms.) 

The length of the cylinder is assumed to be so great that 
the capacity of the ends may be neglected ; this formula is 
applicable to the insulated wire used for submarine cables. 
The capacity of one knot of the English Atlantic cable is 

6087 


x = 4-2 


X 


3 ° 48 _ 228000 (centimetres). 


4-6052 x log 3-28 
6087 is the number of feet in a knot, and 30*48 the number 
of centimetres in a foot; 3-28 is the ratio between the 
diameter of the gutta-percha and that of the wire conductor. 
It follows from the above, that the charge per knot of 
this cable when electrified by 100 Daniell’s cells is -374 
x 328000 = 122670 and every time the cable is charged or 
discharged this quantity per knot flows in and out; thus if 
•01 second be occupied in charging 200 knots the mean 
strength of the current flowing for -oi second will be 
122670 x 200 


100 


245340 units of current. 


§ 10 . The term electric dejisity signifies the quantity of 
electricity per square centimetre on a charged conductor. 
The equations (2), (3), and (4) allow us to calculate this for 
spheres and condensers with flat plates ; equation (4) is 
applicable to any form of condenser in which the curva¬ 
ture is not considerable relatively to the thickness a of the 
dielectric. It is applicable, therefore, to the ordinary Leyden 
jar, with the simple modification that the value obtained 
from it must be multiplied by the number expressing the 
specific inductive capacity of the dielectric. The electri¬ 
cal attraction or repulsion, exerted on a small quantity q 
of electricity close to an electrified surface, is easily calcu¬ 
lated when the electric density on the surface p is known. 
It is perpendicular to the surface, and in air is equal to 

_4 P q = R Q (7) 







Chap. V.] 


Electrostatic Measurement, 


103 


where R is the electrostatic force close to the surface, i.e. the 
force which the charge would exert per unit of quantity on 
the small charge q. 

Between two parallel opposed conducting surfaces, differ¬ 
ing in potential by the amount i, and separated by a small 
distance compared with their size, the resultant electro¬ 
static force R tends to impel any small quantity of electricity 
straight across from one surface to the other, in a direction 
perpendicular to the surface, with a force f which is constant 
in amount. Retaining the previous notation we have 

f=R? = ± e (8) 

The work done on q in crossing is fa — i q. 

The electric density on a small sphere at a given potential 
is much greater than on a large one, for the capacity in¬ 
creases only as the radius, while the area increases as the 
square of the radius; hence an infinitely small sphere 
charged to any sensible potential would have an infinitely 
great electric density on its surface, and the force it would 
exert on electricity in its immediate neighbourhood would 
be infinitely great; it would, in fact, repel its own parts 
infinitely, and we may therefore infer that it would be 
impossible to charge a very small sphere to a very high 
potential. This inference is justified by experiment. The 
distribution of electricity over bodies which have points or 
angles is such that the electric density becomes very great 
on these points, as it would on a very small sphere, even 
when the potential is not high. The result is a great 
repulsion of the electricity for itself, or rather a great re¬ 
pulsion between neighbouring parts of the matter charged 
with it; we then frequently see the electrified matter 
passing off in the condition known as an electric spark, 
or as what is termed an electric brush. Anything tend-, 
ing to produce a great density at any part of the surface 
of a charged conductor tends to produce the spark. Thus 
by approaching a finger to a charged conductor, the density 


104 Electricity and Magnetism. [Chap. V. 

is increased by induction opposite the finger, and may be in¬ 
creased sufficiently to produce the spark. Increased electric 
density by no means necessarily implies increase of potential 
unless the form and position of the conductors are constant. 

§ 11 . There is a real diminution of air-pressure against 
the surface of a charged conductor, due to the repulsion of 
the electricity for itself. This mechanical force can be 
made evident by electrifying a soap-bubble, which expands 
when electrified, and collapses when discharged. If the 
air-pressure per square centimetre be called /, we have 
/ = 2 7rp 2 (9) 

The diminution of air-pressure required before a spark takes 
place between two slightly convex parallel plates has been 
tested by Sir William Thomson, with the results shown in 
the following table : 


Length oLsparks 
in centimetres 

= A 

Electrostatic 
force R close to 
surface in abso¬ 
lute units. 

Vide § 10. 

Electromotive 
force = R x A, 
or difference of 
potential, 
which produced a 
spark 

of length A. 

Pressures of 
electricity from 
either surface im¬ 
mediately before 
disruption in 
grammes weight 
per square 
centimetre = 

R a 

8jtX 981*4. 

■OO254 

5277 

i'34 

11 -290 

•00508 

367*8 

1-87 

5-49 

•0086 

267-1 

2-30 

2-89 

•OI9O 

224*2 

4-26 

2-04 

•0408 

I5I-5 

6-19 

•931 

•0688 

140-8 

9-69 

•806 

•1325 

131 

17-35 

•696 


It is curious to observe that the electrostatic force is not 
constant, as might have been expected; and that the electro¬ 
motive force required to produce a spark does not increase 
in simple proportion to the length of the spark, being less 
per unit of distance between the opposed surfaces for long 
sparks than for short ones. It follows from the measurement in 
§ 8, that 2,600 Daniell’s cells would produce a spark of *0688 









Chap. V.] Electrostatic Measurement. 105 

centimetres between two very slightly convex surfaces : by 
observing the length of spark, which, under similar circum¬ 
stances, can be obtained, say, from a Leyden jar, we may 
roughly estimate the potential to which it has been charged. 

§ 12 . The brushes or sparks which fly off from points 
cf arged to high potentials, show that in all apparatus in¬ 
tended to remain charged at a high potential, every angle 
and point must be avoided on the external surfaces. It is 
easy to draw off, by a silent and invisible discharge from a 
point, by far the greatest part of the charge of a conductor 
without any direct contact with the discharging conductor : 
points are also spoken of as collecting electricity from any 
electrified body held in the neighbourhood ; their action is as 
follows : If attached to an insulated conductor, and held near 
an electrified body a, they become charged by induction with 
the opposite kind of electricity. This flies off in sparks, or 
by a silent discharge, and leaves the insulated conductor 
charged with the same electricity as that contained in a. This 
property of points explains the action of lightning conductors. 
Lightning is an enormous electric spark passing between 
two clouds, or from a cloud to the earth ; in the latter case 
the electrified cloud is attracted towards any prominence or 
good conductor, which becomes electrified by induction, and 
the spark of lightning passes when the difference of poten¬ 
tials is sufficient to overcome the mechanical resistance of 
the air. If the electrified prominence on the earth be 
armed with a point connected, by good conductors, such as 
large copper rods, with the earth, then, as soon as the po¬ 
tential of the point is raised even slightly, the electricity 
passes off from the point into the air; the prominence can 
no more be electrified highly by induction than a leaky 
bucket can be filled with water; the electrified clouds are 
not attracted to the neighbourhood, and even should they 
be driven there in such quantity that the electricity flying 
off from the point is insufficient to prevent a spark from 
passing, the spark will pass from the cloud to the point, 


106 Electricity and Magnetism. [Chap. V. 

inasmuch as the electric density and attraction will be 
greater there than -anywhere in the neighbourhood. Elec¬ 
tricity conveyed by a good metal conductor to the earth 
does no harm, and leaves no trace of its passage; whereas, 
a spark driven through an insulator or bad conductor, tears 
it to pieces on its passage; this fact may be verified by 
sending a spark through glass, which will be cracked and 
shivered, or through paper, which will have a hole tom in 
it. The electromotive force required to produce mechanical 
results of this character is much greater than that required 
to open a passage through a corresponding thickness of air. 
We may, therefore frequently, prevent the passage of sparks 
between two conductors, by covering one of them with 
ebonite, glass, or other hard insulator. 

Sir W. Thomson has found that if a conductor with sharp 
edges or points is surrounded by another, presenting every¬ 
where a smooth surface, a much greater difference of poten¬ 
tial can be established between them without producing 
disruptive discharge, when the points and edges are positive, 
than when they are negative. 

§ 13 . The distribution of electricity over opposing sur¬ 
faces, when these are not of the simplest description, offers 
problems of extreme complication. Generally, we know 
that the density will be greatest where the opposing con¬ 
ductors are close together, and where they have angles or 
points, that it will increase directly as the difference of 
potential and directly as the specific inductive capacity of 
the dielectric. We must especially remember that the charge 
or electric density on opposed surfaces depends on differ¬ 
ence of potential, and not on absolute potential, so that on 
electrifying the outside of a charged insulated Leyden jar„ 
we shall raise not only the potential of the outer, but also 
that of the inner coating; from the same cause the charge 
of any condenser due to contact with two electrodes of a 
battery will be the same, whether one electrode of the battery 
be uninsulated or not, i.e. the quantity which will flow from 


Chap. V.] Electrostatic Measurement. 107 

one armature to the other when joined will be unaltered, 
but the quantity flowing from either armature to the earth 
will depend on the potential of that armature. Any change 
in the total quantity of a charge on a conductor will change 
its potential as a change of its potential will change 
the charge. Putting a charged conductor in contact with 
another conductor at the same potential, will not alter the 
distribution of the charge in either; but if two conductors 
at different potentials are brought into contact, there must 
necessarily be a redistribution of the charge due to the inter¬ 
mediate potential assumed by the two bodies. Mr. F. C. 
Webb in his treatise on electrical accumulation and con¬ 
duction, has given many instructive examples of the dis¬ 
tribution of electricity under different circumstances. The 
theory already stated explains his results. 

§ 14 . The simple laws connecting potential, quantity, 
capacity, density, and electrical attraction or repulsion have 
now been stated, and -the nature of the measurements has 
been indicated, by which potential, quantity, and capacity can 
be defined in terms of length, mass, and time ; a current is 
necessarily measured by measuring the quantity which passes 
per second, and resistances are expressed in terms of that 
resistance which would allow the unit current to pass in the 
unit of time, with the unit electromotive force acting between 
the two ends of the wire. To give some idea of the 
material representation of units of this kind, it may be stated 
that this resistance would be represented by about one 
hundred million kilometres of mercury at o° Centigrade, in 
a tube, the sectional area of which was one thousandth of a 
square millimetre ; electricians when they measure the resist¬ 
ance of the gutta percha envelope of a mile of cable, ob¬ 
serve resistances of about 6 0 ' 0 - <y th of this magnitude; approxi¬ 
mately the insulation resistance of one foot of gutta-percha 
covered wire is of about this magnitude. The unit of current 
is such as would be given by a battery of about 268 Daniell’s 
cells through the above resistance. The unit quantity of elec- 


io8 Electricity and Magnetism. [Chap. V. 

tricity is that on a sphere two centimetres diameter, elec¬ 
trified by one pole of 268 Daniell’s cells in series, the other 
pole being in connection with the earth. This quantity 
discharged per second would give a current equal in 
strength to that flowing through the long mercury conductor 
or gutta percha envelope from the 268 cells. This series of 
units is called the electrostatic absolute centimetre-gramme, 
second series. This electrostatic series is the most con¬ 
venient for calculations concerning electricity at rest, but 
when treating of currents and magnets, a distinct series of 
units is used; this double series of units involves no greater 
inconvenience than the use of the chain, acre, and rod for 
surveying, while the inch, foot, and square inch are used to 
describe machinery. 

§ 15 . The four principal electrostatic units are directly 
determined by four fundamental equations ; from equation 

(1), § 3> we h av e/= from which, if q x = q, we directly 

find the unit of quantity in terms of the unit of force; we 
know by the definition of potential that the work so done 
in conveying the quantity q of electricity between two 
points at potentials differing by the amount i is equal to 
q i or 



This gives the unit difference of potentials in terms of q and 

the unit of work; by definition § 14 the current c = 

where q is the quantity passing in the time t, and from this 
equation we obtain the unit of current in terms of q, and the 

unit of time ; from OhnVs law r — —, by which we obtain 

the unit of resistance in terms of i and c. 

Finally, the unit of capacity is directly derived from that 
of potential and quantity ; the unit of density from that of 
surface and quantity. 


Chap. VI.] 


Magnetism. 


109 


If the capacity of a conductor be called s, we have s = -?, 

where q is the quantity with which it is charged by the 
electromotive force i. 


CHAPTER VI. 

MAGNETISM. 

§ 1 . A magnet in the popular acceptation of the word is a 
piece of steel, which has the peculiar property, among others, 
of attracting iron to its ends. Certain kinds of iron ore 
called loadstone have the same properties. 

If a magnet a be free to turn in any direction, the pre¬ 
sence of another magnet b will cause a to set itself in a 
certain definite position relatively to b. The position which 
one magnet tends to assume relatively to another, is con¬ 
veniently defined in terms of an imaginary line, occupying 
a fixed position in each magnet, and which we will call the 
magnetic axis. The greatest manifestation of force exerted 
by a long thin magnet, is found to occur near its ends, and 
the two ends of any one such magnet possess opposite 
qualities; this peculiarity has caused the name of poles to 
be given to the ends of long thin magnets. These poles 
are commonly looked upon as centres of force, but except 
in the case of long, infinitely thin, and uniformly magnetised 
rods they cannot be considered as simple points exerting 
forces ; nevertheless, the conception of a magnet as a pair 
of poles, capable of exerting opposite forces, joined by a 
bar exerting no force, is so familiar, and in many cases so 
nearly represents the facts that it will be employed in 
this treatise. The magnetic axis, as above defined, is the 
line joining the two imaginary poles. 

§ 2 . Every magnet, if free to turn, takes up a definite 
position relatively to the earth, which is itself a magnet. The 




I 10 


Electricity and Magnetism. [Chap. VI. 


pole, which in each magnet turns to the north, will by us be 
called the north pole of the magnet. The other pole will 
be called the south pole. The two north poles of any two 
magnets repel one another; so do the two south poles ; but 
any north pole attracts any south pole. Hence, the north 
pole of a magnet is similar in character to the south end of 
the earth. The pole which is similar to the south end of 
the earth is sometimes called the positive pole; the other, 
which we call the south pole of the magnet, is the negative 
pole. When a magnet is broken each piece forms a com¬ 
plete magnet with a north and south pole. 

§ 3 . The strength of a pole is necessarily defined as propor¬ 
tional to the force which it is capable of exerting on another 
given pole; hence the force/ exerted between two poles of 
the strengths m and m x must be proportional to the product 
m m v The force /is also found to be inversely proportional 
to the square of the distance d, separating the poles, and to 
depend on no other quantity; hence, choosing our units 
correctly, we have 


/ = 


m m. 


(i) 


The strength of a pole is a magnitude which must be 
measured in terms of some unit. When in the above 
equation we make/and d both equal to unity, the product 
m m x must also be equal to unity hence from equation (i) it 
follows that the unit pole is that which at the unit distance 
repels another similar and equalpole with unit force. 

/will be an attraction or a repulsion according as the 
poles are of opposite or similar kinds. The number m is 
positive if it measures the strength of a north pole and 
negative if it measures the strength of a south pole; hence an 
attracting force will be affected with the negative sign, and 
a repelling force with the positive sign. 

§ 4 . We observe that the presence of the magnet in some 
way modifies the surrounding region, since any other magnet 
brought into that region experiences a peculiar force. The 



Chap. VI.] Magnetism. ill 

neighbourhood of a magnet is often for convenience called 
a magnetic field", and for the same reason the effect pro¬ 
duced by a magnet is often spoken of as due to the mag¬ 
netic field instead of to the magnet itself. This mode ol 
expression is the more proper, inasmuch as the same or a 
similar condition of space is produced by the passage of 
electric currents in the neighbourhood, without the presence 
of a magnet. Since the peculiarity of the magnetic field 
consists in the presence of a certain force, we may numerically 
express the properties of the field by measuring the strength 
and direction of the force, or, as it may be worded, the 
bitensity of the field , and the direction of the lines of force. 

This direction at any point is the direction in which the 
force tends to move a free pole; and the intensity h of the 
field is defined as proportional to the force f with which 
it acts on a free pole ; but this force f is also proportional 
to the strength m of the pole introduced into the field, 
and it depends on no other quantities ; hence, 

f — m h (2) 

and therefore the field of unit intensity will be that which 
acts with unit force on the unit pole. 

§ 5 . The lines of force produced by a long thin bar magnet 
near its poles radiate from the poles ; the intensity of the 
field is equal to the quotient of the strength of the pole 
divided by the square of the distance from the pole; thus 
the unit field will be produced at the unit distance from the 
unit pole. 

In a uniform magnetic field, the lines of force will be 
parallel; such a field can only be produced by special 
combinations of magnets, but a small field at a great 
distance from the pole producing it will be sensibly 
uniform. Thus in any room unaffected by the neighbour¬ 
hood of iron or magnets, the magnetic field due to the 
earth will be sensibly uniform : its direction being that 
assumed by the dipping needle. The dipping needle is a 


112 Electricity and Magnetism . [Chap. VI. 

long magnet supported in such a way as to be free to take 
up its position as directed by the earth, both in a horizontal 
and vertical plane ; it requires to be very perfectly balanced 
before being magnetised, otherwise gravitation will prevent 
it from freely obeying the directing force of the earth’s 
magnetism. 

§ 6. We can never really have a single pole of a magnet 
entirely free or disconnected from its opposite pole, but from 
the effect which would be produced on a single pole it is 
easy to deduce the effect produced by a magnetic field on a 
real bar magnet. In a uniform field, two equal opposite and 
parallel forces act on the two poles of the bar magnet, and 
tend to set it with its axis in the direction of the force of the 
field. This pair of forces tending to turn the bar, but not 
to give it any motion of translation, constitutes what is 
termed in mechanics a couple. When the magnet is so 
placed that its axis is at right angles to the lines of force 
in the field, this couple g is proportional to the intensity of 
the field h, the strength of the poles m , and the distance 
between them /; or ' 

G = m l h (3) 

The product m l is called the magnetic moment of the 
magnet; and from equation (3), it follows that the moment 
of any given bar magnet is measured by the couple which it 
would experience in a field of unit intensity, when it is 
placed normal to the lines of force. A couple is measured 
by the product of one of its forces multiplied into the 
distance between them. The intensity of ?nagnetisation of a 
magnet is the ratio of its magnetic moment to its volume. 

§ 7 . When certain bodies (notably soft iron) are placed 
in a magnetic field they become magnetised, the axis joining 
their poles being in the same direction as would be assumed 
by the axis of a free steel magnet in the same part of the 
field. Thus if the small pieces of soft iron n s are magnet¬ 
ised by the action of the magnet n s producing the lines of 


Chap. VI.] Magnetism. 113 

force shown in Fig. 58, the north pole will be near «, the 
south pole near s in each case. Magnetisation when pro¬ 
duced in this way is said to be induced, and the action is 
called magnetic induction. The intensity of the magnetisa¬ 
tion (except when great) is nearly proportional to the in¬ 
tensity of the field. We have seen in Chapter III. § 13, that 
soft iron, round which a current of electricity circulates, 
becomes magnetised. When, therefore, we can calculate the 
intensity of the magnetic field which we now see is produced 
by the electric current, we shall be able to calculate the 
intensity of magnetisation of the soft iron core. When the 
magnetisation approaches the limiting intensity which the 
soft iron is capable of receiving, it always falls short of that 
calculated on this principle. 

Bodies in which the direction of magnetisation is the same 
as that of the field are termed paramagnetic. Iron, cobalt, 
and nickel, chromium and manganese, are paramagnetic; 
some compounds of iron are also paramagnetic. Some 
of these bodies retain their magnetism, so that we can 


Fig. 58. 



approaches iron in this respect more nearly than any other 
material. Certain other materials, such as bismuth, anti¬ 
mony, and zinc, are magnetised by a magnetic field, so that 

1 








1 14 Electricity and Magnetism. [Chap. VI. 

the direction of magnetisation is opposite to that of the 
field : they are called diamagnetic. None of these bodies 
can be so intensely magnetised as iron, nor do they retain 
their diamagnetism when removed from the field. 

§ 8. One consequence of magnetic induction is that when 
a number of similar magnets are laid side by side we obtain 
a compound magnet stronger indeed than any of the com¬ 
ponent magnets, but much less strong than the sum of the 
strengths of the separate magnets used. For when a magnet 
n s is brought near another n' s', as in Fig. 59, the north pole 
n tends to induce a south pole at n' and similarly n' tends to 
induce a south pole at n. The result is that N and n' by 

Fig. 59. Fig. 6a 


N_8 >' 55 



—.g 

f= 

- 0 

N' 

S' 



f=. 

r—^ 

r — 

— 


their mutual action weaken one another, if n be sufficiently 
strong relatively to n', it may actually reverse the polarity of 
the weak magnet. If on the other hand two equal magnets 
are placed, as in Fig. 60, n and s' mutually strengthen one 
another by induction, but since they tend to induce opposite 
and equal magnetic fields the result is to weaken the re¬ 
sultant field in the neighbourhood, and if the magnets are 
allowed to touch, the strength of the field will be reduced 
to an insensible amount. When the magnets are not equal 
the weaker magnet will reduce the strength of the magnetic 
field due to the stronger. 

§ 9 . When soft iron is magnetised by being placed in a 
magnetic field a sensible time elapses before it assumes the 
maximum intensity of magnetisation which the field will 
produce. Similarly, when the bar of soft iron is withdrawn 
from the field it does not lose its magnetism instantly ; the 
magnetism decreases as gradually as it increased, and in 
almost all cases some traces of magnetism will remain for 















Chap. VI.] Magnetism. 115 

hours or perhaps for ever after the iron has been withdrawn 
from the magnetic field. This remnant of magnetisation is 
often called residual magnetism ; most ordinary pieces of iron 
show residual magnetism very distinctly, especially in large 
masses; but very perfectly annealed iron of certain qualities 
shows very little, and is valuable on that account in the con¬ 
struction of telegraph instruments. The cause of this phe¬ 
nomenon is called coercive force. The slowness with which 
iron in any mass gains or loses its magnetism is a serious 
impediment to the construction of quick-working telegraphic 
apparatus. The term 1 soft iron ’ is applied to denote iron 
which loses its magnetism rapidly, or in other words iron 
which has little coercive force. 

§ 10 . The conception of electric potential has been ex¬ 
plained at length in Chapter II. Magnetic potential is an 
analogous conception. If we move a single magnetic pole 
from one point to another of the magnetic field, we shall 
find that the forces in the field perform work on the pole, or 
that they act as a resistance to its motion according as the 
motion is with, or contrary to, the forces acting on the pole; 
if the pole moves at right angles to the force, no work is 
done. The difference of magnetic potential between any two 
points of the field is measured by the work done by the 
magnetic forces on a unit pole moved against them from 
the one point to the other, supposing the unit pole to 
exercise no influence on the field in question. A point 
infinitely distant from the pole of any magnet must be at 
zero magnetic potential, and hence the magnetic potential of 
any point in the field is measured by the work done by the 
magnetic forces on a unit pole during its motion from a 
point infinitely far off from all magnets to the point in 
question, with the same limitation as before. 

An equipotential surface in a magnetic field is a surface 
so drawn that the magnetic potential at all its points shall be 
the same. By drawing a series of equipotential surfaces, cor¬ 
responding to the potentials 1, 2, 3 . . . ;z, we may map 



116 Electricity and Magnetism. [Chap. VI. 

out any magnetic field so as to indicate its properties. The 
unit pole in passing from one such surface to the next against 
the magnetic forces will always perform one unit of work. 

The direction of the magnetic force at any point is per¬ 
pendicular to the equipotential surface at that point; its 
intensity is the reciprocal of the distance between one sur¬ 
face and the next at that point; i.e. if the distance from 
surface to surface be measured in units of length, the in¬ 
tensity of the field will be 4. 

§ 11 . The magnetic field may be mapped out in another 
manner: this second method is due to Faraday. 

Let a line whose direction at each point coincides with that 
of the force acting on the pole of a magnet at that point be 
called a line of magnetic force. By drawing a sufficient 
number of such lines we may indicate the direction of the 
force in every part of the magnetic field; but by drawing 
them according to a certain rule we may also indicate the 
intensity of the force at any point as well as the direction. It 
has been shown 1 that if in any point of their course the 
number of lines passing through a unit area is proportional 
to the intensity there, the same proportion between the 
number of lines in a unit of area and the intensity will hold 
good in every part of the course of the lines. 

If, therefore, we space out the lines so that in any part 
of their course the number of lines which start from unit of 
area is numerically equal to the number measuring the in¬ 
tensity of the field there, then the intensity at any other part 
of the field will also be numerically equal to the number of 
lines which pass through unit of area there; so that each 
line indicates a constant and equal force. 

The lines of force are everywhere perpendicular to the 
equipotential surfaces; and the number of lines passing 
through unit of area of an equipotential surface is the re¬ 
ciprocal of the distance between that equipotential surface 

1 Vide Maxwell on ‘Faraday’s Lines of Force,’ Cambridge Phil. 
Trans. 1857. 


Chap, vi.] Magnetism . 117 

and the next in order—a statement made above in slightly 
different language. 

§ 12 . In a uniform field the lines of force are straight, 
parallel, and equidistant, and the equipotential surfaces are 
planes perpendicular to the lines of force, and equidistant 
from each other. 

If one magnetic pole of strength m be alone in the field 
its lines of force are straight lines, radiating from the pole 
equally in all directions, and their number is 4 7 r m. The 
equipotential surfaces are a series of spheres whose centres 
are at the pole and whose radii are m, \m , &c. In 

other magnetic arrangements the lines and surfaces are 
more complicated. 

Since a current exerts a force on the pole of a magnet 
in its neighbourhood it may be said to produce a mag¬ 
netic field, and we may draw magnetic lines of force and 
equipotential surfaces depending on the form of the circuit 
conveying the current, and the strength of that current. 
When the current is a straight line of indefinite length like 
a telegraph wire, a magnetic pole in its neighbourhood is 
urged by a force tending to turn it round the wire, so that at 
any given point the force is perpendicular to the plane pass¬ 
ing through this point and the axis of the current. The equi¬ 
potential surfaces are therefore a series of planes passing 
through the axis of the current and inclined at equal angles 
to each other. If the unit current be defined as that current , 
the unit leiigth of which acts with unit force on the unit 
magnetic pole at the unit distance , then the number of the 
equipotential planes surrounding the wire is 4 7r c where 
c is the strength of the current. Thus if the strength c 
were 1 *909 we should have 24 such planes ; if tt c is not 
a whole number, c must be expressed in units so small that 
the error involved in taking the nearest whole number 
may be neglected. The lines of magnetic force are circles 
having their centres in the axis of the current and their 
planes perpendicular to it. The intensity R of the magnetic 



118 Electricity and Magnetism. Chap. VI. 

force at a distance k from the current is the reciprocal 
of the distance between two equipotential surfaces ; we have 

therefore R = . . . . 4 0 . 

§ 13 . In most telegraphic instruments magnets or soft 
iron armatures are moved by forces due to the passage of 
electric currents in certain wires. The apparatus should be 
sensitive so that it may be worked even by feeble currents ; 
in designing the apparatus it should therefore be our en¬ 
deavour so to arrange the wire conveying the current as to 
produce the most intense magnetic field which that current 
is capable of producing, and to place the magnet or soft 
iron acted upon in the most intense part of that field. By 
so doing, and by reducing the forces opposing the motion 
of the soft iron or magnets as much as possible, we render 
the apparatus as sensitive as it can be made. 

When the magnet to be moved or acted upon is large it 
will occupy a large portion of the magnetic field, and will 
therefore experience a larger force than if it were small; but 
the force which it experiences per unit of volume can seldom 
if ever be made so great as when the magnet itself is small, 
for a small and intense magnetic field can be produced with 
a much less current than a large and equally intense mag¬ 
netic field. Hence, we find all very sensitive apparatus 
characterised by small moving parts. The inertia of large 
masses is also injurious in all rapidly moving parts, for not 
only are the large masses acted upon with less force, but 
owing to the increased distance of the greater portion of 
their bulk from the axis on which they must oscillate their 
moment of inertia is increased even more than their bulk. 

Similarly, when a wire conveying a current, or a magnet, 
or a soft iron armature is to move under the influence of a 
magnet, it must be our aim so to arrange that magnet as to 
produce the most intense magnetic field possible at the 
spot where the moving piece is placed. 

The mapping out of magnetic fields due to different 


Chap. VI.] Magnetism. 119 

forms of magnet and different arrangements of wires con¬ 
veying currents has therefore a great practical interest for 
the electrician. 

§ 14 . The poles of a magnet are not at its extremities, but 
generally a little way from the end. It is not necessary that 
a magnet should be magnetised in the direction of its length; 
a bar may be magnetised transversely or indeed in any direc¬ 
tion. Some magnets have more than one pair of poles. 

If a long thin magnet be broken each part becomes a 
distinct magnet having its axis in the direction of the old 
axis ; from this it appears that all parts of the magnet are 
in some peculiar polarised condition, and the actual poles of 
any given magnet are simply the result of the combination 
of all these polarised parts. 

A piece of soft iron which is a magnet by induction can 
again induce magnetism in another piece of soft iron : thus, 
a magnet may sustain a long string of nails each hanging to 
its neighbour. This chain of nails has its pair of poles near 
the ends of the first and last nails in the series, and affords 
an example of what is meant by saying that all parts of a mag¬ 
net are in a polarised condition; each nail when detached 
from the series will remain a magnet for some little time in 
virtue of its coercive force § 9. If a magnet be plunged 
in iron filings and withdrawn, these adhere most abundantly 
near the poles. They stand out from the magnet in tufts, 
largest where the field of force is strongest, that is, near the 
poles, and the direction of the chains or strings which they 
form corresponds to the direction of the lines of force; each 
separate filing becomes a small magnet for the time being. 

§ 15 . Magnets are made from one another by taking 
advantage of this coercive force, which is found to be greatest 
in ha/d steel. A piece of steel may be magnetised by 
being stroked once or twice in the same direction by a 
powerful magnet, or even touched at one end by that 
magnet. Better results are obtained by placing the two 
opposite poles of equally strong magnets in the centre of 




1 20 Electricity and Magnetism. [Chap. VI. 

the bar to be magnetised, and drawing them simultaneously 
away from the centre to the two ends. This operation is 
repeated two or three times, and the bar then turned over 
and treated in a similar way on the other face. The bar 
magnets may, with advantage, incline from one another 
while being dragged apart. A still more complete magneti¬ 
sation is given by placing the bar a b between two powerful 
magnets n s and n' s' as shown, and then drawing the oppo- 


Fig. 6i. 



site poles of two other magnets from the centre of a b towards 
the ends. There are other methods of preparing magnets 
but they all consist in placing every part of a bar of steel in 
the strongest possible magnetic field and trusting to the coer¬ 
cive force of the steel to retain the induced magnetism. 

§ 16. The name electro-magnet is given to a magnet 
formed of a rod or bundle of rods of wrought iron, round 
which an electric current circulates in a coil of wire, as in 
Fig. 40. The electric current so arranged produces an 
intense magnetic field, and the most powerful magnets are 
produced in this manner. It is found that there is a limit 
to the amount of magnetism which in this way or any other 
can be induced in soft iron; when this limit is approached, 
the soft iron is said to be saturated with magnetism. Steel 
is sooner saturated than wrought iron; and as it resists the 
acquisition of magnetism more than soft iron does, so it 
retains more of the magnetism it acquires. This resistance 
to magnetisation is also attributed to coercive force. Electro¬ 
magnets can be made of any form. The two most common 






Chap. VI.] Magnetism . 121 

are the straight bar, in which the poles are as far apart as 
possible, and the horse-shoe, in which they are brought close 
together. 

A piece of soft iron joining the poles of a magnet is 
called an armature; it adheres to the poles and diminishes 
very much, while in its place, the intensity of the magnetic 
field in the neighbourhood. An electro-magnet formed as a 
complete ring produces no sensible magnetic field in its 


Fig. 62. 



neighbourhood; nevertheless, although without poles, it is 
certainly a magnet, and produces many of the magnetic 
phenomena. A series of equal magnets arranged (as in 
Fig. 63) so that the north pole of each is in contact with 
the south pole of its neighbour will also produce no magnetic 
field. An armature is found to diminish sensibly the loss 
of magnetism which is continually taking place in ordinary 
steel magnets. The armature is used to suspend weights 
from horse-shoe magnets, as in Fig. 62. 

§ 17 . The strength m of the poles of a long soft 
iron bar of one square centimetre section held horizon¬ 
tally in the magnetic field due to the earth alone in Eng¬ 
land will be equal to about *175 x 32-8 or 574 units, 










122 Electricity and Magnetism. [Chap. VI. 

each pole would attract a pole of opposite name with a 
force / = , so that if the distance between the poles 

were one mbtre, the force exerted would be 5 74 x 5 _7 4 

ioo 2 

= 32*9 x io -6 = *00329 absolute units of force equal to 
the weight of *000266 grain. In order that this should 
be even approximately true the prism must be so long that 
the magnetisation of the middle does not interfere with that 
of the end. We should be able to calculate the strength of 
the poles of any bar short or long if we were able to find 
the magnetic effect produced by a series of equally magnetised 


Fig. 64. 

S s * a n a s 3 n A N 



elements in a row. Let the black part of each element 
represent a southern pole and the white part a northern 
pole; then if each element were so magnetised that the 
black and white parts were symmetrical and if the strength 
of each pole were a certain multiple of the intensity of the 
field, then n x would exactly cancel s 2 ; n 2 would cancel s 3 , 
and so forth, leaving s at one end and n at the other as 
the effective poles of the magnet; but in fact the action of 
each little element extends to all the others, and the sum¬ 
mation of all these effects is so complex that we must 
abandon all attempt to calculate the strength of the poles 
from the intensity of magnetisation, except in certain very 
simple cases. The calculation given above applies sensibly 
to all long thin bars the cross section of which is small 
compared with one-twelfth of their length; thus our bar 
of one centimetre cross section would have to be at least 
five or six metres long before the formula would apply. 

The magnetic moment (§ 6) of a long thin bar is, k h s /, 
where h is the intensity of the field, s the cross section of 





















Chap. VI.] 


Magnetism. 


123 


the bar, l its length, and k the coefficient of.magnetic induc¬ 
tion ; the magnetic moment of a sphere in the same field 
will be 


%7rr*H 


k 

1 + f irk 


• • ( 5 ) 


and from this formula the intensity of magnetisation of a 
given piece of steel or other metal can easily be calculated 
if k be known, or k may be determined from actual obser¬ 
vation of the magnetic moment. 

§ 18 . The coefficient k is constant only for low magnetic in¬ 
tensities, and gradually diminishes according to an unknown 
law as the maximum intensity for each material is approached. 
The maximum intensity of magnetisation for iron can be 
obtained from an experiment by Dr. Joule, who found that 
the maximum attraction he could produce between an 
electro-magnet and its armature was 200 lbs. per square inch 
of surface. Calling this maximum attraction f, the intensity 
i, and a the area of the surfaces between which the attraction 
is exerted, we have, when the distance between the surfaces 
is very small 

F = 27TZ 2 A ... (6) 


200 lbs. per square inch is 14061 grammes per square centi¬ 
metre, or about 13,800,000 absolute units of force per square 
centimetre. Giving this value to f in the above equation 
when a is unity, we find for i the value of about 1490, as the 
maximum intensity of magnetisation of which iron is cap¬ 
able. If the value of 32*8 k were constant, a magnetic field 
of the intensity of about 45 would be sufficient to magnetise 
iron to saturation. Probably k can only be regarded as 
sensibly constant while the magnetisation of the iron is 
below one quarter of its maximum value, and from some 
experiments by Muller 1 we might infer that the value of k 
near the point of saturation is about one-third of the value 
given above, so that a field of magnetic intensity equal to 

1 Pogg. Ann. vol. Ixxix. 1850. 



124 


Electricity and Magnetism. [Chap. VI. 


about 135 would be required to give an electro-magnet 
the maximum possible strength. 

§ 19 . The relative intensity of magnetisation in the same 
field for different substances has not been very fully studied ; 
in other words, the values of k for different materials and 
different values of i are not well known. The following 
table is deduced from relative values obtained by Barlow, 
to which I have added nickel and cobalt, from relative 
values given by Pliicker: 

Soft wrought iron . 32*8 Soft cast steel . 23*3 

Cast iron . . . 23 Hard cast steel . 16*1 

Soft steel. . . 21*6 Nickel . . 15*3 

Hard steel . . 17'4 Cobalt . .32*8 

These values can only be approximately true. A complete 
table of the values of k would require to contain a set of 
values for each material, and each value of i; whereas the 
value of i for which the above values hold good is not 
known. The maximum intensity of magnetisation for hard 
steel is less than for soft iron, and from some experiments 
of Pliicker, 1 it appears that this difference is about 37 per 
cent., but a much greater intensity of field is required to 
produce the maximum of magnetisation. 

With small values of z, the value of k for nickel was found 
by Weber to be five times that of iron, but with higher values 
of i it rapidly became smaller than for iron, reaching a 
maximum when i is about 30, increasing after this only about 
2 per cent, when i was doubled. 

§ 20 . According to experiments made by Pliicker I 
estimate the value of k for water at 

— 10-65 x IO ~ 6 * 

The following values of k for different diamagnetic sub¬ 
stances are calculated on this assumption from relative 
values obtained by Pliicker: 

Water.— 10-65 x IO “ 6 

Sulphuric acid (spec. grav. 1*839) . — 6-8 x io~ 6 

\ Pogg. Ann. vol. xciv. 


Chap. VI.] 


Magnetism. 


125 


Mercury.. 33.5 x IO -e 

Phosphorus.— 18-3 x io~® 

Bismuth.- 250 x 10 6 

From an observation by Weber, the value of k for bismuth 
is about — 16 *4 x io -6 . 

These figures are given to show very roughly the relative 
value of magnetic and diamagnetic action ; they cannot be 
relied upon as even approximately true. Different observers 
give different relative values of k, differing twenty for the 
same substance. It must also be remembered that they 
are intended to indicate the value of k for equal volumes, 
not equal weights, of the substances. 

§ 21 . It follows from equation (6) above, that the attrac¬ 
tion between a magnet and its keeper or armature is propor¬ 
tional to the square of the intensity of the magnetisation, and 
therefore in an electro-magnet to the square of the current 
multiplied into k. 

It also follows that where the intensity of magnetisation 
is the same throughout the mass of iron, the attraction will 
be simply proportional to the cross section of the iron. The 
object of increasing the length of an electro-magnet is to get 
a uniform field and to place the poles so that they do not 
interfere with one another. 

By rounding or pointing the ends of a magnet, a more in¬ 
tense magnetisation is produced at the ends than elsewhere ; 
hence a greater attraction per square centimetre of surface. 

The attraction between a magnet and a keeper is directly 
proportional to the intensity of the magnetism induced in the 
keeper, if the keeper does not by its mass or great intensity 
of magnetisation react on the magnet, altering its intensity. 
The relative attraction of a large magnet for small volumes of 
different substances does therefore truly measure the relative 
values of k for each substance, if the volumes are the same 
and the intensity of the magnetic field the same throughout 
all the volume; but these values of k are almost useless 
unless the value of i in absolute measure is also determined. 


126 


Electricity and Magnetism. [Chap. VII. 


CHAPTER VII. 

MAGNETIC MEASUREMENTS. 

§ 1. Before proceeding to study further the laws of the 
action of currents upon currents, it is convenient to examine 
the methods by which the forces exerted by magnets one 
upon another can be definitely measured or expressed in 
numbers depending solely on the centimetre, gramme, and 
second of time. To do this, we require to measure 
two things only: ist, the intensity or strength, T, of 
magnetic field which a given magnet or arrangement of 
magnets produces at a given point. 2nd, the magnetic 
moment, m = ml, of the magnet which is acted upon by the 
assumed magnetic field. Knowing these two quantities, we 
can, in virtue of the laws already stated, calculate the couple 
experienced by the magnet in the field. The simplest expe¬ 
rimental determination of the magnetic strength of a field 
requires that the field shall be sensibly uniform throughout 
the space in which the experiment is to be tried. The 
magnetic field due to the earth is sensibly uniform within 
the space occupied by the experiment, and after giving a 
general description of the magnetic field due to the earth’s 
magnetism, we will proceed to examine how its intensity is 
to be measured. 

§ 2 . The direction of the lines of force in this field is not 
horizontal except at some places near the equator. The 
earth may be (very roughly) conceived as a large bar magnet, 
and Fig. 58 shows that the lines of force are parallel to the 
axis of the magnet only at points half-way between the 
poles. The inclination of the lines of force at any place to 
the plane of the horizon is called the dip or magnetic incli¬ 
nation at that place. If a magnet were suspended by its 
centre of figure, and were free to assume any direction, it 


127 


Chap. VII.] Magnetic Measurements. 

would not remain horizontal, but its axis would lie in the 
direction of the lines of force; in the northern hemisphere 
its north pole would point downwards, and the angle which 
this axis makes with the horizontal plane is the dip or in¬ 
clination. 

The lines of the earth’s magnetic force do not usually 
lie in planes running due north and south. The vertical 
plane in which they lie at a given place is called the magnetic 
meridian of that place; the magnet points to the magnetic 
north. This magnetic north is not any one point, i.e. the 
magnetic meridians at different parts of the earth’s surface 
do not cut at one point as the true meridians do. 

The geographical or true meridian of a place is the plane 
passing through the place and containing the true axis of 
the earth. The angle contained by the magnetic and true 
meridians is called the magnetic declination at that place; 
the declination is said to be east if the north pole of the 
magnet points east of the true or geographical meridian. 
The declination is west if the north pole of the magnet 
points west. The north and south points of the mariner’s 
compass indicate the magnetic meridian. 

§ 3 . The declination and dip, or inclination, not only vary 
from place to place, but also at any one place from hour 
to hour and from day to day. There are some irregular varia¬ 
tions, but there are others which are evidently periodic. 

1. There are secular variations, the duration of which is 
not accurately known. In 1580, the declination at Paris 
was n° 30' E. ; in 1814, this had become 22 0 34' W., and 
since then the needle has gradually returned towards the E.; 
in 1865 the declination was 18 0 44' W. In certain parts of 
the earth the magnetic and geographical or true meridians 
coincide ; these points may be joined by an imaginary line, 
called the agonic line, or line of no variation. 

2. There are annual oscillating variations of declination 
not exceeding 15' or 18', and varying at different epochs. 

3. There are diurnal oscillating variations of declination 


128 


Electricity and Magnetism. [Chap. VII. 

amounting at Paris on some days to about 25, on others 
not exceeding 5'. 

4. There are accidental variations or perturbations said 
to be due to magnetic storms. These variations occur with 
great rapidity, causing deflections to the right and left, com¬ 
parable in their rate or period of alternation with ordinary 
telegraphic signalling; accidental variations of 70' have 
been observed. 

The dip also varies from place to place; it is greatest in 
the polar regions, being 90° at the magnetic pole. At a 
series of points near the equator there is no dip; the line 
joining these is called the magnetic equator. In the southern 
hemisphere the direction of the dip is reversed, the south 
pole pointing downwards. Lines connecting places where 
the dip is equal are called isoclinic lines. 

§ 4 . The total intensity of the earth’s magnetism is the 
intensity measured in the direction of the lines of force at 
the point where the experiment is made. It is difficult to 
make the experiment in this way, especially as the direction 
varies so frequently. The strength of the horizontal 

FlG ^ 5, component is therefore experimentally determined, 
and the direction of the total force. These two ele¬ 
ments give the intensity and direction of the total 
force; for let h (Fig. 65) be the horizontal com¬ 
ponent, R the total intensity, and 0 the dip, then 


§ 5 . In order to determine the effect of any magnet upon 
another or upon an electric circuit, its moment, m = m /, 
must be determined. Two experiments are sufficient to 
determine at once the moment m and the force h. The first 
of these gives the value of the product m h by an observa¬ 
tion of the directing force which the earth exerts on the 

magnet; the second gives the ratio - by an observation of 

H. 

the relative strength of the magnetic fields due to the 





Chap. VII.] Magnetic Measurements. 


129 


magnet and to the earth. The following are the two 
experiments : 

1. Let the magnet be hung so as to oscillate freely in a 
horizontal plane round its centre of figure, being directed 
by the horizontal component of the earth’s magnetism. Let 
the moment of inertia of the magnet relatively to the axis 
round which it oscillates be called i. 1 The quantity 1 is 
easily calculable for any regular figure, and can, moreover, 
be directly determined by experiment. Let the magnet now 
be allowed to oscillate freely, and let the number of com¬ 
plete or double oscillations per second be n ; then 


In Rankine’s ‘Applied Mechanics,’ (§ 598) we have, equation (5), 
1 = 4?r - -, where M x is the moment of the couple causing gyra¬ 


tion, i x the semiamplitude of gyration in angular measure. Let us call F 
the force of the couple due to the magnetic field ; the arm of the couple 
will be i x L, where L is the distance between the poles; hence 
M i = fi L F; but the moment of the couple due to magnetism when 
the magnet stands straight across the magnetic field is M H, and the arm 


of the couple being then L, the force must be then and always —— = F.. 

1 . 4.7T 2 11 1 i, 1 Air 2 n 2 1 

or F l = m H; hence m 2 — t x M H= 3-L_ or m h = -Q. e. d. 


g 


2 . To obtain fix n s with its axis perpendicular to 


the magnetic meridian, and observe the deflection which 
it causes on a short magnet n s freely suspended so that 
when in the magnetic meridian the prolongation of its axis 
bisects nos (Fig. 66). The deflection 6 of n s will depend on 
the relative magnitudes of h and the field produced by n s. 


1 Rankine’s ‘Applied Mechanics,’ § 571. I have here taken 1 as 
equal to the weight multiplied into the square of the radius of gyration, 
following Professor Rankine’s example. Many writers define 1 as equal 
to the mass multiplied into the square of the radius of gyration, and if 
this value of 1 be used, the divisor g in equation 2 must be cancelled. 






130 


Electricity and Magnetism, [Chap. VII. 


Let r — o s = o n ; then RI = r 3 tan 0 ... (3) 

H 


Let m be the strength of the poles of the magnet N s; then the force 


which s will exert at 0 on a unit south pole will be — ... in the 

v r 2 


Fig. 66 . 



x o s 


direction s 0 ; the pole N will exert an equal force in 
the direction 0 c. Let 0 a and 0 c represent these 
forces in magnitude and direction; then b 0 =■ T will 
represent the magnitude and direction of the lines 
of force of the magnetic field at 0. We have a o : ob 

= os : N s, or if L = NS; % \ t = r : L; or T = 
r 2 

l m m 
r 3 r 3 

Let M x be the moment of the little magnet, the 
couple due to T tending to turn it out of the magnetic 

meridian will be M, T cos 0 = — cos 0 . The 

r 3 


couple due to H tending to bring it back will 
be m x h sin 0; and when one balances the other 

M . sin 0 m 

as 0 : or — = r 3 - ; or 

H cos 0 * H 


From equations (2) and (3) we have 


h = 2 7 r n 


g r 3 tan 0 


and m = 2 7 x n / tan ^ 

V ^ 


• • ( 4 ) 

• • ( 5 ) 


§ 6. By means of the single experiment last described and 
illustrated by Fig. 66 , the moment m of any permanent or 
temporary magnet can be readily determined if h be known, 
for from equation (3) we have m = r 3 h tan 0 ; h is 
sufficiently constant throughout England, and from year to 
year, to give the value of m with sufficient accuracy for most 
practical purposes. This method can be used for horse-shoe 
magnets or magnets of any shape if care be taken to fix n s, 
the line joining the poles of this magnet, exactly perpendicular 
to the magnetic meridian To do this, suspend the magnet 









Chap. VII.] Magnetic Measurements. 131 

by its centre of figure, and let it take up its position on the 
magnetic meridian. Then noting this position turn the 
magnet through exactly 90° and fix it there. 

§ 7 . In order that the values in the above formulas should 
be expressed in absolute measure, consistent with that 
hitherto adopted, we must be careful to measure 1 in cen¬ 
timetres and grammes. As an example, the moment of 
inertia of a rectangular prism of steel, two centimetres long, 
and with a square section, each side of which measures 
two millimetres, and weighing 1*248 grammes is 
i 2 4- *i 2 

I = 1*248 —— = *00416, 

3 

i 2 -4- - i 2 

-— is the square of the radius of gyration. 1 

3 

To convert the value of h found by the above formulae 
into grammes, divide by the value of g in centimetres 
(981*4 at Glasgow). The mean horizontal component h in 
England for 1862 was 0*175 (centimetres, grammes, seconds) 
in absolute measure. If a free unit pole weighed one gramme, 
it would, under the action of the horizontal component of 
the existing magnetism acquire a velocity of 0*175 centi¬ 
metres at the end of a second. To convert this value into 
English absolute measure (grains, feet), we must multiply it by 
21*69. 

§ 8. The value of 1 for a given magnet or other suspended 
mass of simple form can as above be calculated from 
measurements of its figure and its specific gravity or weight; 
but when the form is complex and the suspended mass of 
various materials, it is better to determine 1 experimentally 
by comparison with a body of known moment of inertia. 
To do this, first observe the time of one complete or double 
oscillation t of the magnet (directed by the earth’s force 
alone), and then add some weight of simple form with a 
known moment of inertia ij, and observe the time t l in 
which the compound body completes an oscillation ; then, if 


Rankine’s ‘ Applied Mechanics,’ § 578. 





32 


Electricity and Magnetism. [Chap. VII. 


n be the number of oscillations per second, t = 


have from equation (2) 
M H 




47T 2 


-t *; 


, . ! _ MH 2 . 

1 + 11 “ ^ 1 ’ 


- and we 
n 9 


or 



; whence 
. . ( 6 ) 


The method by which the value of t [or the line 0 fr\ was 
calculated in § 5 enables us to determine the intensity of the 
field at any point due to a magnet, so soon as the moment m 
and length / are known. The action of each pole on a unit 

pole at the distance r will always be equal to — = ‘ 2 ; 

and by compounding the forces due to each pole we obtain 
the resultant in direction and intensity. 

The magnetic moments of two magnets of known mo¬ 
ments of inertia 1 and I, can be compared by means of their 
times of oscillation t and t x in the same magnetic field ; 
it follows from equation (2) that 

M : M > = : • • • (7) 

Similarly, the horizontal intensity of two magnetic fields 
can be compared by observing the times t and t x required 
for a complete oscillation of any given magnet in the two 
fields : 

h : Hj = /j 2 : / 2 . . . (8) 

In making this experiment, we must not assume the 
constancy of any given magnet even for two successive 
days. 

§ 9 . In calculating the effects of a real magnet, we must 
never forget, that although we may experimentally deter¬ 
mine the value of m /, we cannot really separate m from /, 
because we can never feel certain that the length / is equal 




Chap. VIII.] Electro-magnetic Measurement, 133 

to the length of the magnet, or to any given fraction of it. 
If the material were uniformly magnetised, i.e. if it would 
form a number of absolutely equal magnets when cut up 
into a number of absolutely uniform pieces, then, indeed, the 
length / would be the exact length of the magnet. In any 
actual magnet the strength of magnetisation is found to fall 
off near the ends, and this makes l shorter than the length 
of the magnet; moreover, the distribution of electricity is 
such that the magnetic field produced by it is different in 
many respects, from that which could be produced by poles. 


CHAPTER VIII. 

ELECTRO-MAGNETIC MEASUREMENT. ACTION OF CURRENTS 
ON CURRENTS AND ON MAGNETS. 

§ 1. The series of units described in Chapter V. would 
suffice for all electrical purposes, but they are not very well 
adapted for the calculation of the effect of electric currents 
upon one another, or upon magnets. 

We obtained the set of electrostatic units from a series of 
equations which did not involve the forces acting between 
currents and magnets ; starting from the measurement of 
these latter forces, we obtain a distinct system of units, 
which will be termed electro-magnetic units, from a series of 
equations which do not involve the forces of electrostatic 
repulsion and attraction. Electro-magnetic units are more 
commonly used in telegraphy than electrostatic units. In 
Chapter VI. § 12 a definition of the unit current was sug¬ 
gested, depending on the force with which a current acts on 
a magnetic pole. According to this definition, the unit 
current is such that every centimetre of its length acts with 
unit force on a unit magnetic pole at a distance of one cen¬ 
timetre from all parts of the current. To obtain this last 



134 


Electricity and Magnetism . [Chap. VIII. 


condition the wire conveying the current must be bent in a 
circle, at the centre of which hangs the free magnetic pole. 
The force (/) exerted on the pole of a magnet in its 
neighbourhood is proportional to the magnetic strength ( m ) 
of the pole of the magnet, and to the strength of the cur¬ 
rent c; and if the conductor be at all points equi-distant 
from the pole, the force is proportional to the length 
of the conductor l. It is also inversely proportional to 
the square of the distance k of the pole from the conductor, 
and is affected by no other circumstances. Hence we have 

/=T * * ‘ W 


from which c = *L— , giving the definition of the unit 
Lm 

current stated above. 

§ 2 . Let us use the capital letters Q, I, R, c, and s to 
indicate the quantities in electro-magnetic measure which 
were indicated by q, i, r, c, and s in electrostatic measure; 
then, taking the unit of current as determined by the 
equation in § 1, we have, from the equations Q = c /, 

i = —, r = — , and s = — , a complete new^series of 

q c i 

units bearing a definite ratio to the electrostatic units; by 
experiment it has been found that c = 28,800,000,000 c. 
This numerical coefficient will be termed v. 


C= - 1 

q = 2 

i — vi 

1! 

V 1 

V 





. The above series of equations express the relations be¬ 
tween the numbers expressing electrical magnitudes in the two 
series of units ; they all follow directly from the fundamental 
equations. The relations of the electro-magnetic units to 
one another, and to the mechanical units may be summed 
up as follows : The unit current conveys a unit quantity of 
electricity per second across any section of the circuit. The 
unit current will be produced in a circuit of unit resistance 






Chap. VIII.] Electro-magnetic Measurement. 135 

by the unit electromotive force. The unit current in a con¬ 
ductor of unit resistance produces an effect equivalent to the 
unit of work per second. Lastly, the unit current flowing 
through a conductor of unit length will exert the unit force on 
a unit pole at a distance of one centimetre. It is this last 
condition which is peculiar to the electro-magnetic series. 

§ 3 . Let a very short magnet n j(Fig. 67), say £ inch in length, 
be freely hung at the centre of a circular 
coil a, of considerable relative diameter, 
say 18 inches, and let the plane of the 
coil be placed in the magnetic meridian, 
then the value c in electro-magnetic 
measure of any current passing through 
the coil and deflecting the magnet 
through the angle 0, is given by the fol¬ 
lowing expression: 

c = tan e ... (2) 

L 

where h is the horizontal component of the earth’s magnetism 
and l is the length of the wire forming the coil. All dimen¬ 
sions must be in centimetres if h is measured in the units 
already adopted. 

From this equation we see that the current will be pro¬ 
portional to the tangent of the angle of deflection, and a 
galvanometer of this construction is therefore called a tangent 
galvanometer ; moreover, knowing the value of h, we shall, 
with tangent galvanometer, be able directly to measure 
currents in absolute measure, independently of any know¬ 
ledge of the magnetic moment of the needle employed, and 
independently also of any peculiarity in the instrument used. 
A current so measured in Australia is therefore at once com¬ 
parable with a current measured in England. 

The resultant electro-magnetic force (/) exerted at the centre of a 

C L 

circular coil of radius k, by the current c, will by equation 1 be/= — : 

the two poles of a short magnet hung in the centre, with its magnetic 
axis in the plane of the circular coil, will experience equal and opposite 


Fig. 67. 







136 


Electricity and Magnetism. [Chap. VIII. 


forces, each equal to f m, where in is the strength of each pole of the 
magnet. If / be the distance separating these poles or forces (equal 
sensibly to the length of the magnet), then the magnet experiences what 

is termed a couple, the moment of which \sfml= C L n 


& 


Let N s 


Fig. 68. 


*;■.. 

< 


i \ 






*- Si 

\£' 




|° 






f'3 

c 

J 



y s 


xs now cos 0 


c L m l 


be the plan of the magnet (Fig. 
68) as it hangs in the plane of 
the coil of wire, and let N x Sj, 
making an angle 6 with N s, be 
any new position which it takes 
up under the influence of the 
current. Then, supposing the 
magnet to be small compared 
with the diameter of the coil, 
the poles remain sensibly at the 
centre ; the force f remains the 
same, but the perpendicular dis¬ 
tance N x c between the poles on 
which the equal and opposite 
forces are exerted is now equal 
to / cos 0, and hence the couple 

This couple is opposed by the directing couple 



due to the earth’s magnetism. Let us call H the horizontal component 
of the earth’s magnetism at the place in question ; then the force due 
to its action on each pole will be H m; the perpendicular distance s x c 
separating the two parallel forces will be l sin 0, and whole couple will 
therefore be sin 0 H m l ; and when the magnet is in equilibrium, under 
the combined forces of the directing current and the earth’s magnetism, 
we have 

cos 0 = sin 0 h m l; whence 

C -SLf iL* = tan 9 . 

COS 0 L L 


§ 4. All the relations between force and currents of a given form and 
strength may be deduced mathematically from the following theory, 
due to Ampere. 1. The force with which two small lengths or elements 
of currents act upon each other is in the direction of the line joining the 
centres of these elements, and this force is inversely proportional to the 
square of the distance between the elements. 

2. Let there be two short wires m n and m x n x (Fig. 69), parallel to one 


















*37 


Chap. VIII.] Electro-magnetic Measurement . 


another, and perpendicular to the line d joining their centres. Let 
the current c flow through m n, and c x through m x n x ; then the force 
with which these two little elements of currents attract one another if 
flowing in the same direction or repel Fig. 69. 

\ I.*.I 1 


one another if going in opposite direc¬ 
tions is x 


d 3 


n 


3. If the two short wires be placed as in Fig. 690, so as to lie in the 
direction of the line d joining their centres, the force acting between 
them is half the above: it is a repulsion if 

the currents flow in the same direction, an Fig. 69a. 

attraction if they flow in opposite directions. VHH. .-i?- 

4. If the two short wires be placed so as to 

be both perpendicular to the line d, but so that m n is also perpendicular to 
m x n u as in Fig. 69^, then the currents neither attract nor repel one another. 

5. If one element lies along d, and the other is perpendicular to it, 
the currents neither attract nor repel one another. 

6. Let A B (Fig. 69^) be any short wire con¬ 
veying any current 1 
to the short 
current c x . Let the line d join the centres of " 

a B and A x Bjl ; draw the line x x in the direction of d and draw y x per¬ 
pendicular to x lt and of such magnitude that the resultant of two forces 
y x and x x would be equal to the current c lf and lie in the direction 
a x Bj. On a similar plan draw y parallel to y x , and draw x and 2, 
rectangular components such that if y, x, and z were forces, their re- 


Fig. 69 b. 


rrent c in any direction relatively ' 7 t ^ n x 

wire Aj Bj, conveying another •... 7 ^ 


Fig. 69 c. 



sultant would be equal to c, and lie in the direction a b. Then 
the resultant action of the current in A b on the current in A x B 1} will 
be the sum of that of the three currents^, x, and z on the two currents 
y % and x x . We may observe that this reduces itself to the sum of the 
action of x on x 1} which we can calculate from 3. above added to the 
action of y on y 1} which we can calculate from 2. above: for z is 
inoperative on y X} y does not attract or repel x x , nor does y x attract 














138 Electricity and Magnetism. [Chap. VIII. 


or repel x. In dealing with wires of any considerable length, the 
action of each little element of one wire on all the elements of the other 
must be taken into account, and the results summed. This summation 
or integration gives the results detailed in the following paragraphs; 
and these results, being confirmed by experiments on closed circuits, 
establish the truth of the theory as applied to closed circuits. 

It follows from the above theory, that the action of a small closed circuit 
at a distance is the same as that of a small magnet having its axis placed 
perpendicularly to the plane of the current, and having a moment equal 
to the product of the current into the area encompassed by the circuit j 
thus, if the circuit be circular, the moment of the magnet will be C ir k 2 . 
Let two small circles, with radii k and k lt be placed at a great distance 
D from one another, in such a manner that their planes are at right 
angles to each other and that the line D is in the intersection of the 
planes. Let an equal current c circulate in each of these conductors; 
forces will act between them, tending to make their planes parallel and 
the direction of the currents opposite; these forces will produce a 
couple, of which the moment will be 


M 


C ir k ? x C tt k-f 
D® 


( 3 ) 


If now, M, D 3 , 7r k 2 ,7 r ki 2 be all made unity, this will give a value for the 
unit of current C, which will be the same as that founded on the action 
between a current and a magnet. It also follows that the unit current 
enclosing a circle of unit area will produce the same couple on a magnet 
at a distance as would be produced by a small magnet of unit moment. 

§ 5 . We found one means of measuring the strength of a 
current by comparing the magnetic field it produced with 
the horizontal component of the earth’s magnetism h. We 
may determine or measure the strength of a current in the 
same units by measuring the action between different parts 
of the current itself as determined by Ampbre’s theory. 

Let a coil of wire a be hung inside a larger coil b (Fig. 70), 
and so directed by means of its suspension that, when no cur¬ 
rents pass through the two coils, the plane of a is perpendicu¬ 
lar to that of b. When one and the same current is allowed 
to flow simultaneously through a and b, they experience a 
deviating couple proportional to c 2 , and depending for its 
absolute value on the value of the diameters k and k x of 
a and b, and on the number of turns v and v x in these 



Chap. VIII.] Electro-magnetic Measurement. 139 


coils. If the plane of the coil b be so turned that, when 
the current is passing, the plane of a lies in the magnetic 
meridian, then the only couple tend¬ 
ing to bring a back into its original 
position will be that due to its sus¬ 
pension. Then calling the deflec¬ 
tion or angle between the planes 
of the coils 0 , expressed in circular 
measure, we have 

c = A / “ ° j r • • • W 

V cos 6 

where a is a constant, varying in 
different instruments, but which for 
any one instrument can be found experimentally or deter¬ 
mined once for all by the maker. This method was first 
employed by Weber, and the instrument is called Weber’s 
Electro-Dynamometer. 


Fig. 70. 



Let us call the directing couple G and the deviating couple M. When 
the coil A is in equilibrium, m = g. The value of G depends on the 
mode of suspension ; if it be by a single wire, the torsion varies simply 
as the angle of deflection 6 , or 

G = fi e . . . ( 5 ) 
where u stands for the expression 

4 « 2 1 _ 4 *- 2 1 _ 4 *1 /*) 

g gi> ‘ V ' 

in which the several letters have the same meaning as in Chapter VII. 
§ 8 ; I being now the moment of inertia of the suspended coil instead of 
the suspended magnet, and i x the moment of inertia of a mass of simple 
form added to determine experimentally the value of 1. 

The value of the deflecting couple is given by the equation 
M = f 3 c 2 cos e . . . (7) 


in which B is a constant determined by Ampere’s theory. Let k be the 
radius of the large coil B, k 1 the radius of the small coil A. Let k xx be 
the distance from the centre of coil a to the periphery of coil B ; k lx = k 
when the coils have a common vertical axis ; let v be the number of turns 

of wire in the large coil; v the number of turns in the small coil, then 

b 3 

B _ 11 _... ( 8 ) 

2 V v z/ k l k x * v 1 








140 Electricity and Magnetism . [Chap. VIII. 

Since M = G from equations (7) and (5) we have 


C = 


y 


fl e 

fj. cos Q 


( 9 ) 


The values of and fx are evidently constant for any one instrument. 

If the suspension is bifilar, equations (5) and (6) must be modified : 
we then have 

G = u sin Q . . . (10) 

and 



where w x is the weight of the added mass and w the weight of the 
coil A. 

Then from equations (10) and (7) we have 

C = A tan 0 • • • (12) 

for both cases, where 0 is small, 

C = v/T7 

0 being in circular measure. 

§ 6. The following is another method, due to F. ICohl- 
rausch, of measuring currents in absolute measure by means 
of a tangent galvanometer and a single coil suspended by 
two wires. 


Fig. 71 . 



A 


Let a coil a (Fig. 71) of k radius and n turns be hung by a 
bifilar suspension, with its plane perpendicular to the plane 









Chap. VIII.] Electro-magnetic Measurement. 


141 


of the magnetic meridian. Observe the deflection 0 pro¬ 
duced in this coil by the current c and the simultaneous 
deflection produced by the same current on the needle 
of a tangent galvanometer b of radius k l9 then 

C= a/ tane. tane, . . . (13) 

The coil A, when the current c flows through it, is equivalent to a 
magnet of the moment C n tt k 2 ; and calling H the horizontal com¬ 
ponent of the earth’s magnetism, the couple experienced by the coil 
when deflected through the angle 0 will be H C n ir k 2 cos 0 . The 
directing couple due to the bifilar suspension is n sin 0. Hence, when 
the one balances the other, 

H C nir k 2 cos 0 = n sin 0 

and c = --—— tan 0 . . . (14) 

H . n 7r k~ 

The value ot [l can be found as by the last section. From this 
equation alone we might find c in terms of H; but we have also, 
calling 0 X the deflection produced by the same current c passing through 
the tangent galvanometer of radius k Xi 


hence, eliminating H, we have equation (14) as given above (eliminating 
C, we might find H from the same equations). It should be observed 
that n tt k 2 is more strictly the sum of the areas enclosed by the turns 
of different diameter of which the coil is composed. 

§ 7. Let a current traverse two wires in succession, each 
bent so as to enclose a circle of the radius k. Let these 
wires be hung in parallel planes at the distance a, with their 
centres in the same axis. Then, if the current be sent 
round the wires in the same direction, they will attract one 
another; if in the opposite direction, they will repel one 
another with a force 

f = 4 tt c 2 | . . . (15) 

If two coils, each containing n turns, be thus hung, the 
force with which they attract or repel each other will be 

F n = 4 tt n 2 c 2 j . . . (16) 






142 


Electricity and Magnetism. [Chap. VIII. 



hence, knowing the current, we can determine the force, or, 
weighing the force, can measure the current. 

By placing two fixed parallel coils, a and b, opposite each 
other, as in Fig. 72, and passing a current round them in 

opposite directions, we 
obtain a sensibly uni¬ 
form field of magnetic 
force between the flat 
coils. If a third flat coil p 
be hung between them it 
will be attracted by one 
and repelled by the other, 
and a good electro-dy¬ 
namometer may be con¬ 
structed on this principle. 
The actual value of the 
current corresponding to a given couple experienced by the 
suspending wires e and /, indicated by the torsion of a wire, 
is experimentally determined once for all by comparison with 
a standard instrument. A second suspended flat coil D t is 
required to make the system independent of the earth’s 
magnetism, and this coil Dj may advantageously be placed 
between two more fixed flat coils 
arranged so as to double the couple 
experienced by the suspended system. 

§ 8. The intensity of the magnetic field 
produced by a circle at any point B on an axis 
perpendicular to the plane of the circle is 
given by the following formula : 

Let A c (Fig. 73), the radius of the circular 
conductor, be = k. Let C = the current. 
Let a b = x. Let F = the intensity of 
the field. 
tt c k 2 


Fig. 73. 



(& + * 2 )t 

At a, the centre of the coil, the intensity is 

_ 2 T C 

T >"— ' • 


(17) 


(18) 










143 


Chap, viii.] Electro-magnetic Measurement . 

Let an insulated wire be wound round a cylinder of the length 2 /, 
forming a spiral. Let the distance of the point M (Fig. 74) from the 


Fig. 74. 



nearest end of the cylinder = mo = a. If the point were inside the 
spiral, a would be affected with the negative sign. 

Let the line joining an element of a spiral with M = e. 

Let the number of turns be n, then the intensity of the magnetic field 
at M is 

t = c v n ( a + 2l _ a ^ 

l \ a/ & + {a + 2 If V JP + a 2 ' 

Let the angle A M o — \f/, and the angle B m o = ; then 

C if n , , , . 

T = —j— (COS </> — rf/j). 

This applies to inside as well as outside, remembering that cos 
will be negative inside the spiral, so that we have virtually cos + 
+ cos 

The force is at a maximum in the centre. 

Call the diagonal of the spiral 2 d; then the intensity of the magnetic 
field at the centre will be 

„ 2 C 7 v 11 

m ^ 

If the length of the spiral be 40 times its diameter, the intensity of 
the magnetic field does not vary by one per cent, throughout £ of its 
length, and not 1 per cent, throughout of its length. 

§ 9 . A long spiral of insulated wire of small diameter 
relatively to its length is commonly called a solenoid, 
although, strictly speaking, this name applies only to a series 
of perfectly parallel and equal rings all perpendicular to a 
common axis and in all of which an equal current is flow¬ 
ing. The material representation of the solenoid differs 
experimentally little from its hypothetical type. We have 
seen that a current flowing round a circle or a series of 












144 


Electricity and Magnetism . [Chap. VIII. 

circles in one plane acted upon a magnetic pole or upon an 
electric current at a distance as if it were a short magnet of 
the moment c n tt k' 2 , where n is the number of turns. 

If a solenoid beginning at a were very far prolonged 
towards b, it would act on all points 
within a finite distance of a, as if at a 
1 IflftiMMtiMfflfW B there was a magnetic pole of the strength 
c n 7r £ 2 , in which n is the number of 
turns in the solenoid per centimetre. 

An actual solenoid acts as if two such endless solenoids 
were superposed, having the same current flowing through 
them in opposite directions; one beginning at a and the 
other at b. Then we should have one north pole, say at a, 
and one south pole at b, and all the rest of the turns 
cancel one another; hence the magnetic moment of 
the solenoid is c n k k 2 l, where l is its length. 

If keeping the actual number of turns constant we 
shorten the length l, we increase n just as we diminish l, 
so that the moment does not vary. 

Imagine a watch hung in a solenoid in such a position 
that the current circulates with the hands of the watch. 
Then the south pole will be at the end towards which the 
face of the watch is turned. 

§ 10 . If a magnet be hung with its north pole downwards 
over the centre of a vertical solenoid in which the current 
is circulating in the direction of the hands of a watch 
(looking at spiral and watch from above), then the north 
pole will be attracted when outside the solenoid, as if by 
a south pole; it will continue to be sucked into the solenoid, 
even after entering in it, although the force with which it 
is pulled down will diminish. The south pole of the 
magnet is repelled upwards, but with less force than the 
north pole is sucked downwards. When the centre of the 
magnet has reached the centre of the solenoid, the magnet 
will be in equilibrium so far as magnetic forces are con¬ 
cerned ; if allowed to fall further, the magnetic forces will 


145 


Chap. VIII.] Electro-magnetic Measurement. 


resist the motion, and if the current be powerful enough, 
these forces will carry the weight of the magnet and prevent 
it from falling further. 

Feilitsch made the following experiment, showing how 
the force diminishes, using a magnet io*i centimetres 
long, 2-03 centimetres diameter, weighing 23-678 grammes, 
and a spiral or solenoid of 126 turns, 29-5 centimetres long, 
and 12*9 centimetres internal circumference. The following 
table gives the distances a of the centre of the magnet from 
the centre of the spiral, and g the force in milligrammes : 



The poles of the magnet when in equilibrium inside the 
solenoid are placed relatively to the spiral, as if the spiral 
had magnetised a piece of soft iron of the same length. Soft 
iron is therefore drawn in just as the magnet would be, and 
the' north pole of the soft iron corresponds to the north pole 
of the solenoid. 

§ 11 . A hollow magnet does not in this respect resemble 
a solenoid. 

If the north pole of a magnet a were introduced into the 
interior of a hollow magnet b at its south pole, a would be 
repelled from b after it had penetrated to a very short 
distance ; and if a rod of soft, iron was placed inside a hollow 
steel magnet, the north pole of the magnet would induce a 
south pole in the end of the iron next it. 

This experiment proves conclusively that we cannot re¬ 
gard a magnet as simply produced by a series of currents 
. circulating round its exterior periphery; but 
it agrees with the hypothesis that the 
magnet consists of an immense number of 
little solenoids lying side by side. In fact, 
conceive a number of such solenoids, side 
by side, the end views of which are shown, 
as in Fig. 76, with the current flowing in 
the direction shown by the arrows, then all the elements of 

L 


Fig. 76. 



146 Electricity and Magnetism. [Chap. VIII. 

each little circuit inside the ring would move in the direc¬ 
tion followed by the hands of a watch; all the elements 
outside would move in the opposite direction. On a point 
at y the former would be most powerful; on a point at x, 
the latter; the radial currents counteract one another, for 
there are as many in one direction as in the other. 

§ 12 . For general purposes, we may regard a solenoid as 
equivalent to a magnet, so far as regards all points outside 
of the cylinder; the effect of introducing soft iron into the 
interior of the cylinder is to make the field of force outside 
the cylinder, more intense. It may thus become as much as 
about 32-8 times more intense than before. The direction 
of the lines of force is very little altered. Fig. 77 shows 


Fig. 77 . 



Fig. 7 8 . 



roughly the field of force due to a solenoid, Fig. 78, the field 
of force after a soft iron wire has been introduced. The soft 
iron wire concentrates the lines of force near the poles, 
and thus over a limited space enables the current passing 
through the solenoid to produce very powerful effects; its 
action in this respect is somewhat analogous to that of a 
lens used to concentrate light on a spot where illuminating 
action is required. 







Chap. IX.] 


Electro-magnetic Induction . 


H7 


CHAPTER IX. 

MEASUREMENT OF ELECTRO-MAGNETIC INDUCTION. 

§ 1 . A description of the principal phenomena of magnetic 
induction has already been given, and we will now con¬ 
sider how to estimate numerically the effects produced 
under various circumstances. 

Electro magnetic force .—When the intensity of a given mag¬ 
netic field produced by a magnet or by electrical currents, 
has been determined, the induced current produced in a con¬ 
ductor moving in that field is easily determined. Every part 
of the conductor moving in a field and conveying a current 
(induced or not) is acted upon by a force perpendicular to 
the plane passing through its own direction and the lines of 
magnetic force in the field. This force is equal to the 
product of the length of the conductor into the strength of 
the current in electro-magnetic measure, the intensity of the 
magnetic field, and the sine of the angle 
between the lines of force and the direc¬ 
tion of the current. Thus, if a b (Fig. 

79) be the element of the conductor, 
and the lines of force be in the plane 
of the paper as dotted, then the direc¬ 
tion of the force due to the field and 
current is perpendicular to the plane of 
the paper. Let the intensity of the magnetic field = t, 
the strength of the current in a e = c, the angle a b c = a, 
and f = the force. 

Then / = tc x ABsina . . . (1) 

The force is exactly the same as if the conductor, instead 
of being of the length and in the direction a b, were really 
of the length and in the direction a c. Let a b (Fig. 80) 


Fig. 79. 



0 B 







148 Electricity and Magnetism. [Chap. IX. 

represent a piece of the conductor in which a current c is 

flowing from a to b. Let d o 
be the direction of the lines of 
magnetic force so that a mag¬ 
net n s would place itself in the 
field as shown in the figure. 
The force f experienced by the 
conductor will tend to lift it 
perpendicularly to the plane 
a o d. Let fo represent in 
magnitude and direction the 
current c and d o the magni¬ 
tude and direction of the intensity of the magnetic field, 
then f per unit of length = tc sin a, but c sin a = the 
perpendicular distance from EFtooD and t =* do; hence 
the area of the parallelogram efod= /per unit of length- 

A current flowing from east to west is lifted by the earth’s 
magnetism. The following is a rule by which to remember 
which way the magnetism of any field would impel any cur¬ 
rent. Place a corkscrew perpendicular to the plane efod 
and turn it, as shown by the arrow s, from the direction of 
the current to the direction in which the north end of the 
compass needle would point, the screw will then move in 
the direction of the force. 

§ 2 . Electromotive force. —If the conductor a b is moved 
along the plane in which ofed lies, its motion is perpen¬ 
dicular to the forces acting upon it, and no work is done 
either by or upon a b. When this is the case no induced 
current can be produced in a b, either in augmentation or 
diminution of the original currents, for no work is done by 
the motion or required to produce the motion; a current 
can only be increased by the exertion of energy upon it, and 
diminished by expending its energy. 

If, however, the conductor moves in the direction o h 
(Fig. 80), or across the dotted lines in a direction perpen¬ 
dicular to the paper (Fig. 79), the motion is either helped 







Chap. IX.] Electro-magnetic Induction. 


149 


by the force or opposed by it. To move the conductor 
against the force, we must do work. The measure of this 
work is the product of the force into the distance moved 
against it. If the conductor moves obliquely across the 
lines of force it is resisted with a force proportional to that 
component of the motion which is perpendicular to the lines 
of force, and the work done is equal to the force multiplied 
into this perpendicular distance. 

The work done on the conductor is found by observation 
to be represented by an increment or diminution in the cur¬ 
rent flowing through that conductor; now the work done 
by a current is by definition equal to e q = e c /, where 
e = the electromotive force acting between the ends of the 
conductor. 

If a unit length of the conductor be moved a distance l 
across the lines of magnetic force in a field of intensity h, 
the work done will be /l = c h l : hence, as the work done 
by the current must be equal to the work expended in 
moving the conductor, we have ec/ = chl 

or e = iHl . . . (2) 


Now — is the velocity with which the conductor is moving, 


so that the electromotive force per unit of length is equal to 
the intensity of the magnetic field multiplied into the velo¬ 
city of the motion. 

This law still holds good if the motion be oblique to the 
lines of force, provided l be the component of the motion 
perpendicular to those lines; and if the conductor a b was 
also oblique to the lines of force, the unit length must be 
measured perpendicular to those lines of force. Thus, let 
the direction of the lines of force in a magnetic field be 
represented by o cq ; let (Fig. 81) a b be perpendicular to o o { 
in the plane a o o t , let a a and b b be perpendiculars let fall 
from a and b on the line a b, and let ab be moved to 
the position a 2 b 1} so that po 1( perpendicular to the plane 


ISO 


Electricity and Magnetism, [Chap. IX. 

a o o 1? represents the distance a b has moved across the 
lines of force ; then the e. m. f. due to the motion will be 
h x a b x p oj ^ 
t 

Fig. 82. 



Observe that the unit electromotive force will be produced by 
a rod of unit length moving with writ velocity across a field of 
unit intensity. 

§ 3 . Let there be two fixed rails c d and e f (Fig. 82) in 
a plane perpendicular to the lines of magnetic force oo,. Let 
the bars a b and 1 k, perpendicular to the lines of magnetic 
force, complete a closed circuit abik, round which a current 
might circulate. Then if ab be moved downwards with 
the velocity v, the electromotive force due to induction will 
be h x a B x v; but this product is equal to the number 
of lines of magnetic force subtracted from the area of the 
closed circuit per unit of time ; hence, calling this number n, 

we find that the e. m. f. = The direction of the current 

produced by this e. m. f. would be such as to oppose the 
motion, i.e. from a to b. If 1 k were moved at the same 
rate in the same direction there would be an equal e. m. f. in 
it, tending equally to produce a current from 1 to k, and this 
















Chap. IX.] Electro-magnetic Induction. 151 


would balance the e. m. f. in a b, so that no current would ✓ 
flow. In this case the motion of i k would add just as many 
lines of force to those crossing the area a b c d as the motion 
of a b would subtract, so that the total number n added or 
subtracted would be nil, and the electromotive force on the 
whole would also be nil. 

If i k moves fastest, its electromotive force would be 
greatest, and the difference between the e. m. f. in i k and in 

a b would be equal to Nl , calling Nj the number of lines 


cut by i K during its motion; the current would then run 
round the parallelogram from i to k b a. Similarly, if a b 

N — Ni 

moved fastest there would be a resultant e. m. f. = —-— 


sending a current from a to b k i. Hence in both cases the 
e. m. f. in the current would be equal to the number of lines 
of magnetic force added to or subtracted from the area per 
second. Now it follows from the principles developed in the 
previous paragraph that this is true not only of this simple 
case but of all cases whatever. Let the circuit be of any 
shape whatsoever and moved in any direction, the e. m. f. 
tending to send a current round the circuit due to motion 

in a magnetic field will be 

§ 4 . An apparatus for showing the phenomena or in¬ 
duction with a fixed pair of rails would be extremely difficult 
to construct; the motion could not be continued for any 
length of time, and the resistance in the 
circuit would vary at each moment, as 
the stationary portion was shortened 
or lengthened during the motion of the 
bar. Let a closed circuit (Fig. 83) rotate 
in a uniform magnetic field, and for sim¬ 
plicity sake let us suppose the field uni¬ 
form, the circuit circular, and the axis 
perpendicular to the direction of the lines of magnetic 





152 


Electricity and Magnetism. [Chap. IX. 


force. Let the rotation be in the direction of the hands 
of a watch held with its face upwards ; let the direction 
of the lines of magnetic force be perpendicular to the 
plane of the paper, and such that a north pole would 
be impelled from the spectator down through the paper. 
Consider the short elements a b and c d, which are sen 
sibly parallel to the axis and perpendicular to the lines 
of magnetic force. When these are just crossing the 
plane of the paper they are moving in the direction of 
the lines of magnetic force, and a current in them would 
neither be assisted nor resisted ; but when the circle has 
made a quarter of a turn they are crossing the lines of 
force at right angles. If the current in a b is descending, 
the motion of ab will be resisted by the lines of force, for 
a descending current in ab would impel a north pole in 
front of the paper from right to left, and would therefore 
itself be repelled from left to right. (The north pole must 
be in front of the paper to give lines of force which would 
repel a free north pole from the spectator to the paper.) 
Hence while a b crosses the lines of force an e. m. f. is 
produced in it, tending to send a current downwards. The 
same is true of each element in all the semicircle mabn, the 
e. m. f. diminishing in each element proportionately to the 
sine of the angle between the element and the lines of 
force. Next, consider the element CD. This is simul¬ 
taneously crossing the same lines of force in the opposite 
direction. This motion would be resisted by an upward 
current; hence the electromotive force in the semicircle 
n d c m will be from n towards m or upwards through this 
half of the circle. 

Thus in both halves of the circle the e. m. f. tends to 
produce a current moving from m to a b, n, d c, and back 

to M. 

This electromotive force will evidently be strongest at 
all points of the circle when this is crossing the lines of 
force at right angles, i.e. when the plane of the circle is in 


Chap. IX.] Electro-magnetic Induction . 153 

the direction of the lines of force. It will begin feebly as 
the circle in its rotation leaves the position sketched and 
advances as shown by the arrow, for at first the inclination 
of the direction of each element to the lines of force will be 
small; and again, after reaching its maximum, this inclination 
diminishes until it becomes nil after half a turn has been 
made. During the next half-turn, while mabn is behind 
the paper, the e. m. f. will tend to send current up from a to 
m through b a; the direction of the current will therefore, 
during this half-turn, be reversed in the material circuit. 
Relating to a fixed exterior point, the current is, however, 
always in one direction, though varying from zero to a 
maximum at every half-revolution. The circuit might evi¬ 
dently be not a single circle but a coil of wire. The e. m. f. 
would increase with the length of the coil. If, however, the 
only resistance be that of the coil, the current will be 
constant whatever number of turns were taken, for the 
resistance will increase in the same proportion as the elec¬ 
tromotive force. If some exterior constant resistance be 
connected with the coil, by sliding contacts near the 
axis, the current will be larger with many than with 
few turns. 

There is no difficulty in calculating the exact electromotive 
force due to a coil of any given shape rotating in any mag¬ 
netic field, except the mathematical difficulty of summing 
up the different e. m. f. in all the different elements of the 
coil at each moment, or, what comes to the same thing, 
determining the value of n during the motion. 

It is now clear that the electromotive force produced by 
the motion of a closed Circuit in a magnetic field of known 
intensity can be expressed in terms of that intensity and of 
velocity only; this measurement gives the value of the e. m. f. 
in absolute electromagnetic measure. We have also seen 
how to measure the value of any current c in the same 

measure, and since r = - in any circuit, the resistance r 
c 


154 


Electricity and Magnetism. [Chap. IX. 




of that circuit can be experimentally determined by measur¬ 
ing the values of e and c. When the resistance of a single 
circuit has been thus ascertained, a material standard coil 
equal to some multiple of the absolute unit can be prepared 
by comparison with this experimental circuit. When this 
has been done once for all, the resistance of other conductors 
can be easily determined by comparison with this standard. 
The following statements describe the experiments by which 
such a standard has been prepared. 


§ 5. Let us consider a circular coil of radius K rotating with an 
angular velocity A in a field of the intensity H. Then during each half¬ 
revolution the number n, equal to it k 2 H, will be alternately added and 
subtracted. Every addition and subtraction tends to send a current in 
the same direction relatively to an external point. Let n be the number 


added and subtracted per second will be 4 tt k 2 h x — = 2 A k 2 h. 

2 T 


of turns per second, then n = —, and the total number of lines of force 

27 T 


The e. m. F. due to this will be 2 A k 2 h, and the equivalent current 

2 A K 2 H 

produced-, where R is the resistance of the circuit. If there be 

R 

m turns the length of the wire in the coil L = 2* Km, and the area 
enclosed = it K 2 m = The number of lines added per second ex¬ 


pressed in this manner will be — L K and the current = ALKI !. This 

TT IT R 

current may be measured on a stationary electrodynamometer or gal¬ 
vanometer, and when it has been thus measured in absolute measure 
the only remaining unknown quantity is R. 

§ 6 . The determination of R by this method requires a knowledge 
of the intensity of the magnetic field H, and a contemporaneous measure¬ 
ment of the absolute value of a current. 

These two observations can be dispensed with by hanging, accord¬ 
ing to Sir William Thomson’s method, a small magnet in the centre of 
the rotating coil and observing its deflection. The induced currents 
will all deflect this magnet in the direction of the rotation of the coil; 
the couple exerted on a magnetic needle of the moment m l, when 

deflected to die angle d, will be EEE m / C os d. The equal and 

4 K 2 R ^ 






Chap. IX.] Electro-magnetic Induction . 15 5 

opposite couple exerted by the earth’s magnetism will be H m l sin d; 
hence 

tan d = TA. or 

4K 2 r 

r = —- 2A — . . . (3). 

4 K 2 tan d 

This gives a simple expression for the resistance of the circuit in 
absolute measure in terms of known and simple magnitudes. In prac¬ 
tically making the experiment several corrections have to be introduced, 
as for the inductive effects of the magnet on the coil. The experiment 
was carefully carried out by a committee of the British Association, and 
the absolute resistance of a certain standard determined in this way serves 
to determine the absolute resistance of any other circuit. 


§ 7 . When the induction takes place, not in consequence 
of the motion of a wire in a magnetic field, but in con¬ 
sequence of the sudden creation of a magnetic field, as 
when a neighbouring current is suddenly commenced, the 
effect is exactly as if the wire had been suddenly moved 
from an infinite distance to its actual position on the new 
magnetic field. The electromotive force is in this case also 


equal to 


2., where n is the additional number of lines of 
t ’ 


magnetic force introduced into the circuit in the time t; 
when the induction takes place in consequence of the cessa¬ 
tion of a current, the electromotive force is in the opposite 


direction, and is equal to - ; where n is the number of lines 
t 

withdrawn. If / be made very small, the e. m. f. tending to 
produce an induced current may be indefinitely increased ; 
and similarly if a current can be made to reach its full strength 
in a very short time, it will produce an e. m. f. in a wire close 
beside it much greater than that required to produce the 
original current. The wire in which the inducing current 
circulates, is often called the primary wire; the one in 
which the current is induced is called the secondary wire. 

§ 8. In order to determine the electromotive force 



156 Electricity and Magnetism. [Chap. IX 

produced in a secondary circuit by the commencement or 
cessation of a current c in a primary circuit, we require to 
calculate the number n of lines of force produced, cutting 
the surface inclosed by the secondary circuit. (Of course 
lines of force going in opposite directions through the 
surface must be reckoned positive and negative, and their 
addition made accordingly.) This number n divided by t 
gives the electromotive force. It is extremely difficult to 
determine /, for no current begins instantaneously, and the 
laws of its increase are extremely complex. The fact that 
the current is employed to induce a current or currents in 
secondary conductors, increases t. The statical induction, 
when sensible, increases /, and magnetisation due to 
currents increases t. The actual determination of the 
e. m. f. in any secondary circuit will not be here attempted, 
but the notions given serve to show how we may increase 
or diminish this e. m. f. in designing inductive apparatus. 

§ 9 . I have now shown how, theoretically, resistance, elec¬ 
tromotive force, and currents can all be measured in abso¬ 
lute electro-magnetic measure. Quantity can be measured 
either by observing the total current which it produces 
when flowing away, for which purpose a simple method 
will hereafter be given, depending on the use of galvano¬ 
meters, or it may be measured by observing its electro¬ 
static effects, and being then known in electrostatic measure, 
it may be converted into electro-magnetic measure by mul¬ 
tiplication into the constant 28,225,000,000. Capacity is 
obtained by observing the quantity which the given con¬ 
ductor contains when electrified to a potential e. Theo¬ 
retically, therefore, we may be said, while studying the laws of 
electro-magnetic induction, to have discovered how it is pos¬ 
sible to measure all electrical magnitudes in this series of 
units. The practical methods adopted will be described 
hereafter. 

§ 10 . The examples given of the modes of calculating 
induced currents in the two simple cases of a straight bar 


Chap. IX.] Electro-magnetic Induction. 157 

moving across a uniform field, and a circular coil rotating 
in such a field, serve to show how all similar problems must 
be attacked. The exact solution of them requires mathe¬ 
matical analysis of the highest kind ; but correct views of 
the general nature of the effects to be expected are very 
readily obtained from the general elementary propositions 
now laid down. Thus it is easy to examine whether the 
electromotive force in some parts of the circuit is acting in 
a direction opposed to that in others; if so, it is easy to see 
that to reduce the opposing action we must reduce the 
velocity of those parts, and place them in the weakest por¬ 
tion of the magnetic field, while the efficient portions of the 
circuit must be placed in the strongest portions of the field, 
and made to move with the greatest velocity. The best 
direction of motion is also easily ascertained. The general 
effect of adding * to the length of the wire or coil in which 
induction is taking place is also easily perceived, and the 
object of making the coil of materials which have but little 
electrical resistance. Increasing the thickness of the wire 
does not at all increase the electromotive force, but inas¬ 
much as it diminishes the resistance, a thick and short wire 
may give a very considerable current, if outside the moving 
coil there be no considerable additional resistance to over¬ 
come. But if we desire a considerable or even sensible 
current through an external wire of great length, or of great 
resistance, then our inducing coil must be long in order to 
give great e. m. f., and in such a case its internal resistance 
will not greatly diminish the current, because it will not 
greatly increase the resistance of the whole circuit. If cur¬ 
rents of very short duration are required, we may move oui 
coil or wire rapidly across a magnetic field of small size but 
great intensity, whereas if a current of longer duration is 
required, the motion must be prolonged, and it will be neces¬ 
sary to have a large magnetic field. 





158 


Electricity and Magnetism. 


[Chap. X. 


CHAPTER X. 

UNITS ADOPTED IN PRACTICE. 

§ 1. In the last chapter I have described the manner in 
which the strength of a current may be measured in electro¬ 
magnetic measure. The method, although not offering any 
extreme difficulty, is yet too complex for continual use, 
and currents will certainly not be commonly expressed in 
this manner, until electrodynamometers are habitually sold 
of such construction that by simply multiplying the observed 
deflection into a constant number, the strength of the 
current is obtained. 

The direct measurements of electromotive force and of 
resistance in the same series of units are still more com¬ 
plex. It is unnecessary that each electromotive force or 
resistance should be directly measured in absolute measure 
by these complicated methods. A standard of electrical 
resistance approximately equal to one thousand millions 
of absolute units of resistance (centimetre, gramme, second) 
has been prepared by a committee of the British Associa¬ 
tion. This standard is an actual wire of the required re¬ 
sistance. The measurement of any other resistance' x 
in absolute measure consists, therefore, in a comparison 
of x with this standard or a copy. The process in this 
case is the same as that of measuring length in mbtres. 
Theoretically the measurement of a length a; in metres 
means the comparison of a with a certain diameter of the 
earth; practically it means the comparison of x with a 
measure authorized by Government to be called a mbtre. 

§ 2 . The standard of resistance has been called an ohm , 
and is now in common use. 

Gauges of electromotive force ought for similar reasons to 
be issued, and might be of various forms. Thus the gauge 
might indicate a given difference of potential in virtue of the 


Chap. X.] Units adopted in Practice. 159 

attraction which two opposed plates exert on one another, 
or, even more roughly, in terms of the distance at which 
sparks pass across air between two given balls. There can 
be no doubt that within a few years gauges of this kind 
will be issued with the same authoritative stamp as attaches 
to the ohm. Meanwhile electromotive force or difference 
of potential is often expressed in terms of the electro¬ 
motive force produced by the special form of voltaic 
battery known as the Danielbs cell. The e. m. f. of this 
cell is about 100,000,000 absolute units, centimetre, gramme, 
second, and is fairly uniform. A much better standard of 
electromotive force is the cell introduced by Mr. Latimer 
Clark, and described by him as follows, (Proceedings R. S. 
No. 136, 1872) : ‘The battery is composed of pure mercury 
as the negative element, the mercury being covered by a 
paste made by boiling mercurous sulphate in a thoroughly 
saturated solution of zinc sulphate, the positive element 
consisting of pure zinc resting on the paste.’ ‘ Contact with 
the mercury may be made by means of a platinum wire.’ 
‘The element is not intended for the production of currents, 
for it falls immediately in force if allowed to work on short 
circuit. It is intended to be used only as a standard of 
electromotive force with which other elements can be com¬ 
pared by the use of the electrometer, or condenser, or other 
means not requiring the use of a prolonged current.’ The 
electromotive force of this cell is, in electro-magnetic units, 
i*457 xio 8 (centimetre, gramme, second), or 1*457 xio 5 
(metre, gramme, second). There is already a unit of 
electromotive force in practical use called a volt. The volt is 
intended to represent io 8 absolute units, centimetre, gramme, 
second ; the e. m. f. of Latimer Clark’s cell is 1*457 volt. 

The capacity of a given conductor can be determined in 
absolute measure with less trouble than either the electro¬ 
motive force or the resistance, and condensers of the 
approximate capacity of 10,000,000,000,000 or 10 13 absolute units, 
and called microfarads , are in common use. 



160 Electricity and Magnetism . [Chap. X. 

§ 3 . We thus find that in ordinary electrical measure¬ 
ments, even when we require to calculate the relations 
between forces, work, or heat and electrical magnitudes, we 
need only compare these electrical magnitudes with known 
standards, these standards having been chosen with 
distinct reference to the units of force and work. To the 
ordinary electrician it is therefore much more important to 
know how to compare accurately one resistance with an¬ 
other, one current with another, and so forth, than to be 
able to determine resistances or currents in absolute mea¬ 
sure. Indeed, when an electrician is said to measure a 
current or a resistance, it is this comparison with a re¬ 
cognised unit, which is in all cases understood. The 
unit employed is important only so far as it is widely 
adopted and allows a more or less ready application of 
the measurement in formulae, involving other electrical 
magnitudes. The series of units most generally adopted in 
Great Britain have received distinctive names, and are all 
based on the absolute system. They are, however, all 
multiples or submultiples of the absolute units, which are 
themselves of inconvenient magnitudes. 

§ 4 . The unit of resistance is termed an ohm and = io 9 
absolute units (centimetre, gramme, second). 

The unit of electromotive force is termed a volt = io 8 
absolute units. 

The unit of capacity is termed a farad = -^absolute unit. 

The unit of quantity is that which will be contained in 
one farad when electrified to the potential of one volt: 
it has no distinctive name, and may be called a farad 
also. 1 This unit of quantity = y 1 ^ absolute unit. The 
absolute units referred to throughout are those based on the 
centimetre, gramme, and second. There is a strong objec¬ 
tion to the use of the words absolute unit, inasmuch as they 
do not indicate the series of fundamental units on which 

1 Mr. Latimer Clark calls it a Weber. 


Chap. X.] Units adopted in Practice . 161 

the derived unit is based. The volt, farad, and ohm are 
free from this ambiguity. 

The unit of current is one farad per second; it is one- 
tenth of the absolute unit of current, and is frequently 
termed for brevity a farad, just as in speaking of velocity 
we often speak of a velocity of ioo feet, the words per 
second being understood. 

§ 5 . Inasmuch as the electrician deals with magnitudes 
differing in greatness very widely from one another, it is 
convenient to use multiples and submultiples of the above 
units, each having its appropriate name. 

The megavolt = one million volts. 

„ megafarad = „ farads. 

„ megohm = „ ohms. 

Similarly, 

The microvolt = one millionth of a volt. 

„ microfarad = „ „ farad. 

„ microhm = „ of an ohm. 

The following table (p. 162) gives the value of each unit 
in three systems of absolute units, in which the mbtre, 
centimetre, and millimetre, and in a fourth in which the milli¬ 
gramme is substituted for the gramme, are respectively made 
the basis or starting-point. 

When we require to convert measurements expressed to 
absolute units based on any given system of fundamental 
units into absolute measurements based on some other 
system, it is necessary, in order to calculate the multiplier or 
divisor to be used for the conversion, that we should know 
what are called the dimensions of the units. In other words, 
we must know at what power each fundamental unit enters 
into the particular derived unit ; thus, in the case of velo¬ 
city, which is perhaps the simplest derived unit, the dimen¬ 
sions are said to be-, or a length divided by an interval 
T 

of time, because the magnitude of the unit is directly pro- 

M 


162 


Electricity and Magnetism. [Chap. 



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Chap. X.] 


Units adopted in Practice . 


163 


portional to the magnitude of the unit used to measure 
length, and inversely proportional to that of the unit used 
to measure time. Similarly the absolute unit of force is 
directly proportional to the unit of length and the unit of 
mass employed; it is inversely proportional to the square 
of the unit of time used; hence the dimensions of the unit 

of force are 

When we wish to convert a measurement expressed in 
absolute units based on the units l, m, t, (say foot, grain, 
second) into an absolute measurement based on some other 
system of units /, 7/2, /, (say metre, gramme, second), we 

require to know the ratios of the actual mag- 

l m t 

nitudes of each pair of units. Thus in the example chosen 

T 


j = °' 3 ° 48 , ^ = -0648, j = 1 ; 


then to effect the conver¬ 


sion from English to French measure we must multiply the 
number expressing the measurement in English measure by 
each ratio raised to the power at which the corresponding 
letter appears in the expression for the dimensions of the 
unit. If the power is negative, we divide by the ratio 
instead of multiplying; thus to convert a velocity expressed 
in English measure into a velocity in French measure, we 
multiply by 0*3048, and divide by 1 : to convert a measure 
of force (foot, grain, second) into French measure we multi- 


ply by 


•3048 X *0648 _ 

(lp 


01975- 


The following table of dimensions and constants is taken 
from the British Association Report on Electrical Standards 
1863. 

Fundamental Units. 

Length = L. Time = T. Mass = M. 

Derived Mechanical Units. 

7 =* k!^ 1 . Force = F = kkL Velocity - v - k. 

T 2 T 2 j T 


Work 


M 2 



164 


Electricity and Magtietism. 


[Chap. X. 


Derived Magnetic U?iits. 
Strength of the pole of a magnet 
Moment of a magnet .... 
Intensity of magnetic field 


m = L* T ~1 
ml = T "1 

H = L“i T "1 


Electro-magnetic System of Units. 


Quantity of electricity . 
Strength of electric current . 
Electromotive force 
Resistance of conductor 


. Q = L* 

. C = i 3 T~l 
. E = L$ T “2 M* 
. R = L T "1 


Electrostatic System of Units. 

Quantity of electricity . 

Strength of electric currents .... 
Electromotive force ..... 
Resistance of conductor .... 


q = ii T "1 
c = L$ T “2 m* 
e —■ T "1 

r L~l t 


Table for the conversion of British (foot grain second) system to 
centimetrical (centimetre gramme second) system. 



Number of 
centimetrical 
units 

contained in a 
British unit. 

Log. 

Log. 

Number of 
British units 
contained in a 
centimetrical 
unit. 

1. For m ■ . 

0-0647989 

2-8115678 

1-1884321 

I 5-43235 

2. For l, v. r , i& v 
r 

30*47945 

I -4840071 

2*5159929 

•03280899 

3. For F (also fori 
foot grains and > 
metregrammes J 

1-97504 

0-2955749 

1 7044250 

•506320 

4. For w 

60*198 

1 -7795820 

2-2204179 

•01661185 

5. For H and elec 1 
tro - chemical l 
equivalents J 

•0461085 

2-6637804 

I -3362196 

21-6880 

6. For Q, c and e . 

1-40536 

0-1477874 

7 - 8522 I 25 

•711561 

7. For E m q and e 

42-8346 

1-6317949 

2-3682051 

•0233456 

8. For heat - 

0'0359994 

2-5562953 

I '4437046 

27-7782 


British system.—Relation between absolute and other units. 











Chap. X.] 


Units adopted in Practice. 165 


Let v be the ratio of the electro-magnetic to the electrostatic unit of 
quantity = 28-8 x io 9 centimetres per second approximately, and we 
have 


\ C — V c 

' ,-L«| 

r =L r 

1 

V 1 

v 2 


{ 5 } = in London. 

In London {^ e ^ t ot °^ l a f n ram | = 32-1889 absolute units of {^k. 

One absolute f force "1 _ 1 /unit weight "1 , 

unit of \ work J ~ g \ unit weight and unit length J evei 7 w ere * 

g in British system = 32*088 (1 + 0*005133 sin 2 A ), where A = the 
latitude of the place at which the observation is made. 

Heat. The unit of heat is the quantity required to raise the temper¬ 
ature of one grain of water at its maximum density i° Fahrenheit. 

Absolute mechanical equivalent of unit of heat = 24861 = 772 foot 
grains at Manchester. 

Thermal equivalent of an absolute unit of work = *000040224. 
Thermal equivalent of a foot grain at Manchester = *0012953. 
Electro-chemical equivalent of water = *02 nearly. 

Metrical system. Relation between absolute and other units. [Centi¬ 
metre gramme second .) 


One absolute f force "1 _ 
unit of \work j — 


•0010195 { wei 8 ht of a E ramme \ 
centimetre gramme / 


^ p- {SnZr} - 980-868 {“] 


at Faris. 

force. 

work. 


One absolute / force \ _ 1 / unit weight \ 

unit of \ work J “ g \unit weight x unit length i ever ^ vhere ' 

g in metrical system = 978*024 (1 + 0*005133 sin 2 A), where A = the 
latitude of the place where the experiment is made. 

Heat. The unit of heat is the quantity required to raise one gramme 
of water at its maximum density i° centigrade. 

Absolute mechanical equivalent of the unit of heat = 41572500 = 
42354*2 centimetre grammes at Manchester. 

Thermal equivalent of an absolute unit of work = *000000024054. 
Thermal equivalent of a centimetre gramme at Manchester = 
•0000236154. 

Electro-chemical equivalent of water = *00092 nearly. 




Electricity and Magnetism. [Chap. XI. 


166 


CHAPTER XI. 

CHEMICAL THEORY OF ELECTROMOTIVE FORCE. 

§ 1 In Chapter III. § 15, the phenomenon of electrolysis 
was described and water was shown to be an electrolyte; the 
decomposition of water is much facilitated by the addition 
of a little acid, which has the effect of diminishing the 
resistance of the liquid and of allowing a larger current to 
pass from a given battery than would traverse pure water. 
The acid is not decomposed, or, if it is, the elements re¬ 
combine so as never to appear at the electrodes , as the 
metal terminals plunged in the liquid are called. Platinum 
or gold electrodes are used to show the decomposition of 
water ; otherwise the oxygen carried to the positive electrode 
would not be set free, but would oxidise the metal instead 
of appearing in the test tube (Fig. 41). Three or four 
galvanic cells are usually employed to decompose water. 
The electromotive force of one of the usual DanielFs cells 
is insufficient for the purpose, and this we shall be able to 
prove from a consideration of the chemical affinity of the 
materials employed, and of the work required to be done, 
measured in absolute measure. When the tubes are gra¬ 
duated so that the volume of the gases can be measured, the 
apparatus shown in Fig. 41 is called a voltameter. Owing 
to the absorption of gas by the water, neither the true 
relative nor absolute volumes of the gases appear in the 
test tubes. 

With very few exceptions, electrolysis occurs only in 
liquids. Fused saline bodies are electrolytes, and probably 
many fused oxides are electrolytes, but the reoxidation 
takes place so readily that this is not easily verified. 
Conduction through electrolytes is subject to Ohm’s law, 


Chap. XI.] Chemical Theory of Electromotive Force. i 6 y 

so far as is known. Electrolytes apparently conduct very 
small currents without being decomposed. 

§ 2 . Electrolytes are not necessarily decomposed into 
simple or elementary substances. Many electrolytes are 
decomposed into two groups of components; each group, or 
each simple element, is called by Faraday an ion ; with any 
given electrolyte, the same group, or ion, always appears at 
the same electrode, so that ions may be classed as electro¬ 
positive or electronegative; the electropositive ion appears 
at the negative electrode, and the electronegative ion at the 
positive electrode. 

When the electrolyte is changed, an ion may change its 
electrode, and ions can be classed in a list such that each is 
electropositive to all which follow; so that an ion such as 
sulphur, which is electronegative towards hydrogen, is electro¬ 
positive towards oxygen. 

Hydrogen and metals are electropositive relatively to 
acids and oxygen: oxygen is the most electronegative, and 
potassium the most electropositive element. 

§ 3 . The bases of salts may practically be classed as 
electropositive ions. When we decompose salts composed 
of two or of three elements, we find the base at the 
negative electrode and the acid at the positive electrode; 
but this classification is not strictly scientific, for chemists do 
not consider the decomposition of sulphate of potassium, for 
instance, as consisting in the separation of the base potash 
from the sulphuric acid, but rather as the separation of 
potassium from the other constituents of sulphate of potash. 
When, however, the potassium appears at the negative pole, 
it decomposes water and combines with oxygen to form 
potash, while at the other pole sulphuric acid and one 
element of oxygen appear. When the decomposition goes 
on rapidly, oxygen and hydrogen in small quantities do 
appear at each electrode; otherwise they recombine and 
form water. The practical result is that the base behaves as 
an electropositive and the acid as an electronegative ion. 


168 Electricity and Magnetism. [Chap. XI. 

§ 4 . The following table is an electro-chemical series, 
in which the most electropositive materials come last:— 


Oxygen 

Chromium 

Silver 

Manganese 

Sulphur 

Boron 

Copper 

Aluminium 

Nitrogen 

Carbon 

Bismuth 

Magnesium 

Fluorine 

Antimony 

Tin- 

Calcium 

Chlorine 

Silicon 

Lead 

Barium 

Bromine 

Hydrogen 

Cobalt 

Lithium 

Iodine 

Gold 

Nickel 

Sodium 

Phosphorus 

Platinum 

Iron 

Potassium 

Arsenicum 

Mercury 

Zinc 



§ 5 . The quantity of any electrolyte decomposed by a 
current is proportional to the strength of the current and to its 
duration ; in other words, to the whole quantity of electricity 
which during decomposition passes through the electrolyte. 

The weights of different electrolytes decomposed by a 
constant current are in direct proportion to their combining 
numbers. Tables of these numbers are given in all works 
on chemistry. 

It follows from the above propositions that if we know the 
weight of any electrolyte which has been decomposed by 
any known current in a known time, we can calculate the 
weight of any other electrolyte which in a given time will 
be decomposed by any given current. It does not follow that 
a given battery will decompose two electrolytes at such rates 
that the quantities decomposed in a given time are simply 
proportional to the combining numbers ; the resistance of 
one electrolyte may be so different from that of the other, 
that in order to obtain the same current very different 
batteries may be required in the two cases. 

The quantity of each electrolyte decomposed by the unit 
current in a second is perfectly definite and constant; we 
shall denote this quantity by the symbol e, and call it the 
electro-chemical equivalent of the substance. Since the weights 
of the electrolytes decomposed by the unit current are pro¬ 
portional to the combining numbers of the compounds, 


Chap, xi.] Chemical Theory of Electromotive Force. 169 

the weights of the ions appearing at each electrode will be 
proportional to these numbers, and hence, knowing the 
weight of any one ion produced at either electrode by the 
unit current in a given time we can calculate the weights of 
all the others; in other words, we can calculate the electro¬ 
chemical equivalent of each ion, and therefore of all simple 
bodies. The following is a table of the electro-chemical 
equivalents of some bodies expressed in grammes and 
calculated from that of water experimentally determined to 
be -00092; that is to say, the table is calculated on the 
assumption that one absolute electro-magnetic unit of current 
(centimetre gramme second) will in one second decompose 
•00092 gramme of water. 


Aluminium 


•00141 

Iron . 

. -00186 

Antimony . 


•00624 

Lead 

. *01058 

Arsenicum 


•00383 

Magnesium 

. -00123 

Barium 


•00700 

Manganese 

. -00280 

Bismuth . 


•01073 

Mercury . 

. *01022 

Boron 


•00056 

Nickel 

•OO3OI 

Bromine . 


•00409 

Nitrogen . 

. -00072 

Calcium 


•00204 

Oxygen 

•00082 

Carbon 


•00061 

Phosphorus 

•OOI58 

Chlorine . 


•00181 

Platinum . 

•01007 

Chromium. 


•00268 

Potassium . 

. -OOI99 

Cobalt 


•00301 

Silicon 

•OOI43 

Copper 


•00324 

Silver 

. -00552 

Fluorine . 


•00097 

Sodium 

. -00118 

Gold 


•01007 

Sulphur 

•00164 

Hydrogen . 


•00010 

Tin . 

. -00604 

Iodine 


•00649 

Zinc . 

•00342 


§ 6. When a current is passed from metal electrodes 
through an electrolyte and decomposes it, the current per¬ 
forms an action equivalent to the performance of work or 
expenditure of energy—an action which may be measured in 
the units employed to measure energy. Let 1 be the electro¬ 
motive force between the two electrodes, and Q the quantity 
of electricity passing, then the work done by the electricity 







1 70 Electricity and Magnetism. [Chap. XI. 

is, as we know, necessarily equal to 1 q ; and if this energy is 
wholly spent in decomposing the electrolyte, this product 
measures the energy which must be expended on the electro¬ 
lyte to overcome the chemical affinity of the ions. In ex¬ 
pending work in this manner on the electrolyte, we may be 
said to add intrinsic energy to the ions : after being decom¬ 
posed they possess a potential energy in virtue of which 
they can recombine, and during the recombination they 
must manifest in some form the energy given them when 
they were decomposed. They may manifest this energy in 
the form of heat, and if allowed to do so, the total amount 
of this heat of combination must be equivalent to the energy 
expended in decomposing them. Thus, calling 0 the heat 
produced by the combination of a unit of weight of one ion 
with the other, and e the electro-chemical equivalent of the 
first ion, then 0 e will be the heat produced during the 
combination of as much of that ion as would be decom¬ 
posed by the unit quantity of electricity, and j 0 e will be 
the mechanical equivalent of that heat where j is 41572500, 
being Joule’s coefficient, or the number of absolute units 
of work equivalent to the heat which will raise one gramme 
of water one degree centigrade. Thus the equation ex¬ 
pressing the equivalence between the heat resulting from 
the combination of two ions, and the work done in decom¬ 
posing them, will be— 

1 Q = QJ 0 £, 

or 1 = j 0 e.i° 

This equation gives the value of the electromotive force which 
is absolutely necessary to effect the decomposition. If we 
have less electromotive force than this, 1 q can never equal 
Q j 0 £; or the work done by the current, no matter what the 
resistance may be, can never be sufficient to separate the 
weight Q £ of the ion from its electrolyte. If a greater 
electromotive force than this be maintained between the 
electrodes, the decomposition will proceed very rapidly, but 



Chap. XI.J Chemical Theory of Electromotive Force. lyi 

since i q will be greater than q j 0 e, some of the energy of 
the current will be spent otherwise than in decomposing 
the electrolyte. 

§ 7 . If we look on the work done in separating two ions 
as a product of two factors, one factor being the weight of 
one ion m, and the other factor the chemical affinity e, 

then ME=iQ,orE = i_ 

Q 

But the ratio ^ is equal to e ; hence e = i e, or - = i, so 

that the chemical affinity of the ions per electro-chemical 
equivalent is equal to the electromotive force required to just 
decompose the electrolyte. 

§ 8. The ions which by their combination form an electro¬ 
lyte. may generate a current instead of producing heat. If 
the whole energy due to chemical affinity is so employed, the 
value of the energy will, as before, for each electro-chemical 
equivalent e be the product j 0 e. The mechanical equivalent 
of the current produced is i, Qj, where i x and Q x are the 
electromotive force and quantity of electricity produced by 
the combination of the ions ; but the electromotive force 
just required to decompose the ions is exactly balanced by 
the e. m. f. which the combination of the ions can produce. 
In other words, ij = i, and therefore qq = q. Hence the 
electromotive force due to the combination of any pair of 
ions is equal to j 6 e or the mechanical equivalent of as much 
of the chemical action as goes on with the unit of the current 
in the unit of time. 

e may be taken for either ion. 6 e is constant, whichever 
is taken. 

A table giving the values of 0 is required before we can 
calculate from the table of electro-chemical equivalents the 
e. m. f. which any given combination will produce. 

§ 9 . When a series of chemical actions take place in a 
circuit, some of these may tend to produce an e. m. f., the 
others to resist it. We express this fact by saying that the 


172 Electricity and Magnetism. [Chap. XI. 

respective values of 1 for the several reactions may be posi¬ 
tive or negative. The resultant value or actual electromotive 
force tending to produce a current, or to resist decomposi¬ 
tion, is the algebraic sum of all the values of 1. Thus, in 
the galvanic cell known as Daniell’s cell, the electrodes are 
copper and zinc; next the copper there is a saturated solution 
of sulphate of copper, and next the zinc a solution of sul¬ 
phate of zinc. The chemical action is as follows : 1. The 
zinc electrode combines with oxygen. 2. The oxide thus 
formed combines with sulphuric acid and forms sulphate of 
zinc. 3. Oxide of copper is separated from the sulphate. 
4. The copper in this oxide is separated from the oxygen. 

The oxygen of the water is separated at the zinc electrode 
from the hydrogen, and at the other electrode this hydrogen 
recombines with the oxygen from the oxide of copper, 
but this alternate decomposition and recombination of the 
elements of water can neither increase nor decrease the 
e. m. f. of the cell, the actions being opposite and equal. 

1. The heat evolved by the combination of one gramme of 
zinc with oxygen is 1,301 units. 

2. The heat evolved by the combination of the 1*246 
gramme of oxide thus formed with dilute sulphuric acid is 369 
units. 

3. The heat evolved by the combination of the equivalent 
quantity -9727 of a gramme of copper with oxygen is 588*6 
units. 

4. The heat evolved by the combination of 1*221 gramme 
of the oxide thus formed with dilute sulphuric acid is 293 
units. 

The thermal equivalent of the whole chemical action due 
to one gramme of zinc is therefore 1301 + 369 — (588*6 + 
2 93) = 788*4; but we require the thermal equivalent of a 
weight of zinc equal to e, and this we obtain by multiplying 
788*4 into *00342, giving for 0 e the value 2*696 ; next, to 
obtain the value of 1, this product is multiplied by j or 
41572500, and we then obtain for the electromotive force of 


Chap. XI.] Chemical Theory of Electromotive Force. 173 

a DanielPs cell about 112,000,000 units, a value which 
agrees closely with the result of direct experiment. This 
theory and example are taken from Sir W. Thomson’s 
paper in the ‘ Philosophical Magazine’ for 1851. 

§ 10 . The separation of substances into ions which appear 
separately at the two electrodes is a fact made useful in 
many ways. The elements or elementary groups gather 
at the electrodes in a state of great purity, and hence 
the process of electrolysation is made use of to obtain 
pure chemicals. Metals may be deposited in this way on an 
electrode of any form which it is desired to copy. The 
metal copy thus formed is called an electrotype. The nobler 
metals are often deposited on electrodes of baser materials 
for the sake of ornament. These electrodes are then said to 
be electro-plated with the nobler metals. Some substances 
can only be decomposed by electrolysis, and some ions 
can only be maintained in a state of separation while the 
current is passing. 

§ 11 . The passage of an ion from the place where it is 
first decomposed to the electrode appears to take place by 
a series of combinations and decompositions. Thus, when a 
molecule of water half-way between the electrodes is decom¬ 
posed, neither the hydrogen nor oxygen cross the water as 
Fig. 84. 

IkkkkkxjL 

a b c d e f g 

free gases, but the hydrogen of d, shown by the white half of 
the molecule, Fig. 84, combines with the oxygen of c , shown 
by the black half of that molecule. This sets the hydrogen 
of c free to combine with the oxygen of b , and finally 
the hydrogen of b combines with the oxygen of a. , leav¬ 
ing the hydrogen of a free at the negative electrode. A 
similar series of compositions and decompositions leaves the 





£ 74 Electricity dnd Magnetism . [Chap. XI. 

oxygen of g free at the positive electrode. This is shown 
by the fact that ions can be transmitted through materials 
for which they have a strong chemical affinity without com¬ 
bining with them. 



Thus, put a solution of sulphate of sodium into a, Fig. 85 ; 
dilute syrup of violets into b, and pure water into c; pass a 
current from an electrode in c to an electrode in a. The 
sulphate in the vessel a will be decomposed. Soda will be 
found in a, and sulphuric acid, which must have come from 
a, will be found in c. Nevertheless, the colour of the solu' 
tion in b will not have been altered ; whereas the addition 
of a very small quantity of free acid to b will produce a dis¬ 
tinct red colour. 


CHAPTER XII. 

THERMO-ELECTRICITY. 

§ 1 . When the junctions of a circuit made of two metals 
are at different temperatures, a current of electricity gene¬ 
rally flows through the circuit. The electromotive force 
producing this current depends, 1, on the metals employed; 
2, on the difference of temperature between the junctions; 
and, 3, on the mean temperature of the junctions. 

When the mean temperature of the junctions is kept the 
same for circuits containing pairs of metals in various com¬ 
binations, and when the difference of temperatures between 
the junctions is small and constant, the electromotive 





















Chap. XII.] Thermo-Electricity . 175 

force of each circuit depends only on the metals employed. 
Let us call 6 (a b) the numerical factor by which the 
difference of temperature r between the junctions must be 
multiplied to give the e. m. f. of a circuit composed of two 
metals a and b at the mean temperature t, and let us call the 
value of this numerical factor, when t is equal to unity, the 
thermo-electric power of the circuit a b at the temperature t. 
Then, calling $ (a c) and <j> (b c) the thermo-electric powers 
of the pair a and c and of the pair b and c, we find experi¬ 
mentally that (p (b c) = 0 (a c) — <p(a b). This equation ex¬ 
presses the fact that the thermo-electric power of any pair of 
metals is equal to the difference between the thermo-electric 
powers of those metals relatively to some one standard 
metal a. In order therefore to calculate the thermo-electric 
power of any pair of metals it is sufficient that we determine 
experimentally the thermo-electric power of all metals 
relatively to some one metal used as a standard. In what 
follows lead will be taken as the standard metal. 

§ 2 . We call a metal thermo-electrically positive to 
another, when the e. m. f. in a circuit of these two metals 
sends a current from the first to the second across the 
hot junction; the difference of temperatures r being sup¬ 
posed small. It follows from § 1 that the metals may for 
any one mean temperature t be arranged in a series such 
that each will be positive relatively to that beneath it; it 
follows, moreover, that a number may be assigned to each 
metal proportional to its thermo-electric power relatively, 
say, to lead, and such that the algebraic difference be¬ 
tween these numbers for any two metals will express in any 
arbitrary units the e. m. f. of a circuit of those two metals 
when the junctions are at the mean temperature t , but differ 
by a small constant difference r or, say, by unity. The 
thermo-electric series printed in most books give approxi¬ 
mately numbers of this kind, but the experiments on which 
they are based have generally been conducted without 
reference to the condition that the mean temperature t 


176 


Electricity and Magnetism. [Chap. XII. 


should be constant, and this temperature is seldom given. 
The thermo-electric series differs entirely at different tem¬ 
peratures. The following is compiled from Dr. Matthies- 
sen’s experiments, and is such that approximately the ther¬ 
mo-electric power relatively to lead is expressed in microvolts 
per degree Centigrade. % 


Bismuth pressed com- 


mercial wire . 
Bismuth pure pressed 

+ 97 

wire 

89 

Bismuth crystal axial . 
Bismuth crystal equa r 

65 

torial 

45 

Cobalt 

22 

Argentine . 

11 75 

Quicksilver 

•418 

Lead .... 

0 

Tin .... 

_ • j 

Copper of commerce . 

— *i 

Platinum 

- ’9 

Gold .... 

— 1*2 


Pressed Antimony wire 

- 2-8 

Silver pure hard 

- 3 

Zinc pure pressed 

- 37 

Copper galvanoplasti- 


cally precipitated . 

- 3*8 

Antimony commercial 


pressed wire . 

- 6 

Arsenic 

“ I 3-56 

Iron pianoforte wire . 

- I 7'5 

Antimony axial 

— 22*6 

Antimony equatorial . 

- 26*4 

Red Phosphorus 

- 29 7 

Tellurium 

— 502 

Selenium 

— 807 


The mean temperature for which these numbers are 
approximately true may be taken at from 19 0 to 20° Centi 
grade. 

$ 3 . Any two metals joined by a third metal so as to form a 
circuit have an e. m. f. equal to that which they would have 
had if directly joined, provided both junctions with the third 
metal are at one temperature; thus in Fig. 86 the three 
circuits all have the same e. m. f.— that due to zinc and 
antimony alone. The copper wire might be replaced by 
any complex arrangement of substances without interfering 
with the e. m. f. of the circuit, provided the junctions 
were all at one temperature, except those intended to be 
effective. Thus the e. m. f. of a thermo-electric pair—such as 
zinc and antimony—may be tested by observing the current 
flowing through a complex circuit composed, for instance, 
of the copper wire of a galvanometer having brass terminals! 




Chap. XII.] Thermo-Electricity. 177 

and of German silver resistance coils. We must, however, in 
such cases test the equality of the temperatures at the other 
junctions by observing whether any current is produced 
when the thermo-electric element is removed, and the 
copper, brass, and German silver connections joined so as 
to make an independent circuit exactly similar to that 
1 previously used except as regards the removal of the zinc 
and antimony, or other thermo-electric pair. 


Fig. 86. 



§ 4 . The thermo-electric powers of different combinations 
not only change with a change of mean temperature, but 
they change in very different proportions. Thus the 
thermo-electric power of copper-silver differs little for tem¬ 
peratures between o° and ioo°, but the thermo-electric 
power of iron-copper varies rapidly ; so rapidly, indeed, 
as to fall to zero at about 23o°, and then again to increase, 
but with the opposite sign ; so that whereas copper is posi¬ 
tive to iron below 230°, it is negative to iron above that 
temperature. It follows that, if we are to possess accurate 
knowledge as to the thermo-electric relations of metals over 
a considerable range of temperatures, we must have suffi¬ 
cient knowledge to construct such a diagram as is shown in 
Fig. 87, where the vertical ordinates indicate temperatures 
in degrees Centigrade, and the horizontal ordinates the 
thermo-electric powers in microvolts of the metals relatively 
to lead. 


N 


























Chap. XII.] Thermo-Electricity. ijg 

This diagram may be looked upon as simply one mode of 
tabulating the thermo-electric powers of metals relatively to 
one another at different temperatures, the horizontal scale 
being so arranged that the distance between the two lines of 
any given metals at any temperature gives the thermo¬ 
electric power of the two metals at that temperature.* 

Thus the thermo-electric power of copper and iron at 50° 
is nearly 11-4, and at 260° is zero, and at 400° it is —7*6. I 
here call the thermo-electric power + when the current is 
from the first-named to the second-named of a thermo¬ 
electric pair across the hot junction. 

§ 5 . For any very small differences of temperature the 
electromotive force of a pair is equal to the product of the 
difference of temperature between the junctions into the 
thermo-electric power, so that the area of a narrow strip 
(approximately a parallelogram) represents this e. m. f. on 
the diagram. When the breadth of this strip is unity, or the 
difference of temperature i°, the electromotive force is 
simply equal to the ordinate or to the thermo-electric power. 
When the difference of temperatures is considerable—say 50° 
—the electromotive force is the same as if we had 5 pairs of 
junctions arranged as in Fig. 88; thus if while a a x were 


5 ° 


6o° 6o° 70* 

3111 


mm. 


Fig. 88. 
70° 8o° 8o° 


zmrnt 


aiiK 



joined we were to complete a circuit by joining the junctions 
b b±, we should in this circuit have an electromotive force 
equal to the parallelogram aa x in Fig. 89, where m n and o p 
represent the thermo-electric lines for copper and iron. 

* The first diagram of this kind was given by Sir William Thomson 
in the Bakerian Lecture on the electro-dynamic qualities of metals, Phil. 
Trans. 1856, p. 708. 






l8o Electricity and Magnetism. [Chap. XII. 

If we now were to break the circuit at a a x > Fig. 88, and 
leaving b b x joined were to join cc x , we should have a circuit 
bb x c x c, in which the e. m. f. would be represented in Fig. 89 
by the parallelogram bb x . Similarly in the circuit dd x cc x , 
Fig. 88, the e. m. f. would be represented by the area c c . in 
Fig. 89, &c. 

Fig. 89. 



Now when a a x are joined, and f f x are joined, and all the 
other cross connections broken, the e. m. f. of the series is 
the sum of all the electromotive forces of each of the little 
circuits a a x b b x , b b x c c l9 c c x d d x , &c., and is consequently 
represented by the area a a 1 f x f in Fig. 89. Thus the 
electromotive force of any pair with the two junctions at any 
two temperatures can be calculated by calculating the area 
enclosed between the two thermo-electric lines of those 
metals, and the ordinates corresponding to the two extreme 
temperatures. 

§ 6. In taking out this area we must, however, observe 
that if the areas to the left of any point where two lines cut 
are called positive, those to the right must be termed nega¬ 
tive, for they represent an e. m. f. tending to send the current 
in the reverse direction. If, therefore, the two junctions are 








Chap. XII.] Thermo-Electricity. 181 

at such temperatures that the areas are equal, no e. m. f. 
will be produced in the circuit. 

The points where the two lines for any metals cut are 
called the neutral points for those metals, because at that 
temperature the metals are neither positive nor negative re¬ 
latively to one another, their thermo-electric powers being 
equal. When the lower junction is so far from the neutral 
point that the triangular area intercepted by the ordinate of 
its temperature is greater than the triangular area cut off by 
the ordinate of the higher temperature, the current will go 
from the metal highest on the scale below the neutral point 
to the other through the hot junction. The direction of the 
current will be the opposite if the triangular area above the 
neutral point is the greatest. 

§ 7 . So far, we have been following Sir William Thomson. 
Professor Tait, led by theoretical considerations, has experi¬ 
mentally proved thatthe thermo-electric linesarein most cases 
approximately straight between o° and 300° Centigrade, and 
probably at much higher temperatures. This greatly facilitates 
the calculation of e. m. f., because the areas to be dealt with 
are simply triangles, or trapezes. Let m be the distance sepa¬ 
rating the lines of the two metals forming the pair at the mean 
temperature of the junctions; let /, — t 2 be the difference 
of temperatures : then m (t x — t 2 ) is the E. m. f. of the 
pair under those conditions, being the area of the trapeze, 
or triangle, above described. It follows from the above, 
that when the mean temperature of the two junctions is 
that of the neutral point, no current will flow through the 
circuit. This gives a means of determining the neutral 
points of metals with great accuracy. Professor Tait has 
also established the curious fact that the thermo-electric 
line of iron, whether pure or commercial, when prolonged 
towards red heat, is a sinuous or broken straight line, so that 
there may be two or more neutral points in one circuit when 
iron or steel is one of the two metals. 

The e. M. f. of any pair may be calculated in microvolts 


182 


Electricity and Magnetism. [Chap. XII. 


from the diagram (Fig. 87), taking the measurement of the 
mean distance between the lines of the metals by the hori- 
lontal scale, and the vertical measurements in degrees 
Centigrade; but it is obviously more convenient to calculate 
than to measure the length of the mean distance between 
the lines, and for this purpose the following table is given, 
containing the tangents of the angles at which the lines are 
inclined. Let k x and k 2 be the tangents for two given 


Prof. Tail's Thermo-electric Table (converted to give E.M.F. in microvolts). 


1 

Metals. 

Neutral Point with 
Lead. 

Degrees Centigrade. 
n 

Tangent ot Angle with 
Lead Line. 
k 

Cadmium . 

-69 

- *0364 

Zinc .... 

-32 

- -0289 

Silver 

- ”5 

— *0146 

Copper 

-68 

— -0124 

Brass 

+ 27 

— *0056 

Lead .... 

_ 

— 

Aluminium 

-113 

+ *0026 

Tin .... 

+ 45 

+ *0067 

German silver 

— 314 

+ -0251 

Palladium . 

—181 

+ *0311 

Iron .... 

+ 357 

+ *0420 


Note .—The straightness of the thermo-electric lines has not been 
verified below o°; hence the table must only be used to calculate 
e. m. f. for couples between o° and 400° or 500 0 Centigrade. 

The metals used were not chemically pure. 

This table is calculated from the iron series in Prof. Tait’s table, 
P* 599- Proc. R.S.E. 1871-72, taking the e.m.f. of a Grove’s cell 
as 1 ‘93 volts. 

metals. Let n x and n 2 bz the temperatures of their neutral 
points with lead. Let t m be the mean temperature of the 
junctions; then the mean ordinate or m is given by the 
formula 

m = k x (n l - Q - k 2 (n 2 - t n ) 

Thus, let the mean temperature of a pair of copper-iron 
junctions be 50°, and the difference of the temperatures of 
the junctions ioo°; then (50 -j- 68) ( — -0124) = — 1-46 is 













Chap. XII.] Thermo-Electricity. I S3 

one portion of the mean ordinate (for copper), and 
(50 — 357) (*042) = — i2’9 is the other (for iron). 
Their difference is 11-43, and this multiplied into ioo° gives 
1143 as the e. m. f. of the copper-iron pair in microvolts. 
When the thermo-electric lines of two metals are nearly 
parallel, the e. m. f. produced by a pair of those metals will 
be nearly proportional to the difference of temperatures 
maintained between their junctions. For metals or alloys, 
the lines of which diverge, no such law even approximately 
holds good, and it is necessary, before the e. m. f. can be cal¬ 
culated, that we should know not only the difference of tem¬ 
peratures, but the actual temperatures of the junctions. 

§ 8. A number of thermo-electric pairs, or elements, may be 
joined in series, so as to give an e. m. f. which is the sum of 
the electromotive forces of all Fig. 90. 

the elements. To do this it 
is only necessary to join the 
metals, as shown in Fig.90, and A 
keep all the junctions on one 
side, as at a, warm while the ^ 
other side is cold. .Batteries-^ 
of this kind are easily made 
with exceedingly small resist¬ 
ance, so that when the other 
resistances in the circuit are also small, considerable currents 
will be produced—-greater currents than could be obtained 
under similar circumstances from a Daniell’s cell of moderate 
size. A bismuth-antimony pair may be prepared having, say, 
an e. m. f. of 100,000 microvolts, or about T V the e. m. f. of a 
Daniell’s cell, while the resistance might be reduced to almost 
any desired extent by increasing the section of each element. 
Thus, if each element were about 2 centimetres in length, 
and a tenth of a square centimetre in section, the resistance 
of the pair would be about 3,370 microhms, and the resist¬ 
ance of 100 such pairs would be 337,000 microhms, or 
•337 ohm, so that through a short circuit they would give 







184 


Electricity and Magnetism. [Chap. XII. 

a greater current than any except the largest sized Daniell’s 
cell. There are thermo-electric pairs which give a much 
greater e. m. f. than the above, but generally the increase in 
e. m. f. is to a great extent counterbalanced by an increase in 
the internal resistance of the pair. 

§ 9 . Thermo-electric currents are produced bynon-metallic 
substances. Metals and fusible salts form powerful pairs, 
which are generally held to be thermo-electric, and Becquerel 
has constructed a battery of the artificial sulphuret of copper 
and German silver, in which the salt is used without being 
fused. 

Thermo-electric currents are also produced in circuits of 
metals and liquids, and probably in simple liquid circuits. 

§ 10 . The chief practical use to which thermo-electric bat¬ 
teries have been put is the measurement of small differences 
of temperature. Melloni introduced this method of ob¬ 
serving changes of temperature. A thermo-electric battery, 
Fig. 91, is connected by the terminals t t x with a galvano- 

Fig. 91. 



meter having a very small resistance; one series of junctions 
n is maintained at one temperature as nearly as possible, 
being enclosed in a metal case; the other series of junc¬ 
tions a is exposed to radiation from the objects the tem¬ 
peratures of which are to be compared. The junctions are 




















Chap. XII.] Thermo-Electricity. 185 

screened by tubes from the radiation of other objects ; 
these tubes are shown removed from the battery in Fig. 91. 

When any substance warmer than the space opposite b is 
allowed to radiate heat upon the junctions a, the galvanometer 
is immediately deflected. When the junctions a radiate heat 
to a colder substance than b, so as to become colder than 
b, a deflection to the opposite side is produced ; for small 
differences of temperature the currents produced are pro¬ 
portional to the differences of temperature. This arrange¬ 
ment is so sensitive, that by its aid the heat radiated by 
the fixed stars has been detected. 

§ 11 . In accordance with the doctrine of the conservation 
of energy, heat is transformed into electricity in the thermo¬ 
electric circuit; the work done by the current is precisely 
the equivalent of the heat so transformed. If the whole 
work of the current consists in heating the conductors, the 
effect is merely a transference of heat by means of elec¬ 
tricity from one part of the circuit to another; so that, in 
accordance with the law of dissipation of energy, the parts of 
the circuit are, on the whole, more nearly at one tempera¬ 
ture than if no current had been produced, and heat had 
merely been conducted along the wires. If the current is 
employed to do mechanical work, an equivalent amount of 
heat is abstracted from the circuit, and reappears in the 
bearings of the working machine and the materials it works 
upon ; similarly a portion of the work done may be electro¬ 
chemical. In whatever form the work is done, in the whole 
circuit this work will be equal to 1 Q § 2, Chap. VIII. 

The heat is transformed into electricity at the hot junction, 
and also at unequally-heated portions of one or both metals. 
Peltier discovered that a current flowing through a circuit of 
two metals heated one junction and cooled the other. Now, 
the current which flows in a thermo-electric circuit flows in 
such a direction in general as to heat the cold junction and 
cool the hot one; so that for some time it was considered 
that the heat producing the current was wholly absorbed at 



186 Electricity and Magnetism. [Chap. XII. 

the hot junction, and given out at the cold junction dimin¬ 
ished by radiation, and by an amount equivalent to the work 
done in the rest of the circuit. 

Sir William Thomson pointed out that this explanation 
was incomplete, for when a junction is at the neutral point 
no Peltier effect can occur ; the two metals are then thermo- 
electrically identical; nevertheless when the hot junction is at 
the neutral point and the other junction at a lower tem¬ 
perature, a current is observed, increasing as the tempera¬ 
ture of the lower junction is diminished, and the direc¬ 
tion of the current is such as to heat the cold junction. 
Heat must therefore be absorbed at other parts of the 
circuit than at either junction. 

§ 12 . We may, perhaps, best conceive qf the manner in 
which this heat is absorbed by considering what would occur 
if a current were passed through a series of metal pieces, 
arranged as in Fig. 92, where each is in succession more posi¬ 
tive than that which precedes it, a being the least and k the 
most positive. If a current is passed from a to k , it will flow 
in the direction opposed to that in which a current would 

Fig. 92. 

abedefghi j k 

l 1 1 1 1 t 1 1 1 I I I 

flow across any of the junctions, if that were the hot junction 
of a circuit made of those two metals, and therefore every 
junction would be heated; whereas if the current were 
passed in the other direction, as shown by the arrow, every 
junction would be cooled. If the Peltier effect at every 
junction were the same, the bar would be heated and cooled 
uniformly ; but if the Peltier effect increased from a towards 
k, then the bar would be unequally heated or cooled by the 
passage of the current. The current in the direction of the 
arrow would cool the bar most near k so as apparently 
to heap up heat towards a , whereas a current in the opposite 





Chap. XIII.] 


Galvanometers. 


IS 7 


direction would heap up heat towards k; in other words, 
in such a bar as this, positive electricity might be said to 
carry heat with it. Now, a copper bar, or wire, with the end 
k cooler than the end a , behaves as if it were composed of 
an infinite number of such little elements ; a current from 
hot to cold heats it and carries heat with it; whereas an 
iron bar behaves as if when the end k were the hotter it 
were the more positive, so that a current from cold to 
hot heats iron. The heaping up of heat in iron goes in 
the direction opposed to that of the current. We see that 
a current from hot to cold in iron absorbs heat, and one 
from cold to hot absorbs heat in copper; and hence, when a 
pair is formed of copper and iron with its hotter junction 
at the neutral point, the current goes from cold to hot in 
the copper and hot to cold in the iron. Hence the copper 
and iron both absorb heat, and the electromotive forces of 
the two are added. With most pairs of metals the e. m. f. 
in the one unequally heated metal is opposed to that in the 
other. In this case the stronger e. m. f. overcomes the 
weaker, and the resultant current is due to the difference of 
electromotive forces. The discovery of the absorption or 
evolution of heat due to the unequal temperatures of metals 
and its convection were predicted from theoretical conside¬ 
rations by Sir William Thomson, who afterwards yerified his 
conclusions by experiment. 


CHAPTER XIII. 

GALVANOM.ETERS. 

§ 1 . A galvanometer is an instrument intended to detect 
the presence of a current and measure its magnitude ; all 
forms of the instrument consist of a coil of insulated wire and 
a magnet freely hung or pivoted so as to be easily deflected 
by the passage of a current through the coil. The wire 
forming the coil is so wound that each turn lies in a plane 
approximately perpendicular to the axis of the undeflected 



188 Electricity and Magnetism. [Chap. XIII. 

magnet. The current, in passing through the coil, or bobbin, 
of insulated wire, produces a magnetic field in the space in 
which the magnet hangs, and the couple tending to deflect the 
magnet is directly proportional to the strength of this field 
and to the moment of the magnet. The opposing couple 
tending to bring back the magnet to its undeflected position 
may be due to various causes. 

In one class of galvanometers the magnet is suspended 
or supported in a horizontal plane, and the opposing couple 
is simply due to the earth’s magnetism. In instruments of 
this class, no increase in the moment of the suspended 
magnet will increase the sensibility of the instrument—that 
is to say, it will not increase the deflection due to a given 
current—for by just as much as the deflecting couple is in¬ 
creased, by so much is the opposing couple also increased. 
The complete magnetisation of the needle therefore is 
not of much consequence, and a change in the magneti¬ 
sation of the needle does not alter the sensibility. A 
small, light magnet will also in this class of instruments be 
deflected through the same angle as a large, heavy one, and 
will have the following advantages : ist. That the small 
magnet will require only a small coil to surround it, and that 
this small coil will for the same number of turns produce a 
more intense magnetic field (§ 8, Chap. VIII.) than the 
large one, and offer much less resistance than the large 
coil, if made of the same wire. 2nd. That the inertia of the 
small magnet being less relatively to the magnetic moment, 
it will reach its maximum deflection more quickly, and will 
come to rest more rapidly than the large magnet. It will 
also indicate transient currents which do not last long 
enough to deflect the large magnet. 

§ 2 . In a second class of galvanometers, the couple oppos¬ 
ing the deflection is due not to magnetism, but to weight. 
The magnet is pivoted in a vertical plane, and has one end 
slightly weighted, so as to hang upright when undeflected. 
In these instruments any increase in the magnetic moment 



Chap. XIII.] 


Galvanometers. 


189 

of the magnet increases the sensibility, assuming the counter¬ 
balance or directing weight to remain constant. Hence in 
these instruments, to ensure the greatest sensibility the 
needles should be magnetised to saturation, but, in order 
to ensure constant sensibility, the magnetism of the needle 
must remain constant, and these two conditions can rarely 
oe realized together. The vertical component of the 
earth’s magnetism exerts a certain directing force on the 
needles, but its effect is usually nearly insensible in com¬ 
parison with that of the weight. These instruments are not 
generally intended for the indication of such small currents 
as those described in § r. With very small magnets it is 
difficult to diminish the friction of the pivots and the counter¬ 
balance proportionately to the diminution of the magnetic 
moment. Hence in some forms of the second class it may 
be disadvantageous to diminish the size of the needle. 

§ 3 . In choosing a galvanometer for any special purpose, 
we must first consider the character of the circuit into which 
it is to be introduced. The introduction of the coil of the 
galvanometer into the circuit will in all cases increase the re¬ 
sistance of the circuit, and therefore diminish the current. If 
ihe coil has a small resistance relatively to that of the other 
portions of the circuit, the diminution of the current will be 
small, and may in some cases be altogether neglected; but 
if the resistance of the original circuit be small, the mere 
introduction of the galvanometer intended to measure or 
indicate the current may reduce that current a thousandfold 
or more. In all cases there is some advantage in using a 
galvanometer coil of small resistance, but in order that a 
small current may produce a sensible magnetic field, it is 
desirable that it be led round the coil as often as possible, a 
condition antagonistic to the former. We can readily see 
that for circuits of small resistance the galvanometer giving 
the largest deflection will be an instrument having a coil 
with few turns of thick wire; but for circuits of large resistance, 
galvanometers having thousands of turns of thin wire will be 


190 Electricity and Magnetism. [Chap. XIII. 

on the whole most advantageous. In some writings these 
two classes of instruments are spoken of as adapted to two 
different classes of currents instead of to two different 
classes of circuits. The instrument with numerous turns of 
fine wire is said to indicate intensity currents, the other class 
to indicate quantity currents. These two old names survive, 
although the fallacious theory which assumed that there 
were two kinds of currents is extinct; the term ‘intensity 
galvanometer ’ is used to signify an instrument with thousands 
of turns'of thin wire in its coil, and ‘ quantity galvanometer * 
an instrument with few turns of thick wire. I shall name the 
two varieties ‘ long coil ’ and ‘ short coil' galvanometers. 

§ 4 . The student must clearly understand that equal de¬ 
flections on the same galvanometer always indicate equal 
currents. These currents may be flowing through very 
different circuits, and any given change may produce very 
different effects in the two circuits; but so long as the 
currents produce the same deflection in the same or equal 
galvanometers, the currents are equal, though the circuits 
may be very different. Thus, using a short coil galvano¬ 
meter having a resistance of, say, o*i ohm, and no 
other external resistance in circuit, a thousand voltaic 
cells in series will produce about the same deflection as one 
cell of the same kind. The thousand cells produce 1,000 
times the electromotive force that one cell does, but the 
resistance of each cell, which we may assume as 4 ohms, is 
much greater than that of the short coil galvanometer. 
Hence, the resistance of the thousand cells added to that of 
the galvanometer will be about 1,000 times greater than that 
of one cell added to the galvanometer, being 4000*1 in one 
case, and 4*1 in the other. The resistance varies in nearly 
the same proportion as the electromotive force, and there¬ 
fore the galvanometer shows nearly the same deflection, 
indicating nearly the same current in the two cases. In 
the example taken above, the thousand cells would give 
a deflection greater than that of the single cell in the 


Chap. XIII.] 


Galvanometers . 


191 

proportion of 41 to 40 nearly. When a long coil galva¬ 
nometer, having a resistance of, say, 8,000 ohms, is em¬ 
ployed, very different results follow. With one cell perhaps 
no deflection is observable, whereas with one thousand cells 
the needle is violently thrown against the stops limiting its 
deflection. The cause is simple. With one cell the resist¬ 
ance of the whole circuit, which will be 8004, including the 
long thin wire of the galvanometer, was so great that the 
e. m. f. of one cell did not give current enough to deflect the 
needle; but when a thousand cells were employed, the 
electromotive force was a thousandfold greater, and the 
whole resistance of the circuit was 8000 -}- 4000, or 12000 
ohms. Hence if the e. m. f. of each cell be taken as one 

volt, the current in the first case will be —- - or nearly 

8004 

0-000125 farads per second; whereas in the second case 

it will be 1000 or 0*0833, or about 666 fold greater. The 
12000 

couple deflecting the magnet of the galvanometer will also 
be 666 fold greater in the second than in the first case. 
Remark, however, that neither current will be so strong as 
that produced when the short coil galvanometer was used; 

for in that case, with a single cell the current would be — 

4*i 

= 0*244 farad per second, or roughly three times that due 
to the thousand cells as above ; nevertheless the couple ex¬ 
erted on the magnet of the long coil galvanometer would 
be far greater with 0*0833 farad than that exerted on the 
short coil galvanometer by 0-244 farad simply because to 
produce the same couple the long coil galvanometer would 
only require about three times as many turns as the short 
coil galvanometer, whereas in practice it would have several 
hundred times more turns. The greatest deflection with 
any given circuit is obtained by using a galvanometer, the 
coils of which have a resistance equal to that of the other 
parts of that particular circuit. 


192 Electricity and Magnetism . [Chap. XIII. 

§ 5 . The sensibility of any galvanometer the needle of 
which is directed by a magnetic field may be increased 
by diminishing the intensity of the magnetic field. The 
opposing couple is due to the intensity of this field, and 
by its diminution the deflection due to a feeble current 
may be indefinitely increased. This diminution of the 
intensity of the original magnetic field is most easily 
brought about by laying a powerful magnet near the gal¬ 
vanometer, in such a position as to counteract the earth’s 
magnetism, i.e. in the magnetic meridian, with its north 
pole pointing north. This magnet, often called a com¬ 
pensating magnet, is best placed in the same meridian as 
the suspended magnet. As the intensity of the field 
diminishes under the influence of this magnet, the rate 
of oscillation of the suspended magnet diminishes, and by 
observing this rate we can determine the increase of sensi¬ 
bility. The period of oscillation is inversely proportional 
to the square root of the intensity of the field, and as the 
directing couple is directly proportional to this intensity, 
and the sensibility inversely proportional to the directing 
couple, we have the sensibility directly proportional to the 
squares of the periods of oscillation. So long as the 
magnetism in the needle of a galvanometer remains un¬ 
altered, its relative sensibility with the compensating magnet 
at different distances can be roughly computed in this 
manner; I say roughly, because the number of swings 
which can be counted is small when the sensibility is great, 
owing to the resistance of the air, and this resistance would 
also necessitate a correction in the above series of propor¬ 
tions. This method of obtaining a sensitive galvanometer 
has the following defect: Inasmuch as the directing field is 
due to a difference between two nearly equal magnetic fields, 
a very small change in the direction or intensity of either pro¬ 
duces a great change in the difference; and as the direc¬ 
tion and intensity of the earth’s magnetism is perpetually 


Chap. XIII.] 


Galvanometers. 


193 


varying, it is nearly impossible to keep the needle pointing at 
a constant fiducial mark or zero, or with a constant sensibility. 

The zero should be adjusted by a much smaller 
magnet called an adjusting magnet, placed across the 
lines of force of the magnetic field or pointing east and 
west, and fixed so as to be capable of adjustment by 
turning in a plane perpendicular to the magnetic meridian, 
and with its centre in the meridian of the suspended mag¬ 
net. This adjusting magnet does not, when turned, alter 
the intensity of the field near the suspended magnet, but 
only alters the direction of the lines of force. 

The suspended magnet in very sensitive instruments should 
be hung by a single silk fibre, such as can be obtained from 
the silk threads in a common silk ribbon. The viscosity and 
torsional elasticity of this fibre put a limit to the possible 
diminution of directing force as described above. 

§ 6. The most sensitive instruments employed are those 
known as Astatic galvanometers. In these instruments two 
magnets joined as in Fig. 93, with the north pole of one 


Fig. 93. Fig. 94 



over the south pole of the other, form one suspended system. 
If the two magnets had exactly equal moments with axes 
precisely parallel, they would hang in equilibrium in any 
direction in any uniform magnetic field. The moment of one 

0 




















194 Electricity and Magnetism. [Chap. XIII 

magnet always slightly exceeds that of the other, and by this 
excess directs the system. A single galvanometer coil may sur¬ 
round one needle, or, as is obviously better, each needle: 
may have its own coil, the two coils being so joined that 
the current must circulate in opposite directions round the 
two so as to deflect both magnets similarly. In one 
common form of the astatic galvanometer, needles about 
a couple of inches long are used, and their deflection is 
observed by means of a pointer or glass needle, a b, Fig. 93, 
rigidly connected with the astatic system by a prolongation 
of the brass rod c d. This pointer oscillates over a gradu¬ 
ated circle, and its position is observed by a microscope or 
simple magnifying glass. The coils are made flat, of the; 
shape indicated in Fig. 93. To allow the introduction of 
the needle, the top and bottom coils are made in two 
halves, placed side by side, with just sufficient space between ] 
them to allow the rod c d to hang freely. 

In Thomson’s mirror astatic galvanometer, Fig. 94, the 
magnets are much reduced in size, being only about £ in. long.! 
They are connected by a strip of aluminium c d, and are fre- j 
quently compound magnets, that is to say, the top magnet is. 
replaced by four little needles, all magnetised to saturation 
and placed with their poles in one direction while the 
bottom magnet is replaced by four similar little neediest 
having their poles also all placed in one direction opposed] 
to that of the upper system ; the coils are made circular ; 
the upper and lower coils are each made in two- halves, 
placed side by side. This arrangement gives the most 
sensitive galvanometer yet constructed. 

§ 7 . A galvanometer with a single magnet directed by any 
uniform magnetic field, and made with a coil large in 
diameter relatively to the length of the magnet hung in 
the axis of the coil, is called a tangent galvanoi?ieter, be¬ 
cause the tangents of the angles to which the needle is 
deflected by the currents are proportional to the currents 
causing the deflections. This law has been proved above, 
§ 3> Chap. VIII. The best form of tangent galvanometer is 


Chap. XIII.] 


Galvanometers. 


195 


that in which there are two coils in parallel planes, Fig. 95, 
separated by a distance equal to one-half their diameter. 
The magnet, which should be short, is hung in the common 
axis of the coils half-way between them. 

The object of this arrangement is to do away with the 
error due to the sensible length of the magnet, and to 
any small deviation from a truly central position. 

The deflection is observed by means of a light glass 
pointer oscillating over a graduated limb. 

§ 8. A galvanometer, whether astatic or not, with mag¬ 
nets directed by any uniform magnetic field, and having 
the coils constructed so as to be capable of turning on 
the axis round which the magnet turns, is called a sine 
galvanometer, because, if the coils be turned by hand so as 
to lie in a vertical plane parallel to that passing through 


Fig. 95. 



the magnet when deflected by a current, then currents 
deflecting the magnet to angles d and 0! will be to one 
another in the ratio of sin 6 and sin 0j : this follows from 
the considerations explained in § 3, Chap. VIII. Sine gal¬ 
vanometers can be easily made much more sensitive than 
tangent galvanometers, because they may be astatic, and 
because the coils may closely surround the magnets. They 
























196 Electricity and Magnetism. [Chap. XIII. 

are inconvenient for many purposes, because an observation 
with them occupies a longer time than with any other 
galvanometer: each adjustment of the coils moves the 
magnet also, and many trials are necessary before per¬ 
fect parallelism of the planes is arrived at. This paral¬ 
lelism is attained by bringing a fiducial mark attached to 
the coils vertically under a pointer attached to the magnet. 
A vernier is attached to the coils, and the angle through 
which they are turned from the position indicated by the 
fiducial mark when no current was passing to that indicated 
by the fiducial mark when the current flows is read off on a 
graduated circle. This can be done with great accuracy. 
The coils are generally moved by a tangent screw. 

§ 9 . The form of the coil in a galvanometer is not a 
matter of indifference. The coil may be too broad and flat, 
or it may be too narrow, to give the greatest intensity of 
magnetic field which can be produced by a given length of 
wire wound into a coil. For a given length and size of wire 
there is always one form giving the best effect. This form 
has only been determined for the simple circular coil used in 
the mirror galvanometer. 

Fig. 96. 



The form of the curve, bounding the best section of the 



















Galvanometers. 


Chap. XIII.] 


197 


coils, is given by the following equation, due to Sir William 
Thomson : 

x 2 = (a 2 y)§ — y 2 

where x is the ordinate measured in a direction parallel to 
the axis of the coil, y the ordinate perpendicular to that axis 
and a the distance O B. The origin of the co-ordinates is at 
centre of the coil, where the magnet hangs. Fig. 96 shows 
the theoretical curve and a longitudinal section of a practi¬ 
cable coil. A portion of the area enclosed by the curve near 
the magnet is necessarily omitted to give room for the magnet 
to move; a practical approximation is made to the best 
form by winding the wire on a bobbin of the proportions 
shown, and filling with wire that portion which is cross- 
hatched. 

Fig. 97. 



To get the best result the wire should not be all of one 
gauge, but should increase with the diameter of the coil, so 
that the cross section of the wire may be directly propor¬ 
tional to the diameter of the coil at each point: the resist¬ 
ance of every turn of the coil will then be equal. It is prac¬ 
tically impossible to follow this plan rigidly, but three or four 
sizes of wire may very properly and easily be employed in 
winding a galvanometer coil. 

§ 10 . Sir William Thomson has given the name oigraded 
galvanometer to an instrument constructed as above, and 
having also a moveable arm or lever by which one of the two 
terminals t, Fig. 97, can be connected by an arm a c , 




198 Electricity and Magnetism . [Chap. XIII. 

hinged at c, with the several stops, 1, 2, 3, 4, so as to 
include in the galvanometer circuit either the whole of 
the wire, or J, or or but in all cases so as to use the 
most efficient part of the wire for the degree of sensibility- 
required. The relative sensibility of each grade is easily 
determined by experiment, and is constant. 

§ 11 . Sir William Thomson has given the name of dead 
beat galvanometer to a mirror galvanometer having the 
following peculiarities :—1. very light mirror; 2. four small 
magnets at the back instead of one of equal weight; 3. 
the cell in which the mirror moves only just large enough 
in diameter to allow the mirror to deflect; 4. the front 


Fig. 98. 

Sectional Elevation. 



and back of the cell so close as each separately to act 
as a stop, preventing deflection of the mirror beyond the 
angle required to bring the spot of light to the end of the 
scale. The mirror does not strike the stops in actual use. 








































Chap. XIII.] 


Galvanometers . 


199 


With instruments so made the spot of light moves to the 
final deflection without oscillation being checked by the 
viscosity of the air. The same end is much less per¬ 
fectly attained in some instruments by a vane of light 
material hanging from the magnet. This vane sometimes 
dips in water, and Mr. Varley has made galvanometers in 
which the cell containing the magnet and mirror is full of 
water. 

§ 12 . The Mar me galvanometer is a galvanometer adapted 
for use at sea. It must be so constructed that neither the 
motion of the ship nor the change of direction produces 


Sectional Plan. 



sensible deflections. This result has been obtained by 
Sir William Thomson in the following way : The magnet 
and mirror of a mirror galvanometer are strung on a 
bundle of straight silk fibres, stretched between a and b, 
Fig. 98. The suspended system is balanced so that the axis 








































200 Electricity and Magneton. [Chap. XIII. 

of the fibres passes through its centre of gravity. A power¬ 
ful directing horse-shoe magnet, not shown in the drawing, 
embraces the coils, and serves to overpower the directive 
force of the earth’s magnetism, the effect of which on the 
suspended magnet is moreover much weakened by a 
massive soft iron case, enclosing the whole system every¬ 
where except at the little window d, by which the rays of 
light reflected by the mirror enter and return. An adjusting 
magnet N s is worked by a ratchet and pinion f. 

§ 13 . The differential galvanometer has two equal coils, 
so arranged that when the same current or equal currents 
pass through the two coils in opposite directions, the 
magnet is not deflected. The effect of one coil is com¬ 
pletely neutralised by that of the other. The differential 
galvanometer is most easily made by winding simultaneously 
two equal wires on the coil. These two wires are sometimes 
arranged in a sort of ribbon or plait, being joined by the 
silk used to insulate them. The accurate equality of the 
magnetic fields produced by the two coils -is easily tested, 
for if a current pass from the battery first round one coil 
and then round the other in the opposite direction, it 
should, no matter how great its strength, produce abso¬ 
lutely no deflection. In most cases a small deflection will 
be observed, but this is easily remedied by adding a few 
turns to the weaker coil. If after this has been done the resist¬ 
ance of one coil exceeds that of the other, a length of wire 
can be added to the coil of least resistance, and placed in 
such a position as not to tend to deflect the magnet; the 
instrument will then be in perfect adjustment. This is a 
very useful instrument, as we shall see in a future chapter, 
for the purpose of comparing resistances. The coils are 
sometimes made of German silver instead of copper. 
German silver has a much greater resistance than copper, 
but its resistance varies much less with changes of tempera¬ 
ture. In differential galvanometers intended to be used in 
circuits otherwise of great resistance, the total resistance of 


Chap. XIII.] 


Galvanometers. 


201 


the coils is of small importance, but the equality of the 
resistance of the two coils is very important. 

§ 14 . The sensibility of a galvanometer may be varied 
! in a very simple manner by the use of what is termed a 
, shunt. A shunt is a resistance coil, or coil of fine wire 
j used to divert some definite portion of a current, taking 
it past a galvanometer instead of through its coils. Thus let 
G, Fig. 99, represent the galvanometer 
coils, and let s represent the shunt. Let c 

the resistance of the shunt be -|th that of 
the galvanometer; then, of a total cur¬ 
rent passing from c to D, 9 parts go 
through the shunt and do not deflect 
! the needle, while 1 part goes through 
the galvanometer: only y^th of the 
I whole current is therefore effective in 
deflecting the needle, and the deflec¬ 
tion (supposing a mirror galvanometer u 

be used) is only y^th of what it would 
j have been had no shunt been used. Similarly by making the 
j shunt equal in resistance to ^th of the galvanometric coil, 

I we reduce the sensibility of the instrument to the y-^th part 
of its original sensibility. Most galvanometers used for 
| measuring currents are now sold with shunts = -Jth, y$th, 
and -g-^th, of the galvanometer coil: by these the sen¬ 
sibility of the instrument can be varied iooofold. The 
shunts must be made of the same metal as is used for the 
coils, and should be placed so as to be as nearly as possible 
at the temperature of the coils. Calling s the resistance of 
the shunt, and G the resistance of galvanometer coil ; 
calling d the deflection without the shunt, and d x the 
deflection with the shunt, we have quite generally, witjj| a 
given constant current and assuming that the deflections 
shown by the instrument are proportional to the currents : 

. d : d Y = G + s : s. 

It must be remembered that adding the shunt will in all 







202 Electricity and Magnetism. Chap. XIII. 

cases diminish the resistance of the circuit, so that unless 
this resistance is so great that the resistance of the galvano¬ 
meter forms no sensible part of it, the deflections will not be 
altered in the above proportion. Let r be the resistance of 
all parts of the circuit except the galvanometer. Then, if 
the E. M. f. remain constant, we have r + G as the total 

resistance when no shunt is used, and r + —2JL when the 

g + s 

shunt s is used. The currents c and Cj will therefore be in 

the proportion of r + - G S ■ to r 4- G; and compounding 
G -f- S 

this ratio with that given above, we have for d and ^de¬ 
flections due to a constant e.m. f. with and without the shunts 
d : d y = r (g + s) + g s : (r + g) s. 

§ 15 . Galvanometers intended for circuits of extremely small 
resistance sometimes consist of a single thick ring of copper. 
The cell or battery used with such a galvanometer as this 
must be of such construction as to have very small internal 
resistance, or no deflection will be observed. A Grove’s 
cell (vide infra, Chap. XIV. § 14) with large plates will give 
a current which can be observed with a single ring galvano¬ 
meter. Galvanometers intended for thermo-electric experi¬ 
ments must have very small resistance, and are frequently 
made with twenty or thirty turns of No. 20 wire Birmingham 
wire gauge, the diameter of which is nearly 0-09 centimetres. 
The resistance of these galvanometers may be less than 
a quarter of an ohm. Galvanometers intended for use in 
circuits of great resistance are frequently made with wire 
of No. 30 or No. 36 b.w.g., corresponding to the diameters 
0*0305 and o*o 106 centimetres, and the resistance of these 
galvanometers is frequently as much as 8,000 ohms. About 
half a yard of the No. 36 gauge copper may have a resist¬ 
ance of one ohm, so that the above resistance would require 
4,000 yards of copper wire. The resistance in itself is a 
defect, but it is impossible to get a large number of turns 



Chap. XIV.] 


Electrometers. 


203 


into a small space without great resistance. It is very im¬ 
portant that every coil of the galvanometer should be per¬ 
fectly insulated from its neighbour : if any two coils touch or 
are connected through the silk, they are, in technical lan¬ 
guage, said to be short-circuited ; the current does not then 
flow round any of the intermediate turns, and the effect of 
these is lost. When there is no actual metallic contact there 
may be imperfect and uncertain insulation, and this is the 
worst defect a galvanometer can have : its resistance becomes 
uncertain and variable; the shunts can no longer be de¬ 
pended upon as equal to definite fractions of the resistance, 
and the instrument is useless for accurate observations. 
The insulated wire should not only be thoroughly covered 
with silk, but should also be baked so as to be very dry 
before being wound on ; and after a few layers have been 
coiled, the bobbin should be baked again and dipped in 
pure melted paraffin. When the.coiling has been completed 
the whole coil should be again baked, and its resistance 
compared with the calculated resistance of the wire wound on. 

Contact between coils of a differential galvanometer is 
obviously a radical defect; and when two or more 
distinct coils are wound on the same bobbin, as is some¬ 
times done, these coils must be very carefully insulated. 
Serious errors in testing have arisen from bad insulation 
between different coils and different parts of the same coil. 


CHAPTER XIV. 

ELECTROMETERS. 

§ 1. Electrometers indicate the presence ofa statical charge 
of electricity by showing the force of attraction or repulsion 
between two conducting bodies placed near together. This 
force, depending in the first place on the quantity of electricity 
with which the conducting bodies are charged, ultimately 
depends on the difference of potential between them; an 



204 Electricity and Magnetism. [Chap. XIV. 

electrometer is therefore strictly an instrument for measnrmg 
difference of potential. It is used often simply to indicate 
the presence of electricity, but it does not measure quantity, 
and when used to compare quantities it can do this only 
because under given circumstances the differences of 
potential produced between the two conductors are propor¬ 
tional to the quantities on the bodies by which one of the 
conductors of the electrometer is successively charged. 

The usual repulsion electroscopes have already been de¬ 
scribed. They are known as the pith-ball or Canton's electro¬ 
scope ; the gold leaf or Bennet’s electroscope and the Peltier 
electroscope. Bohnenberger’s electroscope, which consists of a 
single gold leaf hanging between two symmetrically disposed 
knobs maintained one at a positive potential, and the other at 
an equal negative potential, belongs to a different class, 
called by Sir William Thomson heterostatic electroscopes— 
or instruments in which, besides the electrification to be 
tested, another electrification, maintained independently of 
it, is taken advantage of. In Bohnenberger’s instrument the 
independent electrification maintaining the two knobs at a 
constant difference of potential is produced by a kind of 
galvanic battery called a dry pile, consisting of thin plates 
of two metals soldered together, and separated by paper 
which remains very slightly moist in consequence of contain¬ 
ing some deliquescent material. Sometimes the metal plates 
are replaced by metals in powder adhering to the paper. So 
long as the gold leaf is neither positive nor negative, it is 
neither attracted to the right nor left; positive electrification 
deflects it to the negative knob, and vice versa. 

A modification of Bohnenberger’s electroscope, Fig. ioo, 
may be made, in which the heterostatic charge may with 
advantage be given to the gold leaf, instead of to the two 
symmetrically disposed bodies a and b. Any difference of 
potentials between a and b will be indicated by the attrac¬ 
tion of the gold leaf to one side. The higher the potential 
of the gold leaf the more sensitive the instrument. The 



Chap. XIV.] 


Electrometers. 


205 

high potential is most easily maintained by connection with 
a Leyden jar. 


Fig. ioo. Fig. 102. 



§ 2 . The most perfect form of heterostatic electrometer yet 
constructed is Sir William Thomson’s quadrant electrometer. 
In this instrument the Bohnenberger’s gold leaf is replaced 

















































206 Electricity and Magnetism. [Chap. XIV. j 

by a very thin flat aluminium needle, u, shown in plan, Fig. j 
ioi, and (to a smaller scale) in elevation, Fig. 102. This flat j 
needle spreads out into two wings, shown dotted in the plan, 
and is hung by a wire s from an insulated stem q inside a 
Leyden jar. This Leyden jar contains a cupful of strong 
sulphuric acid, the outer surface of which forms the inner 
coating of the Leyden jar. A wire z, stretched by a weight, 
connects u with this inner coating. 

A mirror, hidden in Fig. 102 by the metal cover /, 
is rigidly attached to the needle u by a rod. The mirror 
serves, as in the reflecting galvanometer, to indicate the de¬ 
flection of the needle u by reflecting the image of a flame 
on to a scale. The needle u hangs inside four quadrants, 
abed , insulated by glass stems, i i l ; the quadrant a is in 
electrical connection with d, and c is in connection with b, 
as shown in plan. Above and below the quadrants two 
tubes, v and u 1 , at the same potential as u, serve to screen u 
and the wires in connection with it from all induction ex¬ 
cept that produced by the quadrants abed. These quad¬ 
rants replace the bodies a and b in the elementary form, 
Fig. 100. Let us suppose u charged to a high negative po¬ 
tential—then, if the quadrants are symmetrically placed, it 
will deflect neither to the right nor to the left, so long as a 
and c are at the same potential. If c be positive relatively 
to a, the end of u under c and a will be repelled from a to c , 
and at the same time the other end of u will be repelled 
from d to b. The motion will be indicated by the motion 
of the spot of light reflected by the mirror. Moreover the 
field of force produced inside the quadrants is sensibly 
uniform just over the narrow slit separating them, so that 
the deflection will be sensibly proportional to the difference 
of potential between a and e. The number of divisions 
which the spot of light traverses on the scale will therefore 
in an arbitrary unit measure the difference of potential 
between a and c. This instrument is therefore an electro¬ 
meter, and not a mere electroscope. Two terminals /, of 


Chap. XIV.] 


Electrometers. 


20 7 


which only one is shown in the drawing, serve to charge a 
and c : they can be lifted up out of contact with a and c after 
charging them. A third terminal, /, serves to charge the 
Leyden jar. It is usually disconnected from the inner coat¬ 
ing by being turned back, so that the tongue m is discon¬ 
nected from the metal rod behind s. 

With good glass, carefully washed in distilled water and 
dried before the fire, before being filled with sulphuric acid, 
the Leyden jar can be made to insulate so well as not to lose a 
quarter per cent, of its charge per diem. Sir William Thom¬ 
son adds a little inductive electrical machine inside the jar 
(§ i, Chapter XIX.), by which the charge can be increased 
or diminished at will, and also a gauge by which the 
constancy of the charge can be measured. An instrument 
of this class may be made so sensitive as to give a deflection 
of ioo divisions for the difference of potential between zinc 
and copper. 

§ 3 . The essential parts of Sir William Thomson’s portable 
electrometer are shown in Fig. 103. g is a flat insulated 
disc to which the charge to be measured may be communi¬ 
cated. h is a second insulated disc, having an opening at 
the centre filled by a very light aluminium plate /, supported 
by a stretched wire i z, and carrying an index arm below 
the plate h. This plate and wire are shown in Fig. 57, 
p. 100. If now g and h are at the same potential, there 
will be no charge on the opposed faces, and/will neither be 
attracted nor repelled by^*. If a charge of electricity be com¬ 
municated to g or /z, so that the potentials differ, f will be 
attracted or repelled by g, and the consequent motion can be 
read by observing at / the position of a little hair, fixed to the 
index arm. Unless, however, the charges on g and h are 
very great, the forces will be very small, and this arrange¬ 
ment would offer little advantage : its sensibility is enor¬ 
mously increased by the following device A considerable 
permanent charge is given to /z, which is maintained in 
permanent connection with a highly charged perfectly 





208 


Electricity and Magnetism. [Chap. XIV. 

insulated Leyden jar; then if g be in connection with the 
earth, a charge will be induced on g, and f will be attracted 
by that charge with a very sensible force. Let the torsion of 
the wire i i be adjusted so as to depress f or elevate the hair 
near /, then there will for a given potential of/^beone distance 


Fig. 103. 



Fig. 103 a . 



between g and h, at which the electrical attraction will just 
balance the torsion of the wire. The distance of the plate 
g from the plate h can in the instrument be adjusted by a 
fine screw, and this position is read off by a divided scale and 
vernier. Let.g' next be disconnected from the earth and con¬ 
nected with the body the potential a of which is to be tested, 
i.e. compared with that of the earth—a new charge will be 
induced on ^proportional to the difference between the poten¬ 
tial of h and a ; if a be positive, assuming the potential of h to 
be positive also, the charge will be less than that due to the 
earth, and plate g must be lowered. If, on the contrary, a be 
negative, the charge will be greater than that due to the earth, 
and to bring the hair at / back to its fiducial mark g will have 




































Chap. XIV.] 


Electrometers . 


209 

to be raised—the difference of potential between a and the 
earth will be proportional to the distance through which g 

is moved ; for, from § 7, Chapter V., we have/ = v * M • 

87 r ar 3 

where v is the difference of potential between two plates at 
a distance a. When / is at the fiducial mark, / determined 
by the torsion of the wire is constant, and the quotient 
y2 v 

-j = - must also be constant, so that the difference of po- 

CL Ct 

tential v must vary in direct proportion to the distance a 
between the plates, in order to balance this constant force. 

Each 1 ooth of an inch corresponds therefore with a given 
potential of the plate h to a perfectly definite and constant 
difference of potential, so that if with one body a the disc^- 
requires to be raised o-oi above the position when the 
earth reading was taken, and with a second body b the same 
plate requires to be raised o-i above the same position, we 
know that the potential of b is ten times that of a, both 
potentials being above or below that of the earth. By 
making the potential of h in all cases large, the distance a 
may also be large for a constant force f and a great range 
of measurement is thus combined with great sensibility. 

The plate h h forms part of the inner armature of a 
Leyden jar, the glass of which is lettered m ?n ; the micro¬ 
meter screw b serves to raise and lower the insulated plate g 
by means of a slide which need not be specially described 
here. The position of g is read off bya vertical scale not shown, 
still further subdivided by the divided ring at q ; the plate g is 
connected with a terminal s, shown in Fig. 1030, projecting 
outside the Leyden jar through an opening in the case. This 
rod t serves to charge the plate g, and is usually covered 
with a cap, t , of special form, intended to prevent the influx 
or efflux of air. When the instrument is not in use, the 
cap t is pushed down, closing the Leyden jar entirely. 
When the instrument is in use, the cap t is raised, and 
being then wholly insulated it serves as the terminal by 



210 Electricity and Magnetism. [Chap. XIV. 

which to charge g. A lead case for pumice stone and 
sulphuric acid is placed inside the Leyden jar to dry the 
air. The Leyden jar can be charged by an insulated 
rod, introduced temporarily through a little opening pro¬ 
vided for the purpose in the top of the case. When the jar 
is once charged this hole is closed by a screw. When pro¬ 
per glass is chosen for the jar, well washed with distilled 
water, and dried by evaporation before the fire before being 
finally closed, the Leyden jar will not lose J per cent, of its 
contents per diem. Care must be taken to remove the pu¬ 
mice stone once a month and bake it, otherwise the sul¬ 
phuric acid diluted with water attracted from the atmosphere 
will overflow and spoil the instrument. The difference of 
potential produced by the contact of zinc and copper may 
be detected on this instrument, and the electromotive force 
of 20 or 30 Daniell’s cells can be measured with considerable 
accuracy. The value of each division of the instrument 
alters as the charge in the Leyden jar varies. The instru¬ 
ment is not an absolute electrometer, but is used to compare 
potentials as galvanometers are used to compare currents. 
It is specially adapted for experiments o\ the potential of 
the atmosphere. If a burning match be attached to the 
terminal j, the plate g is rapidly brought to the potential of 
the air at the point where the match bums. The instrument 
is held in one hand, the position of the hair at l relatively to 
the fiducial mark observed through the magnifying glass, and 
the plate g adjusted by moving the screw head w. In the 
manufacture of the instrument so much torsion should be 
given to the wire as wall just leave the plate / in stable 
equilibrium when / is at the fiducial mark. When very little 
initial torsion is given, the directing force of the wire varies 
very rapidly with the increased angle through which it is 
turned by the attraction or repulsion of plate /, and the 
equilibrium is then very stable. As more initial torsion is 
given, the change of directing force due to a deflection from 
the fiducial point is less, and the equilibrium may easily be 


Chap. XV.] 


Galvanic Batteries. 


211 


made quite unstable. The torsion used should be a little 
less than that giving instability for the lowest position in 
which g will be used. 

§ 4 . The absolute electrometer is an instrument much 
like the portable, but on a larger scale, and so arranged that 
the actual force on the moveable disc can be measured. 
Then, calling v and the two differences of potentials which 
give the same force f with the two distances d and t>i be¬ 
tween the parallel plates, and calling a the area of the move- 
able plate, we have 



by which equation the difference of potential v — Vj is 
given in absolute electrostatic units : from measurements of 
this kind we can determine the constant multipliers required 
to convert the indications of a quadrant or portable elec¬ 
trometer into absolute measure. 


CHAPTER XV. 


GALVANIC BATTERIES. 


§ 1 . The simplest form of galvanic cell practically in use 
consists of a plate of zinc and a plate of copper, immersed 
in water slightly acidulated by the addition of a little 
sulphuric acid. The zincs and coppers are generally 
soldered together in pairs, and placed in a long stoneware 
or glass trough, divided into separate cells by partitions as 
shown in Fig. 104. This battery is made more portable by 
filling the cells with sand, which supports the plates and 
prevents the liquid from splashing about when the trough is 
moved. In this form it is called the common sand battery. 
The copper is advantageously replaced by platinum or 
platinized silver; this battery without sand is then known 





212 


Electricity and Magnetism. [Chap. XT. 

as Smee's battery. The rough surface of the deposited 
platinum seems to have the effect of diminishing polarisa¬ 
tion. Fig. 105 shows a common form of one cell of 


Fig. 104. 



Smee’s battery ; the plate of platinized silver hangs from a 
wooden bar between two plates of zinc amalgamated with 


Fig. 105. 



Fig. 105 a. 



mercury; the brass terminals serve to hold the three plates 
together. 

In Walker's battery the copper is replaced by graphite. 

§ 2 . The following are the chief merits of a galvanic cell : 

1. It should produce a high electromotive force. 

2. It should have small and constant internal resistance. 

3. Its electromotive force should be constant whether it 
be employed in producing a large or small current. 

4. The materials it consumes should be cheap. 

5. No materials should be consumed except when the 
battery is employed to produce a current. 













































Chap. XV.] 


Galvanic Batteries. 


213 


6. The form should be such that the condition of the 
cells can easily be seen, and fresh materials added when 
required. 

No one battery combines all these advantages in the 
highest degree, and the special requirements of each case 
should guide us in the choice of the design to be preferred for 
any given purpose. 

§ 3 . No single-fluid cell can give a constant electro¬ 
motive force because of the polarization of the plates, § 9, 
Chapter IV. The electromotive force due to the metals 
in the batteries above described diminishes with extra¬ 
ordinary rapidity as soon as the poles are joined, especially 
when the current flowing is considerable. This diminution 
is due to an opposed e. m. f. consequent chiefly on the 
presence of free hydrogen on the copper or platinum 
plate. The effect of gases in setting up an electromotive 
force is easily shown by the voltameter, Fig. 41, p. 67. Let the 
wires a and b be joined by a wire, part of which is the 
coil of a galvanometer. A current will be perceived 
opposed in direction to that which decomposed the water; 
i it will come from the hydrogen, through the water to the 
oxygen. This current is accompanied by the recombina- 
| tion of oxygen and hydrogen forming water. The direction 
I of the current from this gas cell is such as would be pro- 
|; duced if hydrogen were a negative metal electrode, and 
| oxygen a positive electrode, as shown in Fig. 105^. 
j Provided the oxygen and hydrogen have no chemical 
affinity for the metal employed to join them, this metal will 
have no effect on the e. m. f. of the gas cell; the hydrogen 
plays the part of the zinc plate, being oxidised by the 
water, and the hydrogen set free appears at the positive 
electrode (oxygen) and combines with it. The fact that 
hydrogen and oxygen joined by a metal conductor will 
recombine, whereas when simply in presence of one 
another they will not recombine, is probably due to the 
electromotive force set up at the junction between the 
metals and the gases Thus the junction between the 





214 Electricity and Magnetism. [Chap. XV. 

platinum and hydrogen makes the hydrogen positive; the 
oxygen is either less positive or negative : thus the difference 
of potentials produced by the contacts tends to produce a 
current from the hydrogen electrode to the oxygen elec¬ 
trode through the water, and this would decompose the 
water, sending hydrogen to the oxygen electrode, and 
oxygen to the hydrogen electrode. The result is, that the 
decomposition of the water is balanced by the recomposi¬ 
tion at the electrodes, and the gas gradually absorbed. 
The whole of the gas cannot be thus absorbed consistently 
with the theory of dissipation of energy. The above 
illustration of the action of the gases certainly is not a 
complete or accurate hypothesis. If it were, the electro¬ 
motive force of the gas cell or polarized platinum plates 
would be constant, whereas it is much increased if the 
decomposition of the water has been effected by a high 
E. m. f., and gradually diminishes as the recombination of 
the gases occurs, as we should expect from the theory of 
dissipation of energy. 

The electromotive force called up by the deposition of 
gases on electrodes is within limits nearly proportional to 
the e. m. f. employed in producing the deposition. This 
is most clearly seen when the electrodes are so formed that 
the gases cannot easily escape—when, for instance, the 
electrodes are small surfaces of metal, surrounded by an 
insulator, such as are produced by boring a hole so as to lay 
bare a small portion of the copper of a guttapercha-covered 
wire. We may, perhaps, conceive the highE.M. f. produced 
in reaction against p, great decomposing e. m. f. as due to the 
decompositions of a row of molecules forming a number of 
gas cells in series imperfectly insulated from one another. 

§ 4 . The sand battery is the worst of all batteries as regards 
constancy of electromotive force, the polarization being 
greater in this battery than in any other because the gas 
cannot readily escape. The common copper and zinc cell 
is the next in order of demerit. Its electromotive force can 
at any time while it is producing a current be greatly in- 


Chap. XV.] 


Galvanic Batteries. 


215 


creased by mechanically brushing the gases off the metals, 
or even by shaking the battery. The Smee battery is better 
than the copper zinc battery because it is found that hydrogen 
does not stick to the finely divided platinum on the surface 
of the plates so much as to the copper. The carbon or 
graphite plate in Walker’s battery performs the same func¬ 
tion of facilitating the liberation of the free hydrogen. 

When any of these single fluid batteries are left with the 
electrodes free or insulated so that no current passes, the 
full electromotive force is gradually restored, partly by the 
liberation of the hydrogen, partly by its recombination 
with oxygen. The process of restoration may be assisted 
by passing a current through the cells against their e. m. f. 

For some purposes a constant current is not required ; 
—for instance, where batteries are employed to ring bells in 
houses or on railway lines they have long intervals of 
repose; for such purposes single fluid batteries are still 
employed cn account of their simplicity. 

§ 5 . If the voltaic theory of the cell were absolutely 
correct, the electromotive force of the cell would depend 
wholly on the electrodes or plates in the electrolyte, and 
not at all on the solution or electrolyte employed to connect 
them. We might then form a list or potential series (§22, 
Chapter II.) in which the difference of potential between 
each successive material being known, the e. m. f. pro¬ 
duced by a cell made with any two materials would simply 
be equal to the difference of potential obtained by summing 
up the differences due to all the intermediate materials. 
These differences of potential have not been determined 
by experiment, though potential series have been deter¬ 
mined so far as to give the order in which the materials 
come; but it has been found that this order is slightly 
changed by the solution employed to join the plates or 
electrodes; in order to account for this fact it is necessary 
to treat the voltaic theory as incomplete. The following 
are potential series for some of the more important solu¬ 
tions :— 




F araday 


216 


Electricity and Magnetism . [Chap. XV 































































Chap. XV.] 


Galvanic Batteries. 


217 


The positions occupied by the several materials with 
the first five solutions do not differ so much as to 
invalidate the theory of potential series. We know from 
thermo-electric experiments that not only the chemical 
condition but the molecular condition of the metals (what 
may be called their tempering) affects their position in the 
potential series : remembering this fact, and also the effect 
of polarization, no surprise need be felt at the change in 
relative position of cadmium and tin, or bismuth and 
antimony. We perceive also a general law that the 
materials having the greatest affinity for one constituent of 
the solution are most electro-positive, and this agrees with 
the chemical theory of electromotive force already stated. 
The last potential series obtained with a yellow solution of 
sulphide of potassium is quite anomalous and inconsistent 
with the simple potential series theory. 

§ 6. The true absolute values of the electromotive force 
produced by unpolarized single fluid elements are not 
accurately known, and owing to the polarization produced 
by any current cannot be determined by galvanometric 
observations. This is of less consequence, because, not 
being constant, the value of this electromotive force could 
not be used in any formulae depending on Ohm’s law. The 
available electromotive force in a Smee’s element is about 
o*47 of a volt. 

The solution employed has little effect on the electro¬ 
motive force, but has a great effect on the resistance. 
Pure water has a much higher resistance than any of 
the solutions employed in batteries : hence a cell with pure 
water or nearly pure water will give only a very feeble 
current through an external circuit of small resistance; 
when salt, or sulphuric or nitric acid are added, the current 
is increased at once. This is due merely to the change in 
the total resistance of the circuit, not to any increase of 
electromotive force. A solution of sulphuric acid and 
water containing thirty per cent, of sulphuric acid has a 





218 


Electricity and Magnetism. [Chap. XV. 



smaller resistance than a solution with either less or more 
sulphuric acid; but, when used to charge a battery, it gives 
rise to useless oxidation of the zinc—useless because it 
produces no current outside the cell. Much weaker 
solutions, of about one part in twelve, are therefore com¬ 
monly employed; solutions of common salt and of sulphate 
of zinc are also employed to charge the battery; the first 
because of its small resistance and the second because the 
action of the cells causes no change in the constituents of 
the solution. 

§ 7 . Some useless oxidation of the zinc or other electrode 
which is consumed in the cell almost always occurs, and 
is due to what is called local action. This local action 
arises from inequalities in the condition of the zinc exposed 
to the liquid. These inequalities cause certain points of the 
zinc to be electro-negative to certain other points. These 
points being in metallic connexion through the mass of the 
zinc constitute with the fluid a galvanic cell of small e. m. f., 
but also of very small resistance, and a current is produced in 
a local circuit as indicated by arrows in Fig. 106 : that portion 
of the zinc which is most electro-positive is eaten away, 


and the current produced is con¬ 
fined to the cell, and cannot be 
utilized. This local action is 
very much increased by dimi¬ 
nishing the resistance of the 
fluid. It is much diminished by 
amalgamating the surface of the 
zinc. This is done by cleaning 
the surface of the zinc plates 
with dilute sulphuric or hydro¬ 
chloric acid, and then rubbing a 
little mercury over the surface 


Fig. io6 . 



with a brush. The surface being then composed of a uni¬ 
form material not susceptible of those differences of temper 
described by the words ‘ hard ’ and £ annealed ’ is not attacked 















Chap. XV.] 


Galvanic Batteries . 


219 


by the solution until the external circuit is closed : no zinc 
is consumed except in producing useful currents. Several 
forms of battery are in use in which the zinc plate is kept 
permanently in contact with a small supply of mercury. 

§ 8. Single fluid batteries are subject to another incon¬ 
venience besides that of polarization; the solution usually 
employed # cannot by any convenient means be kept in 
uniform condition. For instance, the sulphuric acid used 
in most forms of the cell is gradually used as well as the 
zinc, so that the resistance of the battery is perpetually 
increasing, and the cell requires from time to time to be 
refreshed, as it is termed, by the addition of sulphuric acid. 
Single fluid batteries are subject, therefore, to three defects : 
their electromotive force is enfeebled by polarization; it is 
not constant; and their resistance is not constant. 

§ 9 . All these defects are remedied in the two fluid bat¬ 
teries, of which the DanielVs cell was the first invented, and 
is a good typical example. In the most constant form of 
this cell, the zinc is plunged in a semi-saturated solution 
of sulphate of zinc, the copper in a saturated solution of 
sulphate of copper, and these two solutions are separated 


Fig. 107. 

Z D D C 



either by a porous earthenware barrier or by taking advan¬ 
tage of the different specific gravities of the two solutions. 
Fig. 107 shows three DanielFs arranged with porous cells, 
as used in telegraphy. The glass trough a a has glass 





































220 


Electricity and Magnetism. 


[Chap. XV. 


Fig. 108. 


partitions b b, which separate it into distinct cells, insulated 
from one another. In these cells stand the porous earthen¬ 
ware pots e e e, containing a saturated solution of sul¬ 
phate of copper, and sur¬ 
rounded by a semi-satu- 
rated solution of sulphate 
of zinc. A thick plate 
of zinc is joined by a 
connecting strap to a 
thin plate of copper at 
d d ; the coppers stand 
in the porous cells, the 
zincs in the sulphate of 
zinc. The terminal plate 
of copper c forms the 
positive pole of the bat¬ 
tery, and the terminal 
zinc z has a copper wire 
soldered to it, which 
forms the negative pole. 
In one common form, 
called Muirheads, and 
shown in Fig. 108, the 
glass trough a a contains 
ten cells, which stand 
inside a teak case with a 
lid, through which gutta¬ 
percha-covered wires 
pass at the ends. Crys¬ 
tals of sulphate of copper 
of the size of a hazel 
nut are placed in the 
porous cells to maintain 
the solution in a satu¬ 
rated condition. The copper connecting strap is cast in the 
zinc, having been tinned to ensure adhesion. The plates 
































Chap. XV.] 


Galvanic Batteries . 


221 


may be four inches long, and two inches wide, and the 
copper plates about four square inches. The zinc should 
hang on the upper part of the cell, and not reach to the 
bottom. 

§ 10 . The chemical action in the Daniell’s cell when in 
perfect working order has already been described, chap. xi. 
§ 9; the result of the series of actions there described is 
that the sulphuric acid and oxygen of the sulphate of zinc 
are transmitted to the zinc, combine with it, and form fresh 
sulphate of zinc ; the sulphuric acid and oxygen of the sul¬ 
phate of copper are transmitted to the zinc, set free by the 
above process, and reconvert it into sulphate of zinc; the 
copper of the sulphate of copper is transmitted to the copper 
electrode, and remains adhering to it. The whole result 
is therefore the substitution of a certain quantity of sul¬ 
phate of zinc for an equivalent quantity of sulphate of 
copper, together with a deposition of copper on the copper 
or negative electrode. Sulphuric acid and oxygen have a 
stronger affinity for zinc than for copper, otherwise there 
would be no source of power in the substitution. 

The result differs in two material respects from that given 
by single fluid batteries, i. No free hydrogen appears at the 
copper electrode. It is impossible to say whether water is 
or is not decomposed at some stage of the process, but if 
it is, the oxygen and hydrogen recombine without becoming 
visible. In the single fluid batteries described, the oxygen 
of the decomposed water combines with the zinc or other 
electropositive metal, leaving the equivalent of hydrogen 
free. In the Daniell’s cell no oxygen is required from the 
water, the supply coming from the sulphate of copper. 
Consequently no free hydrogen appears. 2. It is com¬ 
paratively easy to keep the solutions in a sensibly constant 
condition. The sulphate of copper solution is maintained 
by the presence of crystals of sulphate of copper. The 
sulphate of zinc solution, if it be saturated in the first 
instance, simply deposits the sulphate of zinc which is 
formed. Practically it is found better to work with semi- 


222 Electricity and Magnetism. [Chap. XV. 

saturated solution of zinc, because a crust of sulphate of zinc 
crystals forms at the edge of the saturated solution and this 
impairs the action of the battery if it touches the zinc, and 
injures the insulation of the battery by forming a conducting 
film all round the edges of the cell, and on the copper junc¬ 
tion straps. 

§ 11 . The Danielhs cell will give a constant electromotive 
force, and retain a nearly constant resistance, for weeks to¬ 
gether. To ensure this result, the following precautions must 
be taken : 

The solutions must be inspected daily and kept in the proper 
condition by the addition of crystals of sulphate of copper and 
the removal of sulphate of zinc solution, water being added 
to replace the liquid withdrawn. No sulphate of zinc or dirt 
must be allowed to collect at the lips of the cells. The zinc 
plate must not touch the porous cell, or copper will be 
deposited upon it, which will set up local action. The 
sulphate of copper must be free from iron. To detect 
iron, add liquid ammonia to the solution; both copper and 
iron will be at first precipitated, making the solution appear 
cloudy; but as more ammonia is added the copper will be 
redissolved, forming a bright blue solution, and leaving the 
iron as a brown powder. No acid should be used to set 
the battery in action ; it should be charged with sulphate of 
zinc from the first (unless a very low resistance, not con¬ 
stancy, be the object in view). The plates should be clean. 
Copper plates, if dirty, may be cleaned by being made red 
hot, and dipped in weak ammonia. The card used in 
cotton factories is a good brush for batteries. Porous cells 
must be examined to see that they are not cracked; if set 
aside for a time after being used, they must be kept moist, 
or the crystallization of the sulphate of zinc they contain 
will crack them. The solution of sulphate of copper must be 
watched to see that it does not rise in the porous cells so 
high as to overflow the edges. This action by which 
liquid is drawn from one side of the porous diaphragm to 


Chap. XV.] 


Galvanic Batteries. 


223 


the other is called osmose. The resistance of the cell 
described above with very porous Wedgwood pots may 
perhaps not exceed 4 ohms; 6 or 10 ohms is a much 
more common resistance. 

§ 12 . The various constructions of Daniell’s cell are very 
numerous. When the cells are large, a separate glass or 
earthenware jar is generally used for each cell. The porous 
cells are cylindrical, and the zincs and coppers are likewise 
parts of cylinders. Sometimes the zincs and sometimes 
the coppers are placed inside the porous cell; but the 
zinc should always be in the largest receptacle. Sometimes 


Fig. 109. 



the copper electrode is made the jar to hold the sulphate 
of copper, the zinc being then inside the porous cell. This 
form of cell cannot be recommended, as the copper is fre¬ 
quently eaten away at the corners and allows the liquids to 
run out. 

A more distinct form of the Daniell’s cell is that in which 
the porous cell is replaced by sawdust; the copper lies at 
the bottom of the cell covered by crystals of sulphate of 
copper ; on this sawdust is placed, moistened with the 
copper solution at the lower part of the cell and with the 
zinc solution near the top of the cell. On the top of all lies 





























224 


Electricity and Magnetism. [Chap. XV. 


the zinc plate. This form of battery was first used by Sir 
William Thomson, who made the lower coppers in the form of 
trays, which rested directly on the zinc of the cell beneath. 
This form would be very convenient for plates of large size, 
if the copper were not occasionally eaten through. This 
defect he has remedied by making the trays of wood covered 
with lead, electrotyped with copper at the bottom. Fig. 109 
shows three of these square trays, in which the zincs are 
forty-one centimetres long and broad. The trays are seven 
centimetres deep inside. The resistance of one of these 
cells is about o’2 ohm. 

The zinc is made in the form of a grating to allow 
bubbles of gas to escape, and is supported on blocks of 
wood w at the corners. 

§ 13 . Fig. no shows a slight modification of the sawdust 
battery, commonly known as Menotii's ele?nent. * In an earthen- 


Fig. iio. 



ware or glass cell, a flat circular plate of copper c is laid, 
with a piece of guttapercha-covered wire soldered to it; this 
wire comes out of the cell and forms the positive pole. The 
copper is covered with crystals of sulphate of copper and 
sawdust as above described, and the zinc lies on the top. 
A little oil is sometimes added to prevent evaporation. 

* This element differs in no respect from one introduced for testing 
the Atlantic cable, by Sir William Thomson, in 1858. 










Chap. XV.] 


Galvanic Batteries. 


225 

The cells are usually about 10 centimetres diameter inside 
and 12 centimhtres high. The metal plates are then made 
about centimetres diameter This form of battery is 
portable, and has a constant e. m. f. Its resistance is high, 
being usually about 20 ohms when in fair condition. It 
is chiefly used for purposes connected with testing. The 
sawdust cells are well adapted for use at sea, where the 
wash of the solution tends to disturb the electromotive 
force and to produce variable polarization; for even in a 
Daniell’s cell there is practically always some polarization. 

Gravitation batteries are like the Minotti’s with the 
sawdust removed. They must be kept perfectly still, and 
are found difficult to manage. 

§ 14 . The following double fluid batteries are in practical 
use :—1. Marie Davy's element , which consists of a carbon 
electrode in a paste of proto-sulphate of mercury (H g 2 so 4 ,) 
and water contained in a porous pot, and a zinc electrode 
in dilute sulphuric acid, or in sulphate of zinc. The 
chemical action is similar to that of the DanielFs cell; 
sulphate of zinc is formed, and mercury deposited at the 
carbon electrode. 

The sulphate of mercury is apt to rise by capillary action 
to the junction of the carbon and copper; it then attacks 
the copper and destroys the continuity of the circuit. This 
is prevented by filling the pores of the charcoal at the top 
with melted paraffin; the sulphate of mercury is expensive, 
but very little mercury need be wasted, and it is easily 
re-converted into proto-sulphate. This material is poison¬ 
ous. The e. m. f. of this element is about 1*5 volts, but 
its resistance is greater than that of a Daniell’s cell. 

2. Grove's cell .—This well-known and very useful element 
consists of a platinum electrode plunged in nitric acid, 
more or less diluted, and a zinc electrode plunged in sul¬ 
phuric acid diluted with about twelve parts of water: the 
two solutions are separated by a porous cell. The zinc is 
converted into sulphate of zinc, the oxygen required being 
Q 


226 Electricity and Magnetism, . [Chap. XV. 

obtained from the water; the hydrogen is prevented from 
remaining free at the platinum pole by forming, with the 
nitric acid, water and hyponitrous acid gas. This gas is in 
part dissolved, and in part appears as nitrous fumes. These 
fumes are not only disagreeable, but poisonous. The 
electromotive force of this battery varies from nearly two 
volts, when the nitric acid is concentrated and the sulphuric 
acid solution has the specific gravity ri36 (20 parts sulphuric 
acid in 100 by weight), to 1*63 volt, when the nitric acid 
solution has the specific gravity 1*19 (26*3 parts n 2 o 5 in 
100 solution), and the sulphuric acid the sp. gr. 1*06 (9 parts 
in 100 by weight). 

With the zinc in sulphate of zinc, and the nitric acid 
solution sp. gr. 1*33, the e. m. f. is 1-67. 

With the zinc in solution of common salt, and nitric acid 

sp. gr. 1*33 (45 parts in 100), the e. m. f. is 1*9 volt. 

The e. m. f. of this cell is very high, but its great merit 
is its low resistance which may with moderate-sized cells be 
reduced to J of an ohm. The resistance of a cell con¬ 
structed as follows was *212 ohm; area of zinc plate 27^3 

sq. in. : area of platinum plate 13-8 sq. in. ; sp. gr. of sul¬ 
phuric acid 1’06; nitric acid 26-3 parts by weight in 100 
of solution. The double e. m. f. is easily got by doubling 
the number of Daniell’s elements, but the size of these: 
elements must be immensely increased to reduce the resist- 
ance to that of a small Grove’s cell. 

3. Bunsen’s cell. —This element is exactly similar to 
Grove’s, except that the platinum is replaced by porous 
carbon. In both Bunsen’s and Grove’s cells the zinc must 
always be amalgamated, or the local action causes intoler¬ 
able fumes and waste of zinc. The electromotive force of 
Bunsen’s- cell is rather greater than that of Grove; but the 
resistance is also greater, and there is occasionally difficulty 
in securing a good contact between the carbon electrode and 
the metallic strap or wire used to connect it with the next 
zinc or with the terminal, of the battery. The carbons are 


Chap. XV.] 


Gatva7iic Batteries. 


227 

! specially prepared for all carbon batteries, and vary much in 
quality. The upper part of the carbon should be impregnated 
jj with stearine to prevent the junction from being corroded. 

Faure puts the nitric acid inside the carbon pole, which is 
made in the form of a bottle closed by a carbon stopper. 
The carbon performs the double part of porous pot and 
electrode. The nitrous fumes rise inside the bottle, and by 
! their pressure assist in forcing the nitric acid through the 
| porous carbon. 

The resistance of an ordinary Bunsen’s element 12 centi¬ 
metres high with the carbon outside the zinc is given by 
Blavier as equal to from 2 to 3 ohms when partially charged, 
but to double this amount after a few hours. 

4. The Chromate of potassiuvt element is thus de- 
1 scribed by Mr. Latimer Clark: ‘ Prepare two solutions, 
‘ the first to be made by dissolving 2 ounces of bichromate of 
I ‘potash in 20 ounces of hot water, and when cold add 10 
‘ ounces of sulphuric acid. As this addition will cause the 
‘ solution to become warm, it must be allowed to cool before 
‘ being used. The second is a saturated solution of common 
; ‘salt. To charge the battery with these solutions the 
; ‘ bichromate solution must be poured into the porous jar 
‘ containing the carbon, until it reaches about half an inch 
‘ from the top; then pour the salt solution into the outer 
‘ vessel containing the zinc until it reaches the same level.’ 

The electromotive force is said to be 2 volts. 

The chlorine of the common salt unites with the zinc, 
forming chloride of zinc, while at the carbon electrode the 
sodium replaces hydrogen in sulphuric acid, forming sul¬ 
phate of sodium. The nascent hydrogen reduces chromic 
acid (produced by the action of sulphuric acid on the 
bichromate of potash), so that sulphate of chromium is 
produced. In chemical notation, 

3 Zn; 6NaCl; 6 H 2 S 0 4 ; 2Cr0 3 
gives 3 ZnCl 2 ; 6 H 2 0 ; 3 Na 2 S 0 4 ; Cr 2 (S 0 4 ) 3 . 



228 Electricity and Magnetism . [Chap. XV. 

5. The Leclanche battery ; a zinc carbon element. The 
zinc is plunged in a solution of ordinary commercial sal 
ammoniac, and the carbon is tightly packed in a porous pot, 
with a mixture of peroxide of manganese and carbon, in the 
form of a coarse powder. Its e. m. f. is about 1 *48 volt. 
The zinc unites with chlorine, forming chloride of zinc; 
ammonia is set free at the negative electrode, while the 
nascent hydrogen from the ammonium reduces the peroxide 
of manganese to sesquioxide. The chemical notation of 
the change is that Zn; 2NH4CI; 2 Mn 0 2 is changed into 
ZnCl 2 ; H 2 0 ; 2NH3; Mn 2 0 3 . 

6. Mr. Latimer Clark’s cell of constant electromotive force; 
this element has already been described, Chap. X. § 2. 

§ 15 . With all batteries it is of the utmost importance that 
during any delicate experiments the whole battery should be 
perfectly insulated, and each cell perfectly insulated from 
its neighbour. For telegraphic purposes this is less essential, 
but it is always desirable. When a battery gives no current 
or a much feebler current than was expected, the following are 
defects which should be looked for: 1, solutions exhausted; 
for instance, sulphate of copper in the Daniell’s cell entirely 
or nearly gone, leaving a colourless solution; 2, terminals 
or connections between the cells corroded, so that instead 
of metallic contact we have oxides of almost insulating 
resistance intervening in the circuit; 3, cells empty or 
nearly empty; 4, filaments of deposited metals stretching 
from electrode to electrode. Intermittent currents are 
sometimes produced by loose wires or a broken electrode 
which alternately makes and breaks contact when shaken. 
Inconstant currents are also produced when batteries are 
shaken, unless they are in first-rate condition : the motion 
shakes the gases off the electrodes, increasing temporarily 
the e. m. f. 



Chap. XVI.] Measurement of Resistance. 


229 


CHAPTER XVI. 

MEASUREMENT OF RESISTANCE. 

§ 1 . In order to measure a resistance we must compare it 
with a standard recognised as the unit of resistance. In 
telegraphy the measurement of resistance plays a very 
important part, regulating the choice of materials and enabling 
the electrician to test the quality of goods supplied. The 
ohm (Chap. X. § 4) is the unit of resistance almost universally 
adopted in this country. Multiples and submultiples of the 
ohm are so arranged in boxes of resistance coils that any 
given resistance from one ohm to 10,000 or 100,000 ohms 
can be readily obtained for comparison with any other resist¬ 
ance. The general arrangement of these boxes is shown in 
the diagram, Fig. 1 t 1. 


Fig. in. 



Between two terminal binding screws t and Tj secured on 
a vulcanite slab, are fixed a series of brass junction pieces, 
<7, b, c, d\ each of these is connected by a resistance coil to 
its neighbour, as shown at 1, 2, 3, and 4. A number of 
brass conical plugs with insulating handles of vulcanite are 
provided, which can be inserted between any two successive 











230 


Electricity and Magnetism. [Chap. XVI. 


junction pieces, as between t and a, or a and b. Conical 
holes are bored for this purpose at the opening between the 
junction pieces. When the plugs are withdrawn, no electrical 
connection exists between the junction pieces except through 
the coils. 

Let us assume that the resistance of the first coil is one 
ohm, that of the second two ohms, that of the third 
three ohms, and that of the fourth four ohms. • Then if the 
plugs are arranged as in the figure the whole resistance 
between t and will be 4 ohms, because the resistance of 
the large metallic junction pieces directly connected by 
plugs would be insensible between c and t. If all the plugs 


Fig. 112. 



were withdrawn, the resistance between t and d would be 
10 ohms, and obviously by properly arranging the plugs we 
could obtain any resistance from 1 to 10 between t and d. 
Now suppose that d ,, instead of being the final terminal 
of the set of resistance coils, were connected by a thick 
copper bar to t as in Fig. 112, showing a plan of the 
lid of the box containing the coils; and that a similar 
series of junction pieces were used to connect coils of 10, 
20, 30, and 40 ohms, precisely as a ,, b, c, and d connected 
the coils 1, 2, 3, and 4; then between t and d u if all the 




















Chap. XVI.] Measurement of Resistance. 231 

plugs were out, we should have a resistance of 100 units, 
but by inserting the proper plugs we could at will have 10, 
20, 30, 40, 50, 60, 70, 80, or 90 units. Thus for 80 units, 
withdraw the 1st, 3rd, and 4th plug, giving 10 + 30 + 40 or 
I 80 units. Now between d x and t we can obviously by proper 
plugging obtain any number of units between 1 and no ; d x 
is connected by a thick bar with t u the last of five junction 
pieces joining coils of 100, 200, 300, and 400 units, by means 
' of which, between d x t and t, we can get with the twelve plugs 
any number of units from 1 to mo; similarly with four 
more junction pieces and four more coils we have between 

and t, the final terminals of the box, a series of sixteen 
coils and sixteen plugs, by the proper arrangement of which 
we can between t and t x obtain any number of units of re¬ 
sistance from 1 to lino ; when all the plugs are in their 
places the resistance between t and t x ought to be very small 
relatively to the resistance of one ohm; and, if this is not 
the case, the plugs and holes must be well cleaned, as any 
resistance observed when all the plugs are in, can only be 
due to imperfect metallic contact between the holes and plugs. 

§ 2 . Many other arrangements of resistance coils may be 
adopted. Thus, instead of the 1, 2, 3, 4 series, we might have 
had ten equal coils in each row of junction pieces, but this 
would have required 40 plugs instead of 16. We might 
also have arranged ten coils in a circle, and joined them to 
11 equidistant junction pieces, as in Fig. 113. Then the re¬ 
sistance between the wires t and t x would be 2 if the arm a 
was on the second stop, or 5 if on the fifth stop. The 
end of the arm a may be so arranged that, before leaving 
one junction piece, it makes contact with the next, so that 
the circuit between t and t x is never wholly broken. 

In all boxes of resistance coils the following precau¬ 
tions should be observed during the manufacture. Large 
gauges of wire should be used for the smaller coils instead 
of short pieces of fine wire. Better adjustment and less 
liability to derangement by a powerful current is thus ob- 



232 


Electricity and Magnetism. [Chap. XVI. 

tained. The metal used for the wire must be such that its 
resistance varies little with changes of temperature. German 
silver is a good material. The wires should be insulated with 

Fig. i 13. 



two coatings of silk saturated with solid paraffin or other 
suitable insulating mixture. No solderings should be per¬ 
mitted inside the coils—above all, no 
solderings in making which acid is used. 
The wire should be wound double, so 
that the current makes as many turns from 
left to right as from right to left. There is 
no self-induction (Chap. III. § 21) in a coil 
so wound, nor does the current affect gal¬ 
vanometers in the neighbourhood. The 
junction pieces must be firmly fixed, well 
insulated, and so formed that the vulcanite 
on which they stand can be easily cleaned. 
It is a good plan to make the bobbins 
hollow, and rather of large than small 
diameter, to promote uniformity of temperature. All the 
bobbins should be in one box. 




Chap. XVI.] Measurement of Resistance. 233 

§ 3 . Let two points a and b, Fig. 114, be joined by two 
conductors having resistances r and r lf these conductors 
are said to be joined in multiple arc ; with a difference of 
potentials 1 between a and b. 

The current c through r will be equal to and similarly 

the current through r x will be — ; the whole current be- 

r \ 

tween a and b will be — + or • this current will 

r r x rr x 

be the same as if a and b had been joined by a single re¬ 
sistance equal to ——, which is therefore the resistance of 
r + r x 9 

the two conductors joined in multiple arc. With three wires 
r, r \u connecting the same points by a multiple arc, the 

resistance between a and b will be - r r - n - 

r r x + r x r n + r r n 

If a galvanometer with the resistance G be shunted by a 
shunt of the resistance s, the resistance of the shunted galvano- 

• G S G “ 4 " S 

meter will be -. Let u — ———, then the sensibility 

G -j- S S 

of the shunted galvanometer will be to that of the un¬ 
shunted galvanometer as 1 to u; then calling c the current 

flowing in other parts of the circuit, - will flow through 


the galvanometer, and —c will flow through the shunt; the 

G 

resistance of the shunted galvanometer will be 

u 

Example. —We have a galvanometer with a resistance of 
8,000 ohms, and wish to find the shunt which will reduce its 

-t. r 11 8,000 + s 8,000 

sensibility 100 fold, u — 100 = l -——, or j =— l -= 

s 99 

8o-8. 

The resistance of the galvanometer when shunted will be 

o 8,000 
80 = —- 











234 


Electricity a 7 id Magnetism. [Chaf. XVI. 


§ 4 . Definition .—The conductivity of a given wire or con¬ 
ductor is the reciprocal of its resistance. 

That is to say, if a be the resistance of the wire, i is its 

conductivity; if the resistance of a conductor is io ohms, 
its conductivity is o*i. 

The conductivity of a number of wires joining two points 
in multiple arc is the sum of the conductivities of the several 
wires. For the current in each wire with a unit differ¬ 
ence of potential between the ends is \ 

The sum of all the currents is 


- + i 4 - — + . • . 

** r \ r n rn 


which is the same current as if a single conductor joined 

the two points with a conductivity of (— 4* — + — ... + —) 

r r \ r lt rg 

The resistance of the wires in multiple arc is the reciprocal of 
the conductivity of the multiple arc. This rule gives the 
same expression for the resistance as is given in § 3. 

Example .—Let two points be joined by wires in multiple 
arc with resistances of 2, 18, 27, and 64 ohms respectively. 

The conductivities are 0*5, 0-05555, *° 37 ° 4 > ‘01562. The 
sum of the conductivities is 0-6082 ; and the resistance of 


the four wires in multiple arc = ——— = 1*644 ohms. 

*6082 

§ 5 . We may compare one resistance with another by 
comparing the deflections produced by a given battery 
through the same galvanometer, but with the different 
resistances in circuit. Thus, let G be the galvanometer 
resistance, b the battery resistance, R a resistance chosen at 
pleasure from those at our disposal in the box of resistance 
coils, and x the unknown resistance which we wish to measure 
or compare with r. Let us first observe the deflection d ob¬ 
tained with a circuit containing g, b, and r only, arranged in 



235 


Chap. XVI.] Measurement of Resistance* 

any order, and next the deflection d Y , obtained with G, b, and 
x only in circuit: then, if the galvanometer be a mirror 
galvanometer, the deflections of which are proportional to the 
currents flowing through it, we have, by Ohm’s law, the pro¬ 
portion 

g + b + r:g + b + # = ^i : d\ 
for the e. m. f. being the same in both cases, the currents and 
therefore the deflections must be inversely proportional to 
the total resistances. From the above we find 

X = i- (G + B + R) - (G + b) . . . 1 °. 
d x 

When G and b are so small that they can be neglected 

relatively to R, we have approximately x = y R- This case 

seldom arises ; but frequently, as, for instance, when x is the 
resistance of some insulating substance, we may neglect 
G + b as insensible relatively to x , and then we have 

_ d ( g + b + r) # 2 °. 
d x 

The number d (g + b + r) is in telegraphy called the con¬ 
stant oi the instrument with the given battery. If^=l, we 
shall have the whole resistance of the circuit x =d (g + b 
-f r) ; hence the constant is often defined as the resistance 
of the circuit with which the given battery would give the 
deflection 1 . Obviously when a tangent galvanometer is 
used, we must write tan d and tan d x in the above formulae 
instead of </and d\ ; and if a sine galvanometer is used, 

we must write sin d and sin d x . 

§ 6. By the use of shunts the application of this method 
is greatly extended; calling the resistance of the shunt 
s, the resistance of the shunted galvanometer becomes 

G s • hence if the shunt be used when both d and d x are 

G + s ' . GS 

observed, we must in equation 1 substitute for g, 



236 Electricity and Magnetism. [Chap.. XVI. 

the only effect being to diminish the resistance of the galva¬ 
nometer ; but when d is observed with the shunt in, and d l 
without the shunt, the sensibility is different in the two cases. 

Then let the ratio ^±- S be called u as before ; we have by 
s 

Ohm’s law :— 

— + B + R I G -{- B + # — d j , U d. 

u 

or x — u % /- + b + r) - (g + b) . . . 3 0 . 
d\\u 

The constant of the unshunted galvanometer or resistance 

for which d x = 1, is u d (- + b + r). 

u 

Thus with a shunt reducing the sensibility ioo-fold, a 
deflection of 90 divisions, with G = 8000, b = 20, and 
r = 4000, the constant will be 36,900,000 ; this will be the 
whole resistance of the circuit including g and b with which 
the battery used would give the deflection 1 on the galvano¬ 
meter used without a shunt. In practice r is chosen so that 

- + B + R may be some whole convenient number; thus 

u 

in the above case an experienced observer would have made 
r = 3900 when the constant would have been 36,000.000. 
A series of shunts are usually sold with each galvanometer of 
such resistance that u may by them be made 10, or 100, or 
1000 at pleasure. The constant is determined at the 
beginning of the experiment when the galvanometer is not 
shunted, and the value of the resistance in circuit giving a 
deflection d x is obtained by simply dividing u times the 
constant by d x . To get x, the resistance of G + b must 
be subtracted from the whole circuit, but when the sum of 
G + b is small, this subtraction is often omitted. 

This mode of measuring a resistance is much used in test¬ 
ing insulating materials, such as gutta-percha. The battery 
and wire covered with gutta-percha are arranged as in Fig. 


Chap. XVI.] Measurement of Resistance, 237 

The negative current flows from z through the shunted 
galvanometer to the copper wire inside the gutta-percha; 
then through the gutta-percha to the 
water in the tub t, and from t to the 
copper pole of the battery. The resistance 
x is the resistance of the gutta-percha. 

§ 7 . The value of r in the above equa¬ 
tions is always known, and the value of g 

or of - is also generally known, and can 

always be directly determined by experi¬ 
ment ; for instance, it may be measured as 
any other resistance would be measured, 
a second galvanometer being used for the 
purpose. The value of b should be de¬ 
termined at least once a day, since the 
resistance of any battery is found to vary 
considerably from day to day. There are 
several methods of determining the value 
of b. The following is the most com¬ 
mon :— 

Make a* circuit consisting of the battery b, the galvano¬ 
meter g, and a set of resistance coils r ; shunt the galvano¬ 
meter with a piece of short thick wire connecting the ter¬ 
minals ; put all the plugs of the resistance coils in their 
places so as to reduce r sensibly to zero ; let the wire shunt 
be so short and thick as to have no sensible resistance 
relatively to the battery, but adjust it of such length that a 
sensible deflection d is shown by the galvanometer; the 
greater part of the current is shunted, but enough goes 
through the sensitive galvanometer to give the deflection 
d ; under these circumstances the whole resistance of the 
circuit is b, that of the battery, for r is reduced to nothing, 
md the resistance of the shunt is insensible ; now increase 
:he resistance in the box to r by taking out plugs until a 
deflection D! is obtained ; then 


Fig. 115. 
G 














238 


Electricity and Magnetism. [Chap. XVI. 


r + b 


b = d : d,, or b = 


R Dj_ 
D — D, 


If Dj = — we have b = r 
2 


This method has the defect that the battery resistance is 
measured when a powerful current is passing, increasing the 
polarization. Moreover the current is very different when 
d and d x are taken, and the polarization very different. 
Consequently Ohm’s law is seldom strictly applicable, be¬ 
cause the e. m. f. of the battery is not strictly constant 
throughout the experiment. With a battery of very small 
resistance, this method would be liable to injure the re¬ 
sistance coils. 

The following is a second method by which the sum 
b 4- g is determined. Observe two deflections D and 
given by the battery when the two circuits are b + G 4- R 
andB + G + R!; then we have G + b + r : g 4 - b 4* Ri 
= Dj : d, and 

G + B = R ' Dl ~ R ° . . . . S° 

D — B l 

Mr. Varley recommends that three deflections d, d 1? and 
d u , be taken with additional resistance r, k 1} and R n for 
the purpose of testing whether polarization interferes much 
with the experiment; if there be no polarization, adjusting 
the values of r, r 1? and R n so that d u = 4 d and Dj — 2 
D,we should have r = 3 r x — 2 r u . 

The following is a third method. Arrange the connec¬ 
tions as in Fig. 116; let d be the deflection when the cir¬ 
cuit is b 4 - R 4 - G; next insert the shunt of known resistance 
s, by making contact at a ; reduce r to Rj until the deflec¬ 
tion is the same as before, then 

R — Rj 


B = S 


6 C 


G + Ri 

or, fourthly, leaving r unaltered, let D! be the deflection 
observed when contact is made at a ; then 





Chap. XVI.] Measurement of Resistance. 


239 


B = S 



7 


o 



G 


or approximately 



This method is especially applicable to batteries of very 
small resistance. 

§ 8. The accuracy with which a resistance can be mea¬ 
sured by any of the above methods is limited by the accu¬ 
racy with which a deflection can be observed. If we cannot 
make certain that any deflection is correct within one per 
cent., still less can we feel confident that the resistance 
calculated from the deflection is correct within one per cent. 


Fig. 117. 


Fig. 116. 


f 



The following methods, which may all be termed differential 
methods, admit of much greater accuracy. The simplest 
differential method has already been described (Chap. IV. 
§ 3), and the arrangement of the connections is shown in Fig. 
117. With a sensitive galvanometer it admits of extreme 
accuracy, for by increasing the battery power we may increase 
at pleasure the deflection which the difference between the 






























240 


Electricity and Magnetism. [Chap. XVI. 

currents in the two branches produces. We may also shunt 
either branch of the galvanometer so as to reduce its resist¬ 
ance and sensibility u times. Calling the resistance of each 
branch of the instrument G, we then have, when the galvano¬ 
meter is undeflected on completing the circuit, assuming that 
the known resistance is connected with the shunted branch 
of the galvanometer, 

4 -G : x + = 1 : u 

u 

or x = u (r + g) — - . . . . 9 0 
u 

If, as in the figure, x is connected with the shunted branch, 
we have x 

u 

Resistances one thousand times greater or one thousand 
times less than r, are easily measured in this way. In order 
that the plan should give accurate results, it is necessary that 
the ratio u be accurately known and that it remain constant. 

Now u — ———: and if the resistance of either g or s varies 
s 

during the experiment fallacious results are given. 

When the wire of a differential galvanometer is made of 
copper the shunts must be of copper also, in order that the 
ratio u may be constant at all temperatures; but even 
with this precaution, the very current employed in testing 
disturbs the value of u, for a much larger current flows 
through s than through g, and hence more heat is generated 
in the shunt than in the galvanometer coil, and this heat is 
concentrated in a comparatively small mass of metal; the 
consequence is that the resistance of the shunt is increased 
relatively to that of the galvanometer by every current 
which passes, and this seriously impairs the value of the 
method. Diffeiential galvanometers made of German 
silver give much more accurate results than copper wire 
instruments, because their resistance and that of their shunts 
are less affected by temperature. The circuit should be com¬ 
pleted for the shortest possible time by making contact with 




Chap. XVI.] Measurement of Resistance. 241 

a key at a , and breaking it as soon as a deflection to right or 
left has been observed. This may, however, lead to error if 
the unknown resistance x is so formed that any self-induction 
can take place, or if x has any sensible electrostatic capacity 
like a gutta-percha-covered wire in water. In either of these 
cases the currents in the two branches will not increase at 
the same rate when contact is first made. Assuming the coils 
in r to be properly wound, while ^ is a simple bobbin of 
wire not wound double, the current in x will lag behind, 
and hence a momentary contact at a will always show x as 
greater than r when it is really equal to it. The first jerk 
of the galvanometer needle must, in this case, be neglected, 
and x measured by means of the permanent deflection 
arrived at after the currents in the various branches have 
become constant. 

§ 9 . When a steady current c through a resistance r is 
due to a difference of potentials 1 between the ends of the 
conductor, then the difference of potentials i between any 
two intermediate points separated by a* resistance r must be 
equal, by Ohm’s law, tore; the smaller the resistance be¬ 
tween the two points the less the difference of potential 
between them, and if one end of the conductor be at zero 
potential or uninsulated, the potential of any point in the con¬ 
ductor will be proportional to the resistance r between the 
earth and the point in question, and equal to r c. In the 
diagram Fig. 118, if the line a e represents to any scale the 

Fig. 118. 


P 

-- 1 ) 



z c 


length of a uniform conductor separating the battery c z 
from the earth at e, and if the line or ordinate p a represent 
the e. M. f. of the battery to any scale : then, joining p e by 
a straight line, the ordinate f h will represent the potential 

R 






242 Electricity and Magnetism, [Chap. XVI. 

of the conductor at the point f. If, for instance, pa is 
equal to 12 volts, and f is half-way between a and e, f h 
will be equal to 6, and 6 volts will be the potential of the 
conductor at that point. 

If a were separated from e by several conductors of dif¬ 
ferent resistances, we must draw a e so as to represent the 
total resistance instead of the mere length of the conductor. 
Then as before, f h will represent the potential at the point 
f, separated from e by a resistance equal to f e ; if f is so 
placed that the resistance of f e is equal to that of a f, the 
potential at f will be half that at a, in whatever manner 
the resistances a f and f e are made up. 

The difference of potential between b and f is equal to 
the difference of the length of the lines b d and f h. 

Let us now suppose that the two ends of the resistance 
a d b are joined to the two poles of an insulated battery, 
and that at the middle of the resistance at d the conductor 
is connected with earth, Fig. 119. The potential here will be 
zero; but the difference of potentials between a and b must be 

Fig. 119. 



equal to nearly the whole e. m. f. of the battery, assuming the 
resistance between a and b to be large relatively to that of the 
battery. Hence a will be equal to half that e. m. f., and 
b p u , a negative ordinate, will be equal to the same quantity. 
The sum of the lengths b p h + a Pj = a p, calling a p the 
e. m. f. of the whole battery as shown in Fig. 118. The 
ordinates f h and f 1 h 1 show the potentials at points f 
and Fu one positive or measured upwards, the other nega¬ 
tive or measured downwards. The difference of potentials 
between f and f 2 is the sum of h f and h x f^ This differ- 






243 


Chap. XVI.] Measurement of Resistance. 

ence will be exactly the same whatever point of a b be put to 
earth, if the battery is insulated. If F t were put to earth 
instead of d, then p x p xi would be the line showing the 
potentials, and f h , the difference of potentials between f 
and f u is equal to f h -f- f l 

§ 10 . Let us assume that the same difference of potentials 
is maintained by a battery between the ends of two con¬ 
ductors of different resistance represented by the lines a e 
and A x e 1? Fig. 120, and for simplicity’s sake we will further 
assume that the potential at e is zero. If we now choose any 
two points b and B! so placed that ab : b e = a x Bj * b 1 E b 
we shall have the line b d equal to b x d 1? showing that the 
potentials of b and b x are equal. Hence, if we join b and 
Bj by a conductor, no current will flow from b to Bj ; and if 
a galvanometer Gwere inserted in the wire joining b and Bj, 
it would remain undeflected, although the e. m. f. represented 
by ap and producing the currents through a e and a l e x 
might be very great and the galvanometer very sensitive. 
If, however, the wire or bridge, as it is called, joins b with 
a point in a x Ej between B] and e x , we shall have a current 
from a e which runs through the bridge ; and on the contrary, 
if the bridge joins b with a point between b x and a x , the 

Fig. 120. 



current will flow in the opposite direction through the gal¬ 
vanometer, i.e. from a x e x through the bridge. 

If then we know the ratio a b to b e, as we shall do if 






244 


Electricity and Magnetism. [Chap. XVI. 


these two resistances are made up of graduated resistance 
coils, we shall be able to divide a resistance in the 
same ratio by simply seeking the point b ^ at which no 
current flows across the bridge. 

And if Aj Bj is a known resistance, we can experimentally 
find a resistance Bj E! which shall bear the same ratio to 
A! B! as be does to AB. 

§ 11 . The principles laid down in the two preceding 
sections give the most convenient method of measuring 
resistance. The Bridge , as it is technically called, is ar¬ 
ranged as in Fig. 121. 

Four conductors, ab, be, ab 1( and Bj e, are joined at a 
and e to the poles of a battery, the current from which 
flows round a be and aBjE, corresponding to a be and 
Aj Bj Ei in Fig. 120. The difference of potentials between a 
and e depends on the battery used, but is obviously the 
same for the ends of the two circuits. The resistance be¬ 
tween a and b we will call r; that between a and b 1? Ri ; 
that between b and e, r ; and that between and e, x the 
unknown resistance to be measured ; r, r 1? and r are 
usually resistance coils. 

A convenient constant ratio is chosen for r and r, such 


Fig. 121. 



G 


as equality, 1 to 10, 1 to 100, or 1 to 1,000 ; and then r, is 
adjusted until no current flows through the galvanometer g ; 







Chap. XVI.] Measurement of Resistance. 245 

when this is’the case we have r ; r = Rj \ x or x = — r x ; 

R 

so that if r — , x will be equal to 

100 100 

The convenience of this method is very great. Any gal¬ 
vanometer can be employed; but the more sensitive the 
instrument the more delicate the measurement of x. The 
constancy of the resistance of the galvanometer is of no con¬ 
sequence. The coils R, Ri, and r , are made of German silver 
or some other alloy varying little in resistance with a 
change of temperature. Two keys are inserted, one at a and 
one at b ; the current is wholly cut off the four conductors 
until contact is made at a ; and then, after the currents in the 
four conductors have come to their permanent condition, 
contact is made at b to test whether any current flows 
through the galvanometer. If none flows, making contact 
at b does not disturb the currents in the four conductors 
at all. R and r are usually so arranged as to give any 
decimal ratio between 1,000 to 1 and 1 to 1,000 : the two 
keys at a and b are often arranged so that the same finger- 
piece moves both, making contact at b a little after contact 
has been made at a. 

The three resistances r, r 15 and r, and the resistance of 
the galvanometer, should be small if # is small, and great if 
x is great. When x is very small, a b e is frequently made 
of a single wire of constant diameter; R! is kept constant, 
and the point b slipped along the wire a be, until no 
current flows through g. Then the ratio of the resistances 

- is the ratio of the actual lengths — measured on a 

R AE 

scale over which the wire abe is stretched. An alloy 
of silver with 33-4 per cent, of platinum makes a good wire 
for this purpose. It must be a stout wire, or else the wear 
and tear of shifting the contact piece b will soon destroy the 
uniformity of its section and therefore of its resistance. 

When * is small, great care is necessary to prevent the 



246 Electricity and Magnetism. [Chap. XVI. 

resistance of mere connections between r, /*, Rj, and x from 
being sensible. These connections may be made of stout 
copper rods centimetre diameter, and junctions made by 
dipping the ends of these rods in mercury cups, the ends 
of the rods being amalgamated. 

The bridge is applied to measure the resistance of the 
gutta-percha sheath used to insulate the conducting wire of 
submarine cables : for this purpose e is connected with 
earth, the battery carefully insulated, and the wire to be 
tested is connected with b„ but insulated at the other 
end instead of being connected with e ; the insulated wire 
is submerged in an uninsulated tank or in the sea, and thus 
the only connection between B t and e is through the insu¬ 
lating cover or sheath. The resistance of this insulating 
cover is therefore the resistance x. 

After the wires have been arranged thus we can, by 
joining the end of the conducting wire with e, measure the 
resistance of the copper conductor immediately before or 
after measuring the resistance of the insulator. 

When no current flows across the bridge, the position 
of the battery and of the galvanometer may be inter¬ 
changed, and no current will flow from a to e through the 
galvanometer. 

§ 12 . KirchhofPs laws. —If a number of currents c x c 2 c 3 . . . c„ are 
flowing some to a point A (Fig. 122) and some from that point; then, 
since the whole quantity arriving at the point must be equal to that taken 
away, the sum of all the currents coming to the point must be equal 
to the sum of those going away from it: hence, calling the first series, 
positive and the second series negative currents, the algebraic sum of al'l 
the currents must be equal to zero, a result written as follows, 

2c = o, 

the letter 2 signifying that the sum of all the values of c are to be taken. 

Let there be several sources i x i 2 i 3 of electromotive force in a circuit 
(Fig. 123), some acting in onedirection and some in another, and joined by 
resistances r 4 R b R c . Let the currents flowing through each be c a c b c c . 
Let the difference of potential or e.m.f. between the two ends of R, be 
P„ — A »that between the two ends of R tl , P b — / b ; and that between the 
two ends of R ( ., p,. — p, . 



Chap. XVI.] Measurement of Resistance. 247 

Then by Ohm’s law, c a R a = p a -/ a , c b R b = p, -p b , c c R c = p c ~p c 
or C a R a + C b R b + C c R c = (P, — + P b — p b + P c _ P, ) = (p a — p Q ) 

+ ( p t -A ) + (p c —A). 

Now p a _ p c is the difference of potentials produced by the electro¬ 
motive force i 2 ; for however high or low the absolute value of the po- 

Fig. 122. Fig. 123. 




tentials P„ or p c may be, by definition the difference of potentials must 
be equal to the electromotive force between them. Similarly p b — / a = i 3 , 
and P c -p b = h : 

hence l 1 + l 2 + i 3 = c. R a +Cb R b +c r c , 

or 2 1 = 2 c R . . . 9. 

The sum pf all the electromotive forces is equal to the sum of the 
products of each current into the resistance which it traverses. 

One obvious application of this law of Kirchhoff’s is to those cases 
in which the electromotive force in a circuit, instead of being due to a 
certain difference of potentials produced at one point of the circuit, as 
by a battery, is due to an e.m.f. distributed throughout the length of the 
whole or part of the conductor, as when the E.M.F. is due for instance 
to electromagnetic induction, where we only know for each part of the 
circuit that the E.M.F. is so much per centimetre of length. We now 
see that we need only add up all the . electromotive forces in each unit 
of length, and then, knowing the whole E.M.F., we find that the current 
multiplied into the whole resistance of the circuit will be equal to the 
electromotive force thus calculated—in other words, Ohm’s law is per¬ 
fectly applicable to this case. 

The results arrived at in sections 1 and 2 of this chapter are easily 
proved from Kirchhoff’s equations. 




24B 


Electricity and Magnetism. [Chap. XVI. 


§ 13 . The theory of the bridge may be proved as follows 
from KirchhofFs laws : 

Let five conductors r , r b r u , r m , r iy , be arranged as in Fig. 
124 with a battery 1 connected with a and e by conductors, 
as shown in the figure. 

Let c, c b c ib c m , c iy , c be the six currents, in the six parts of 
the circuit, c being the current in r , c i the current in r b etc. 
Then at a and e we have c = 4 + c m = c a + c iy 

,, at b and Bj ,, ,, c — c j c b s ® ; q v c j^. 

In the circuit a b Bj we have c r = % r m — q r b 

„ BEBj „ c r aa c a r b - c iy r iy ; 

eliminating c i c u c m and c iy we have from the above equa¬ 
tions : 

£ __ _ ^*iii f'ii ^"iv _ ^ 

(n + r m ) (r u 4. r iy ) +r (r L + r h + r m + r iy ) 

This gives the value of the current produced in the bridge 
r in terms of the whole current c produced by the battery. 
If there is no current in r , we must have 

>ra - r x r iy = oorr i :r ii = r m : r ly . 

§ 14 . The specific resistance of a material referred to unit 
of volume is the resistance of the unit cube to a current 

Fig. 124. 


B 



between two opposed faces. The following table contains 
the specific resistances of several metals and alloys at o° C. 








249 


Chap. XVI.] Measurement of Resistance. 

The specific resistances given are those of a cubic centi¬ 
metre of chemically pure metals calculated from experiments 
by Dr. Matthiessen. The resistances of commercial metals 
are always higher, and frequently very much higher. It is 
not at all uncommon to meet with copper having 50 per 
cent, more resistance than that in the table. This is due to 


Table. Specific Resistance of Metals and Alloys at o° Centigrade, from 
Dr. Matthiessen 1 s experiments. 


NAMES OF 
METALS. 


Resistance of one 
^ cubic centimetre to 
conduction between 
s opposed faces. 

q> Resistance of a wire 
one metre long and 
j* one millimetre in 
diameter. 

O Resistance of a 
tr wire one metre 

3 long, weighing one 
gramme. 

q Resistance of a wire 
g* 1 foot long, ToV.oth 

3 of an inch in dia¬ 

meter. 

Resistance of a wire 

§ one foot long,weigh- 

3 ing one grain. 

Silver annealed 


I'52I 

0*01937 

0-1544 

9 -I 5 I 

•2214 

„ hard drawn 


1*652 

0*02103 

0*1680 

9*936 

•2415 

Copper annealed 


I * 6 l 6 

0*02057 

0*1440 

9718 

•2064 

,, hard drawn 


1*652 

0*02104 

0*1469 

9*940 

•2106 

Gold annealed . 


2*081 

0*02650 

0*4080 

12*52 

■5849 

,, hard drawn 


2*118 

0*02697 

0*4150 

1274 

•5950 

Aluminium anneale 

d 

2-945 

0*03751 

0-0757 

1772 

•1085 

Zinc pressed 


5*689 

0*07244 

0*4067 

34*22 

*5831 

Platinum annealed 


9*158 

o*n 66 

1*96 

55*09 

2*810 

Iron annealed . 


9:825 

0*1251 

0*7654 

59 *io 

1*097 

Nickel annealed 


I2*6o 

0*1604 

1 *071 

75 78 

i*535 

Tin pressed . 


13*36 

0*1701 

0-9738 

86*36 

1-396 

Lead pressed . 


19*85 

0*2526 

2*257 

119*39 

3*236 

Antimony pressed 


35*90 

0-4571 

2*411 

216* 

3*456 

Bismuth pressed 


1327 

1*689 

13*03 

798* 

18*64 

Mercury liquid . 


99*74 

1*2247 

13*06 

578*6 

18*72 

Platinum silver . 
Alloy hard or an- - ] 
nealed, 2 parts 
silver, 1 platinum J 
German silver hard 1 
or annealed . j 

Gold-silver alloy j 

i 

24*66 

0*3140 

2-959 

148*35 

4*243 

: 

I 

21*17 

0*2695 

1*85 

127*32 

2*652 

hard or annealed, | 
2 parts gold, I 1 
silver . . . J 

1 

io *99 

0*1399 

i*668 

66*io 

2*391 





















250 


Electricity and Magnetism .. [Chap. XVI. 

the presence of other metals in small quantities. Lead, tin, 
zinc, and cadmium, when alloyed with one another, conduct 
electricity as if the component parts had remained separate 
and were arranged as a bundle of conductors, each having 
a uniform section throughout. Alloys of bismuth, antimony, 
platinum, palladium, iron, aluminium, gold, copper, silver, 
mercury, and probably most other metals, have a much 
greater resistance than the mean resistance of their com¬ 
ponent parts. The resistance of a wire one mhtre long, 
and one millimetre in diameter, is given in the table : this is 
equal to the specific resistance multiplied into or 

12732. The resistances of the wires are given in ohms, 
the specific resistances in microhms. 

Notes .—In the above table the numbers underlined are direct obser¬ 
vations by Dr. Matthiessen, B. A. Report, 1864. 

The numbers given in Col. II. (metre, millimetre) are obtained by 
calculating the value in Column III. for lead from the specific gravity 
11 *376 (Table II., Electric Conducting Power of Alloys) and making 
the other numbers in the column inversely proportional to the conduct¬ 
ing powers given by Dr. Matthiessen, when hard drawn silver is 100, 
and gold silver alloy 15*03. Column III. is next filled in by calculating 
the values for zinc, platinum, iron, nickel, tin, antimony, bismuth, 
mercury, from Column II. by their specific gravities; the three 
alloys from specific gravities given by Dr. Matthiessen; the silver, 
copper, and gold, by proportion, from the hard drawn metals. Except 
in the case of lead, the underlined values do not agree with Column II., 
and the true specific gravity. Column IV. is calculated from Column 
II. by simply multiplying the numbers by 472*45 ; and Column V. 
from Column III. by multiplying the numbers by 1*4337. Column I. 
is calculated from Column II. by dividing the numbers in Column II. 
by 12,732. 

§ 15 . The specific conductivity of a material is the re¬ 
ciprocal of its specific resistance. Thus the specific conduc¬ 
tivity of hard silver in ohms is . wo = 605300. 
There is a common but most reprehensible practice of 
referring conductivities to some material such as silver. 
The result has been that numerous most careful experiments 
by skilled electricians are found to be valueless, for no two 


251 


Chap. XVI.] Measureme 7 it of Resistance. 


of them take as their standard metal a metal with the same 
conductivity. Nor are the relative conductivities of the 
standards known. Even Dr. Matthiessen’s experiments 
do not allow the construction of a perfectly satisfactory 
table. 

It should be observed that while copper has the greatest 
conductivity or smallest resistance of any known metal 
relatively to its volume, aluminium has the smallest resist¬ 
ance for any length of a given weight , a matter frequently 
of considerable importance. 

§ 16 . The specific resistance of all metals increases as 
the temperature increases, and for all pure metals except 
iron and thallium, Dr. Matthiessen found that the rate of 
increase was the same. The resistance R of a metal or 
alloy at the temperature t expressed in degrees Centigrade 
may be calculated from the resistance r at o° Centigrade by 


the following formula: 

R = r (1 + a t + b t 2 ) . . 

The following are the values of a and b : 


Most pure metals . 

,, Mercury 
,, German silver 
,, Platinum silver 
,, Gold silver . 


a 

•003824 

•0007485 

•0004433 

•00031 

•0006999 


. H° 
b 

+ -00000126 

- -000000398 
+ -000000152 

— -000000062 


According to experiments by Dr. C. W. Siemens, the 
resistance r for any temperature up to one thousand degrees 
Centigrade is expressed by the general formula r =a t* + 
(3 t -f- y (Bakerian Lecture, 1871). 

Very slight impurities increase the specific resistance of 
metals considerably, and they diminish the change of 
specific resistance with a change of temperature. 

The copper wire obtained commercially for submarine 
cables has usually a specific resistance from 5 to 8 per cent, 
higher than that of pure soft copper. It is usually tested at 
24 0 Centigrade, at which temperature the resistance of a foot 




252 Electricity and Magnetism. [Chap. XVI. 

grain of pure soft copper is 0*2262. The specified resist¬ 
ance of the French Atlantic cable at that temperature was 
0*2456 ; the actual mean resistance per foot grain at 24 0 
was 0*2388 ; calling r the resistance per knot, w the weight 
in lbs. per knot, and j* the resistance per foot grain, 

R = 1£9 ¥*J . . . Ia - 

w 

The resistance of iron used in telegraphy is given by 
Latimer Clark as 7 times that of pure copper, or at 24 0 
Centigrade 1*58 per foot grain: different specimens vary 
considerably. 

§ 17 . The specific resistance of insulating materials does not 
admit of being tabulated in the same manner as that of metals, 
because slight differences in the preparation of the materials 
cause great differences of specific resistance, and because of 
the effects of electrification* and of age. Gutta-percha and 
India-rubber as applied to insulate submarine cables have 
been the subject of an immense series of careful experiments. 
The resistance of a cubic centimetre of gutta-percha, a fort¬ 
night old, and tested at 24 0 Centigrade after one minute’s 
electrification, varies from about 25 x io 12 ohms to 500 x 
io 12 or more. The mean value of the specific resistance of 
the gutta-percha employed for the 1865 Atlantic cable was 
342 x io 12 (ohms) after one minute’s electrification. India- 
rubber when in good condition has a still higher resistance. 
The Persian Gulf cable made by Hooper had a specific 
resistance of about 7500 x io 12 ohms. 

Let r be the resistance of a length l of gutta-percha cover¬ 
ing to conduction, from the wire inside to the water outside, 
that resistance being what is commonly called the insula¬ 
tion resistance of the covered wire or core of a submarine 
cable; let m be the specific resistance of the material referred 

to the unit of volume; and let B be the ratio between the 

a 

diameter of the covering and that of the covered wire : then, 

* The effect of electrification or polarisation in causing an apparent 
increase of resistance is described in Chap. IV. § 10. 




Chap. XVI.] Measurement of Resistance. 


253 


r = -3665 


, D 

M 

I, 


13 ° 


L and m must be expressed in the same system of units. 
The resistance R k of a knot of cable is 

= ... 14 0 

Rk ~ 506300 

where m is the specific resistance referred as above to centi¬ 


metres. The value of—^— adopted by Mr. Latimer 
506300 

Clark for gutta-percha at 75 0 F is 769, corresponding to a value 
for m equal to 389 x io 6 megohms. This is a high value. 
The resistance of g.p. increases under pressure. Let r p be 
the resistance at the pressure p expressed in pounds per 
square inch, and r the resistance at the atmospheric pres¬ 
sure : then, approximately, 

r p . = r (1 + 0-00025 p.) . . . 15 0 

The constant 0*00023 probably varies for different speci¬ 
mens and at different temperatures. 

The resistance of G. p. also increases very considerably with 
age, if kept under water. This has not been observed with 
India-rubber. The resistance of some specimens of India- 
rubber tested by Dr. Siemens decreased under pressure. 

§ 18 . We may calculate the resistance of an insulating 
material separating two conductors in the following way. 
Let a body of known capacity s measured in microfarads be 
charged to the potential p measured in any unit, and let it 
be gradually discharged through a great resistance r such 
as the gutta-percha covering of a submarine cable offers to 
conduction through the insulating envelope, from the wire 
inside to water outside—the potential of the water being 
zero. Let the potential of the charged conductor fall to p 
in the time t measured in seconds; then in megohms 

R = - * —= °'4343 -p . . . . 16 0 

s log,] slo g/ 








254 


Electricity and Magnetism. [Chap. XVI. 

The capacity in electrostatic measure of covered wire, 
neglecting the ends, is given by the equation 6, Chap. V.; to 
convert this into electro-magnetic measure, we must divide 
the value by v 2 (§ 2, Chap. VIII.); and to express the result 
in microfarads the quotient must be multiplied by io 15 (Chap. 
X. § 5): hence the value of s for one knot or 6087 ft. expressed 
in microfarads is 

g _ 4-2 x 6087 x 30^48 x io 15 __ 0*2038 

4-6052 x (28-8) 2 x io 18 x log log ^ ’ 17 


Substituting this value for s in equation (16), we have for 
the resistance per knot, 


R* = 2*13/ 


*** 


i8 c 


This formula is the more convenient as d, d, p, p may be 
measured in any units as the ratios only are required. More¬ 


over, log is a constant for any one cable. 


The values of p 


and p may be observed on any electrometer, or by means of 
galvanometers, using the method described in the chapter on 
the Measurement of Capacity. 

The specific resistance of very short specimens of wire in¬ 
sulated by different materials may be calculated by the above 
method, when the current traversing the material would be 
insensible even on the most sensitive galvanometer. 

The method described in this section is only correct if r 
be constant throughout the experiment; we know that under 
electrification it actually increases from minute to minute, so 
that the result given by the formula is intermediate between 
the resistance when the experiment began and when it 
ended. 

§ 19 . A rise of temperature invariably causes a decrease 
in the resistance of insulators. Within the limits of o° and 





255 


Chap. XVI.] Measurement of Resistance. 

24 0 Centigrade the law of the decrease for gutta-percha is 
approximately expressed by the following empirical formula: 

Let r be the resistance of the material at the higher 
temperature, and r the resistance at the lower temperature, 
and let t be the difference of temperature in degrees Centi¬ 
grade: then 

R = r a 1 or log -= tloga . . . 19 0 ; 

r 

where a is a constant varying with different specimens of 
gutta-percha and also with variations in the time of electri¬ 
fication. The value of log a increases as the time of elec¬ 
trification increases, and is also higher at the lower tempera¬ 
tures. The following table gives values of log a for different 
times of electrification and also for two ranges of temperature, 
from o° to 12 0 and from 12 0 to 24 0 , derived from a series of 
experiments made on a knot of French Atlantic cable. 


Time of electrification 
in minutes. 

Between o° and 12 0 . 

Between 12 0 and 24° 

1 

•0562 

•0532 

2 

*o6l 

•0544 

5 

•0657 

•0554 

IO 

•0686 

•0560 

15 

•0706 

'057 

20 

•0725 

•0574 

25 

•0729 

•0578 

30 

•0736 

•058 

60 

•0765 

*0600 

90 or more 

•0747 

•0618 


Thus the resistance r, after one minute’s electrification 
at o°, was 7,540 megohms. Then, to find the resistance 
r at io° after the same time of electrification, we have 


log 5 =2 10 x 0-0562; whence r — = 2070 

r 3*040 

The following is a table of the relative resistances ato° and 

24 0 after various times of electrification. 



256 


Electricity and Magnetism. [Chap. XVL 


Minutes’ electrification. 

1 

2 
5 

IO 

20 

30 

60 

90 


Resistance at o°. 
7540 
9650 
I 2300 
I 44 OO 
I 74 OO 
189 OO 
219 OO 
24 OOO 


Resistance at 24 0 . 

369 

401 

457 

477 

493 

499 

5°9 

512 


It should be observed that the difference in resistance 
produced by electrification is much greater at the low tem¬ 
peratures : or, putting the same statement in another form, 
there is a much greater change of resistance produced by a 
change of temperature after long electrification than with 
short electrification. Experiments have been most frequently 
made after one minute’s electrification. 

R 

The following are a series of values of — for the tempera- 

r 

ture of o° and 24 0 from different observations. 


Name of cable. 

R 

f 

Log a. 

Persian Gulf 

36-5 

•0651 

Cores in which thickness of 

G.P. does not exceed -ii 

in. .... 

23-62 

•0572 

French Atlantic 

20-43 

•0545 

Willoughby Smith’s im- 

proved G.P. . 

28-14 

•0604 

Silvertown India-rubber 

17-84 


Hooper’s India-rubber 

3-01 

•OI 99 


The experiments on the Silvertown India-rubber seem to 
show that the increase of resistance does not follow the law 
expressed by equation (19). The resistance of Hooper’s 
material on the contrary, according to Mr. Warren’s experi¬ 
ments, does admit of being calculated by that formula up to 
the temperature of 38’33 Centigrade : the resistance is halved 
by a further increase of 18*33°. 



Chap. XVI.] Measurement of Resistance. 257 

The electrification of Hooper’s material is still more 
remarkable than that of gutta-percha ; with one specimen 
the apparent resistance had increased fourfold at the end of 
10 minutes, and after 24 hours’ electrification the resistance 
was 23 times greater than at the end of one minute. 
According to Mr. Warren, if Rj is the resistance after one 

minute, and R t the resistance after the time /, the ratio — 1 is 

constant for all temperatures with this material. 

§ 20 . The specific resistance of other insulating materials 
than India-rubber and gutta-percha has been very little tested; 
that of glass varies immensely in different specimens. Ley¬ 
den jars may be found which do not lose more than ^J-^th 
of their charge per diem, and the greater part of this loss 
appears to be due to conduction over the surface, or creep¬ 
ing as it is called, rather than conduction through the mass 
of glass. The specific resistance of some kinds of glass 
is therefore nearly infinite ; but many specimens of glass, 
especially those which contain lead, hardly insulate as well 
as gutta-percha. Vulcanite, porcelain, and paraffin are good 
insulators, but I am aware of no experiments determining 
their specific resistance. Liquid paraffin and some oils are 
also good insulators. 

§ 21 . Graphite and gas coke are used as conductors in 
batteries, and according to experiments by Matthiessen their 
specific resistance referred to the unit of volume is from 
about 1,450 to 40,000 times that of pure copper. Tellurium 
and red phosphorus have still higher specific resistances. 
The following table gives Dr. Matthiessen’s results expressed 
in the units now adopted. 


S 



258 


Electricity and Magnetism. [Chap. XVI. 


Specific Resistance of bad Conductors , computed from experiments by Dr. 
Matthiessen. 


Materials. 

Resistance in 
• Microhms. 

1 

Temperature 

Centigrade. 

Graphite, specimen 1 

2390 

22° 

,, 2 

3780 

22° 

>, 3 

41800 

22° 

Gas coke ..... 

4280 

25 ° 

Bunsen’s Battery, coke 

67200 

26-2° 

Tellurium .... 

212500 

19*6° 


ohms. 


Red Phosphorus 

132 

20° 


§ 22 . The specific resistance of liquid electrolytes is not 
very accurately known, though many experiments have been 
made with them. The phenomenon of polarization intro¬ 
duces a source of inaccuracy, and all observers hitherto 
have contented themselves with comparing the resistance of 
the liquid with some metal assumed as a standard, instead of 
determining the resistances in units. The author has endea¬ 
voured to reduce the results obtained to the resistances in 
b a units, and now gives a series of tables computed from 
Becker’s experiments on some of the solutions most em¬ 
ployed in batteries (‘Ann. d. Chem. u. Pharm.,’ vols. 73 and 
75). These experiments agree fairly with those of other 
physicists, except as to the small change introduced by the 
dilution of the sulphate of zinc solution: possibly some 
misprint or misunderstanding has occurred here. The rise of 
temperature diminishes the resistance in all cases. Sulphuric 
acid when diluted with water has a minimum resistance when 
of the specific gravity 1 *25, or, according to other experiments, 
when 45-84 grammes of so 3 are mixed with 100 cubic centi¬ 
metres of water. 









Chap. XVI.] Measurement of Resistance. 


259 


Sulphate of Copper. 


Percentage 
of salt in 
solution. 

I 4 ° 

16° 

18° 

20 ° 

24° 

28“ 

30 ° 

Centigrade. 

8 

12 

16 

20 

24 

28 

457 

36*3 

31*2 

28-5 

26-9 

247 

437 

34'9 

30*0 

27*5 

25*9 

23-4 

41*9 

33'5 

28*9 

26*5 

24-8 

22-1 

40-2 

32-2 

27-9 

25-6 

23-9 

21-0 

37 -i 

29-9 

26-1 

24*1 

22-2 

18-8 

34’2 

27-9 

24-6 

227 

207 

16-9 

32*9 

27'0 

24-0 

22-2 

20-0 

16*0 

Resistance 
of a cubic 
► centimetre 
expressed in 
ohms. 


Sulphuric Acid — diluted. 


pecific 

ravity. 

o° 

4 ° 

8° 

12° 

16 0 

20° 

24 0 

28° 

1 

Centigrade. 

1*10 

i ’37 

I *17 

I -04 

•925 

• 84.5 

786 

737 

709 


Resistance 

I‘20 

i *33 

I’ll 

•926 

792 

.666 

’567 

•486 

•411 


of one cubic 

1-25 

1 31 

1*09 

•896 

743 

•624 

•509 

•434 

758 


centimetre to 

1*30 

1*36 

1-13 

*94 

* 79 

•662 

•56I 

■472 

‘394 

! 

y conduction be¬ 

1-40 

1-69 

1-47 

i " 3 ° 

1 -16 

1-05 

•964 

•896 

•839 

1 

tween opposed 

1*50 

274 

2-41 

2-13 

1 -89 

172 

i-6i 

1-52 

1 ‘43 

1 

faces, express 

i*6o 

4-82 

4*16 

3-62 

3 ' 11 

275 

2 ‘46 

2*21 

2-02 

! 

ed in ohms. 

170 

9-41 

7-67 

6*25 

! 5 -12 

4-23 

3'57 

3-07 

27I 


1 


The resistance of solutions of sulphate of copper and 
sulphate of zinc increases steadily from the point of satura¬ 
tion as they are more and more diluted, but the solution of 
common salt has a minimum resistance when the solution 
contains about 24 per cent, of salt. 


Sulphate of Zinc. 


96 grammes 
in 100 C.C. 
of solution. 


io° 12 0 14 0 16 0 18° 20 0 

22'7 21 - 4 20*2 19*2 i8‘i 17*1 


22 ° 

16-3 


24 ° 

15-6 


Centigrade. 
Resistance of 
one cubic 
centimetre 


The same so¬ 
lution with 
an equal 
volume of 
water. 




21*1 20*3 19*5 18*8 i 8 *i 17*3 


expressed' ill 
ohms. 















































260 Electricity and Magnetism. [Chap. XVII. 

Nitric Acid. 

2° 4° 8° 12° 16° 20° 24 0 28° Centigrade. 

f t Resistance | 
1-94 1-83 1*65 1-50 1-39 1*3 1*22 1-18] of one cubii 

] centimetre i] 
( ohms. 

The specific resistance of water (res. of cubic centimetre) when pure is 
9320 ohms, computed from experiments by Pouillet. The presence of 
5o^ s th of sulphuric acid reduced this resistance to 155°. The tempera-, 
tures were not given by Pouillet. 

§ 23 . When the resistance of insulators is being mea¬ 
sured, care must be taken to prevent conduction over the 
surface of the insulating material between the two conductors 
separated by that insulator. If, for instance, a conductor 
c, Fig. 125, supported by a long vulcanite stem, be charged, 
and the gradual fall of potential tested by observing the 
potential on an electrometer, the insulation resistance of 
a b will not really be tested, for conduction will take place 
almost wholly by creeping over the slightly damp or dirty 
surface from a to b. Similarly the insulation resistance of a 
short length of covered wire, Fig. 115, will be very incorrectly 
indicated by a galvanometer g, unless the surface of the 
gutta-percha near a separating the wire from the water 
is such as to allow no creeping. Surfaces have no special 
conducting power, but the slight film of damp or dirt 
conducts in proportion to its sectional area and the con¬ 
ducting power of the particular kind of dirt. Thus brass 
filings or salt with a little moisture form a highly conducting 
film. The surface of glass being hygrometric will always be 
covered with a conducting film, unless the atmosphere be 
artificially dried in the neighbourhood. The outer layers of 
gutta-percha, soon after being exposed to the air, become 
so far changed as to insulate badly, so that the surface 
should always be fresh cut when experiments are being 
performed. Old vulcanite is often found covered with a 
conducting film resulting from the decay of the material. 
The surface of old glass which has been exposed to the 


Chap. XVII.] Capacities , Potentials , and Quantities . 261 

weather conducts better than new glass. Mr. Varley gives 
the following recipe for preserving and renewing the insu- 
! lating power of ebonite or vulcanite supports :— 

First, wash the ebonite with water, rubbing it well till dry; 
secondly, moisten the surface of the ebonite with anhydrous 
paraffin oil. To prepare this, put a quart of common 
paraffin and an ounce of sodium into a bottle. 

A glass support or the inside of a Leyden 
jar is best cleansed by being washed with 
distilled water and dried at a fire without 
being wiped. A stem such as a b may then 
be made to insulate admirably by setting it 
in a deep narrow tube with a little concen¬ 
trated sulphuric acid at the bottom. To 
increase the resistance of the conducting film, 
its sectional area must be diminished as much 
as possible, and its length increased : hence 
a long rod a b , Fig. 125, will insulate better 
than a short one, and a rod of small surface 
better than one with a large surface. 

The resistance of a film of dirt does not appear to follow 
Ohm’s law. When the potential of the charged and insulated 
conductor is increased, the loss by creeping increases in a 
much higher ratio : probably the conduction is partly due to 
numberless small discharges from one speck of dirt to its 
neighbour. 


Fig. 125. 
C 



CHAPTER XVII. 

COMPARISON OF CAPACITIES, POTENTIALS, AND QUANTITIES. 

§ 1 . The relative throw or swing of a galvanometer needle 
caused by the charging or discharging of two conductors 
gives a very convenient method of comparing their capacities 
when these are sufficiently large. Thus let xy, Fig. 126, 










262 Electricity and Magnetism. [Chap. XVII. 

represent the plates of a condenser separated by a dielectric 
from the opposed series of plates a b ; let a b be connected 

Fig. 126. j 



with the earth, and let x y be connected with the body of the 
key m ; the contacts p and o of this key serve at will to con¬ 
nect x y with the. zinc pole of the battery z c, the copper pole 
of which is to earth, and with the one terminal of the galva¬ 
nometer g, the other terminal of which is also to earth. If 
the handle at m be lifted, the condenser x y will be charged 
with negative electricity. On depressing m this charge will 
flow to earth through the galvanometer g ; this flow will 
throw the needle of the galvanometer to one side by an 
impulse of very short duration. If the needle is impeded by 
no friction, calling s and s r the capacity of two condensers, 
which, when charged by the same battery, throw the needle 
to the angles i and i l9 we have 

. • i • i\ 

s . Si :: sin— : sm —1 
2 2 

The current is proportional to the capacities, the impulse 
is proportional to the current, and the sines of half the angles 
are proportional to the impulses: hence we have the above 
proportion. Instead of observing the discharge we might have 
placed the galvanometer g between m and the plates x y of 






Chap. XVII.] Capacities , Potentials , and Quantities. 263 

the condenser; in that case, on raising m we should observe 
the throw of the needle produced by the charge when flowing 
in instead of when flowing out; the throw in the two cases 
is the same if there is no leakage from x y to a b. We 
might substitute for the earth any other conductor, joining 
E e x and e 2 without in any way affecting the observation. 

§ 2 . The galvanometer g may be shunted when one con¬ 
denser is observed, and less shunted or not at all shunted 
when a second condenser is tested; but in that case it is 
necessary to take care that the resistance of the shunts bears 
the same relation to that of the galvanometer for transient 
currents as for permanent currents. The self-induction of 
the shunt and the galvanometer may be very different, and 
may seriously affect the proportion in which the current is 
subdivided between the shunt and the galvanometer. 

§ 3 . A differential galvanometer may be made use of to 
compare two condensers, the capacities of which are nearly 
equal. The charges given to the two condensers by the 
same battery must, for this purpose, be passed simul¬ 
taneously through the two coils of the galvanometer; the 
sine of half the throw will then be proportional to the dif¬ 
ference between them. In making this experiment it is not 
necessary that the coincidence between the times occupied 
by the passage of the charges should be absolute ; it is 
sufficient that both charges pass while the magnet is still 
sensibly at rest. A similar comparison may be made, using 
a simple galvanometer, by the following device:— 

Pass a current from a battery c z, Fig. 127, through a con¬ 
siderable resistance r R t . Connect one point of the resistance 
r Rj with earth at e, the rest of the system being insulated. 
Then two points a and b separated from e by equal resistances 
will be at equal and opposite potentials. Now let the two 
condensers to be compared be charged respectively by 
simultaneous contact with a and b, then if they are equal they 
will receive opposite and equal charges. Next connect the 
two condensers one with another (after removing both from 




' 

264 Electricity and Magnetism. [Chap. XVII. 

a and b) ; then the two equal charges will exactly neutralize 
one another, and no charge will be detected in either con¬ 
denser. The absence or presence of a charge may be 
observed by galvanometer or electrometer. The proportion 


Fig. 127 



between two condensers may similarly be measured by 
observing the proportion between the resistances a e and e b 
required to produce charges which exactly neutralize one 
another. The capacities will be inversely proportional to 
the resistance a e and e b. These resistances must be 
considerable, or the potentials at a and b will be insufficient 
to charge condensers in such a way as to be measured by 
the electrometer or galvanometer. 

The points a and b may be connected by sliding pieces 
to successive terminals subdividing r r,. 

§ 4 . For small capacities Sir William Thomson’s platy- 
meter and sliding condenser may be used (vide Gibson and 
Barclay, spec. Ind., cap. Paraffin—Phil. Trans. 1871). 

Let there be two equal condensers p and p l9 Fig. 128, the 
outer armatures of which are insulated and the inner armatures 
connected with an electrometer. Let a and B be the two 
condensers which are to be compared; connect the outer 
armatures of a and b with p and p l respectively, and their 
inner armatures with the earth. 

Let a be so constructed that its capacity can be varied at 
will. Charge the outer armature of a positively, and at the 












Chap. XVII.] Capacities, Potentials, and Quantities. 265 

I same time connect the point q with the earth; the outer 
armature of p will take a positive charge, its inner armature 
a negative charge; /, will remain uncharged. Now break 

Fig. 128. 



contact between q and the earth; the electrometer will not 
deflect, for the charge in p will be unaltered. 

Connect the outer armatures of a and b ; if the ratio of p 
to a is the same as that of p x to b, the potential of q will 
remain unchanged, and the electrometer will not be de¬ 
flected; if - is greater than , the potential of q will be 

raised ; if ^ is less than ^ , the potential of q will be 

lowered by the connection of the outer armatures of a and 
b. The deflections of the electrometer due to the raising 
or lowering of the potential of q allow us to adjust the 

capacity of a until the ratio and if p — p x , we 

shall then have a = b. a can therefore be adjusted until 
it is exactly equal to b. 

This appears to be the best method for copying standard 
condensers, because it does not depend on the accuracy of 
any other instrument. Any error in the adjustment of p and 
p x can be detecfed and allowed for by reversing the position 













266 


Electricity and Magnetism. [Chap XVII. 

of a and b. The relation of equality is not required. In 
order that no deflection be produced by free electricity at q, 
it is sufficient if 

p : Pi — a : b. 

The analogy with the Wheatstone’s bridge is obvious. 

§ 5 . The absolute capacity in electrostatic measure of any 
small condenser is obtained by comparison with that of a 
sphere of known dimensions enclosed within another sphere 
of known dimensions. 

The absolute capacity of larger condensers in electro¬ 
magnetic measure is obtained from the throw i of the needle 
of a galvanometer through which an instantaneous dis¬ 
charge is passed; we have the capacity, 


7 r Rj 

Where t is half the period or time of a complete oscillation 
of the needle of the galvanometer when no current is pass¬ 
ing, and the resistance of a circuit in which the e. m. f. 
used to charge the condenser would produce the unit de¬ 
flection ; i has the same meaning as in § i. In a reflecting 
galvanometer half the deflection may be taken as equal to 
sin ^ i. This formula follows from the formula for the im¬ 
pulse produced by the current on the magnet, and the 
formula for the throw produced by a given impulse. In 
order that it should be applicable, the impulse must be very 
short when compared with the time and the resistance of 
the air must be insensible. This latter condition is only 
fulfilled when successive oscillations of the needle are 
sensibly equal. A galvanometer with a heavy needle should 
therefore be used in making this observation. The absolute 
value of the difference between two condensers detected by 
the method described m § 3 can be determined in this way. 

§ 6. The comparison of potentials of two batteries may 
be made indirectly by observing the currents which the two 
batteries are capable of maintaining through known resist- 




Chap. XVII.] Capacities , Potentials , and Quantities. 267 

ances; but this method has the defect that the electromo¬ 
tive force of most batteries varies when the resistance in 
circuit is changed, being higher with a large resistance and 
lower with a small resistance in circuit. The potentials can 
be directly compared by comparing the deflections which the 
two batteries produce on the same electrometer. If the 
difference is great, a graded electrometer must be em¬ 
ployed, or the following method may be used : charge a 
condenser with the higher potential • insulate the condenser; 
and then diminish the potential in a known and convenient 
ratio by connecting a second condenser with the first, the 
ratio between the condensers being previously determined. 
In this way the reduced potential may be brought within 
the range of the electrometer employed to measure the 
lower potential. If the condenser is large, the electrometer 
may be dispensed with and a galvanometer used to 
indicate the relative potentials, to which the condenser is 
successively charged by two batteries. The two discharges 
are proportional to sin \ i; and as the capacity of the 
condenser is constant, the potentials charging the con¬ 
densers are proportional to sin J i, or in the case of mirror 
galvanometers to the throw of the spot of light; by the use 
of shunts on the galvanometer this method is extended to 
the comparison of potentials differing 100 or 1000 fold. 

§ 7 . A quantity of electricity is seldom measured directly. 
A known current flowing for a given time conveys a de¬ 
finite quantity of electricity, and a body of known capacity 
charged to given known potential also contains a known 
quantity of electricity. The relative quantities per unit of 
surface on a conductor can be measured by the proof plane 
and an electrometer as already described. The quantity of 
electricity producing a given amount of heat or chemical action 
is best measured by the measurement of heat or of the weight 
of material electrolyzed. The quantity Q of electricity in a 
very short current flowing through a galvanometer is given 
in electromagnetic measure by the following formula :— 



268 


Electricity and Magnetism. [Chap. XVIII. 



Where Cj is the permanent current which produces the 
unit deflection on the galvanometer. This equation follows 
from equation i. 


CHAPTER XVIII. 


FRICTIONAL ELECTRICAL MACHINES. 


§ 1. The simplest of these is the electrophorus, which 
consists of two parts : i. a disc of ebonite, or similar material, 
a, cemented into a brass disc b, uninsulated ; 2. a brass plate 
c which can be held in the hand by an insulating stem d. 
When the surface of the ebonite a is rubbed with flannel, 
silk, or a catskin, it becomes negatively electrified ; if the 
disc c be now superposed on the electrified disc a, and 
connected with the earth by being touched with the finger, 
some of the negative electricity on a is conducted to earth. 
Some of the negative electricity remains on a, partly because 
there is not perfect contact all over the surface between a 
and c, and partly because the electricity on a is not wholly 


on the surface, but being 
attracted by the disc b, has 
penetrated the mass of the 
vulcanite in the manner 
indicated by the electrifi¬ 
cation described Chap. V. 
§ 6. The negative electri¬ 
city remaining on and in a 
attracts a positive charge 
to the lower surface of c. 
If the finger be now re¬ 
moved and the disc c lifted, 


Fig. 129. 



it retains its charge of positive electricity, which may be 








Chap. XVIII.] Frictional Electrical Machines. 269 

seen passing to earth in a spark if the knuckle or any other 
blunt conductor is brought near the edge of c. The dis¬ 
charged disc c may be again charged by being placed as 
before on the disc a and touched by the finger, and this 
process may be repeated until by gradual conduction to b 
and c the original charge on a is dissipated. It is certain 
that the electricity which is effective in inducing a charge on 
c does not lie on the surface of a, for the addition of one 
or two little brass pegs f passing from the surface of a to b, 
improves the action of 
the electrophorus : this 
little brass peg serves to 
conduct any negative 
charge which may accu¬ 
mulate on the surface of 
a to the earth. The elec¬ 
trophorus therefore acts 
as if the parts were 
arranged as in Fig. 130, where the simple vulcanite disc 
a is replaced by a metal conducting disc a a, electrified 
with negative electricity, and separated from c by a thin 
layer of dielectric, and from b by a thicker layer of the same 
dielectric. 

An electrophorus will continue to give sparks in rapid 
succession for a considerable period, and may be used to 
charge Leyden jars. A cheap electrophorus may be made 
by using a cake of resin instead of vulcanite, and wooden 
discs covered with tin foil instead of the brass pieces b and c. 

§ 2 . The frictional electrical machine, Fig. 131, consists 
of a vulcanite or.glass disc or cylinder a, made to revolve 
between cushions or rubbers of leather or silk BBp By the 
friction the (silk) rubbers become negatively, and the glass 
positively electrified. The difference of potential depends 
on the substances used as rubbers and disc; if one of 
these be put to earth, the other will be raised or lowered in 
potential to twice the extent by which it would have been 


Fig. 130. 










270 Electricity and Magnetism. [Chap. XVIII. 

raised or lowered if both were insulated, having been at 
the potential of the earth before commencing the experi¬ 
ment. This action is precisely analogous to that which occurs 

Fig. 131. 



with a galvanic cell; when both poles are insulated, one is 
raised above the potential of the earth, and the other 
lowered beneath it. Let one pole be put to earth, the po¬ 
tential of the other is immediately doubled, the difference of 
potentials remaining what it was before. Let us assume 
that the rubbers in an electrical machine are put to earth, 
then the positive electricity of the glass is collected by a 
series of points d d 1? placed close to the glass, and con¬ 
nected with a conductor f or a Leyden jar. The glass points 
are sometimes described as acting by induction thus : the + 
electricity on a induces — electricity on the points, which 
springs across to the glass, neutralizing the + electricity on 



















Chap. XVIII.] Frictional Electrical Machines. 


271 


the glass, and leaving the conductor or Leyden jar positively 
electrified. There is neither theoretical nor practical differ¬ 
ence between a negative spark passing from d to a, and 
a positive spark passing from a to d, and we may 
therefore correctly use the more simple statement given 
above. The positive electricity which the glass loses is 
supplied through the rubber; a stream of negative elec¬ 
tricity flows from the rubber to the earth while the con¬ 
ductor or jar is being charged; and this is only saying in 
other words that positive electricity flows from the earth to 
the rubber, whence it crosses to the glass and so to the 
conductor f or to a Leyden jar. It is just as essential to the 
effective working of the electrical machine in charging a jar 
that the outside of the jar be to earth, as that the rubber be 
to earth; and if the outside of the jar and the rubber be 
connected, it is unnecessary that either should be to earth. 
It is necessary in order to charge a jar or conductor as 
highly as the machine is capable of doing, that the electric 
circuit should be complete, except across the dielectric used 
to insulate the conductor to be charged. It is of no import¬ 
ance whether the earth form part of that circuit. The 
parts must be arranged as in Fig. 132, where b represents 
the rubber, a the rubbed glass, GG! conducting wires or 
chains, f and c the two opposed coatings of the Leyden iar 
and d the dielectric; c may Fig X13> 

be a mere brass ball, f the 



walls of a room, and d the air 
of the room. The case will 
not differ from* that of an ordi¬ 
nary Leyden jar except as to 
the capacity of the conductor 


c. The machine b a will 
produce the full difference of 

potential it is capable of producing between f and c. The 
charge given to c will simply then be proportional to its 
capacity. The circuit may all be insulated; it may be put 









272 Electricity and Magnetism. [Chap. XVIII. 

to earth between b and F, or it may be put to earth between 
a and c. The only effect of these changes will be to alter 
the absolute potential of f and c, but not to alter the 
difference. If, however, G and are both put to earth, the 
circuit is destroyed and no effect will be observed at f or c. 
Similarly, if g or G! are broken, the circuit will be destroyed ; 
but in this case some less perfect circuit is generally com¬ 
pleted, which will lead to the observation of some electrical 
difference between f and c if either g or g, are entire. 

§ 3 . In electrical machines sold by opticians, large brass 
conductors f f, insulated on long stems, are usually con¬ 
nected with the collecting points d d 2 Fig. 131. These large 
conductors have a sensible capacity, and allow the machine 
to produce long sparks and other phenomena requiring the 
accumulation of a considerable quantity of electricity. 
The addition of a large pasteboard cylinder with rounded 
ends covered with tin foil insulated from the earth by a 
single long stem and connected to DDj by a wire through 
the air, allows the volume of the spark obtained from 
the machine to be greatly increased. The insulating stems 
are best made of vulcanite, and should be kept clean, 
as described in § 23, Chapter XVI. No points or sharp 
angles must form part of the system of conductors 
attached toDD b if phenomena requiring great differences 
of potential are to be observed. Glass stems and discs are 
old-fashioned. They are weak, hygroscopic, and when 
rubbed with hot cloths to dry them become covered with 
fluff which conducts the electricity to earth. 

§ 4 . The friction of globules of [jure water suspended in 
steam against wood and other insulators may be made use 
of to produce electricity. This fact was discovered by Sir 
William Armstrong, whose apparatus was made as fol¬ 
lows :— 

The steam issuing from a high-pressure boiler by the 
pipe a passes in a series of tubes (not shown) through the 
box b, which is supplied with cold water; from these tubes 


Chap. XIX.] Electrostatic Inductive Machines . 


2/3 


the steam charged with condensed globules issues through 
the jets ccc. These jets are lined with wood. The friction 
charges the steam with 
positive electricity, which Fia I33> 

is gathered by a series of 
points at d attached to the 
insulated conductor f. The 
globules of water must be 
pure, or only charged with 
insulating materials. The 
resistance of pure water is 
so great that it may be 
looked upon as an imperfect insulator of the same class as 
flannel; the material against which the water rubs exercises, 
as might have been anticipated, a great influence on the 
amount and sign of the electricity produced. When tur¬ 
pentine is mixed with the water, the vapour becomes nega¬ 
tively electrified. 



CHAPTER XIX. 

ELECTROSTATIC INDUCTIVE MACHINES. 

§ 1. The action of the electrophorus, described in § i, 
Chapter XVIII. may be imitated by arrangements no part of 
which requires to be electrified directly by friction; and, more¬ 
over, the apparatus can be arranged so that the inducing 
charge shall be continually strengthened by the action of 
the machine. Inductive machines of this kind have been 
invented by Bennett, Nicholson, Mr. Varley, Sir William 
Thomson, and others. Mechanical energy in these instru¬ 
ments is converted directly into an accumulation of elec¬ 
tricity at different potentials, the work done being expended 
in overcoming electrostatic forces. The following is Mr. 
Varley’s design:— 




274 Electricity and Magnetism. [Chap. XIX. 

A series of metal conductors, c, c, c (Fig. 134), which will 
be called earners, are attached by means of a vulcanite disc b 
to the axle a, which can be made to rotate at pleasure. The 


Fig. 134. 



disc and carriers rotate between two pairs of metal insulated 
cheeks, e and e v which will be called inductors. The knobs h 
and h x are in connection with the earth, and are grazed by 
the carriers c c as they revolve. There are also contact 
pins at g and g x , which put each carrier successively in con¬ 
tact with e and with e x for an instant in passing. 

Let a small charge of positive electricity be communicated to 
e , the rest of the apparatus being at the potential of the earth. 
The plate e will induce a negative charge in c as it rises 
past h , the positive electricity flowing to the earth through h. 
The carrier c conveys this negative charge to g 1 , giving up 
almost the whole of it to the surrounding inductor plates e v 
This redistribution of the charge leaves c almost neutral, 
and the inductor e x next induces a negative charge in c as 
it descends past h x ; the carrier conveys this to e through 
the pin g, and so augments the original positive charge. 






Chap. XIX.] Electrostatic Inductive Machines. 27 5 

When it again passes h , it receives by induction a greater 
negative charge than before, which again augments the 
negative charge in e lf and this induces a new positive charge 
on c , which is transferred to e. Each turn thus augments the 
charge on both inductors in a continually increasing ratio; 
and the only limit to the charge which can thus be accumu¬ 
lated on the inductors is that determined by the escape of 
electricity from them in the form of sparks or brushes. A 
continuous supply of sparks may be drawn from e or e x . The 
knobs h and h x need not be in connection with the earth, 
provided they are in connection with one another. In that 
case, when passes h , and^, immediately opposite, passes h x , 
c and c x are connected for an instant. A positive charge is 
induced in c lf and a negative charge in c. When this arrange¬ 
ment is adopted, one of the inductors may be in connection 
with the earth. 

The arrangement adopted by Sir William Thomson to 
replenish Leyden jars, Chap. XIV. § 2, in which he wishes 
to maintain a constant potential, is very compact. The 
inductors are metal plates ee x bent so as to form cylindrical 
surfaces, as in Fig. 135. The axis a supports two carriers 
c Ci, which are also parts of cylinders not exactly concentric 
with the inductors. In the fig. the axis and carriers are shown 
removed from their positions inside the inductors. The 
connectors are shown at h and h v The springs ^and^j 
correspond to the pins with the same letter in Mr. Varley’s 
arrangement. In the mouse mill , another arrangement used 
by Sir William Thomson to give a rapid succession of sparks, 
the inductors are parts of cylinders and the carriers are 
long strips like the staves of a barrel. The smallest con¬ 
ceivable charge on one inductor of these machines is 
sufficient to start them ; indeed, it is difficult, if not impos¬ 
sible, so completely to reduce e and e v to the same potential 
that after a few turns of the carriers they shall not be highly 
charged. 

§ 2 . Holtz’s electrical machine is an inductive machine in 



2 76 


Electricity and Magnetism . [Chap. XIX. 


which the carriers are replaced by the imperfectly conducting 
film which usually covers a disc of glass, or by the external 
film of the glass itself considered as a body caoable of 


Fig. 135. 



receiving a charge, though not of conducting electricity. 
This film must be a sufficiently good insulator not to allow 
the escape of the charge it has taken. The theory of the 
machine will be more readily understood if we replace the 
imaginary film by a series of insulated carriers similar to those 
described for Mr. Varle/s apparatus. 

Let there be a fixed disc, Fig. 136, of insulating material 
b and a rotating disc of insulating material a ; on each 
side of the disc a let there be a series of metal carriers c 
and d all insulated from one another. On the disc b let there 
be two inductors e and e lf the first positively and the 
second negatively charged, e and e l cover both sides of 
disc b for a short distance, and there are two openings F 
and f 1? as shown. The fixed rods h and h x serve to join 
successive pairs of carriers d and d l as they come opposite 
e and e v The rods h and h x are shown with a couple 
of little balls, which can be separated to show sparks pass- 











Chap. XIX.] Electrostatic Inductive Machines. 277 

ing along the connecting rods h and h x . There are also 
shown two springs g and g lt which serve to connect each 
carrier c in succession with e and e x . 

Now let the disc a revolve so that the 
side nearest us moves in the direction of 
the arrow; when c is opposite e , and 
c l opposite e X} d and d x being connected 
by h and h x , there will be a positive 
charge induced on the external surfaces h 
of d and c lf a negative charge on the 
external surfaces of d x and c. As the ro- I 
tation continues, each of these carriers 
will become disconnected from h and ▼ 
h x , and will carry with it its «charge of 
electricity without any considerable 
change in the distribution. d x and c x 
will, after a fraction of a revolution, 
come opposite f, where they are shown 
as c a . and d a . The positively charged 
carrier c a will come in contact with the 
spring g ; at the same time c and d will 
have come to the position c b and d b ., 
and the negatively charged carrier c b will come in contact with 
the spring g x . There will then be a redistribution of elec¬ 
tricity. The capacity of c a and c b is diminished by the absence 
of the plate b at f and f 1? and the result of the redistribution is 
to remove the greater part of the positive electricity from c a to 
e, of the negative electricity from c b to e u to set free negative 
electricity on d a and positive electricity on d b . When, therefore, 
d a comes under h into the position of d, , the negative elec¬ 
tricity flies to d X y or, in other words, positive electricity flies to 
d x from d , and the cycle of operations recommences. The 
rods h, h x , the carriers c } c x , &c., the inductors e, e x , and the 
contact springs g , g x , all play exactly the same part in Holtz’s 
machine as in Varley’s, with the exception that in the new 


Fig.136. 



















278 Electricity and Magnetism . [Chap. XIX. 

arrangement the connectors h , h x , instead of joining c, c x 
directly, join a new set of carriers d f d u &c., on which c , c x 

The actual Holtz’s machine has no 
carrier. There is a fixed disc of glass b 
and a rotating disc of glass a. At the 
openings f and Fi there are the in¬ 
ductors e and e u made of paper ; the 
connecting-pieces g and g x are also of 
paper, and merely point at the place 
where the carriers should be ; the con¬ 
nectors h , h x are brass rods ending in 
points opposite c and c x ; the part of the 
carriers is played by the surface of the 
glass ; the action is identical with that 
described for carriers. The openings 
at F! and f serve to insulate the positive 
from the negative parts of b as well as 
to alter the capacity of each portion 
of the surface of a as it passes them ; 
the rods h and h { are arranged so that 
they can be withdrawn, leaving a space 
at n across which sparks pass; if the 
space be gradually increased between h 
and h x at n, after the machine has been set in action by charg¬ 
ing e or e u a splendid violet brush of some inches in length 
may be observed passing at n. If Leyden jars are hung on 
h and h x to increase their capacity, this brush is replaced 
by a torrent of brilliant sparks. With large Leyden jars on 
h and h x one spark of extraordinary length and volume 
passes at sensible intervals of perhaps one or two seconds. 

In the figures the openings f and Fi are shown as if they 
were near together, because the whole series of inductions 
can thus be better brought into one view. In the machine 
itself, as shown in Fig. 138, the openings are diametrically 
opposite one another, and the electricity is collected from 


induce charges. 


Fig. 137. 


















Chap. XX.] Magneto-electrical Apparatus. 279 

the glass by a comb or series of points h and attached to 
the rods h and h v The openings f and f x are behind the 
transparent Dlate a, though shown in the full lines. 

Fig. 138. 



The dark portions of the figure e and e x are the paper 
armatures which are on both sides of b. The gear is 
omitted by which a is driven. The plate b is carried by four 
supports touching its edge. 


CHAPTER XX. 

MAGNETO-ELECTRICAL APPARATUS. 

§ 1 . The phenomenon described in Chapter III. § § 18 and 
19, and more fully explained in Chapter IX., is often de¬ 
scribed as magneto-electric induction when the current is 
induced by the motion of a wire in a field produced by a 
magnet , the term electro-magnetic induction being reserved 
for the case in which an electric current induces magnetism. 
The 1 distinction in this sense is rather popular than scientific, 

1 An essential and scientific distinction can be drawn between the 
two cases by applying the name, magneto-electric induction, to all those 













280 Electricity and Magnetism. [Chap. XX. 

but it is convenient to retain the name magneto-electrical 
apparatus for those arrangements in which powerful electric 
currents are induced in wires moved across a magnetic field 
produced by permanent magnets or electro-magnets. 

In magneto-electric apparatus the moving coils of wire 
must be driven by some external source of power. 

The term electro-magnetic apparatus is used, on the 
contrary, for those arrangements in which the battery pro¬ 
ducing a current is the source of power which produces 
motion. An electro-magnetic engine is one which may be 
employed to drive machinery. 

§ 2 . Arrangements giving electric*currents by the relative 
motion of magnets and coils were invented by Pixii and 
Ritchie. The apparatus which will be now described is 
generally known as Clarke’s : In front of a powerful horse¬ 
shoe magnet a, Fig. 139, there are two bobbins b and B! of 
insulated wire; these two bobbins are carried by one 
frame v, which rotates round a horizontal axis, being 
driven by a pulley. The two coils of wire are continuous, 
so that a single current may flow round both; but they 
are so joined that the current flows in a right-handed direc¬ 
tion round one and flows in a left-handed direction round 
the other. Each bobbin has a core of soft iron, and these 
cores are joined by iron at the back; that is to say, at 
the ends farthest from the horse-shoe magnet. Two ends of 
the wire on b and Bj are directly joined, but the two other 
ends are connected through a set of springs rubbing on suit¬ 
able contact pieces on the axis, with two fixed terminals t and 
Tj, and the circuit is not complete till these are joined. We 
will suppose this to be done.- As the coils rotate, each soft 
iron core is successively magnetised in opposite directions; 
thus coil b, when opposite a north pole, has its south pole 
near the magnet and its north pole at the back, and this 

cases which require relative motion, and using electro-magnetic induction 
to denote only those phenomena of induction which result from the 
change of currents or magnetism without relative motion. 


Chap. XX.] Magneto-electrical Apparatus. 281 

arrangement of the magnetism is reversed when b is opposite 
the south pole; thus in every revolution a magnet is, as it 
were, introduced into b, withdrawn, and replaced with its 
poles in the opposite direction, and again withdrawn. 


Fig. 139. 



The withdrawal of a magnet having its north pole at one 
end of b, and the introduction of a magnet having its south 
pole at the same end, both tend to induce a current in one 
direction ; but the withdrawal of this second magnet, and the 
introduction of the reversed magnet, induce a current in the 
opposite direction. Thus from the instant the coil b begins to 
leave the pole s, to that instant at which it arrives opposite 
n, a current in one and the same direction is being induced; 
but as soon as b begins to leave n and return to s the direc¬ 
tion of the current is reversed, and continues reversed until 
opposite s. Thus two equal and opposite currents are 
induced in b during each revolution. The same statements 
hold good of Bj, but when the current induced in b is right- 



































282 Electricity and Magnetism. [Chap. XX. 

handed that in b x will be left-handed. When the coils are 
joined as described, the two currents are added to one 
another; the currents can be observed and utilised on that 
portion of the circuit which is interposed between t and iq. 
With the connections as described the currents will be 
reversed between t and at every half-revolution ; but it is 
easy to arrange a set of contact pieces in the axis so that 
although the currents must necessarily be reversed in the 
coils, they flow always in one direction between t and Tj. 

§ 3 . Even when flowing in one direction the currents 
between t and t 1? must rise to a maximum and decrease to a 
minimum once during each half-revolution. 

The maximum current occurs at those points where the 
armature (as the soft iron continuous core may be termed) 
resists the motion most strongly. At these points the 
greatest change of magnetism is taking place in the armature. 
The motion of the coils alone without a core would give 
rise to similar but much weaker currents. The best length 
and thickness of wire depends on the resistance through 
which the current is required to flow between t and Tj. 
If this resistance is small, the coils b and Bj should be made 
of thick wire; if the external resistance is great, then the 
coils should be composed of many turns of thin wire. 

§ 4 . Instead of a simple pair of bobbins and a single 
horse-shoe magnet, we may arrange any convenient number 
of bobbins on a ring moving in front of the poles of a series 
of magnets also arranged in a circle. Still better, we may let 
the ring of coils rotate between two rings of magnets, each 
coil having its own core, which is alternately magnetised in 
opposite directions ; each coil being then connected with its 
neighbour, so that the current flows alternately in a right- 
handed and left-handed direction, we add the electro-motive 
forces due to all the coils. 

The coils may be joined in series, or the pairs may be 
joined in multiple arc, the former plan being adopted if 
the object is to get a great e. m. f. between t and ; the 


Chap. XX.] Magncto-electrical Apparatus. 283 

latter plan if our object is to obtain a moderate e. m. f., with 
a very small resistance in that part of the circuit which 
forms part of the magneto-electric machine. Great heat 
would soon be developed with the latter plan. With the 
former (coils in series) very perfect insulation is required 
between the separate layers of the coils, or sparks will 
perforate the insulating substance and destroy the action 
of the coils. The following is a description of a machine of 
this class constructed by Mr. T. Holmes, and successfully 
used by him to produce the current for a large electric 
lamp :— 

The coils, eighty-eight in all, are fixed in the rim of a 
wheel about five feet in diameter, with their axes all parallel 
to the axis of the wheel. They are arranged in two rings, each 
containing forty-four equally spaced bobbins. The centre 
of each bobbin in one ring corresponds with the centre of the 
space between two bobbins in the other ring. This wheel 
is driven at about no revolutions per minute. Horse-shoe 
magnets are fixed in a frame round the circumference of the 
wheel in three planes, or rings, containing twenty-two each. 
The two poles of each magnet are in the same plane, or ring. 
The distance between their poles is equal to the distance 
between the bobbins, or coils. The magnets in the two 
outside rings have similar poles opposite one another. The 
magnets in the inner ring are placed with opposite poles 
facing the two similar poles of the outer rings. The two out¬ 
side rings have compound magnets of four steel plates ; the 
magnets of. the inner ring between the two sets of bobbins 
have six plates. The weight of each plate is six pounds. 
Alternate coils have their iron cores magnetised in oppo¬ 
site directions, but the wires are so connected in series that 
the induced currents flow all in the same direction relatively 
to the wire. The length of the hollow iron core inside each 
bobbin is 3^ inches. Its external diameter, ij inch; its 
internal diameter, 1 inch. Two copper wires, *148 inch in 
diameter, forty-five feet long, are wound round each core 


284 Electricity and Magnetism. [Chap. XX, 

and connected in double arc. These wires are equivalent to 
one wire ‘2 inch in diameter of the same length. The iron 
core and brass bobbin surrounding it are split; that is to say, 
an open slit is left down one side 1 of each cylinder. This 
prevents the induction of currents in the bobbin and wire 
where they are not wanted. 

Each ring induces forty-four distinct currents during one 
revolution of the wheel, and the maximum current from one 
ring coincides with the minimum current from the other; and 
as each current lasts a very sensible time, and by a commuta¬ 
tor is transmitted always in one direction, their combination 
does not produce a series of sparks, but a nearly constant and 
uniform current. One and a quarter horse-power is re¬ 
quired to drive the machine when in action, and much less 
when the circuit is broken so as to stop the induced current. 
This machine offers a striking example of the transformation 
of work into a current of electricity. 

§ 5 . If the change of magnetisation could take place in¬ 
stantaneously, there would be no limit to the electromotive 
force which these machines could produce, except the limit 
imposed by the difficulty of insulating the wire and of driving 
the coils against a great mechanical resistance; the electro¬ 
motive force induced in the coils would increase in direct pro¬ 
portion to the speed at which they were driven. Practically 
owing to the coercive force of even the softest iron and the 
self-induction of the wire on the bobbins, the change of 
magnetisation and of direction of the current occupies a very 
sensible time, and if the speed be increased beyond that at 
which the greatest change of magnetisation occurs, the elec¬ 
tromotive force will fall off instead of increasing. The effect 
of the coercive force is diminished as stated above by making 
the core hollow, and the effect of useless induction is dimin¬ 
ished by splitting it from end to end. 

§ 6. Obviously the magnets used to induce the currents 
might be electro-magnets ; but if these were excited by an 
independent battery, the induced current would be obtained 


Chap. XX.] Magneto-electrical Apparatus. 285 

at a much greater cost than would give the same current 
directly from a battery. 

Mr. Wilde conceived the happy idea of using a current in¬ 
duced by permanent magnets to excite a large electro-magnet 
which is used to induce a second current, which can be so 
much greater than the first as the electro-magnet is more 
powerful than the permanent magnet. The second current 
may be used to excite a second electro-magnet still more 
powerful than the first, and this second electro-magnet used 
to induce a third current greater than either of the two 
others. Dr. Siemens and Professor Wheatstone simultane¬ 
ously invented a further extension of the same idea. They use 
the current induced by the permanent magnet to convert 
this magnet itself into an electro-magnet. The effect is very 
remarkable. However weak the permanent magnetism in 
the inducing magnet may be in the first instance, a few rapid 
turns of the coils with their armatures induces a current 
which increases in geometrical proportion, increasing the 
magnetism of the inducing magnet at the same time, until 
the resistance of the armatures as they pass the poles is 
such as to balance the driving power. The current in 
the main circuit may be directly utilised, or one portion 
of it may be shunted for use while the other branch 
maintains the magnetism of the electro-magnet. Mr. Ladd 
modifies this arrangement by having two distinct coils on 
his armature, one of which is used to excite the electro¬ 
magnet, while the other conveys the induced current which 
is to be utilised outside the machine. Ladd's, Wilde's, and 
Siemens’ machines will produce currents capable of fusing an 
iron rod an inch in diameter and a foot long. The arma¬ 
tures and coils become themselves so hot that they must 
be artificially cooled, or the machine can only be worked for 
short periods without being permanently injured. 

§ 7 . The armature used in these new machines is generally 
of the form introduced by Messrs. Siemens, which is much 
superior to that in Clarke's apparatus. 




286 


Electricity and Magnetism. [Chap. XX. 

The compound horse-shoe magnets are arranged in a pile 
of considerable depth, each separated from its neighbour by 
a sensible space, as shown in Fig. 140. The armature a A t 
rotates round the axis x y between the poles in a position 
where the magnetic field is much more intense than that 

Fig. 140. 

Sectional Elevation. 



A 



occupied by Clarke’s armature. This armature is a long bar 
of soft iron of an W section, as shown in plan at a (Fig. 140), 
and is magnetised transversely. The wire is wound round it 
longitudinally, passing up one side and down the other. 

As this armature rotates round the axis x y its magnetism 
is reversed, and at each reversal a current is induced in the 
enveloping wire. The intensity and uniformity of the mag¬ 
netic field in which the wire is placed cause this arrangement 
to give much better results than those obtained by Clarke’s 
arrangement. 

§ 8. It is unnecessary that the armature either of Siemens’ 
or Clarke’s or any magneto-electric machine should com¬ 
plete one or more revolutions in order to induce a current: 



















Chap. XX.] Magneto-electrical Apparatus . 287 

the smallest motion about the axis is sufficient to produce 
some electromotive force, because it will change the intensity 
of the field in which the armature is placed. With Siemens’ 
armature especially a very small deviation in one direction 
from the position shown in the plan, Fig. 140, will give a 
powerful current. The wires of the coil move almost directly 
across the lines of magnetic force, and the armature will be 
so magnetised as to help the induction so produced. A slight 
motion in one direction will induce a positive current, a 
slight motion in the opposite direction a negative current. 
Keys for sending electric signals without batteries are con¬ 
structed on this principle. 

§ 9 . The Inductorium , or Ruhmkorff’s coil, is strictly 
speaking an electro-magnetic apparatus, inasmuch as the 
inducing magnet is not moved, but is magnetised and de-mag- 
netised by the passage and interruption of a current from a 
battery. It is used to obtain by induction a great electro¬ 
motive force from a battery of small electromotive force. The 
inductorium consists of an electro-magnet excited by a com¬ 
paratively short coil of thick wire called the primary coil : a 
long coil of fine wire, called the secondary coil, is wound 
round the same electro-magnet; the primary circuit, which 
is completed by a battery of small resistance such as Grove’s, 
is alternately made and broken with great rapidity; the 
secondary circuit is always complete, or interrupted only by 
such a space that the electromotive force induced in the 
secondary is sufficient to cause the passage of a spark. 
When the primary circuit is closed, the electro-magnetism of 
the core induces a current in the secondary wire in a direc¬ 
tion opposed to that of the primary circuit. When the 
primary circuit is interrupted, the diminution of the mag¬ 
netism in the core induces a current in the same direction 
round the wire as the primary current, and therefore in a 
direction through the secondary coil opposed to the current 
previously induced. 

The electromotive force per foot of the wire in the 


288 


Electricity and Magnetism. [Chap. XX. 

secondary coil depends on the intensity of the magnetic 
field produced and on the rapidity with which it is produced. 
The sum of the electromotive forces thus induced in a long 
coil is enormously greater than the e. m. f. of the inducing 
battery; the longer the secondary coil the greater the 
electromotive force. 

§ 10 . Sparks many inches in length can be obtained from 
the secondary circuit of a large inductorium, but in such 
apparatus the greatest care is requisite in the insulation of 
the secondary coil. Each wire must be insulated from its 
neighbour by layers of some hard insulator which a spark will 
not easily pierce, and care must be taken so to wind the coil 
that no two portions of the secondary coil at very different 
potentials are near together: this is effected by winding the 
coil in successive compartments a, b, c,as in Fig. 14T, where 
each compartment is insulated from its neighbour by discs 


Fig. 141. 



of vulcanite. In order to facilitate the rapid change of mag¬ 
netism, the core should be either a hollow split cylinder or a 
bundle of iron rods insulated from one another. 

The making and breaking of the primary current is gene¬ 
rally effected by a little oscillating hammer having a small 
armature of soft iron at its head : this hammer is placed so 
as to be attracted when the iron core is magnetised; by its 
motion towards the core it breaks the primary circuit; the 
core being no longer magnetised allows the little hammer to 
fall back and so once more to complete the primary circuit; 
this re-magnetises the core, and the hammer again breaks the 
circuit, and this action repeats itself indefinitely. There are 











Chap. XX.] Magneto-elcctrical Apparatus. 289 

adjustments by which the rapidity of the oscillations of the 
hammer can be regulated until the best result is obtained. 
The limit to the speed at which the successive currents can 
be induced depends on the coercive force of the iron core 
and the self-induction of the secondary coil. The work 
done in the secondary coil by the induced current is neces¬ 
sarily less than that done in the primary coil by the battery, 
however much greater the electromotive force may be. 

The following is a description of an inductorium made by 
Messrs. Siemens :—The core is made of iron wires 1*3 m.m. 
diameter and 95 centimetres long. These are cemented to¬ 
gether and form a cylinder 60 m.m. diameter. Two layers of 
copper wire 2*5 m.m. diameter form the primary coil. This 
coil and the iron core weigh 35 lbs. They are placed in a 
tube of hard vulcanite 26 m.m. thick at the ends, and 12 
m.m. thick at the middle : along this tube 150 thin discs of 
vulcanite are fixed at equal intervals, and the ends are 
covered with thick discs of the same material. Each sub¬ 
division between the little discs is filled with a coil of fine 
silk-covered and varnished copper wire 0*14 m.m. diameter : 
these coils are connected in series, so that the current flows 
from the outside to the inside of one compartment and from 
the inside to the outside of the next, in order that no two 
portions of wire at greatly differing potentials may ever be 
in close proximity. The length of the secondary coil is 
10,755 metres, and it makes 299,198 turns round the 
cylinder. The weight of the copper wire is 58 lbs. and its 
resistance about 155,000 ohms. 

There is some difficulty in arranging a good make and 
break piece acted upon by the hammer on account of the 
large sparks which pass between the contacts tending to 
fuse them together and oxidise them. Messrs. Siemens 
make contact between a platinum point and a platinum or 
silver amalgam covered with alcohol. 

When long sparks are wanted, the make and break appa¬ 
ratus is driven slowly, by clockwork or by a separate 

u 


290 Electricity and Magnetism. [Chap. XX. 

electro-magnetic engine, so as to give a long contact, which 
is then suddenly broken. The above apparatus will give 
sparks of from one to two feet in length, with six large 
Grove’s elements in the primary circuit: 50 miles of fine 
wire have been used in some induction coils. 

§ 11 . A Leyden jar or some other form of condenser is 
frequently attached to the secondary circuit when this is 
used to give sparks. The one armature of the condenser is 
connected with one end of the secondary wire and the 
other armature with the other end of the same wire, near the 
opposed points across which the spark is to pass; the effect 
of this arrangement is that a considerable accumulation of 
electricity takes place near the points before the difference 
of potential is sufficient to cause the spark to pass, and con¬ 
sequently the number of sparks observed in a given time is 
less with the condenser than without, but each spark con¬ 
veys more electricity and is much more brilliant. An electro¬ 
motive force in the coil insufficient to cause any spark to 
pass may nevertheless help to charge the armatures of the 
condenser, and thus some portions of the inductive action 
may be utilised with the condenser which without it would 
be wasted. The dielectric must be thick and strong, or it 
will be pierced by the spark. 

A condenser is also frequently employed, connected with 
the primary circuit. 

§ 12 . The Inductorium may be used to give the sparks 
required for examination by the spectroscope or to give an 
electric light, which is, however, comparatively feeble. It may 
be used to charge Leyden jars and produce physiological 
effects; it may be used to produce the beautiful luminous 
effects which occur when electricity is passed through 
rarefied gases. The gases are enclosed in glass tubes having 
platinum electrodes soldered into the glass and terminating 
in balls at a considerable distance apart: instead of the 
spark observed in air, a diffused light is seen differently 
coloured in various gases and beautifully stratified. These 



291 


Chap. XXI.] Electro-magnetic Engines. 

appearances have been carefully studied by Gassiot, Pliicker, 
and others. The tubes enclosing the gases may be bent 
into very complicated shapes, and filled in different parts 
with different gases, so as to produce a striking and pretty 
appearance when the current from the inductorium passes : 
they are generally called Geissler tubes. The induction of a 
magnet, or of a current of electricity, or of a simple conductor 
outside the tubes, can be observed on the luminous current 
within, causing it to be distorted or move in those directions 
in which the inductive force would act on a solid wire con¬ 
ducting a similar current: for this experiment the tube must 
be wide or nearly spherical, so that the luminous current 
occupies only a portion of the enclosed space. 


CHAPTER XXI. 


ELECTRO-MAGNETIC ENGINES. 


§ 1. The most elementary arrangements by which electricity 
can be made to produce regular motion by electro-magnetic 
force are those in which a short wire or rod conveying a 
current is made to rotate by the direct and continuous 
electro-magnetic attraction to or repulsion from some fixed 
conductor conveying the same or another current. 

Let o p, Fig. 142, be a wire capable of rotation round o, 





and conveying a current from the centre to the circumference 
of a ring-shaped trough of mercury into which the end 








2 Q2 Electricity and Magnetism. [Chap. XXL 

of the wire p dips. Let the same current or another be 
conveyed in a straight wire a b near the edge of the 
mercury ring. Then the wire o p will be attracted by 
a b until p reaches the position Pj, Chap.- III. § 6 ; the wire 
will then be repelled till it reaches the position p in , when it 
will be again attracted, and thus continuous rotation may 
be produced in the direction shown by the arrow, if the 
other portions of the circuit are arranged so as not to neu¬ 
tralise the series of actions described. The force available 
even with very powerful currents is small. 

Again, let the fixed current flow in the circle a b as shown 
by the arrow, Fig. 143; the moveable wire op in which a 
current flows from the centre to the circumference will be con¬ 
tinuously impelled to rotate in a direction opposed to that of 
the fixed current. The force will be very small, but we may 
multiply it by using a coil of many turns for the conductor 
a B. No convenient way has yet been found of multiply¬ 
ing the conductor o p, and the power given out by this 
arrangement is therefore still very small. 

A horizontal circular current also tends to produce con¬ 
tinuous rotation in a vertical current approaching it or receding 
from it. Thus let a moveable system pmp„ Fig. 144, be 

Fig. 144. 



placed in the centre of a fixed ring a b, through which a 
current flows as shown by the arrow. Let the ends p and 
?! dip in a mercury trough, by which the circuit through 











293 


Chap. XXI.] Electro-magnetic Engines . 

o p and o Pj may be maintained : both vertical currents de¬ 
scending to p and Pi are acted upon in one direction by the 
fixed current, and tend to turn p m P t in a direction opposed 
to that of the current in a b. 

§ 2 . Currents can be made to rotate by magnets, and 
magnets by currents, under the influence of continuous 
electro-magnetic attraction and repulsion. Let a magnet n s, 
Fig. 145, be weighted so as to float upright in a vessel filled 


Fig. 145. 



with mercury, and let the upper end of the magnet carry a 
little capsule m of mercury, serving to connect the magnet 
with one pole of a galvanic battery by the point z, and 
yet leave it free to rotate ; the magnet should be well var¬ 
nished, except at its lower end. Let the other pole of the 
battery be brought to the mercury near the magnet by a 
wire c : the magnet will rotate so long as the circuit is 
complete. The cause will be obvious if we consider the 
magnet to be a kind of solenoid, for then a force will act 
between each ring of the solenoid and the current going 
from the centre to the circumference, as in the second ex¬ 
periment of the last §. The force in this case will cause 

































294 


Electricity and Magnetism. [Chap. XXI. 


the ring (the solenoid or magnet) to rotate, the current 
flowing from centre to circumference being fixed. 

If the magnet be fixed and a little wire frame similar to 
that in Fig. 144 be pivoted upon it with the two vertical ends 
p dipping into the mercury near the magnet, the frame will 
be caused to rotate by the magnet. This is explained by the 
third experiment of § 1, if we look upon the magnet as a 
solenoid. 

§ 3 . The power to be obtained from the above arrange¬ 
ments of magnets and currents is so small that they cannot 
be employed to drive any other apparatus, and cannot 
therefore be termed electromotors. By alternately mag¬ 
netizing and demagnetizing electromagnets we can construct 
electromotors giving out as mechanical effect a considerable 
fraction of the whole energy of the electric current. The 
simplest electromotor is Froment’s rotating engine. This 
consists of one or more horse-shoe electromagnets, a a \ } 
fixed as in Fig. 146, radially outside the periphery of a 
drum, D, capable of rotation. On the periphery of this 

Fig. 146. 



movable drum there are a series of soft iron bars 01 
armatures, bbe, etc. As the drum revolves it completes 
a circuit, by suitable make and break pieces, sending a 
powerful current through each electromagnet as each arma¬ 
ture approaches its poles within 15 0 or 20°: the electro¬ 
magnet then attracts the armature and so drives the drum 










295 


Chap. XXI.] Electro-magnetic Engines. 

forward. The circuit is interrupted, and the magnet there¬ 
fore unmade, just as the armature passes the poles ; the drum 
continues its rotation by inertia or by the action of another 
electromagnet, until a second armature approaches the poles 
of the first electromagnet, when the circuit is made as 
before. The make and break pieces and successive elec¬ 
tromagnets are so arranged that the current is not cut off 
from one circuit till it can flow through the next. This has 
the double advantage of tending to produce uniformity in 
the driving action and of preventing the passage of sparks 
when the contacts are made and broken. These sparks 
tend to bum the contacts, and gradually to prevent them 
from closing the circuit. 

Another form of electromotor is constructed, resembling 
the ordinary beam steam engine ; the piston is represented 
by a magnet which is alternately sucked into a hollow coil, 
and repelled as the current in the coil is reversed ; sometimes 
a soft iron piston is used, which is alternately attracted and 
set free. 

§ 4. Much more attention would be directed to electro¬ 
motors than they have hitherto received were it not for the 
fact that they are necessarily at least fifty times more ex¬ 
pensive to maintain in action than the ordinary steam 
engine. Zinc is the cheapest material by the consumption 
of which electricity is produced. The energy evolved by the 
consumption of one grain of zinc is only about x Vth of 
that developed by the consumption of a grain of coal. 
A large fraction of the energy in the case of the zinc can be 
converted into an electric current, whereas we have not 
yet discovered any means of obtaining the energy of coal 
except as heat, and we necessarily waste a great part of this 
heat in the process of transforming it into mechanical energy. 
In the transformation of energy into mechanical effect the 
advantage lies with electricity. The whole of the energy 
either of heat or of an electric current can never be 
transmuted into mechanical effect. In the best steam 


296 Electricity and Magnetism . [Chap. XXII. 

engines not one quarter of the heat is so transformed; more 
frequently about a tenth is so used. It is probable that j 
larger fractions than these of the total energy could be 
transformed by an electromotor into mechanical effect; but j 
this advantage, even if realised, cannot nearly counter¬ 
balance the disadvantage entailed by the cost of zinc, ' 
which is 20-fold that of coal weight for weight, and 200- 
fold that of coal for equal quantities of potential energy. 
In estimating as above that the zinc motor may be only 50 
times as dear as the coal motor, I assume that the electro¬ 
magnetic engine may be four times as efficient as the heat 
engine in transforming potential into actual energy. 


CHAPTER XXII. 

TELEGRAPHIC APPARATUS. 

§ 1. The instruments used in telegraphy may be divided 
into two great classes :—I. Those which transmit signals 
representing the alphabet by signs of a purely conventional 
character. II. Those which transmit signals shown or re¬ 
corded in some ordinary printed alphabet. 

In the first class the apparatus is simpler, because the 
symbols representing the alphabet are chosen with reference 
to the indications most easily produced by electricity in a 
telegraphic circuit. The advantages of the second class 
of instruments are, that the chances of error which 
result from the translation of telegraphic symbols into 
ordinary writing are avoided, and that no special training 
is required to read the messages as they are received. 
Each class is best suited to a special kind of work. For 
the general business of the country, carried on by a 
special staff, the first class is almost wholly employed, and will 
probably retain this pre-eminence. For private telegraphs 
read by untrained persons, and for large stations where 
highly-trained mechanics and electricians can be employed, 




297 


Chap. XXII.] Telegraphic Apparatus. 

the second class of instruments, which show messages in letters 
or print them in type, will probably also continue to be 
employed. 

Both classes may be subdivided into those instruments in 
which a galvanic battery generates the current, and those 
in which the current is induced by a magneto-electric 
arrangement. 

§ 2 . A telegraphic circuit, when a battery is used, consists 
of (i) an insulated wire connecting the transmitting and 
receiving stations, (2) the wire of the receiving apparatus at 
the station where the message is to arrive, (3) the earth, 
which conveys the received current back to the sending 
station, (4) the sending battery , or other rheomotor ,* which 
is alternately allowed to transmit its current into the line, and 
insulated from that line by the manipulator who works the 
sending apparatus. 

The sending apparatus is commonly some contrivance lor 
making or breaking the connection between the battery and 
the line ; so that when the circuit is completed, its resistance 
is the sum of the resistances of the battery, the line, the 
wire in the receiving apparatus, and the tract of earth con¬ 
necting the two stations. When a magneto-electric sender is 
used instead of a galvanic battery, the resistance of its coils 
takes the place of the resistance of the battery. In land lines 
the distinctness of thesignals depends, other things being equal, 
on the strength and uniformity of the currents transmitted ; 
and in order to save the expense of employing batteries or 
magneto-electric arrangements of great electromotive force, 
it is desirable to keep the resistance of all the parts low. 
Thus, the thicker the wire the better will be the signalling 
with all classes of instruments; but the size of the wire is 
of much greater importance on long lines than on short 
ones. The larger the plates of the battery the better, but 
on long lines the resistance of this part of the circuit sinks 

* Rheomotor is the name given by Professor Wheatstone to any 
apparatus which can generate an electric current. 


298 Electricity and Magnetism. [Chap. XXII. 

into insignificance in comparison with that of the line. The 
less the resistance of the receiving apparatus the better ; but 
this also forms a small percentage of the whole resistance 
on long lines. The resistance of the earth between most 
stations is insensible if care be taken to make the two con¬ 
nexions with earth at the two stations by large plates 
buried in damp earth. Occasionally, however, it may be 
necessary to take a wire a long way from the signalling 
station before a suitable spot for a good earth connexion 
can be found. Signals are sometimes stopped altogether 
by a failure in the earth connexion. 

Class I. 

§ 3 . All signals are made by the alternate transmission 
and interruption of currents, and these currents may be either 
positive or negative ; that is to say, they maybe sent from the 
copper or zmc pole of the battery into the line, the other 
pole of the battery being necessarily put to earth at the 
same time. The following are the elements out of which 
every telegraphic alphabet must be compounded in Class I. 

i°. The relative length or duration of the currents sent. 

2 0 . The relative strength of the currents. 

These strengths may range from zero upwards through all 
strengths of positive current, and from zero downwards 
through all strengths of negative current. 

The simplest symbols are those which record merely two 
lengths, one long and one short; and those which record 
merely two strengths, one positive and one negative. The 
Morse alphabet is the standard example of the former class, 
and the single needle alphabet the standard example of the 
second class. 

§ 4 . Morse signals are sent by a simple key, which the 
operator depresses when he wishes to send a current, and 
raises when he wishes to interrupt it. Fig. 147 shows a 
common form. The insulating parts are generally made 
of dry wood, the resistance of which is amply sufficient. 


Chap. XXII.] Telegraphic Apparatus. 299 

A short depression or mere tap sends the short ele 
mentary signal technically called a dot ; a longer depression 
sends the second elementary signal technically called a 
dash. The Morse alphabet is formed by a combination of dots 
and dashes, separated by equal intervals. The letters are 

Fig. 147. 



separated by longer pauses, and wpjjls by still longer intervals. 

The following table gives tfie^Morse alphabet. The short 
lines are dots, the long lines dashes. 


A - — 

A (se)- 

B- 

C- 

D- 

E - 


F- 

G- 

H - - - - 
I -- 



L- 

M- 

N — - ' 

n- 

O- 

6, oe- 

Q*- 

R- 


Pull stop (. ).- 

Colon ( :)- 

Semi-colon ( ;) —-- 

Comma (, )--- — 

Note of interroga- \ 
tion (?) J 




2 - - —- 


3 

4 

5 


S - - - 
T — 

U- 

ii, ue - - — 

V - 

W- 

X- 

Y - 

Ch- 


Note of admi -1 _ 

ration (!) / 
Hyphen (-) — .... 

Apostrophe (’)- 

Parenthesis ( — - — 
Inverted "I 
Commas (“ ”) / 

6 - 

7 - 

8 - 

o- 


-) 


■J’Vvv. vvidbiV 














































3oo 


Electricity and Magnetism . [Chap. XXII. 


Bar of division--— — 

Call signal-- 

Understand message - - -- 

Repeat message--- 

Correction or rub out.- - 

End of message - -—-- — - 

Wait- 

Cleared out and all right - — - * — - - — - 
Begin another line---- 

The positive and negative alphabet may be exactly similar 
to the above; the dash, or long signal, being replaced by a 
mark on the right side of the paper, or by the motion of some 
index to the right, and the dot by a mark on the left side, 
or a motion to the left. 

§ 5 . Ink marks similar to those printed above are made 
on a long strip of paper at the receiving end of a line, by the 
device shown in Fig. 148. 


Fig. 148. 



Let m represent the Morse sending key; l the insulated 
line, reaching from the sending station to the receiving 
station, where the conductor is connected to one end of 
the wire of an electro-magnet r, the other end of that wire 
being directly connected with e, the earth. Let a be a soft 
iron armature hinged at a, and having a narrow roller b con¬ 
tinually revolving in an ink trough b. Let the strip of paper 
p be continually moving in the direction of the arrows. Then 
when m is depressed, making contact at m with one pole of 
a battery c z, the other pole of which is to earth, a current 
will flow through the whole circuit and make the core of r 
magnetic. The end a of the armature will be depressed, the 












Chap. XXII.] T elcgraphic Apparatus. 301 

little roller pressed against the paper, and a black mark 
made, the length of which will depend on the rate at which 
the paper is moved, and the time during which m remains 
depressed. On raising the handle m so that the contact is 
now made at o, the current will cease to flow ; the core of r 
will lose its magnetism: a will rise, pulled up by a little 
spring, and the ink mark will cease on the paper. Thus 
a short depression of m will make a short mark or dot ; 
a long depression of m will make a long mark or dash. The 
handle m is in the diagram shown in a neutral position, 
making contact neither at o nor at m ; in practice it is never 
in this position, but makes contact at o when not depressed 
by hand. 

Fig. 149 shows a complete Morse ink writer as made by 
Messrs. Siemens Brothers. The following is a description 
of the instrument almost in their own words :— e is the 
electro-magnet, through which the received current passes. 
N is a handle by which the clockwork is wound up. 

The clockwork placed inside the instrument turns a small 
milled roller w, and the printing disc d. The friction roller 
Wi is pressed, by means of a spring v, upon w, and turns 
with it. 

The disc of telegraph paper s is placed upon the horizontal 
wheel p, which turns on a hardened pivot a. Horizontal 
wheels for paper were first introduced by Mr. Stroh, and 
are much superior to vertical wheels. The end of the strip 
of paper is led round the roller s 1 , turning on a vertical 
axis, thence under the roller s 11 , over the roller .r, and under 
the small steel roller i, where it is struck by the printing 
disc d, on the armature e being attracted by the electro¬ 
magnet e. From the small roller i the strip of paper passes 
between the friction rollers w and w lf which, when they re¬ 
volve, draw the paper forward in the direction of the arrows. 

The roller w x can be lifted by the small handle x; and it 
will be found convenient to lift it in this manner when in¬ 
troducing the paper between the friction rollers w and w x . 


302 


Electricity and Magnetism 


[Chap. XXII. 

Fig. 149. 










































































































303 


Chap. XXII.] Telegraphic Apparatus. 

a a is a brass vessel for holding a supply of printing-ink, 
the opening to which for putting in the ink is supplied with 
a cover c to prevent dust from getting into it; the vessel 
terminates in an open cup or trough b b , in which the print- 
ting disc d revolves. The vessel a a is fastened to the side 
of the apparatus by means of a screw with a milled head c, 
so that it can be easily removed for refilling or cleaning. 
The spindle on which the printing disc d is fastened revolves 
in an eye at the end of the continuation h of the printing 
lever h h. The spindle is made to revolve by being joined, 
at the end furthest from the printing disc, by a species of 
universal joint, to the end of a short spindle carrying a cog¬ 
wheel in gear with the clockwork. The printing disc is thus 
kept revolving, although free to follow the motions of the 
printing lever. 

Should it be wished to stop the clockwork of the instru¬ 
ment, the handle Q must be pushed to the right, by which 
the spring / is pressed against the small metal collar ^ of 
the regulator t. The release of the clockwork is effected by 
moving the handle Q in the opposite direction. 

The cores of the electro-magnet are of soft iron, united 
by a cross-bar and surrounded by the wire coils. The 
lever h h moving between the points 2 and 3 of the 
screws m and m l9 carries on one arm an armature of iron e, 
and at the other end the continuation h , in an eye at the 
end of which revolves the end of the spindle which carries 
the printing disc d. 

The contact screws m and m x limit the play of the print¬ 
ing lever h h. In order to draw the lever back to its normal 
position as soon as a current has ceased, a spring k is pro¬ 
vided, the degree of tension of which can be regulated by 
means of the nut 0. Another adjustment has been adopted, 
in addition to the above, by which the electro-magnet e has 
been made moveable, and can be raised or lowered by 
means of the milled headed screw n, thereby increasing or 


304 Electricity and Magnetism. [Chap. XXII. 

decreasing the distance between the cores of the magnets 
and the armature e of the printing lever h h. 

When the circuit, Fig. 148, is closed at m a current from the 
copper of the distant battery, after traversing the line, enters 
the printing instrument r, passes through the coils E of the 
electro-magnet, Fig. 149, and leaving the instrument returns 
through the earth to the zinc of the distant battery. As 
long as the current lasts, the iron cores are converted into 
magnets, the free ends of which will attract the armature 
e and thus set the printing lever h h in motion. The con¬ 
tinuation h of the printing lever h h consequently presses 
the disc d against the paper band, upon which it produces 
a dot or a dash, according to the length of time during 
which the armature is attracted by the cores. 

There are many modes of receiving and recording the 
Morse signals besides that just described. In many old 
instruments the roller b, Fig. 148, is replaced by a mere 
steel pointer or style, which makes a little indented line when 
pressed on the paper by the depression of a. In Bain’s 
chemical telegraph, Fig. 150, the electro-magnet r is wholly 
dispensed with. The depression of m sends a positive current 


Fjg. 150. 
L 



through r, c, and l, and then at the receiving station 
through a steel style c, pressing on a band of paper p , 
which has been soaked in a mixture of equal parts of satu¬ 
rated solutions of ferrocyanide of potassium and nitrate of 











305 


Chap. XXII.] Telegraphic Apparatus. 

ammonia. The current next flows to r and through m to 
earth, the handle of m being raised. The diagram shows 
the connections so arranged that all signals can be sent from 
either end. At the receiving station the keys m or m make 
contact at o or o. Prussian blue is deposited so long as the 
current passes through the paper, and thus the long and 
short signals are recorded by short or long blue marks. 
There should be a slight excess of carbonate of ammonia in 
the solution of nitrate. 

Sometimes the Morse signals are indicated to the ear or 
eye without being recorded. Thus, even if the paper at p , 
Fig. 148, be removed, the mere sound of the armature as it 
rises and falls is intelligible to the ear of a skilled operator. 
The soimder, as it is called, is coming into extensive use and 
consists of a Morse receiver without clockwork or paper or 
inking roller. The sound is produced by the tapping of the 
lever h , Fig, 149, against the stops m and in v The mere de¬ 
flection of a galvanometer needle, included in the circuit at 
p, will be equally intelligible to the eye. It is only necessary 
to make the needle light and confine its.'notion within narrow 
limits, so that each current in passing produces a single well- 
marked depression lasting for a longer or shorter time, and 
not a series of unchecked oscillations. 

§ 6. The simplest form of receiving instrument for posi¬ 
tive and negative signals is a little galvanoscope, the index 
of which can deflect only a short distance to right or left of 
its zero, being checked by stops. The inside of one of 
these instruments is shown in Fig. 151. 1 1 are the coils 

fastened to the back of a little door which opens to allow the 
works to be got at; a is a support in which one pivot of the 
needle works ; n p are the keys used in sending; the needle 
s n and pointer a b are shown in Fig. 152. The key by which 
the positive and negative signals are sent from one and the 
same battery is better shown in Fig. 153. l and e are two 
springs connected respectively with the line and with earth. 
They, when untouched by the hand, press against the upper 

x 


306 Electricity and Magnetism. [Chap. XXII. 

bar c, which is connected with the copper pole of a battery. 
Either spring can be depressed by the finger so as to come 
in contact with the bar z, which is connected with the zinc 
pole of the battery. If l is depressed, a negative current 
flows into the line; if e is depressed, a positive current flows 
into the line. The galvanoscope at the other end is so con¬ 
nected that the depression of the left-hand key causes a de¬ 
flection to the left; a depression of the right-hand key a 
deflection to the right. The form of galvanoscope used is 

Fig. 151. 



called the single needle instrument, and the alphabet the single 
needle code. The Morse code given above is often used, 
a dot being a deflection to the right and a dash a deflection 
to the left. 

Sir Charles Bright introduced the bell instrument as a 
substitute for the single needle. His instrument contains 
two bells struck by the depression of the armatures of two 
electro-magnets, one working each bell. Each electro-magnet 
























Chap. XXII.] Telegraphic Apparatus. 


30 7 


was worked by its own relay; one of the relays worked 
when a positive current was received, and the other when 
the received current was negative. This instrument is falling 
into disuse. 

§ 7 . The connections shown above are most suitable for 
comparatively short lines. On longer lines more complex 
arrangements are generally adopted, involving the use of 
relays. The Relay is an instrument which retransmits the 
original signal from a fresh battery : it may be used either 
to send this signal to a distance along a second section 
of line, or simply to send a strong current from a local 

Fig. 152. Fig. 153. 


b 



battery through the receiving instrument. The current 
received from a distance is often so diminished by leak¬ 
age that it is insufficient to work the electro-magnet which 
marks the paper, or to give legible or audible signals, 
and yet it may be sufficiently strong to move an armature 
with sufficient force alternately to make and break an 
electric contact, and thus indirectly to work the receiv¬ 
ing or recording instrument. Fig. 154 shows the con- 


x 2 











308 Electricity and Magnetism. [Chap. XXII. 

nection for a Morse system with relays at each end, worked 
by single currents. 

Corresponding parts at the two stations are indicated by 
the same letters, capitals being used for one station, and 
italics for the other, r is the relay, and c z the sending 
battery; r l is the Morse instrument, and Ci Zj the local 
battery used to work it. The depression of the key m 
making contact at o sends a positive current through the 
line l to m, and through the contact p to the electro-magnet 
r of the relay and thence to earth. The electro-magnet r 
attracts the armature of the relay, making contact at n and 


Fig. 154. 



thus sending a positive current through Rj, the electro-magnet 
of the recording instrument. 

Obviously R t might be at a station 100 miles from r, in 
which case Lj would be the second line, and the portion 
of the circuit from Zj to Rj the earth. 

Relays are constructed so that a very slight difference in 
the strength of a current determines whether the moveable 
tongue or armature makes contact at n, or rests against 
an insulated stop. Care is also taken to provide such adjust¬ 
ments that the tongue may be made to move with any desired 
strength of current: thus the relay may be set so that with zero 
strength the tongue rests on the stop and makes contact when 
the current reaches the strength unity, or it may be set so that 
it rests against the stop when the current has a strength 100, 
and makes contact when the current has a strength 101. 








309 


Chap. XXII.] Telegraphic Apparatus. 

Relays are also often made so that the tongue moves only 
with a current of one sign, remaining unaffected by a current 
of the opposite sign ; the core of the electro-magnet may in 
this case be a hard steel magnet, the polarity of which is 
never reversed by the currents received. Other relays 
are made so that when the tongue has once been de¬ 
flected to make contact, it will not return until a reverse 
current has been sent through it. The best known form of 
this species is the polarized relay made by Messrs. Siemens, 
and shown in Fig. 155. s is the 
south pole of a hard steel magnet, 
the north pole of which is bifur¬ 
cated and ends in the two pieces 
n n lf between which the tongue a 
of the relay oscillates, pivoted at 
d. The coils are wound round the 
two north branches of the magnet 
in opposite directions, so that a 
current in one direction tends 
to brake n } north and n south, 
while the reverse current would 
make n x south and 11 north. The tongue «, made of soft 
iron, becomes a south pole by contact with s s. 

Relays can be arranged so as to send positive and 
negative currents corresponding to positive and negative 
currents received. 

The Morse ink-writer can easily be arranged so as to act 
like a relay, the armature being employed to make the 
necessary contacts instead of to mark paper. With instru¬ 
ments of this class Messrs. Siemens, on the Indo-European 
line, work from London to Teheran, a distance of 3,800 
miles, without any retransmission by hand. There are five 
relay stations in this circuit. 

§ 8. In ordinary Morse signals and in all others where only 
one current is absolutely required, there is nevertheless 
some advantage in using the negative current to draw back 
















3io Electricity and Magnetism. [Chap. XXII. 

the armature and so terminate each signal. This system 
was introduced by Mr. Varley. It considerably simplifies 
the adjustment of the relays and has other advantages. 
Where these reverse currents are not used, the relay tongue 
must be pulled back by a spring or by magnetic attraction, 
and their adjustments require to be continually altered. 
This spring requires continual adjustment to suit the strength 
of the received current, which varies much during each day 
as the insulation of the line varies. With a polarized relay 
and reverse currents, no such adjustment is required, be¬ 
cause the positive and negative currents decrease simul¬ 
taneously; and if there were no earth currents , a good 
polarized relay once set for reverse currents would never 
require to be touched ; practically, all relays require adjust¬ 
ment from time to time. Earth currents are currents 
flowing along the line, not sent by the batteries, but de¬ 
pending either on a difference of potential between the 
earth at the two stations or on induction from passing clouds. 
Currents often flow for hours in one direction through the 
lines, and the signalling currents are superposed on these 
earth currents; the relays then have to be set, so that when 
no signal currents are passing the armature is attracted more 
strongly by one armature than by the other, and the amount 
of this bias must be regulated as the earth currents vary. 

§ 9 . With the connections as shown in Fig. 154, although 
no current is sent direct from the battery through the home 
relay circuit, every signal sent causes the relay at the sending 
station to work, if the line is long and well insulated, or 
if it includes many miles of underground or submarine wires. 
This action is due to the statical charge which accumulates 
on the line l. When contact is made *by the key m at o, 
the line l becomes statically charged. When contact is 
broken at o, and made at p, part of this statical charge flows 
to earth through the relay r, the other portion flowing on 
through the distant relay r; thus the key m as it makes and 
breaks contact causes intermittent currents to flow through 


Chap. XXII.] Telegraphic Apparatus. 311 

the home relay which will work the local Morse instrument R t . 
This action is not only unnecessary, but is detrimental, 
because the currents returned in this way are often so 
strong as to alter the permanent or residual magnetism of the 
relay, which then requires readjustment when signals begin 
to arrive from the distant station, and moreover the local 
battery cq z x is put in action by these return currents when 
not required. The return current is especially great when 
any portion of the line l is formed of wire coated with 
india-rubber or gutta-percha, because lines so formed 
have a much larger electrostatical capacity than the 
ordinary aerial land line. Where this inconvenience 
exists, each station may be provided with an apparatus 
called a switch, by which the connections are altered at 
will, so that when the station m, fig. 154, for instance, is 
sending the relay, r is not in the circuit between p and e, 
which points are then directly connected. 

The sending key m is sometimes so made as to put the 
line to earth for a short time between the two positions 
where it makes contact respectively with o and p. 

A still better arrangement for discharging may be em¬ 
ployed, in which the action of the current sent from the 
home station puts p to earth by means of a separate relay, 
and keeps p to earth by residual magnetism for a very short 
time after the key m has broken contact at o and made con¬ 
tact at p. With this arrangement the distant station can at 
will interrupt the sender. 

§ 10 . The following points must be attended to in the 
construction of telegraphic apparatus :— 

The core of the electro-magnet should be arranged so that 
its magnetism changes rapidly at the commencement 
or cessation of a current; otherwise rapidly alternat¬ 
ing changes produced by rapid signals will not be regis¬ 
tered by the armature. With this object, if soft iron is 
used, the mass should not be great; the core should be 
hollow, and split longitudinally; and the iron should be 


312 


Electricity and Magnetism. [Chap. XXII. 

carefully selected with as little coercive force as possible, j 
The highly magnetized cores of polarized relays gain and 
lose the small increments of magnetism due to feeble ! 
currents with less delay due to coercive force than is ex- j 
perienced with soft iron. The coercive force in the arma¬ 
tures is another source of delay in rapidly alternating 
signals. These armatures should, therefore, be made 
light, and must not pass through very different states of 
magnetization. If allowed, for instance, actually to touch the 
core of the electro-magnet, they become so highly mag¬ 
netized that when the electro-magnet is weakened by the 
cessation of the current, they often adhere to the core under 
the influence of residual magnetism, requiring a very strong 
spring to pull them back, and consequently a very powerful 
current to pull them against the spring to the electro-magnet. 
The most delicate relay is that in which, other things 
being equal, the armature moves in a nearly constant 
magnetic field, which is alternately weakened and strength¬ 
ened by the received current. The alteration produced in 
the magnetic field of the electro-magnet by the passage of a 
current should, however, be the greatest which that current 
can produce, and this condition requires that the iron or 
steel core should not be very small; moreover, some little 
pressure must be exerted at the contacts, or the tongue of 
the relay will be made to tremble by the mere passage of the 
local current, which exercises a repulsion on itself; to obtain 
the necessary force, the armature must have considerable 
bulk: these two last conditions are antagonistic to those first 
mentioned, and experiment alone can determine the best 
proportions. The form of the electro-magnet should be 
such as to give the strongest and most uniform field possible 
with a given intensity of magnetization. This condition is 
entirely violated in the common relay or ink-writer, where 
the armature stretches across the poles of an ordinary horse¬ 
shoe magnet. It is much more nearly complied with in the 
Siemens polarized relay described above. The form of 
the iron or steel core and the distribution of the core on the 


Chap. XXII.] Telegraphic Apparatus. 313 

magnet should be such as to give the maximum intensity of 
magnetization per cubic centimetre of core consistent with a 
given current passing through a given length of wire. This 
condition is probably very imperfectly fulfilled by any 
relay yet constructed. 

The mass of the armature should be so distributed that its 
moment of inertia may be the smallest that is consistent 
with the necessary weight of the armature and position of 
the pivots ; any increase in the moment of inertia pro¬ 
duces a proportional diminution in the angular velocity 
with which the tongue will move under a given force, and 
the rate at which a relay will work depends on this angular 
velocity. If the moment of inertia be doubled, the force 
remaining the same, the angular velocity acquired in a 
given time will be halved, and the angle traversed in that 
time will be halved ; but to traverse the same angle, i.e. to 
pass from one contact to the other, will not require double 
the time, but only 1*414 times the time required by the 
lighter armature, because 1*414= s /2. The moment of 
inertia is the sum of the products of the weight of each 
particle into the square of its distance from the pivot round 
which the mass rotates : it is therefore not only desirable, 
when rapid motion is to be produced by a weak force, that 
the weight should be small, but also that it should be near 
the pivots. 

No harm is done, however, by putting the pivots far from 
the points of contact, because we thereby diminish the angle 
through which the armature has to move between the 
contacts; so that if we halve the angle and double the 
moment of inertia, the one change exactly compensates the 
other. 

The wire on the electro-magnet (or in the coil of the single 
needle instrument) should have a moderate resistance re¬ 
latively to that of the whole circuit : 1 thus on short lines a 

1 One authority says of the resistance of the whole circuit; this 
seems very large. 


314 Electricity and Magnetism. [Chap. XXII. 

thick, short wire should be used for the electro-tmagnet; but 
on long lines, relays with long, thin wires are required. The 
reason for this is the same as that for using galvanometers 
with long coils to test insulation, and galvanometers with 
short coils to observe currents in circuits otherwise of small 
resistance. The common single needle instruments have a 
resistance of about 200 ohms, the coil being made of No. 35 
wire. 

The direct ink-writer used for short lines may be coiled 
with No. 35 wire (0-005 inch diameter), and have a 
resistance of about 500 ohms. 

The electromagnets in local instruments (no line wire on 
circuit) are made with wires of from *022 inch to 0-012 
inch diameter (Nos. 24 to 30). 

A Siemens polarised relay may be made with No. 40 
copper wire, and have a resistance of 500 to 700 ohms. 
These relays sometimes have a resistance of 3,500 ohms. 

All contacts must be made by platinum points, platinum 
being the only metal which is not oxidized or dirtied by the 
passage of the little spark which accompanies the making 
and breaking of the circuit. This spark wears out even the 
platinum contact pieces in time: it may be avoided by 
connecting permanently the two contact pieces through a 
resistance so large that the current passing when contact is 
broken is small enough not to be injurious. The same 
object is gained by placing a small condenser between the 
contact pieces, each contact piece being connected with one 
of the two armatures. 

§ 11 . In place of a voltaic battery, a magneto-electric 
arrangement may be employed to send currents. Thus a 
Siemens armature worked by hand may be employed to send 
Morse signals, the motions of the hand being similar to those 
required for the Morse key. The depression of a handle 
moves the armature in one direction, and sends, say, a posi¬ 
tive current, which by a polarized relay causes an ink-writer 
to begin marking the paper. So long as the armature 


Chap. XXII. ] Telegraphic Apparatus . 31 5 

and handle remain depressed the ink-writer continues to 
mark, though no current is flowing through the relay, the 
tongue of which is held over by the permanent magnetism 
of its magnet; when the handle is raised and the armature 
moved back to its original position, another short current is 
sent in the opposite direction to the first. This second 
current throws back the tongue of the relay, and the ink- 
writer ceases to mark. The current produced is the equi¬ 
valent of the power employed to work the armature ; 
considerable force must therefore be exerted to send a 
current suitable for a long circuit. Other magneto-electric 
arrangements are used to send + and — signals for the 
single needle receiver. The induced currents are of very 
short duration ; and hence, although the e. m. f. which pro¬ 
duces them may easily be made much greater than that of 
the batteries usually employed to signal, yet the actual 
quantity of electricity transmitted for each signal is generally 
much less than is sent by a battery. 

On a long line the received current is longer in duration 
than the sent current, and proportionately feebler. On a 
short line the received current and that sent are both so 
short, that even when strong they may fail to move an 
armature which would work freely with a feebler current 
prolonged for a longer time. The e. m. f. produced by the 
magneto-electric arrangement is so great near the sending 
station, that the leakage is much greater in proportion to 
the whole quantity of electricity sent than when a battery is 
used. This would not be the case if the resistance of the 
faults where electricity escapes followed Ohm’s law, but the 
resistance of faults seldom follows Ohm’s law. More es¬ 
pecially surface conduction, which is the chief cause of leak¬ 
age on land lines, allows much more than double the current 
to pass when the e. m. f. is doubled. On underground or 
submarine linjes the high potential produced for a short 
time by the magneto-electric sender tends to send minute 
sparks through the insulating material, and so to cause faults. 


316 


Electricity and Magnetism. [Chap. XXII. 


Magneto-electric senders, owing to the above causes, are 
not much used on long or important lines. 

§ 12 . The simple Morse or + and — key can be worked 
at the rate of from twenty-five to thirty-five words per minute 
by a skilled operator. Receiving instruments can, however, 
record even more than ioo words per minute (of five letters 
each). Automatic transmitters have therefore been adopted 
in which the messages are prepared by several operators, 
being represented by punched paper or metal types, and 
these types or paper strips passing through the transmitter 
determine the required succession of currents. Sir Charles 
Wheatstone’s automatic transmitter is the most successful 
yet used. In this instrument the messages are represented 
by three rows of holes in a strip of paper. For + and — 
signals a hole on the right-hand side represents a + signal or 
dot, a hole on the left-hand side a — signal or dash. Uni¬ 
formly spaced central holes serve to move the paper on at a 
constant speed. The right and left-hand holes determine the 
contacts made and signals sent very much as the cards in a 
Jacquard loom determine the pattern in woven stuff. The 
contacts are determined by the position of two little plungers, 
which are either kept down by the unpunched paper or come 
up through the holes. "Whenever a plunger rises through a hole 
a current is sent into the line; a 4- current when the hole 
is on the right side; a — current when the hole is on the 
left side. The contacts are pressure contacts, with a slight 
slip at the moment of making contact, which are superior to 
any contact in which the surfaces merely slide one on the 
other. By a somewhat more complex arrangement of 
similar character, the long and short Morse signals are 
sent. A full description of this instrument is given in the 
Fifth Edition of Mr. R. S. Culley’s Hand-book of Prac¬ 
tical Telegraphy. 



Chap. XXII.] Telegraphic Apparatus. 317 

Class II. 

§ 13 . The elementary signals used in those telegraphic 
systems which show or print letters are produced, as in 
Class I., by the alternate transmission or interruption of 
currents, sometimes all of one sign, and sometimes both 
positive and negative ; but these transmissions and interrup¬ 
tions are not themselves the subject of direct observation or 
record : they are used to work the escapement of clockwork 
in what may be termed ‘ step by step ’ instruments, or to 
connect synchronous actions in the sending and receiving in¬ 
struments, which are driven with similar motions at the two 
ends of the line. 

The * step by step’ instruments sometimes print the 
messages, but more frequently show the required letters in 
succession on a dial. The synchronous instruments all 
print the letters, but they effect this by various distinct in¬ 
ventions, the more striking of which are Hughes’s, Caselli’s, 
and Bonelli’s. 

All ‘ step by step ’ instruments are very much alike. A 
ratchet wheel on an axis bearing the pointer is worked by a 
propelment which, as each current passes, turns the ratchet 
through a segment of a circle corresponding to one tooth or 
half a tooth of the ratchet. Fig. 156 shows a form now made 
by Messrs. Siemens Brothers, and very similar to that first 
introduced by Sir Charles Wheatstone : 11 s are two poles of 
a polarized electro-magnet, similar to that used in their rela^ 
(§ 10 above). The soft iron tongue t works between these, 
pivoted at /, being attracted to j by one current, and to n by 
the reverse current. The tongue t carries at its other extremity 
one end of the axis of the ratchet wheel d, having thirteen 
teeth j the other end of the axis is on a fixed bearing, and 
carries the pointer. The play of t is limited by two stops, 
q, q l9 and the rotation of the ratchet is determined by 
tvvo stops p, p u and four springs, h, h u h 2 , h s , two of which, h 
and h v have a catch at their end, adapted to hold the 


318 Electricity and Magnetism . [Chap. XXII. 

ratchet. The tongue t is shown drawn towards n; the ratchet 
is locked by the spring h , so that it cannot turn to the right 
neither can it turn to the left, because it is locked by the stop 
p. The position of the pointer is therefore perfectly definite. 

Fig. 156. 



The next current received will attract t toj; the spring h 
will turn the ratchet ^ of a revolution, and it will then be 
locked by the spring h x and the stop p x \ the following current 
will turn the ratchet an equal distance by moving it towards 
«, and thus each alternate current will carry the pointer 
forward by Jyth of a revolution over the dial, on which there 
are twenty-five letters and one blank. 

These thirteen positive and thirteen negative currents will 
cause the index to make one complete revolution. Let us 
assume that the index is at the letter a, then one current will 
move the index to the letter b, three currents more will move 
it to e, and seven currents will send it to L ; by sending the 
right number of currents and then pausing for an instant, the 
index will be made to travel from letter to letter, and to pause 
at each letter required to be read. The index may be driven 
by clockwork and the teeth of an escapement wheel liberated 





































Chap. XXII.] Telegraphic Apparatus. 319 

by the currents, or the escapement wheel may, as in the 
above example, be replaced by a propelment wheel, such that 
each motion of the armature causes it to move on one tooth. 
The latter is the plan now most in use. 

The right number of currents is sent by means of a dial 
at the sending station, and an index with a handle which 
can be turned from letter to letter; the letters on the send¬ 
ing dial correspond in number and arrangement to those on 
the receiving dial. The handle always moves in one direction 
and sends one current (positive and negative alternately) as it 
passes each letter. When the index of the receiving instrument 
and the handle of the sending instrument have once been set 
opposite the same letter, the sending operator has merely to 
turn his handle at a moderate speed to each letter in succes¬ 
sion which he wishes to send, and by so doing he will send 
just the number of currents required to bring the receiving 
index step by step to the same letter. Should any current 
or currents fail to move the receiving index, the sender and 
receiver, finding that the signals are not understood, put 
their instruments to one letter or mark (sending no currents) 
by a mechanical arrangement contrived for the purpose, and 
recommence the message from the point at which it 
became unintelligible. The currents sent by the handle as 
it is turned round may come from a battery, or, as is more 
commonly the case, from a magneto-electric arrangement. 
Fig. 157 shows the magneto transmitter used by Messrs. 
Siemens. 

The handle h is fastened to the spindle a carrying the 
toothed wheel l, which latter gears into the pinion t of the 
cylindrical armature or keeper e. This armature e is mount¬ 
ed vertically upon pivots between the poles of a series of 
permanent magnets ggg. One revolution of the wheel l, 
or of the handle h fixed thereto, causes the pinion of the arma¬ 
ture e to revolve thirteen times, as the teeth of the former 
are in the proportion of thirteen to one of the latter. As one 
full turn of the armature produces two currents of opposite 



3 20 Electricity and Magnetism. [Chap. XX 11 . 

directions in a coil of insulated wire forming part of the 
cylindrical armature e, twenty-six currents, alternately posi¬ 
tive and negative, are generated during one revolution of 
the handle; the dial is divided, as above stated, into 
twenty-six parts, viz. twenty-five letters of the alphabet (I 
and J being taken as one) and one blank. 



Sir Charles Wheatstone’s magneto-electric letter-showing 
dial step-by-step instrument is perhaps the best yet intro¬ 
duced. 

When a radial arm is employed to- drive the armatures 
of magneto-electric induction coils, the induced currents 
are generally very unequal in strength, because the operator 
naturally begins and ends the motion comparatively slowly. 
Sir Charles Wheatstone, therefore, drives the magneto¬ 
electric armatures continuously, and regulates the number of 
currents admitted into the line by a series of stops, corre¬ 
sponding to thirty letters and symbols arranged round a dial. 
The propelment in the receiving instrument is admirably 
light and accurate, and its workmanship very perfect. These 
little instruments are chiefly used for short private lines, but 
have been employed on circuits of more than ioo miles in 
length. 
























Chap. XXII.] Telegraphic Apparatus. 321 

§ 14. The ‘ step by step ’ printing instrument is made on a 
plan differing little from that of the letter-showing instru¬ 
ment. The pointer is replaced by a ring on which the types 
of the required letters and symbols are placed; this ring is 
turned by the propelment or by an escapement and clockwork, 
so that each required letter is brought in turn opposite the 
paper on which the symbol is to be impressed ; the paper is 
then struck against the letter on the ring by some special 
device differing in different instruments. In one the mere 
pause of the dial suffices to allow the striking or printing 
hammer to act. In another positive currents alone are used to 
work the escapement, and a negative current, sent when the 
desired letter is reached, determines the impression by the 
stroke of a hammer. In a third a second line wire is used 
to give the blow which prints the letter. The paper then 
moves on one step. These instruments have not come 
largely into use. It will be observed that the number of 
alternating currents required for each letter in the 1 step by 
step ’ instruments greatly exceeds the number required by in¬ 
struments of Class I. 

§ 15. The Hughes printing instrument is the typical 
synchronous printer. The principle on which it is based may 
be stated as follows :—Two type-wheels, having letters on their 
periphery, one at the sending and one at the receiving sta¬ 
tion, revolve with equal velocity, and are moreover so placed 
that the same letter in each wheel passes corresponding fidu¬ 
cial marks at the same time. The fiducial mark in the receiv¬ 
ing instrument is opposite a little roller, carrying a strip 
of paper which is struck against the edge of the rotating 
wheel by the release of the armature of an electro-magnet 
whenever a current is received ; a letter is printed by 
the blow without stopping or sensibly retarding the wheel; 
the paper is then pulled on a step by clockwork, the arma¬ 
ture replaced on the electro-magnet, and all is in readiness 
for the next letter. The letter which is printed 
depends on the letter of the wheel which happens to be 


Y 


322 Electricity and Magnetism. [Chap. XXI r. i 

• 

opposite the roller and paper at the moment when the \ 
current arrives. A series of keys like the keys of a piano- j 
forte, and each lettered to correspond with the letters of the ; 
alphabet, are so arranged relatively to the sending wheel that ; 
the depression of the key a causes a single current to be 
sent when a is opposite the fiducial mark at the sending 
station ; the current occupies nG sensible time in reaching i 
the other station, and strikes up the paper when the a on 
the receiving wheel is at the fiducial mark. The letter a is 
therefore printed ; if the operator next touches the key N, 
the sending wheel causes a current to pass when N is opposite 
the fiducial mark; at the same instant N is opposite the 
paper and roller at the receiving station, and the letter N is 
accordingly printed. This action can be repeated inde¬ 
finitely with any series of letters so long as the two wheels ' 
keep perfect time. Each wheel is driven by clockwork, 
and regulated so as to keep very nearly perfect time, by a 
spring pendulum, which vibrates with extreme rapidity, and 
regulates a frictional governor connected with each wheel; 
any trifling deviation from perfect synchronism is corrected 
by every current sent. The act of printing slightly accele-- 
rates the receiving wheel if it is behind time, and slightly 
retards it if it is too fast. This is done by a little wedge 
which, whenever a letter is printed, is forced between the 
teeth of a star wheel fixed to the type wheel. This wheel 
is not rigidly connected with the axis on which it is centred 
but is maintained in its position by friction. This position 
can therefore be corrected without sensibly affecting the 
speed of the clockwork. This instrument is the best of the 
printing instruments hitherto introduced : it has the great 
advantage that only one current is required for each 
letter. 

§ 16. Bakewell’s and Caselli’s copying telegraph appara¬ 
tus requires synchronous motion at the two ends of the line. 
The principle on which their instruments are constructed 
may be explained as follows. 



Chap. XXII.] Telegraphic Apparatus. 323 

The message is plainly written in common ink on a sheet 
of paper, a, covered with thin tin foil, Fig. 158 . A corre¬ 
sponding sheet of paper, b, is chemically prepared, so that 

Fig. 158. 



when a current passes through it from a pointer r to earth, a 
mark is made similar to that used in Bain’s instrument. The 
pointers s and r are drawn across the papers a and b in a 
succession of parallel equidistant lines with a perfectly syn¬ 
chronous motion. A battery is connected with the tinned 
paper, the line l, and the earth, as shown in the sketch. 
When the pointer s touches the tin, the battery is short- 
circuited through the tin; no sensible current reaches b, 
and r leaves no mark; but when s crosses the ink on a the 
current from c z flows through l, and so long as s remains 
insulated from a by the ink a line is drawn by the point r. 

It is easy to perceive that the result must be 
as accurate a copy of the original writing as 
can be produced by a series of fine lines inter- 
rupted in the proper places, as in Fig. 159 . €'# I 

The synchronism required is in Caselli’s 
instrument obtained by a pendulum at each re¬ 
ceiving station; one beat of the pendulum corresponds to each 
line drawn across the paper; the one pendulum controls the 
other by a current which it transmits from the sending 
station through a special circuit temporarily connected with 
the line. 

§ 17. By various differential arrangements messages can 
be sent simultaneously in both directions through one line. 
The currents sent from the two stations do not really travel 







324 Electricity and Magnetism. [Chap. XXII. 

simultaneously in opposite directions through the-line, but 
the effect of the signals on each receiving instrument is 
precisely the same as though the line were being worked in 
only one direction. 

Let the connections be arranged as in Fig. 160. r and r 
represent two relays, each wound with two coils capable of 
producing equal magnetization in the core if equal currents 
are passed through both coils. If equal currents pass in 
opposite directions through the two coils, the poit will neither 
be magnetized nor demagnetized, m and m are two Morse 
keys, so made that the line must always be in contact with 
the earth or the battery, or (for a very short time, as the key 
moves) with both. When the handle at m is untouched, 
there is unbroken connection from the line round the inner 
coil of the relay to earth through the contact o and the wire 
v. There is a second connection between the line and the 
earth from the point n, through the outer coil of the relay, 
and through the resistance coils w. The condenser d is 
connected, as shown, with this branch. 

When the handle m is depressed, contact is made at p, 

Fig. 160. 


r r 



which for an instant short-circuits the battery cz through 
the wires Vj and v, and immediately afterwards contact is 
broken at o, so that the battery c z is connected with w and 
thence with two circuits, one through the line to the distant 





















Chap. XXII.] Telegraphic Apparatus. 325 

station and one through the outer branch of the relay to 
earth at the Home station through w. 

The resistance of w is made equal to that of the line l, 
added to that part of the circuit by which l is connected with 
earth at the distant station; the capacity of d is so chosen 
that W and d may represent an artificial line in all respects 
equivalent to the real line. 

Thus there may be nine arrangements of the positions of 
the keys m and m. 

1. Let m be depressed and m untouched. The battery 
c z sends a current round both coils of r, which does not 
work, as the currents flow in opposite directions; it also sends 
a current through the line l, and thence round the inner 
coil of r and to earth through 0 ; the relay r works and 
gives a signal. 

2. Let m be depressed and m also depressed. The 
currents which each battery would send through the line 
neutralise one another, but each battery sends a current 
through the o.uter coil of its own relay; both relays work, 
and signals are received at both stations. The current sent 
through the outer coil of each relay is equal to that which 
the battery would send through the line and inner coil of 
the distant relay. 

3. Let m be depressed and m untouched. This case is 
similar to the first case; a signal is indicated by the 
relay r. 

4. Let neither key be depressed, both batteries are cut 
off the line and no signal is indicated by either relay. 

5. Let both m and m be in the intermediate position, 
contact made at p and p but not broken at o or 0. No 
signal will be given at either station. 

6 and 7. Let the key at m or m be in the intermediate 
position and the other key not depressed; no signal will 
be indicated at either station. 

8. Let the key at m be in the intermediate position when 
m is depressed, the current produced by ^ jst will be un- 


326 Electricity and Magnetism. [Chap. XXII. 

altered, and the signal will be received through the inner 
coil of R. 

9. If the key at m is in the intermediate position, and m 
depressed, a signal will be received by the inner coil of r. 

In every arrangement of the keys m and w, the effect pro¬ 
duced on the relays is such that when m is depressed r 
receives a signal, when m is depressed r receives a signal. 

This arrangement is a modification of that introduced by 
Messrs. Siemens and Frischen, and is due to an American, 
Mr. Stearns. 

Mr. Stearns finds it advantageous to introduce two resist¬ 
ance coils, v and v, ; v is made equal to the battery 
resistance; and v { is chosen sufficiently large to prevent 
the polarization of the battery when momentarily short- 
circuited through v and v,. 

By short-circuiting the battery, Mr. Steams is able to avoid 
insulating the point n when the key m is in its intermediate 
position. If n were insulated, the received current would 
pass round both coils of the relay and would pass to earth 
through the resistance w. At first sight this latter arrangement 
(which was that used by Messrs. Siemens and Frischen) 
seems perfect, for we have the current diminished to one- 
half by a doubled resistance and at the same time acting 
with double force per unit of current on the relay. This 
reasoning does not take into account the inductive retarda¬ 
tion (Chap. XXIII.) produced by artificially lengthening the 
line. Mr. Stearns, in all positions of the key, signals through 
a line of constant length and capacity. 

BELLS. 

§ 18 . Bells may be classed as a distinct kind of tele¬ 
graphic apparatus. Besides the bells which have already 
been described, in which each signal sent causes the hammer 
to strike one blow, there are two kinds of electric bells :— 
First , those in which the hammer is driven by a weight and 
clockwork; the clockwork remains at rest so long as a certain 


Chap. XXIII.] Speed of Signalling. 32 7 

detent or trigger restrains it, but runs down, striking the 
while, so long as the detent is held back by the armature of an 
electro-magnet actuated by the received current. While the 
current is maintained, the weight runs down and the bell 
continues to ring. Secondly , those in which the hammer is 
attached to the armature of the electro-magnet, and is fur¬ 
nished with contact pieces (as in Ruhmkoff’s coil), such that 
when the armature is attracted to strike a blow, the contact 
is broken, and the current ceasing, the armature returns to 
its original place, makes contact again, and is again impelled 
to strike a blow. This action is repeated so long as a cur¬ 
rent is sent from the sending-station. The second form of 
bell, sometimes called a trembler , is the more convenient, and 
is used for household and hotel purposes. 

Electric bells may with especial propriety be introduced 
into hospitals, and may be employed even in private houses 
by invalids. The effort required to ring the electric bell is 
that of making contact at one part of the circuit. This can 
be done by the smallest pressure on the little button of a 
handle or little box, which can be held in the hand in bed, 
and attached by flexible wires to the wall. This arrange¬ 
ment allows the patient to assume any posture without 
losing command of the bell. Electric bells are also used 
for railway signalling, and in all telegraph stations to call the 
attention of the clerks. 


CHAPTER XXIII. 

SPEED OF SIGNALLING. 

§ 1. Electricity cannot properly be said to have a velocity. 
It is true that when a circuit is completed at any one point, 
electrical effects are not produced at other points of the 
circuit until a sensible time has elapsed; so that, for instance, 
when a signal is sent through the Atlantic cable, it does not 



328 Electricity and Magnetism. [Chap. XXIII. 

produce any effect in Newfoundland simultaneously with the 
depression of the key in Ireland. The distance divided by 
the time occupied in the transmission of the signal may be 
called the velocity with which that particular signal was 
transmitted ; it might even be termed the velocity with 
which a certain quantity of electricity traversed the cable, 
but it is not the velocity proper to or peculiar to electricity, 
for under different circumstances the same quantity of elec¬ 
tricity may be made to traverse the same distance with 
almost infinitely different velocities. 

For about two-tenths of a second after contact is made in 
England, no effect can be detected in Newfoundland even- 
by the most delicate instrument: after ‘4" the received current 
is about 7 per cent, of the maximum permanent current 
which will ultimately flow equally through all parts of the 
circuit. The current will gradually increase until, 1" after 
the first contact was made, the current will have reached 
about half its final strength, and after about 3" it will 
have attained nearly its maximum strength ; during the 
whole time the maximum current is flowing into the cable at 
the sending end. The velocity with which the current 
travels even in this one case has therefore no definite mean • 
ing ; the current does not arrive all at once like a bullet, but 
grows gradually from a minimum to a maximum. The 
time required for any given similar electrical operation on 
various lines is directly proportional to the capacity of the 
unit of length of the conductor, to the resistance per unit 
of length, and to the square of the length intervening between 
the sending and receiving station. Fig. 161 shows the curve 
representing the law of increase of the received currents, 
which is the same on all lines. The vertical ordinates parallel 
to o y represent strengths of current, the maximum or per¬ 
manent current flowing through the circuit after equilibrium 
has been reached being called 100. 

The horizontal ordinates parallel to o x represent intervals 
of time, measured from the time at which contact was first 


Chap. XXIII.] 


329 


Speed of Signalling. 

made, and expressed in terms of an arbitrary unit, a, different 
for different circuits, but constant for any one circuit. For a 
uniform line of the length /, the resistance per unit of length 

Fig. 161. 



r and the capacity per unit of length s, the value of a is 
given in seconds by the expression 

a = ~ 2 -log 6 (ioio) = -02332 skP .... i°. 

Inthis expression absolute measure (gramme metre second) 
is used. When S! is measured in microfarads per knot, R! in 
ohms per knot, and /j in knots, the above expression becomes 
a = -02332 s x Ri /j 2 -T- io 6 . . . . 2°. 

For the French Atlantic Cable we have S! = 0*43 
Rj = 2-93 and /j = 2584; and hence for a the value *196 
second. 

In terms of « the arrival curves for the received current of 
all lines are identical, and the same curve shows the law 


Fig. 162. 



according to which the current at the receiving end dies 
away when at the sending end the line has been put to 
earth. A succession of contacts with a battery and with 
earth at the sending end prolonged each for times equal 
to about 25 a would produce the series of changes in the 







330 Electricity and Magnetism. [Chap. XXIII. ^ 

received current shown in Fig. 162, each curve being a com¬ 
plete arrival curve. 

Fig. 162 a. 



The annexed table shows the value of the vertical ordi¬ 
nates corresponding to successive multiples of a, the maximum 
current being 100. 


t in 
terms 
of a 

Strength of 
current in per¬ 
centages. 

t in 
terms 
of a 

Strength 
• of current 
in per¬ 
centages. 

1 t in 

1 terms 
of a 

Strength 
of current 
in per¬ 
centages. 

t in 
terms 
of a 

Strength 
of current 
in per¬ 
centages. 

•4 

•OOOOOOOO271 

I'l 

•04140636 

3'5 

18-48434 

7-8 

66-95995 

•5 

•OOOOOO51452 

1*2 

•08927585 

3-6 

19-84366 

8-o 

68-42832 

'55 

•OOOOO33639 

i '3 

•1704802 

37 

21 ‘21342 

8-5 

71-82887 

•60 

•OOOOI6714 

i -4 

•2959955 

3’8 

22-59017 

9-0 

74-87172 

•62 

•OOOO29252 

1 '5 

•476336 

3*9 

23-97071 

9-5 

77 - 59 I 33 

•64 

•OOOO49412 

1 -6 

720788 

4 -o 

2 5 35217 

100 

80 -02000 

•66 

•OOOO80817 

17 

I -036905 

4-2 

28-10757 

10-5 

82-18760 

•68 

•OOOI2835 

1 -8 

1 -430252 

4-4 

30-83807 

11 0 

84-12139 

•70 

•OOOI9845 

i *9 

1 *904356 

4-6 

33-52902 

12 

87-38402 

•72 

•OOO29937 

20 

2-460812 

4-8 

36-16892 

13 

89-97752 

74 

•OOO44152 

21 

3-09969 

5 *o 

3874814 

14 

92-03836 

•76 

•OO063776 

2‘2 

3-81846 

5*2 

41 -26032 

15 

93-67565 

•78 

•OOO90371 

2-3 

4-61560 

5-4 

43-70028 

16 

94-97631 

•80 

•OOI25804 

2*4 

5*48661 

5-6 

46 -06449 

17 

96-00951 

•82 

•OOI72272 

2-5 

6-42695 

5-8 

48*35070 

18 

96-83023 

•84 

•OO232333 

2-6 

7 H 3 I 63 

6 -o 

50-55770 

J 9 

97-48215 

•86 

•00308919 

27 

8*49536 

6*2 

52-68501 

20 

98 -ooooo 

•88 

•OO405358 

2-8 

9*61264 

6-4 

54 - 733 I 4 

21 

98-41134 

•90 

•OO525387 

2-9 

JO -77797 

6-6 

5670294 

22 

98-73809 

•92 

•OO673158 

3-0 

11-98582 

6-8 

58-9502 

23 

98-99763 

•94, 

•OO853247 

3 ' 1 

13-23087 

7-0 

60-41164 

24 

99-20379 

•96 

•OIO70646 

3'2 

14-50800 

7-2 

62-15439 

25 

99-36754 

•98 

OI330764 

3'3 

15-81233 

7*4 

63-82523 



1 -oo 

•OI639420 ! 

3’4 

17-13921 

7-6 

65 -42636 































Chap. XXIII.] Speed of Signalling. 331 

When the line is put to earth at the sending end before 
the maximum current is reached, the falling curve is super¬ 
imposed on the ascending one, and a derived curve is pro¬ 
duced as shown in Fig. 162 a, which gives the effect of mak¬ 
ing contact for 5 a and then putting the line to earth. At 
the time 6 a from the beginning of the operations the 
strength of current will be 50*55770 — *01639 == 50*54131; 
and at the end of 7 a it will be 60*41164 — 2*46081 = 
57*95°^3 ) an d i n this manner the whole of the derived curve 
can be traced. If now the line be put in contact with the 
battery again at the end of 7 a, the third curve can be 
derived by again superimposing the original curve on the 
first derived curve; so that at the end of 8 a the strength 
would be 68*42832 — 11*98582 + *01639420; and in this 
manner the effect of any number of operations can be com¬ 
puted. 

§ 2 . It follows from the above, that the result of a series 
of short equal contacts alternately with earth and a battery at 
the sending end will produce a small series of rises and falls 
in the strength of the current, which grow smaller and 
smaller as the length of the contacts diminishes : the mean 
strength of the current will be half the permanent maximum 
produced by a permanent current; and when the alternate 
contacts are made short compared with a, no sensible 
variation can be detected in the current which flows from the 
cable at the receiving end. As the contacts are lengthened, 
the amplitude of variation increases. The following table 
gives some amplitudes due to a succession of simple dots or 
equal contacts with the earth and with a battery. 


Length of pair of contacts ) . 
in terms of a. . . . I 2 ^ 

3 ° 

3*5 

[ 4 ° 

5 ‘o 

0*0 

7 ° 

8-o 

9-0 

10 

Amplitude of variation of] 



6 - 3 . 


14*85 

19-67 


29-11 

33*68 

current in percentages !• 2*69 
of maximum. } 

2*97 

4 ' 5 2 

10*42 

24*42 


The theory of the speed of signalling was first given by 
Sir William Thomson, read before the R. S. May 24, 1855, 
published in the Proceedings, and reprinted in the Phil. Mag., 
February 1856. 













332 Electricity and Mag 7 ietism. [Chap. XXIII. 

§ 3 . Signals sent through land-lines last so long relatively 
to the exceedingly short value of a for such lines, that in all 
ordinary cases the current rises almost to its maximum, and 
falls to zero at each dot. The capacity in electrostatic 
measure of wire of diameter d suspended at a height h above 
a flat plane, and remote from all other conductors, is 


/ 



Taking^=3 metres and ^=0-004 metre, we have s = 0-062, 

or in absolute electro-magnetic measure s = ° °^ 2 - 

8 (28-8 x io 9 ) 2 

or about *013 microfarad per statute mile. There is ex¬ 
perimental reason to believe that the actual capacity is 
about double this amount, or even a little more, owing to the 
induction between the wire and the posts and insulating 
supports. Even taking s as *03 microfarad, and the resist¬ 
ance of a mile of *004 mm. wire as 15 ohms, we have for 
a line 350 miles long 

a = -00126 second. 

This value is so small that even with 20 a for each con¬ 
tact and 40 « for each dot, the dot would only occupy 
'° 5 "i or 20 dots could be made in a second ; and for every 
dot the current would rise almost to its maximum and fall 
almost to its minimum. The above speed would give about 
80 words per minute as a speed at which the effect of what 
is called retardation would be insensible in diminishing the 
rise and fall of the received current. 

Instruments intended for use upon land-lines are therefore 
invariably constructed on the hypothesis that the received 
current will at each signal rise and fall through a consider¬ 
able percentage of its maximum strength. The spring 
attached to the armature of the electro-magnet is adjusted 
so that at some one strength of received current the 




Chap. XXIII.] Speed of Signalling. 333 

armature will rise, and at another strength differing little 
from the former it will fall : in order to work such an 
instrument safely, the received current must rise much above 
the first and fall far below the second strength, and this is 
the case even when 100 words per minute are sent by 
Professor Wheatstone’s automatic sender from London to 
Edinburgh. 

§ 4 . On submarine lines any such condition as a great 
and regular rise and fall in the received current limits 
the speed of transmission very seriously: 40 a for the 
French Atlantic cable corresponds to nearly 8 seconds, 
and two minutes would be required for the transmission 
of each word, if this interval of time were required for each 
dot; whereas from 15 to 17 words have actually been sent 
through this cable in a minute. The duration of a dot at the 
speed of 15 words per minute must have been about *27 
second, or about 1*38 ci. Many of the dots can have pro¬ 
duced no more variation in the received current than is 
equivalent to 10 1 00 th of the permanent current; the theory of 
superimposed signals shows us that the exact effect of any one 
positive or negative dot depends on the 20 or 30 preceding 
signals, so that even very regular sending produces irregular 
results at the receiving end. Signals such as these cannot 
be received by any arrangement of armatures or other 
apparatus which moves at a fixed strength of current, but re¬ 
quire some arrangement which shall be capable of following 
and indicating or recording every change in strength of 
the received current. Sir William Thomson, by his inven¬ 
tion of the mirror galvanometer so constructed that it 
could fulfil this condition, rendered submarine telegraphy 
commercially practicable. The spot of light wanders over 
the scale, following every change of current, and the clerks by 
degrees acquire sufficient skill to interpret the seemingly 
irregular motions. One dot will cause the light almost to 
cross the scale, the second moves it a little farther, the third 
or fourth hardly cause a perceptible motion, but the clerk 


234 Electricity and Magnetism. [Chap. XX III. 

by experience knows that the four very different effects each j 
indicate a simple dot, each sent by the clerk at the other end 
in a precisely similar manner. 

§ 5 . Sir William Thomson’s syphon recorder actually draws 
on paper the curves which we have learnt to construct theo¬ 
retically. Ink is spurted from a fine glass tube on to paper 

Fig. i 6 ^. 



drawn past it with a uniform motion : the glass point of this 
tube moves to the right or left through distances proportional 
at each instant to the strength of the current, and thus the 
signals are drawn on the paper in the form of curves repre¬ 
senting the strength of the current at each instant of time. 
The glass tube n (Fig. 163) is pulled backwards and forwards 






















Chap. XX1I1.] Speed of Signalling. 335 

by being connected through the threads k h and lever i with 
a very light movable coil b b, placed between the two poles 
of a very powerful electro-magnet, not shown. 

A soft iron fixed core a is placed in the centre of the 
coil. The coil oscillates about a vertical axis, being directed 
by a bifilar arrangement ff. The received current passes 
through this coil from the terminals t t x : the vertical arms 
of the coil are impelled across the magnetic field in one 
direction or the other according to the sign and strength of 
the received current. The magnetic field in this arrange¬ 
ment is very intense and very uniform, which gives great 
sensibility to the apparatus. The glass syphon n is strung 
on the wire l l l9 the shorter end dips in the ink-trough tn % and 
the longer end is opposite the paper 0; the syphon can be 
withdrawn from the ink by the slide p; the spring g keeps 
the threads k h taut; the directing force of the bifilar ar¬ 
rangement is adjusted by varying the position of the bracket 
r; the two weights w hang from the coil by the two 
directing threads. 

If the coil is shunted so that there is a comparatively short 
circuit through which the current induced by its motion can 
flow, the electro-magnetic induction of the magnet on the 
coil tends to check rapid oscillations not due to the signals. 

Fig. 164. 



A certain portion of the received current is lost through the 
shunt, which is, however, rarely required, for the capacity of 














336 


Electricity and Magnetism. [Chap. XXIII. 


the cables connected with the coil is such that a very- 
sensible induction takes place even without the shunt. 

The ink is electrified by an induction machine similar in 
principle to that described in Chapter XIX. § i, and is 
thus made to fly to the oppositely electrified strip of paper 
in a succession of fine drops. 

§ 6. If it were necessary to allow the recording point to 
travel over the whole possible range of the received current, 
it is clear that practically dots of only of the maxi¬ 

mum strength would correspond to T ^V?r °f the breadth of 
the paper, and could not be made legible with any practi¬ 
cable breadth of paper. They are legible on the mirror 
galvanometer because the light can range over a length of 
some feet, but £ inch is a broad paper strip for any re¬ 
cording instrument. Mr. Varley’s mode of signalling by 
condensers supplies the means of keeping the light of the 
mirror galvanometer always at one part of the scale, and the 
glass tube end of the recorder within a very narrow strip of 
paper. 

The line l, Fig. 164, is attached to the insulated armatures 

Fig. 165. 


b c d e f q h i j 7c L m.n 



op q 7' St zcvvrjcyx understand 


n and n of two large condensers; the second armature m at 
the sending end is connected to a key k, by which it can at 
will be connected with the battery c z or with earth ; the 
armature m is permanently connected through the receiving 
instrument r with earth. 

When by the key k, m is connected with the positive pole, 
n is rendered negative by induction; a current flows from 
n to n ; n becomes positive and m negative by induction. 




Chap. XXIII.] Speed of Signalling. 337 

and to charge m negatively, a short current flows from m to 
e through r, making the desired signal in one direction; 
the current sent through r begins suddenly, is very small, 
and would gradually die out, even if m were not put to 
earth: the fall in the current is, however, accelerated by 
raising the key and putting m to earth. A negative signal 
is given by connecting m with the zinc instead of the 
copper pole of the battery. 

With this arrangement no electricity flows into or out of 
the cable but by induction: the charge in the cable is re¬ 
arranged at each signal. The current received through the 
instrument r never increases beyond that due to the first 
signal. 

Fig. 165 shows the alphabet, and Fig. 166 shows a 
message sent with condensers and received by the recorder. 

Fig. 166. 

y e $ was t a p p c 7 t gr 

Mr. Varley’s system has the additional advantage that no 
permanent earth currents can flow through the line, for the 
line is not connected anywhere with earth. A sudden change 
of potential in the earth at either end will induce a current, 
but sudden changes are much rarer than slow changes, and 
the latter, however great, are quite cut off by the condensers. 

§ 7 . The time of every electrical operation is proportional 
to a, ortosR/ 2 ; and consequently, whatever instrument is 
employed to record or receive the messages, the speed of 
working must with that instrument be inversely proportional 
to s R /*, and with any cables of uniform construction the 
speed must be inversely proportional to the square of the 
length. 

The speed will, however, differ enormously, according to 
the nature of the electrical operation required for working 

z 


33 ^ 


Electricity and Magnetism . [Chap. XXIV. 


the instrument. Thus the Morse instrument probably requires 
that the dots should occupy a time of from 15 to 20 a, and is 
therefore about 14 times slower than the mirror galvanometer, 
which will show dots of 1 or 1*2 a. The speed of the 
syphon recorder is nearly equal to that of the mirror. 

The speed depends on the weight per knot w of the copper 
and on the weight per knot w of the gutta percha employed, 
and may be calculated from the following formula, where l 
is the length of the cable in knots. 

Speed by mirror in words per minute— 

log (70-4 w + 480 w) — log 64 w . 

=0-2325 w — L - 5 -x 10 

If Mr. Willoughby Smith’s material is used instead of gutta 
percha, the multiplier -275 may be used instead of 0*2325 ; 
and for Hooper’s material, if the specific gravity is such that 


its weight per knot is 


p 2 -d* 
400 


lbs., and its specific induc¬ 


tive capacity 3-3, the above formula becomes 

log (70*4 w + 400 w) — log 64 w c 
•295 w ——- ^2 - L -- X io 6 

The speeds given correspond to 13 words per minute 
through the French Atlantic Cable. As many as 17 have 
occasionally been sent. For Morse instruments the above 
speeds must be divided by 14. 

It will be observed that when a constant ratio is main¬ 
tained between the weights per knot of dielectric and con¬ 
ductor, the speeds of working are directly proportional to 
the quantities of material used. 


CHAPTER XXIV. 

TELEGRAPHIC LINES. 

§ 1 . A telegraphic line is an insulated wire reaching from 
station to station. On land an iron wire is generally used, 
supported on stoneware, porcelain, glass, or vulcanite insula- 






Chap. XXIV.] Telcgraphic Lines. 339 

tors carried by wooden or iron posts. Sometimes underground 
wires are used, and these are generally made of copper insu¬ 
lated with gutta percha or india rubber, and protected by 
tape, leaden or iron tubes, wooden troughs filled with 
bitumen, or an iron wire serving. Submarine lines invaria¬ 
bly have a copper conductor insulated with gutta percha or 
some preparation of india rubber, forming what is called a 
core. This core is served with hemp or jute, and covered 
helically with iron or steel wires, which are further covered 
in many cases with hemp and tar, or a bituminous compound. 
It is desirable that the conductor of a telegraphic line should 
have a small resistance, and that it should be well insulated. 
The smaller the resistance of the line, the smaller the 
battery required to work it, and with a given insulation the 
smaller the leakage. On submarine lines the speed attain¬ 
able is increased by diminishing the resistance of the con¬ 
ductor. Bad insulation or great leakage involves the use of 
large batteries, frequent adjustment of the receiving instru¬ 
ments to suit variations in the received currents, resulting 
from variation in the resistance; bad insulation also involves 
greatly increased difficulty in ascertaining by electrical tests 
the position of any injury occurring to the line. The follow¬ 
ing paragraphs relate chiefly to the modes practically adopted 
for securing moderate resistance and high insulation : 

§ 2 . The iron wire used in land lines is in this country 
generally No. 8, B.W.G. £ inch diameter. 

The following table (p. 340) gives some of the other sizes 
adopted. The weights per statute mile are taken from 
Mr. Clark's tables. There are considerable differences in 
the weights given by different authors, and I am not aware 
that any one set of tables are authoritative. 

Mr. Culley gives No. 8 wire as 0-17 inches diameter; its 
resistance 13*5 ohms, and that of No. 4 as 7*8 ohms. There 
is great difference in different specimens. The strength of 
good iron wire varies from 20 tons per square inch for large 
gauges such as No. 1 to 40 tons per square inch for No. 8 


340 Electricity and Magnetism. [Chap. XXIV. 

and smaller sizes. Mr. Culley gives 1,300 lbs. for No. 8, and 
this corresponds by the above table to 367 tons per square 


Size of wire, 
B.W.G. 

Dia¬ 
meter in 
inches. 

Weight 
in cwts. 
per 

statute 

mile. 

Resist¬ 
ance in 
ohms 
at ordi¬ 
nary tem¬ 
peratures 
per 

statute 

mile. 

Strain 
corre¬ 
sponding 
to 10 
tons per 
square 
inch, 
(cwt.) 

Where used. 

! 

*3 

1245 

4-16 

I 4 -I 3 

(India. Some long 

2 

•284 

III 7 

4‘57 

12 *66 

| lines in England. 

4 

•238 

783 

651 

8-89 


6 

'203 

570 

8-96 

6-47 

Germany 

8 

•165 

376 

136 

4*27 

England and Germany 

10 

•134 

249 

20-5 

2-82 

England, short lines 

4 millimetres 

•157 

340 

15-0 

3-86 

France 

3 millimetres 

*Il8 

192 

267 

2'l8 



inch. The iron wire should be galvanized, and should be 
capable of being bent round itself and unbent without 
injury. It should also stand bending four times, first one way 
and then the other, to a right angle, being held in a vice. 
The wire is stretched 2 per cent, cold before being used. 
This process is called killing , and not only detects weak 
places, but makes the wire less springy and more manageable. 
It should be painted or varnished in smoky places. 

From 25 to 20 poles per mile may be used on straight 
lines, but 16 poles per mile are sometimes used if no more 
than four wires are required. On sharp curves as many as 40 
poles per mile may be required. The fewer the poles the better 
the insulation. For 10 wires or less the diameter of wooden 
poles may be 5 inches at the top; for a larger number of 
wires 6 inches. Creosoted larch is the best material; and 
the batts should be charred and baked to prevent decay, 
and tarred if well-seasoned. The pole above ground should 
be painted. 

The distance between the wires should not be less than 












Chap. XXIV.] Telegraphic Lines. 341 

12 inches vertically, and 16 inches horizontally, with 20 
poles per mile. 

§ 3 . No line can be perfectly insulated. On land lines 
no leakage occurs from the wire to the air, but at every pole 
there must with the best construction be some leakage, 
or, in other words, at every pole there is a connection with 
the earth. The resistance of this connection is very great 
when the wire is well insulated, and small when there is 
bad insulation. 

The wire is always separated from the wooden pole by an 
insulator , and the insulation of the wire depends on the de¬ 
sign, material, and condition of these insulators. Glass of 
certain kinds offers the greatest resistance to conduction 
through its substance of any known material, but it does not 
answer well for telegraphic insulation, because surface con¬ 
duction plays by far the greatest part in the leakage from a 
line, and glass is highly hygroscopic, i.e. it will be found 
covered with a moist film in most states of the weather. 
Ebonite (hard vulcanized india-rubber) has a high insulation 
resistance and does not readily become damp, but rain wets 
it easily, and therefore when employed for insulators it is 
generally covered with a cap of some other material: it soon 
becomes dirty and spongy on the surface. 

Porcelain of certain qualities insulates well; it is not 
nearly so hygroscopic as glass, and rain runs readily from its 
highly glazed surface. The glaze insulates still better than 
the substance of the porcelain, but in some specimens is 
liable to crack with old age, when its value is lost. 

Brown stoneware is an excellent and cheap material for 
insulators : its glaze does not crack, but its substance has not 
so great a specific resistance as highly vitrified porcelain. 
The point of chief importance in all insulators being the 
condition of the surface, porcelain and stoneware are the 
favourite materials; they keep clean, do not change with 
age if well selected, and do not harbour insects. 

The form most used approaches that of a bell, or of 


342 


Electricity and Magnetism. [Chap. XXIV. 


several bells one inside another. In Fig. 167 No. 1 shows 
Latimer Clark’s double-bell insulator; No. 2 Varley’s insu¬ 
lator, made in two pieces ; No. 3 the French cup insulator, 
a very rudimentary design; and No. 4 Siemens’ insulator, pro¬ 
tected and supported by an iron cap. 

Fig. 167. 

4 



The objects aimed at in each design are the following :— 
1. To make any conducting film which may be deposited 
on the surface of the insulator between the wire and the 
pole as long as possible, because, other things being equal, 








































































1 Chap. XXIV.] Telegraphic Lines. 343 

its resistance increases directly as its length. This object 
is attained by the series of bells, for the electricity has to 
run down outside and up inside each, in succession, before 
getting from the wire to the pole. 

2. To make the cross section of the conducting film as 
small as possible. With this object the insulator is kept as 
small in diameter as is consistent with other conditions of 
excellence. 

The thickness of the deposited conducting film depends 
on external conditions, but the larger the diameter of our 
bells the larger will be the cross section of the film, i.e. the 
ring of moisture which we should find outside and inside 
each ring of insulating material if it were sawn across hori¬ 
zontally. 

3. To expose one portion of the insulator to the rain, so 
that it may be cleansed by rain from dust, salt, smoke, 
spiders’ webs, &c. 

4. To protect another portion of the insulator from rain, so 
that when the outside is wet the inside may still insulate. 
These two conditions are fulfilled by the forms 1 and 2. 

5. To prevent the failure of part of the insulator from 
destroying the insulation. With this object some good 
insulators are made in three parts, as shown in Fig. 2—two 
distinct cups and a vulcanite covering to the iron supporting 
pin. 

6. To prevent insects from settling in recesses. This 
object is difficult of attainment, and limits the depths of 
the recesses under the bells. 

7. To provide strength and protection against malicious 
injury. This leads to the adoption of metal caps as in Fig. 4. 

§ 4 . Besides leakage from the wires to the earth, wires 
on poles are subject to the defect of more or less 
electrical connexion one with another, by the surface con¬ 
duction from one insulator to another. To prevent this 
very serious inconvenience a wire from the earth is led up 
the pole and across every portion of it by which electricity 



344 


Electricity and Magnetism . [Chap. XXIV. 


could be conducted from one insulator to the other. A 
short circuit or line of no sensible resistance is thus pro¬ 
vided, so that all leakage finds its way at once to the earth ; 
simple loss weakening the transmitted currents causes much 

Fig. i 68 . 



less inconvenience than cross connections by which the 
message on one wire finds its way partly into its neighbour. 
The earth wire is carried above the pole and forms a 
lightning conductor. 

§ 5 . The insulation resistance of a line is measured by 
Fig. 169. measuring the resistance experienced at 
the end a when the end x is insulated, 
Fig. 168. 

The resistance thus measured is not the 
sum of the several insulation resistances 
be„ c e 2) d e 3 , &c., but is the resistance 
due to the circuits a b Ej, b c e 2 , c d e 3 , 
&c. arranged in multiple arc as in Fig. 
169. We can calculate this total resist¬ 
ance if we know the resistance of each 
elementary part. First find the resistance between the points 
d and e due to a double arc ; next add this resistance to that 
between d and c; next compound the resistance so found 
with that due to the arc c e; this will give the resistance 
due to all the conductors between c and e ; add c b and 
proceed as before till the resistance due to all conductors 
between a and e is obtained. 

When the resistance m of each part of the line between 
two poles is constant, and the insulation resistance i at 
each pole is also constant, we can calculate the difference 











Chap. XXIV.] Telegraphic Lines. 345 

between the current q 0 sent into the line and that received 
at the further end Q n by the following formula. 

Let n be the number of poles, and let z = 2718372 ^7 

then Q n = — Qo - 

z+-.. I<5 

z 

Mr. Varley considers no line well insulated for which the 

fraction is greater than •g-Tnrw This fraction may also be 

defined as the ratio of the resistance of the conductor per mile 
to the insulation resistance of each mile. Q n will be 46 per 

cent, of Q 0 in a line of 400 miles with the above value of -r 

§ 6. On submarine and underground circuits, the insula¬ 
tion depends wholly on the resistance to conduction across 
the sheath of the gutta percha or india rubber covering. 
Surface conduction can only occur at the two extremities of 
the line, and unless by gross neglect, or on very short lines, 
cannot be a sensible cause of leakage. 

Equation i° is applicable to submarine lines, calling m the 
' resistance of the conductor per mile, i the insulation resist¬ 
ance of each mile, and n the length of the line in miles. 

The conductor is invariably a copper strand, and the 
resistance can be calculated for pure copper from the Table, 
§ 14, Chap. XVI. In practice from five to eight per cent, extra 
resistance must be allowed for on account of impurities. 

The smallest conductor in practical use for sea lines 
weighs 73 lbs. per nautical mile of 2,029 yards; the largest 
yet employed (French Atlantic) weighs 400 lbs.. 

The large cores require nearly an equal weight of gutta 
percha as a covering, and the lighter conductors require a 
still larger proportion of insulator; the 73 lbs. of copper 
is generally covered with 120 lbs. of guttapercha. Hooper’s 
india rubber is sometimes used in smaller quantities than 
gutta percha. 

The electrical tests applied to ascertain the quality and 




346 


Electricity and Magnetism. [Chap. XXIV. 


condition of the materials employed in the case of submarine 
cables are—the measurement of the resistance of the core ) 
the measurement of the resistance of the insulator to con¬ 
duction from the copper inside to water outside; and the 
measurement of the capacity of the insulated conductor in 
microfarads. The methods of making these tests have been 
already described. 

The insulation resistance r of a length l of the insulating 
core measured in centimetres is given in terms of the resist¬ 
ance R # of one centimetre cube to conduction between its 
opposed faces by the following formula : 

D 


log 


R = R s - 


d 


•3665 R s log - 

—I - d 


where 


D 


1 '975 R .logv 


27 T L 

? is the ratio of the external diameter of the insula- 
d 

tor to that of the enclosed conductor. From this equation we 
have the resistance r*. of one knot of insulating envelope : 


io° 


r s is what was called in Chap. XV. the specific resistance of 
the material. 

The following table gives the value of R k and r s for 
some important cables at 24° C. after 1 minute’s electrifV 
cation. 



D 

d 

R 

megohms. 

R, 

megohms. 

Malta Alexandria (first) . 

Persian Gulf, mean .... 
Second Atlantic, mean 

French Atlantic, mean 

Hooper’s Persian Gulf (india rubber),> 
mean . . . . ( 

2*95 

3-48 

3-28 

2-92 

115 

193 

349 

234 

8000 

4 X IO 6 
0 x io 6 
342 X IO 6 
256 X IO 8 

7572 X IO 6 


Ihe specific gravity of gutta percha is between 0*9693 
and 0-981. The weight W* of gutta percha per knot in any 
case is 












Chap. XXIV.] 


Telegraphic Lines. 


347 


w 


ibs. 


‘ — a 4 
480 

Where d and d are measured in thousandths of an inch. 
The specific gravity of Hooper’s rubber is about 1*176, 
and the constant divisor for the weight of Hooper’s material 
in the above formula is 400 instead of 480. The weight 
per knot w k of a copper strand of 7 wires such as is used 
for submarine lines is in lbs. 

a * 

w k — 

70*4 

§ 7 . The capacity in electrostatic measurement s of any 
length of wire for a submarine cable may be calculated by 
equation 6, Chap. V. The electromagnetic capacity s is 
more commonly required, and we know (Chap. VIII. § 2) 

that s = - where v — 28*8 x io 9 . Hence in absolute 
V ' 

electromagnetic measure 

KL - KL T> 

x io 18 log^ ; 


4*6052 x 28*8 2 x io 18 xlog 


D = 


d 


3820 


and calling s M the capacity in microfarads, we have 
kl D 

382 x to 4 log-, • * * * 5 ° 


s„ = 


This value of s M is given in terms of l measured in centi¬ 
metres : practically it is convenient to measure the length in 
knots; and as one knot is equal to 185,526 centimetres, 
(6087 feet), we have, calling L k the length in knots, 

Cap. of cable = 7 _ii. L ... 6° 

l0 ^ 

Taking the value of k for gutta percha as 4*2 (vide Chap. V. 
§ 5), we find the capacity of the French Atlantic cable to be 
about o*43 a microfarad, dhis value agrees with the 
result of direct experiment by the ballistic method (vide § 5» 
Chap. XVII.). 







348 Electricity and Magnetism. [Chap. XXIV. 

§ 8. Fig. 170 shows a cross section and a projection of the 
component parts of the Anglo-American Atlantic cable 
drawn full size. In the centre is the copper strand of 7 
wires : round this we have the gutta percha envelope covered 
by a serving of jute, outside which there are ten wires of 

Fig. 170. 



what is called homogeneous iron, each enveloped in fine 
strands of Manilla hemp. 

Fig. 171 shows the more common type of cable, in which 
the hemp-covered steel wires are replaced by iron wires of 
considerable size. These iron wires, laid on as shown in Fig. 






Chap. XXV.] Faults in Telegraphic Lines . 349 

171, are often covered with one or two outer servings of jute 
and a compound of mineral pitch, silica, and tar, known as 
Clark’s compound. 


CHAPTER XXV. 

FAULTS IN TELEGRAPHIC LINES. 

§ 1 . Any impediment to signalling due to the condition of 
the line is a fault. Faults are of three kinds :—1. A defect 
producing bad insulation. 2. A defect producing want 
of continuity in the line, or excessive resistance. 3. Contact 
between two neighbouring conductors used for separate 
messages. 

Defective insulation in land lines may be due to cracked, 
dirty, or otherwise defective insulators, or to contact between 
the line and some conductor in connexion with the eartli. 
In the first case the defect may be distributed over a great 
length of line. We can determine its importance by elec¬ 
trical measurements. In the second case the fault has a 
definite position, and we can determine its importance and 
its position by electrical tests. In submarine cables, defective 
insulation is always due to connexion between the sea and 
the internal conductor at one or more definite points. The 
second class of fault implies a rupture in the conducting 
wire of the line or in the connexions at the stations, or in the 
connexions with the earth at the stations. In many cases 
its position can be ascertained. Frequently the first and 
second faults co-exist: i.e. the line is broken and its end 
is in contact with the earth. The third class of fault seldom 
arises except on land lines. When the connexion arises 
from the actual contact of one wire with another, its position 
is easily found. 

Tests for the position of faults can generally be made 
more accurately on submarine lines than on land lines, 



350 Electricity and Magnetism . [Chap. XXV. 

because the insulation of the undamaged portions of the 
line is generally better. The following descriptions refer 
especially to submarine faults, but the same principles are 
applicable to land lines. 

§ 2 . Let there be a fault in an otherwise well-insulated 
conductor, involving loss of insulation at one point, at the 
distance a b, Fig. 172, from station a. 

If the connexion at b with the earth has no sensible re¬ 
sistance, we have only to measure the resistance a b, and 
divide by the resistance of the line per mile, to obtain the 
distance a b in miles. This measurement may be made by 
the Wheatstone balance, connected as shown, a d and 
n f are the two arms of the balance, f e is the box of resist- 

Fig. 172. 



ance coils. If a d is of d f, and the plugs in the box 
between f and e arranged so as to give 1,500 units when 
the galvanometer g remains undeflected on the completion 
of the circuit, then abEj has a resistance of 150 units: 
and if the line has a resistance of 5 units per mile, b 
is 30 miles from a. It is always desirable to insulate the 
end of the line at c during this test. We can easily as¬ 
certain whether the resistance of b Ej is sensible or not, by 
repeating the test from c. If by the second test we find a 
distance b c, which, added to a b, makes up the whole length 
of the line, b E! can have no resistance. If, on the other 











35 i 


Chap. XXV.] Faults in Telegraphic Lines. 


hand, the sum of the measurements from c and from a gives 
a greater length than a c, this can only be due to the resist¬ 
ance of the fault ; for we have not really measured the re¬ 
sistance of a b and b c, but of ab + b Ej and bc + bEj. 
If then the sum of the two measurements exceeds the resist¬ 
ance a c, the excess will be equal to twice the resistance of 
the fault. Let m be the resistance measured at a, n the 
resistance measured at c, and l the resistance of the whole 
line. 


T , _ „ L + m — n l + n — m 

lhen a b =— -- orBC= —■- . . i 


This method would be perfect if the resistance of the fault 
were really constant while the resistances m and n were 
being measured ; but faults usually vary very much, owing 
to polarization ; and hence, except with great faults of small 
resistance, this method is defective. 

§ 3 . A second method of determining the resistance a b 
is given by the following test, on the assumption that the 
resistance of the fault is constant:—Measure at a the resist¬ 
ance m of the line when c is insulated, and measure the 
resistance e when the end c is put to earth. 


Then ab + f=m ;ab + 


~+— 
/ BC 


= e and ab + bc = l 


therefore a b = e — V (l — e) (m — e) . . . 2° 

This test is even less trustworthy than the preceding one. 
By taking a large number of values of m n and e with 
different poles of the battery, and different strengths of 
battery, and choosing the smallest values obtained as those 
corresponding with one and the same minimum value of f, 
some approach to accuracy can be made. Great experience 
is required in testing to enable the observer to judge of the 
nature of a fault. By noting the polarization obtained with 
positive and negative currents of different strengths the 
character of a fault can generally be determined, and a 
guess made at its probable resistance. 






352 


Electricity and Magnetism. [Chap. XXV. j 

§ 4 . When there is a well-insulated return wire from the s 
distant station c back to a, the position of a leak can be 
determined with great accuracy by what are called loop tests. 
The observer has then both ends of a complete metallic 
circuit before him, and the ratio between the two parts which 
intervene between the two ends and the fault can be deter¬ 
mined by several methods, all independent of the varying 
resistance of the fault. 

Mr. Varley uses a differential galvanometer to ascertain 
when an equal current runs into both ends of the metallic 
circuit and out at the fault. This will only be the case 
when the resistance between the galvanometer and the fault 
is the same by both roads. This condition is fulfilled by 
adding a resistance r between one coil of the galvanometer 

Fig. 173. 



and the defective wire. The resistance r required to bring 
the galvanometer to zero is obviously equal to twice the re¬ 
sistance of the wire between the distant station and the 
fault. 

Perhaps a still better method is given by arranging the 
Wheatstone balance as shown in Fig. 173, where the fault, 
supposed to be at 0, forms part of the circuit connecting the 
pole c to the metallic conductor subdivided at 0. 

The variation of the resistance of the fault does not 
affect the result: it will indeed cause a greater or less 
deflection in the galvanometer until the desired balance is 
effected, but it will not alter the relative resistances of the 









353 


Chap. XXV.] Faults in Telegraphic Lines. 

several parts of the circuit required to reduce the deflection 
to zero. The test is made by adjusting the resistances a 
and b until no deflection is obtained; then, calling c and d 
the resistances of the conductors separating m and ?i respec¬ 
tively from the fault, we have A = 5 . Then the resistance 

B D 

of c -f d being called l, the above equation gives the value of 
c = - A L --. 

L + B 

§ 5 . The following is a plan for determining the position 
of a fault of high resistance in a submarine cable by a simul¬ 
taneous test at each end. It takes into account the uni¬ 
form leakage from each knot of the insulated cable, and 
can be carried out with much greater synchronism than is 
possible for the plans described in §§ 2 and 3, above. The 
r connexions are shown in Fig. 174. g is a galvanometer ; 


Fig. 174. 



s an electrometer at the same station; s x an electro¬ 
meter at the distant station, where the end of the sub¬ 
merged cable is insulated; the battery c z has one pole 
connected with the galvanometer g, and the other pole 
to earth; let k be the resistance of the unit length of the 
conductor, and i the resistance of the unit length of insulated 
wire to conduction across the sheath; then let l be the length 
of the cable. Let \ be the distance of the fault from the 
galvanometer station \ let Pj be the potential at the distant 
station ; let p be the potential at the near station, and c the 
current observed on the galvanometer. 

A a 

















354 Electricity and Magnetism. [Chap. XXV. 

/f 

•* + - C — Pj t al 
a 

al , k 

Pi £“ + ~ C — P 

a 

Then X = — log* - .... 3 0 . 

2 a d 

The measurements must be made in one consistent system 
of units. Absolute measurement in centimetres, grammes, 
and seconds may be used for the whole series. 

The test requires two instruments by which p and p, can 
be measured in absolute measure. 

§ 6. A fault of insulation in a submarine cable is generally 
due to a hole in the dielectric. This hole is gradually en¬ 
larged by the action of the current, although the polarization 
at the fault often seems to seal it up for a time. Rapid 
reversals with 100 cells or more tend to break a fault down, 
i.e. to enlarge it, so that its resistance becomes insignifi¬ 
cant. A current flowing from the copper to the sea 
apparently seals up a fault better than the opposite current. 
It causes the deposit of chloride of copper and oxygen, 
whereas the zinc current causes a deposit of salt and hydrogen. 
The bubbles of gas formed under great pressure in time 
burst the film of deposited salts, and the fault temporarily 
breaks down. When this occurs with the negative current, 
no further damage occurs in general than a slight enlarge¬ 
ment of the fault; but by the positive current a slow but 
certain erosion of the copper is produced, which always ends 
in producing a complete and sudden loss of continuity in 
the conductor. No warning is given of the impending fatal 
injury ; for so long as the slenderest thread of copper remains 
no sensible diminution occurs in the resistance of the line. 
Signallers prefer to keep a cable positive to the sea, because 
they get better signals, the currents received being stronger, 


Let a = 


f = 


d = 


Chap. XXV.] Faults in Telegraphic Lines. 355 

and less liable to the derangements produced by the sudden 
variations of a fault. The practice is, however, reprehensible. 
A faulty cable should always be kept negative relatively to 
the sea. It is possible to send very good signals through a 
cable or line in which there is a fault of such magnitude 
that its resistance is far less than that of the conductor 
between the stations. Nothing is absolutely fatal to com¬ 
munication except a want of continuity in the conductor. 

Sometimes the fault is made by the presence of some 
foreign body in the insulator. When metal, such as a piece 
of broken wire, is driven through the dielectric connecting 
the conducting wire with the sea, or with the metal sheathing, 
a fault of no sensible resistance is produced, and this class 
of fault is easily recognised by the absence of polariza¬ 
tion. 

§ 7 . A fault of the second class, i.e. involving want of 
continuity, may be combined with one of the first class : 
thus the cable or land-line may not only be broken, but may 
be in more or less perfect connexion with the earth at the 
fracture. In this case simultaneous tests at both ends are 
impracticable. We can only measure the resistance of each 
unbroken portion of the cable, and guess from the polariza¬ 
tion what is likely to be the fraction of the whole resistance 
observed due to the fault. We can in any such case safely fix 
a maximum distance beyond which the fault cannot lie. With 
the minimum of polarization the bare copper end of a cable 
usually has a resistance equal to several miles of the con¬ 
ducting wire. 

A fault of the second class not unfrequently occurs with 
perfect insulation. The conductor is broken, but insulated 
at the fracture. In a submarine cable the distance of the 
insulated fracture can then be measured very exactly by 
measuring the capacity of the cable between the fracture and 
the shore. The capacity per mile being known, this test 
gives the distance with great exactitude. On a land line the 

A A 2 


356 Electricity and Magnetism. [Chap. XXV. 1 

insulation is seldom good enough to allow this test to be j 
rigorously applied. 

§ 8. The position of a fault of the third kind—contact 
between neighbouring conductors—can easily be fixed if the | 
contact is local, and of small resistance. We need only ; 
measure the resistance of the loop formed by the contact, ; 
and half this is evidently the resistance corresponding to 
the distance of the fault. When the contact is imperfect, its 
position can be very accurately determined by the aid- of a 
third wire, if this be well insulated : to do this, treat one of 
ihe two wires in contact as an earth, leaving it uninsulated: 
and by the loop test described § 4 above, fix the position of 
the point of contact on the other wire, this contact being 
now in effect an ordinary fault of the first class. 

The position of the contact can also be ascertained with¬ 
out a third wire, by a Wheatstone’s balance test. To do 
this, the connections are arranged as follows, Fig. 124: r t 
and r m are resistance coils, r n and r iy are the two sub¬ 
divisions of one of the two faulty line wires, subdivided at e 
by the contact; the point Bi is the further end of the line, 
and is put to earth ; the branch r is made up of the galvano¬ 
meter, and of the earth at Bj; the wire joining the battery 
with e is the second line wire in contact with the first at e ; 
the further end of the second line is insulated. 

Then, calling a; and y the two subdivisions of the first line 
wire, we have x — r n , y = r iy and r- x : r m = x : y; whence, 
knowing and r m , x and y can be found. 



Chap. XXVI.] Applications of Electricity. 


357 


chaptp:r xxvi. 

USEFUL APPLICATIONS OF ELECTRICITY, OTHER THAN 
TELEGRAPHIC. 

§ 1. Electricity has been applied in so many ways to the 
useful arts that a large separate treatise might be written on 
these applications. In this book a few only of these appli¬ 
cations can be mentioned, and these must be very cursorily 
described, under the heads of Electro-Metallurgy, Electric 
Light, Medical Applications, the Firing of Mines, Clocks, 
governors and chronoscopes. 

ELECTRO-METALLURGY. 

§ 2 . In metallurgy electricity finds a threefold applica¬ 
tion. 1. To electro-plating, such as gilding or silvering 
objects. 2. To the reproduction by metallic casts of 
objects of any form. 3. To the reduction of metals 
from their ores. When our object is to coat a metal 
with a thin metallic film of some other metal, we immerse 
the object to be coated in a solution of some salt of the 
metal to be deposited. We pass a current from the bath 
to the object, so as to decompose the salt and deposit the 
metallic positive ion on the object, which is a negative elec¬ 
trode. By the choice of' a proper salt, a proper strength of 
solution, and a proper strength of current, the film can be made 
adhesive. When copper objects are to be gilt, they are 
treated as follows :—They are first heated, to dispel any fatty 
matter from their surface; they are next plunged while 
still hot in very dilute nitric acid, which removes any coating 
of oxide or suboxide of copper; they are then rubbed with 
a hard brush, washed in distilled water, and dried in gently 
heated sawdust. They are still further cleaned by being 
rapidly immersed in ordinary nitric acid, and next in a 
mixture of nitric acid, bay salt, and soot. The objects thus 



358 Electricity and Magnetism. [Chap. XXVI. 

prepared, so as to have a uniformly clean metallic surface, 
are immersed in a bath containing a solution of some salt ; 
of gold. 

The objects are attached to the zinc pole of a battery 
consisting of three or four elements, the other pole of which 
is connected with an electrode of gold also plunged in the 
bath. The passage of the current decomposes the salt, 
deposits gold on the object, and causes the dissolution of 
an equal quantity of gold from the gold electrode. The 
time required for the operation depends on the thickness of 
coating required. One grain of gold and io grains of 
cyanide of potassium in every 200 grains of water form 
a suitable bath. Silver, bronze, brass, German silver, and 
some other metals can be directly gilt in this manner ; but 
in order to gild iron, steel, zinc, tin, or lead, it is found 
necessary to electroplate them first with copper. The bath 
from which copper is deposited is a saturated solution of 
sulphate of copper. The positive electrode must then be 
a copper plate. A bath for the deposition of silver 
consists of two grains of cyanide of silver and two parts of 
cyanide of potassium in every two hundred grains of water; s 
the positive electrode must be a silver plate. 

§ 3 . The reproduction of objects in metal by electricity is 
effected by a thick deposit of the metal in a mould, the sur^ 
face of which has been so treated as to be a good conductor. 
The deposit is obtained from a bath by the passage of a 
current, precisely as the deposit required for electro-plating 
is produced. 

The mould, if made of metal, should be slightly coated with 
some fatty substance. A brush rapidly passed through a smok 
flame, and then used as it were to dirty the mould, is said 
to be sufficient to prevent adhesion. Ganot mentions Street’s 
fusible alloy, consisting of 5 parts of lead, 8 of bismuth, and 
3 of tin, as suitable for moulds of metallic objects. Stearine 
is used to prepare moulds of plaster objects; these are 
first immersed in melted stearine and withdrawn quickly ; 



Chap. XXVI.] Applications of Electricity. 359 

some of the stearine is absorbed by the pores of the plaster ; 
the surface is next coated with graphite or with black lead 
rubbed on with a brush. The stearine mould can then 
be taken. The interior surface of the mould is covered 
with graphite to make it conduct. 

Gutta percha moulds may be prepared by pressing gutta 
percha heated in warm water against the surface of the object 
to be copied, which should previously be covered with 
graphite to prevent adhesion. The mould must also be 
coated with graphite to make it conduct. Any of these moulds, 
used as a negative electrode in a bath of sulphate of 
copper, will become filled with a copper deposit, which re¬ 
produces the original object. This process is of great use to 
printers. Copper plates are beautifully reproduced by its 
means. 

§ 4 . The reduction of ores has never been carried out on 
any large scale, but several of the rarer metals have only 
become known to us by the decomposition of their salts 
under the action of the electric current. Davy obtained 
potassium for the first time by decomposing a slightly 
moistened fragment of hydrate of potash by a current from 
200 or 250 cells. Sodium can be obtained in a similar way ; 
but other methods are now known, which are commercially 
preferable. 

Barium, calcium, magnesium, aluminium, &c., can be ob¬ 
tained by electrolytic methods. 

The ores of silver, lead, and copper have been treated by 
electric processes, many details of which will be found in the 
‘ Trait 6 d’Electricite' et de Magnetisme,’ by Messrs.Becquerel, 
vol. ii. 


ELECTRIC LIGHT. 

§ 5 . When the points of two pencils of charcoal or graphite, 
attached by thick wires to the two poles of a galvanic battery 
of forty or fifty Grove’s elements, are placed for a moment in 


360 Electricity and Magnetism. [Chap. XXVI. 

contact and then withdrawn, so as to remain about one 
eighth of an inch distant, a current will flow round the circuit 
crossing the arc from pencil to pencil, and at this spot 
emitting a most brilliant light. 

The name voltaic arc is often used to designate that por¬ 
tion of a continuous current where there is a gaseous con¬ 
ductor. The voltaic arc is in most cases luminous. Its 
colour depends on the gas traversed, and its intensity is 
closely connected with the density of the gas. With rare¬ 
fied gases, as in the Geissler tubes described above, a com¬ 
paratively feeble glow is obtained ; in air, the intensity of 
the electric light may be as great as J that of sun-light, 
according to experiments of Fizeau and Foucault. The 
air is much heated at the point of passage, and its resist¬ 
ance thereby reduced ; if the current be momentarily inter¬ 
rupted, the e. m. f. of the battery will be unable to re¬ 
establish the voltaic arc, unless the points are again 
brought very close or into contact, to. be withdrawn as 
before when the current has been established; the reason 
being that the e. m. f. which is sufficient to send the 
current across hot air is insufficient when this air is 
cooled. The carbon of the pencils is consumed in the 
production of the light. The positive electrode is much 
more rapidly consumed than the negative electrode, and 
becomes hollow at the point. In order to render the light 
available for practical use, the graphite pencils must be held 
in a lamp, so constructed that the opening between the 
points remains sensibly in one place. In these lamps there 
must therefore be a feed supplying the pencils in the ratio 
in which they are found to be consumed. The lamp must 
also be furnished with some contrivance by which, if the 
voltaic arc is extinguished from any cause, the graphite 
points will instantly fall together, re-establish the arc, and 
again separate to the normal distance for the greatest inten¬ 
sity of light. Lamps fulfilling these conditions more or less 
perfectly by means of electro-magnetic gearing have been 




Chap. XXVI.] Applications of Electricity. 361 

invented by Mr. F. H. Holmes, M. Serrin, M. Dubose, 
and others. 

Mr. Holmes’s lamp has been used for lighthouse illumb 
nation with success. 

An electromotive force of about eighty volts is apparently 
the least with which a good electric light can be produced, 
and the resistance of the circuit (exclusive of the voltaic 
arc) must not much exceed 12 or 15 ohms. Sir William 
Thomson has produced a good light with eighty Daniell’s 
cells of the construction and dimensions described § 12, 
Chap. XV. These cells remained in good condition for 
several months, so that the light could be obtained at any 
moment by merely closing a circuit. Grove’s cells will 
only act well for a few hours after being filled, and give out 
noxious fumes. 

Mr. Waring produces aji intense electric light by the in¬ 
candescence of mercury vapour. The current is passed 
along a thin stream of mercury, which it volatilizes. The 
mercury is hermetically enclosed. This light has a 
greenish tinge. A rapid succession of sparks from a 
Ruhmkoff coil will also produce a somewhat feeble light. 

The electric light may be made use of in photography, 
and the examination of its spectrum presents many points 
of great interest to the physicist. 

FIRING OF MINES. 

§ 6. This is effected by passing a current through a film of 
semi-insulating substance, which becomes red hot, and fires 
a detonating mixture or gunpowder. A fuse is prepared to 
which two insulated wires are led. The ends of these 
wires are imbedded in a thin solid gutta percha rod : they 
do not join, but end in a little layer of the priming com¬ 
position, which is an intimate mixture of subsulphide of 
copper, subphosphide of copper, and chlorate of potassium. 
The whole is surrounded by gunpowder. A feeble current 
will not heat the priming composition to redness, but a 


362 Electricity and Magnetism. [Chap. XXVI. 

powerful current, even if short, will develop enough heat by 
its passage to ignite the powder. The current is generally 
produced by the discharge of a condenser, and this con¬ 
denser is often charged by a frictional electric machine. A 
vulcanite plate machine as designed by Ebner is much used 
with a condenser consisting of a sheet of india rubber with 
tinfoil armatures rolled up so as to form a cylinder. A 
magneto-electric current or a battery current may be used. 
When the mine or torpedo is to be fired by the discharge of 
a condenser, a fine wire is better than a thick one, in order 
that the capacity of the conductor may be small: with the 
same object the thickness of the dielectric should be con¬ 
siderable, and the very best insulation is necessary. 

The detonating mixture may also be fired by heating 
to redness a fine platinum wire stretched between the two 
ends of the copper wires : the platinum wire should be coated 
with fulminate of mercury. A voltaic battery is required with 
this arrangement, which has the double advantage that the 
condition of the conductors can from time to time be tested 
by feeble currents which will not explode the charge, and 
that it allows several insulated conductors to be laid in one 
cable, which plan cannot be followed when the mine is 
fired by the discharge from a condenser, owing to the power¬ 
ful current then induced in the neighbouring wires, which 
would fire all the mines whenever a current was passed along 
a single wire. The platinum fuse can be fired when the 
insulation of the conductors is very defective. 

MEDICAL APPLICATIONS. 

§ 7 . Electricity in its passage through the body may produce 
very marked physiological effects. The simple passage of a 
current from one hundred cells produces a somewhat dis¬ 
agreeable disturbance or tingling at the point where it enters or 
leaves the body. This feeling is considerably more intense at 
the moment when the current begins and ceases than at any 
other time. When a powerful current of very short duration 


Chap. XXVI.] Applications of Electricity. 363 

is sent through the body, as from a Leyden jar of moderate 
size charged to the potential of Several hundred volts, the 
disturbance is felt throughout the frame, and is well known 
as an electric shock. The disturbance produced may be so 
great as to produce illness or death, and many persons who 
are killed by lightning are killed by the simple shock re¬ 
sulting from the sudden discharge of electricity from their 
bodies, which had been inductively electrified from the 
clouds; the lightning passing from cloud to cloud discharges 
these, and the escape of the electricity from the body pre¬ 
viously charged produces the shock. The rapid succession 
of currents produced by rotating magneto-electric arrange¬ 
ments produce a singular numbness if passed through the 
body, so that a man holding two electrodes from which these 
short rapidly alternating currents flow cannot let them fall, 
but holds them convulsively. The very first discovery of the 
electric current by Galvani was due to the contraction of a 
muscle of a frog under the influence of the current. From 
all these facts it cannot be doubted that electricity may be 
of use as a curative agent; the medical man may find in it a 
means of producing important modifications in the condi¬ 
tion of the body; but the author is unable to speak with 
any confidence of the applications as yet made of this agent. 
Rapidly alternating magneto currents are the most popular, 
but he is not aware that thoroughly scientific experiments have 
been made on the effects produced, or on the real magnitude 
of the currents employed. Valuable results may have been 
and may be attained, but it is for medical men to decide 
how far these have or have not been the results of some 
happy accident. The application of electricity, unhappily, 
can easily be made the subject of quackery without de¬ 
tection. 

The actual cautery can be applied by platinum wire 
heated by an electric current in parts of the body which 
could not be reached in any other way. 


Electricity and Magnetism. [Chap. XXVI 


3 <H 


CLOCKS, GOVERNORS AND CHRONOSCOPES. 

§ 8. There are many other useful applications of electricity. 
Mr. Alexander Bain drives clocks by a small current acting 
on a propelment, the speed of which is regulated by a 
pendulum. The propelment acts like the propelment of the 
dial telegraph instruments. The same inventor followed 
by others controls distant clocks from one standard clock 
by electro-magnets set in action by currents. The pendu¬ 
lum of the distant clock oscillates freely if keeping perfect 
time, but is slightly retarded or accelerated by an electro¬ 
magnet if before or behind time. Time guns or other time 
signals are also given from observatories by the aid of 
electric currents. 

Electricity is made use of in one form of governor to 
regulate the speed of machinery. When the speed is ex¬ 
cessive, the governor balls by their divergence complete 
a contact which permits a current of electricity to produce 
friction by the action of an electro-magnet. 

Electricity is made use of to light the gas in one species of 
motor gas engine, and electric sparks have been lised to 
light gas lamps. 

Electric chronoscopes measure time to thousandths of a 
second, and by their aid the speed of projectiles is ascer¬ 
tained : the plan in general being that the projectile at one 
part of its path interrupts one circuit, and at another part a 
second circuit, by cutting wires. The interruptions deter¬ 
mine sparks which leave their record on prepared paper or 
a metallic surface, moving with known velocity : the distance 
between the records of the sparks serves therefore to 
measure the time occupied by the projectile in passing from 
one wire to the next. In this little treatise these and many 
other important applications can barely be enumerated. 
As the science becomes more familiarly known, the extent 
and number of useful applications will day by day increase. 


Chai\ XXVII.] Atmospheric Electricity. 


365 


CHAPTER XXVII. 

ATMOSPHERIC AND TERRESTRIAL ELECTRICITY. 

§ 1. Not much is known of the distribution of electricity 
on the surface of the earth. According to Sir William 
Thomson the most probable distribution is analogous to that 
which would be produced if the earth’s surface generally were 
charged with negative electricity held as a charge on the inner 
armature of a condenser, the outer armature of which was 
in the upper regions of the atmosphere, the lower part of 
which acts as the dielectric. Electrified masses of air moving 
at no great distance from the earth’s surface are continually 
altering the distribution of electricity, which is, however, gene¬ 
rally found to be negative on the earth’s surface. The 
modes of investigating the density of electrification and the 
sign of the electricity at the earth’s surface are analogous to 
the method of the proof plane. Some conductor in contact 
with the earth is insulated, brought indoors, and the sign 
of its electrification ascertained by an electrometer. We 
here speak of the electrification of the surface, not of the 
potential, at points of the air which must be separately 
investigated. We cannot treat air as we can the earth, 
because it is an insulator, and will not part with its elec¬ 
tricity to any conductor analogous to a proof plane. 

§ 2 . The potential of the earth’s surface is assumed as the 
zero or datum from which all other potentials are measured; 
nevertheless we know that the potentials of different places 
on and in the earth differ considerably, sometimes to the 
extent of several hundred volts, though this is rare. We 
obtain this information from the currents observed to flow 
through wires joining parts of the earth widely separated. 
These currents being known, and the resistance of the 
circuit being known, the e. m. f. due to differences of poten¬ 
tial between the ends of the wire can be inferred with 


366 Electricity arid Magnetism. [Chap. XXVII. 

certainty. The difference of potential between the two 
sides of the Atlantic is often not more than one or two 
volts, and generally points joined by the sea are nearly at 
one potential. This condition is, however, liable to be dis¬ 
turbed from time to time, and these disturbances are 
called electric storms. Statistics of the distribution of po¬ 
tential over the earth’s surface have not yet been compiled. 

§ 3 . Any conductor at the end of which a flame ft 
burning, or any small pipe from which water drops, will very 
soon acquire the potential of the air where the flame burns 
or the water is dropping; for if there is any difference of 
potential between the conductor and the air near the flame 
or tube end, it will cause an accumulation of electricity at 
the flame or tube end, and this electricity will then be 
conveyed away by the particles flying off in the flame or by 
the drops of water until there is no difference of potential 
between the conductor and the neighbouring air. 

This fact enables us to measure the potential of the air at 
any point, or, in other words, to compare its potential with 
that of the earth. To do this, a conductor having a flame 
or water-dropping arrangement at one end is connected with 
one pair of quadrants of the reflecting electrometer ; this 
pair of quadrants is thereby brought to the potential of the 
air at the spot to be tested. The other pair is connected 
with the earth, and the difference of potentials is then 
measured by the deflection of the electrometer in the usual 
way. Other forms of electrometer may be used. Sir William 
Thomson found that the potential of the air varied very 
rapidly near the surface of the earth. Thus he has observed 
a difference of potential between the earth and the air nine 
feet above it, equal to 430 volts in ordinary fair weather, and 
in breezes from the east and north-east as great a difference 
as this per foot of air. The potential is perpetually fluc¬ 
tuating, even in fair weather. Instruments have been in 
action for some time at Kew and elsewhere, recording con¬ 
tinuously the differences of potential between the earth and 



Chap. XXVIII.] The Mariner's Compass. 367 

one point in the air. The potential of the air appears to be 
generally positive in fine weather, and negative only 
during broken or rainy weather. 

§ 4 . The distribution of magnetic force on the surface of 
the earth has already been alluded to in Chap. VII. It is 
conceivable that this force may be wholly due to currents 
flowing round the earth, and maintained by the thermo¬ 
electric action due to the sun, or to some other cause con¬ 
nected with the rotation of the earth. Observation does 
not, however, as yet enable a decided opinion to be given 
on this point. 


CHAPTER XXVIII. 

THE MARINER’S COMPASS. 

§ 1 . The mariner’s compass consists of a card pivotted on 
a vertical axis, and directed by having on its lower surface 
one, two, four, or more parallel magnets with similar 
poles pointing in similar directions. The magnets being 
free to turn in a horizontal plane, place themselves in the 
magnetic meridian. The object of using several magnets 
is to increase the magnetic moment for a given weight of 
steel. The upper surface of the card is divided into degrees 
and also into thirty-two parts, each containing n° 15'; the 
thirty-two rays indicate the thirty-two points of the com¬ 
pass; the line joining the north and south points is parallel 
to the axes of the magnets. The north and south line 
indicates the magnetic meridian at each place. As was 
shown in Chapter VII., the declination varies at different times 
and at different places The declination of the particular 
place at the particular time must be known by means of 
charts or otherwise before the true north or any other true 
course can be determined by the aid of the compass. 

§ 2 . The presence of any iron or steel in the neighbour¬ 
hood of the compass alters the direction df the lines of 
force in the magnetic field, and causes what is termed a 



368 Electricity and Magnetism . [Chap. XXVIII. 

deviatioii of the north and south line from the magnetic 
meridian. In wooden ships, by a little care in placing the 
compass properly, deviation errors of any practical moment 
may be wholly avoided, but in iron ships they must be 
partly allowed for and partly compensated. The deviation 
in an iron ship is due to two causes—ist, the permanent 
magnetism of the ship; 2nd, the magnetism induced by the 
earth’s magnetic force. We can compensate for the effect of 
the permanent magnetism by properly placing a permanent 
steel magnet in the neighbourhood of the compass, exerting 
an equal and opposite couple to that due to the ship. 

We cannot compensate or can only very imperfectly com¬ 
pensate for the effect of induced magnetism, because it is 
impracticable to arrange a soft iron structure near the com¬ 
pass, such that its induced magnetism shall have an opposite 
and equal effect to that of the ship. The induced magnetism 
varies as the ship turns round horizontally. Thus when she 
bears north or south, her magnetic moment is much greater 
than when east or west. By testing experimentally in port 
the deviation on each course, a correction is obtained for that 
particular neighbourhood. The ship’s induced magnetism 
also varies, however, as the direction and intensity of the 
earth’s magnetic force varies; and no safe allowance can 
be made for errors resulting from this cause. Moreover 
the induced magnetism varies as the ship rolls, and 
(to a much less extent) as she pitches. The heeling error 
can be compensated, as was shown by the late Mr. 
Archibald Smith. The Admiralty Compass Manual, written 
by that gentleman in concert with Captain Evans, R.N., 
should be consulted by all who wish to understand the 
mariner’s compass. The mathematical and practical in¬ 
vestigations of Mr. Smith have been of the very highest 
utility in adding both to our scientific knowledge and to 
the practical utility of the mariner’s compass. 

The prismatic compass and azimuth compass are compasses 
fitted with contrivances by which the bearings of objects can 
be taken. 


INDEX 


ABS 

A BSOLUTE electromagnetic capacity 
from throw of galvanometer, 266 

— electrometer, 211 

-principle of Sir William Thomson’s, 

100 

— electrometers, definition of, 21 

— unit of force, 20 
-work, 51 

•— units, compared with others, 162 
Absorption, apparent, by insulators, 90 

— by insulators, effect on resistance, 255 

— in condensers, 98 

— of heat at hot junction of thermo-elec¬ 
tric pair, 185 

-from current through unequally 

heated metal, 186 

Accumulation of electricity on projections 
of conductors, 17 

Acid facilitates electrolysis of water, 166 
Acids behave like electronegative ions, 167 
Addition of coils joined in multiple arc, 233 
Agonic line, definition of, 127 
Air, potential of, obtained by aid of flame, 41 

-how to observe, 366 

-measured by electrometer, 210 

-point in, 40 

— pressure balanced by electric force, 104 
-diminution of, required to produce 

sparks, 104 

Alloys and metals, specific resistance of, 
249 

Alphabet, Morse, 299 

— of Thompson’s siphon recorder, 336 
Amalgamation of zinc plates in galvanic 

cell, 218 

Ampere, discovered laws of attraction and 
repulsion between currents, 58 
Ampere’s theory of forces between cur¬ 
rents, 136 

Amplitude of current indicating dots 
through cables, 331 
Anode, definition of, 67 
Antimony, diamagnetic, 113 


BAT 

Armature, attraction between electromag¬ 
net and,123 

— of a magnet, 121 

— Siemens’, for magnetoelectric arrange¬ 
ments, 283 

Armatures or coatings of condensers, 98 
Armstrong, Sir William; hydroelectric 
machine, 272 

Arrival curve of current, 329 
Astatic galvanometers, 193 
Atlantic cable, Anglo-American, design of, 
348 

-(French), elements of arrival curve 

for, 329 

-speed of signalling through, 333 

Atmospheric electricity, distribution of, 365 
Attraction and repulsion due to static 
electricity, 1 
-induction, 14 

— between currents, 56 

— maximum, between electromagnet and 
armature, 123 

Automatic sender, Wheatstone’s, 316 
Axis, magnetic, 109 


"D AIN’S chemical telegraph, 304 
— electric clock, 364 
— telegraph, printing solution for, 304 
Balance, Wheatstone’s, 244 
-theory of, 243 

Bases of salts behave like electropositive 
ions, 167 

Battery, galvanic, Bunsen’s and Faure’s, 
226 

-chromate of potassium, 227 

-Daniell’s, 219 

-gas, 213 

-general instructions for management 

of, 228 

-Leclanche, 228 

-Marie Davy’s and Grove’s, 225 

-Menotti’s, 224 


B B 






370 


Index. 


\ 


BAT 

Battery galvanic, sand, Smee’s and 
Walker’s, 211 

-Thomson’s and sawdust, 223 

— how to measure resistance of, 237 
B. A. units, 158 

Bell instrument for+and—signals, 306 
Bells, electric, 326 
Bennett’s electroscope, 204 
Bismuth is diamagnetic, 113 
Bohnenberger’s electroscope, 204 
Bridge, Wheatstone’s, 244 
Bright, Sir Charles ; bell instruments, 306 
British Association experiments on electro¬ 
magnetic resistance in absolute measure, 

155 • , 

Brush discharge, 41 
Bunsen’s galvanic cell, 226 


/"^ABLES, design of, 348 

Capacity, absolute electromagnetic 
from throw of galvanometer, 266 

— for electricity, meaning of, 96 

— of a knot of cable, formula for, 254 

— of cores of cables, 347 

— of long cylindrical conductor (insu¬ 
lated wire), 101 

— of spheres and opposed flat plates, 96 

— specific inductive, 97 

— tests, to determine position of fault, 355 

— unit of, electromagnetic, 134 

-electrostatic, 96 

-practical, 162 

Capacities compared by throw of galvano¬ 
meter, 261 

Caselli’s copying telegraph instrument, 322 
Casts taken by electro-deposits, 358 
Cautery applied by electricity, 363 
Charge on spheres and opposed plates, 96 

— proportional to potential of conductor, 36 
Chemical affinity, relation to e. m. f. re¬ 
quired to produce decomposition, 171 

— reaction source of power in galvanic 
cell, 54 

— telegraph, Bain’s Morse, 304 

— theory of E. M. F, 169 
-of galvanic cell, 23 

Chromate of potassium galvanic cell, 227 
Chronoscopes, electric, 364 
Circuit, inductive, in frictional electrical 
arrangements, 271 

— telegraphic, 297 

Circuits, lengths worked by relays, 309 
Circular current producing rotation of 
straight current, 292 

Clark’s compound; used in submarine 
cables, 349 

— insulators for land lines, 342 

— cell, e. m. F. of, 159 

Clarke’s magneto-electric machine, 280 

Clocks, electrical, 364 

Closed circuit, analogy with magnet of, 138 

— circuits, forces exerted between, 138 
Cobalt is paramagnetic, 113 


COR 

Code, Morse, 298 

— single needle Morse, 306 

Coeffic entfor effect of temperature on G. p., 
255 

---metals, 251 

— of magnetic induction for various 
materials, 124 

-in iron, 123 

Coercive force, effect of in telegraphic 
apparatus, 312 

-in magneto-electric machines, 284 

-meaning of, 115 

Coil of galvanometer, best form of, 196 

— rotating in uniform magnetic field, elec¬ 
tromotive force due to, 151 

-used to determine resistance, 

*54 

Coils, resistance, first notion of, 86 

— flat spiral, action of current in, 60 

— long cylindrical, action of current in, 59 

— sizes of wire used in galvanometer, 202 

— used to increase force between currents, 

58 

Compass, mariner’s, 367 
Compound magnets, 114 
Condenser attached to inductorium, 290 

— capacity of, 97 

— definition of, 20 

— Varley’s system of signalling with, 336 
Condensers, absorption in, 98 

— compared by throw of galvanometer, 262 

-differential galvanometer, 263 

-galvanometer and resistance slide, 

263 

— --platymeter, 264 

— used to fire mines or torpedos, 362 
Conductivity, definition of, 234 

— specific; definition, 250 
Conductor, effect of large conductor in 

electrical machines, 272 

— in submarine cable, 345 
Conservation of energy, theory of ; applied 

to thermoelectric pair, 185 
Constant of a galvanometer, 235 
Contact between dissimilar substances pro¬ 
duces electricity, 21 

-wires, one class of fault, 349 

-test to find position of, 356 

— potential series; for metals, 43 

— theory of galvanic cell, 22 
Continuity, want of, one class of fault, 349 
Convection of heat by electricity, 186 
Conversion of British into metrical units, 164 
Copper and zinc single fluid cell, e. m. f. of, 

217 

— called positive pole of galvanic cell, 220 

— resistance in cables, test ©f, by Wheat¬ 
stone’s bridge, 246 

— specific resistance of, in cables, 252 
Copying telegraph instruments, Bakewell’s 

and Caselli’s, 322 

Cores of cables, capacity per knot, 347 

-formula for insulation resistance of, 

346 





Index . 


37i 


COR 


ELE 


Cores of cables, insulation resistance 
changed by temperature, 253 

— of electromagnets split in telegraphic 
apparatus, 311 

Cost of motive power due to electricity, 295 
Couple exerted on magnet by magnetic 
field, 112 

Culley’s rules for iron wire on land lines, 339 
Current, commencement of, in any circuit, 78 

— constant; strength equal in all parts of 
circuit, 77 

— electromagnetic unit of, 117 

— induced by motion of magnet, 69 
-by increase or decrease of neigh¬ 
bouring currents, 72 

-by motion of neighbouring current, 70 

— influence of resistance of battery on, 86 

— intensity of magnetic field produced 
by, 117 

— meaning of strength of, 56 

— nominal direction of in galvanic c.rcuit, 

53 . . „ . . 

— of electricity, definition of, 52 

— produced by galvanic cell, 53 

— produces rotation of a second current, 291 

— resume of various causes producing, 80 

— thermoelectric, first notion of, 79 
transient, in broken circuit, 79 

Currents act on magnets as if solenoids, 
60 

— fundamental experiments on, 57 

— Ampere’s theory of forces between, 136 

— arrival curve for, 329 

— force between, 56 

— heat conductors, 66 

— induction by, 70 

— made to rotate by magnets, 293 

— magnetise iron, 66 

— measured in electromagnetic measure by 
Webef’s electrodynamometer, 139 

-by Kohlrausch’s method, 140 

-in terms of force between flat 

spirals, 141 

— multiplication of force between ; by use 
of coils, 58 

— produce a magnetic field, 113 
-rotation of magnets, 293 


TAANI ELL’S cell, chemical theory of 

E.M.F. Of, 172 

- E . m. f. of; in electromagnetic measure, 

159 r 

-management of, 222 

-practical construction of, 2x9 

-resistance of, 223 

— cells of low Resistance ; Thomson’s large 
trays, 223 

-sawdust used in, 223 

Dash and Dot Morse signals, 299 
Dead beat galvanometer, 198 
Declination, magnetic, definition of, 127 
Decomposition of electrolyte by currents, 
67 


Deflections, equal; indicate equal currents 
in galvanometer, 190 
Density, electric ; definition of, 102 

— of electricity, 16 

— on opposed surfaces depends on differ¬ 
ence of potential, 106 

Dial telegraphic instruments, 317 
Diamagnetic substances, coefficient of mag¬ 
netic induction for, 124 
Diamagnetism, meaning and examples of. 
“3 

Dielectric, meaning of, 18 
Dielectrics, specific inductive capacity of, 
97 , 

Difference of potential,, definition of, 26 

— of potential due to contact of zinc and 
copper ; Thomson’s experiment, 45 

— —— between coatings of Leyden jar, 33 
Differential galvanometer, adjustment of, 

200 

-description of, 83 

-precautions to be observed in using, 

240 

Dimensions of a unit, meaning of the term. 
161 

Dip of magnet, 126 
Dipping needle, 111 

Direction of current induced by motion of 
neighbouring magnet, 70 
-nominal, from galvanic cell, 53 

— of deflection of magnet under influence 
of currents, 61 

Discharge of electricity by points, 40 

— by brush cr spark not subject to Ohm’s 
law, 92 

— by points, due to increased density, 102 

— silent, 105 

Discharging keys for return currents in 
telegraphic circuits, 310 
Distances worked by relays, 309 
Distribution of charge examined by proof 
plane, 15 

— of statical charge, unaffected by mass 
of conductor, 6 

Dot and Dash, Morse signals. 299 
Dots, effect of, sent rapidly through sub¬ 
marine cables, 331 

Dry pile, used with electroscopes, 204 
Duplex sending on telegraphic lines, 322 


T^ARTH currents, cut off line by con 
densers, 337 

-effect of, in telegraphic lines, 310 

— difference of potential between various 
parts of, 365 . 

— function of, in telegraphic circuit, 297 

— magnetic properties of the, 109 

— magnetisation of soft iron bar by, 121 

— potential of ; used as zero, 29 
Earth’s magnetic force, cause of, 367 
Ebner’s machine for firing mines, 362 
Electric density on plates, spheres, and 

points, 102 


B B 2 




372 


Index . 


ELE 


FAU 


Electric light, 359 

— series of insulators each positive to 
successor, 9 

Electrical machine, description of frictional, 
269 

-first notion of, 5 

Electricity, atmospheric, 363 

— charge of, 3 

— conveyed by convection through air ; 
sparks, brushes, 92 

— how produced, 21 

— positive and negative, 7 

— quantity of, 3 

— velocity of, 327 

— vitreous and resinous, 2 
Electrification, change of apparent resist¬ 
ance in cables, due to, 255 

Electrochemical equivalent of water, 165 

— equivalents, 169 
Electrodes, definition of, 49 
Electrodynamometer, construction of, 59 

— theory of Weber’s, 138 
Electrolysis, description of, 67 
Electrolyte, definition of, 44 
Electrolytes decomposed into groups called 

ions, 167 

Electromagnet, definition of, 120 
Electromagnetic engine, Froment’s, 294 

— force at centre of circular coil, 135 

— induction description of, 69 

— measure, relation of volt, ohm, farad, to 
absolute, 160 

— ring produces no magnetic field, 121 

— system of units, dimensions of, 164 

— unit of current, 117 

— units, definition of, 133 

-ratio to electrostatic units, 134 

Electrometer, absolute ; 211 

-definition of, 21 

-principle of Sir William Thomson’s, 

100 

— Thomson’s quadrant, 205 
-portable, 207 

— used to ascertain potential of air, 210 
Electromotive force, chemical theory of, 169 
-definition of, 48 

-due to alteration of neighbouring 

current, value of, 155 

-in terms of heat of combination and 

electrochemical equivalent, 171 

— — on closed circuit rotating in magnetic 
held, 152 

-- produced in conductor moving in 

magnetic field, 148 

■-required to produce decomposition, 170 

-unit of, electromagnetic, 134 

-electrostatic, 95 

-- — practical, 162 

-without difference of potentials, 75 

— series for metals, 43 
Electromotor, Froment’s and beam, 294 
Electromotors, cost of, compared with heat 

engines, 295 
Electrophorus, 268 


Electroplating, 357 

— theory of, 173 

‘ Electropositive,' meaning of, 43 
Electroscope, charged by induction, 15 

— gold leaf, 5 

Electroscopes, Bennet s. Canton s, Bohnen- 
berger’s, Peltier’s, 204 

— gold leaf and Peltier ; used to compare 
difference of potential, 37 

Electrostatic force, relation of, to density 
of electricity on neighbouring conductor, 
102 

— inductive machines, 273 

— measure, meaning of, 94 

— system of units, dimensions of, 164 

— units, actual magnitude of, 107 
-equations connecting, 108 

-of quantity resistance and differ¬ 
ence of potential, or E. m.f., 94 
Electrotypes, 358 

— theory of, 173 

Elementary substances discovered by elec¬ 
trolysis, 173 

Elements, electrochemical equivalents of, 

169 

-series, 168 

E. M. F. necessary to decompose an electro¬ 
lyte, 170 

-of cells, how affected by solution, 217 

-of Clark’s cell, 159 

-of copper zinc, single fluid cell, 2x7 

-of Daniell’s cell, 159 

-in electrostatic measure, 

100 

-of Grove’s cell, and Bunsen’s, 226 

-of Marie Davy’s cell, 225 

-of thermo-electric pair, relation of, to 

thermoelectric power, 179 

-per foot of wire in secondary coil of 

inductorium, 287 

-of bismuth-antimony thermo-electric 

pair, 183 

-unit of, called a volt, 159 

Equality between+and—electricity due to 
any cause, 8 
Equator, magnetic, 128 
Equipotential surfaces in magnetic field, 115 
Equivalents, electrochemical, 169 
Evolution of heat at cold junction of ther¬ 
moelectric pair, 185 


■p ARAD ; unit of capacity, 160 

A Faraday’s potential series of metals 
plunged in solutions, 216 

— how to find position of fault causing 
loss of insulation, 350 

Fault, how to find position of second 
method, 351 

— or loss of insulation, position found by 
aid of return wire, 332 

— position of ; found by simultaneous tests 
at two ends of line, 353 

Faults, description and behaviour of, 354 








Index. 


3 73 


fa a 


HUG 


Faults, in telegraph lines; classification, 
349 

Faure’s galvanic cell, 227 

Feilitsch, experiment on suction of iron into 
coil, 145 

Field, magnetic definition of, in 

Flow of electricity depends on difference of 
potentials, 40 

Foot-pound, relation to absolute unit, 51 

Force and work, units of, 94 

— experienced by conductor moving in 
magnetic field, 147 

— of attraction or repulsion between elec¬ 
trified bodies, 95 

— —_-magnetic poles, no 

Friction between insulators produces 

electricity, 1 

-difference of potentials, 42 

— of water suspended in steam produces 
electricity, 272 

Frictional and voltaic electricity, compari¬ 
son between, 50 

— electrical machine, 269 

Frog, contraction of muscles by electri¬ 
city, 363 

Froment’s electromoter, 294 

Fuse for firing mines by electricity, 361 


ALVA NIC battery ; cells in series and 
' Jr multiple arc, 87 

batteries, chief merits of, 212 

- cell, first notion of, 22 

- — influence of resistance of, 86 

- — produces permanent current, 53 

- — source of power in, 54 
Galvanometer, application of shunts to, 201 

- astatic, 193 

- coils, best form of, 196 

- - — practical construction of, 202 

- dead beat, 198 

- description of Thomson’s mirror, 62 

- differential, adjustment of, 200 
-first notion of, 83 

— effect of resistance of, 189 

— graded ; Thomson’s, 197 

— marine, Thomson’s, 199 

— shunted ; resistance of, 233 

— sine, 195 

Galvanometers, definition and classification 
of, 187 

— how to adjust sensibility of, 192 
-zero of, 193 

— intensity and quantity, 190 

— long coil and short coil, 190 

— size of wire used in coils of, 202 

— vertical, 188 

Gas engines, electricity used in, 364 

— galvanic cell, 213 

Gases, luminous currents through rarefied, 
290 

— perfect insulators, 85 

Gassiot’s experiments on discharges through 
rarefied gases, 290 


Geissler’s tubes, conduction through rare¬ 
fied gases in, 93 

-used with inductorium, 290 

German silver used for differential galvano¬ 
meter, 200 

-in differential galvanometer^ 240 

-for resistance coils, 86 

Gilding, 357 

Glass, hygrometric properties of, 260 

— insulators for land lines, 341 

— resistance of, 257 

— used in frictional electrical machine, 270 
Gold leaf electroscope, 37 

Graphite, resistance of, 257 

— used in electric lamp, 359 

-in Walker’s galvanic cell, 212 

Gravitation galvanic cell, 225 
Grove’s cells used for electric light, 359 

— galvanic cell, 225 

Gutta-percha core, capacity of, per knot, 347 
-resistance of at different tempera¬ 
tures, 253 

-insulation resistance per knot, 346 

— cores, dimensions of, 345 

— moulds for electrotypes, 358 

— resistance of ; measured, as test, 236 

— sheath; resistance tested by Wheat¬ 
stone’s bridge, 246 

— specific inductive capacity of, 97 
-resistance of, 252 


H EAT, amount of, produced by current, 
66 

— generated by flow of electricity, 41 
— mechanical equivalent of, in various 
units, 165 

— of combination, relation to e. m. f. of, 
170 

— of fixed stars detected by thermoelectric 
battery, 185 

— relation of, to mechanical work, 41 
— transformed into electricity by thermo¬ 
electric pair, 185 

Helix, intensity of magnetic field inside, 
142 

Heterostatic electrometers, 204 
Holmes’ electric lamp, 361 
— (T.), magneto-electric machine, 283 
Holtz’ inductive electrostatic machine, 275 
Homogeneous wire, used in submarine 
cables, 348 

Hooper’s india-rubber, specific resistance 
of, 252 . 

— material, insulation resistance per knot 
of core, 347 . 

-capacity per knot of wire, 347 

Horizontal component of earth’s magnetic 
force ; definition, 128 _ 

-determination of, 128 

-value of, 131 

Horse-shoe magnet, 121 
Hughes’ printing telegraphic instrument, 
321 






374 


Index. 


HYD 

Hydroelectric machine of Sir William 
Armstrong, 272 

Hygroscopic properties of glass, 260 

T NCLINATION, magnetic definition of, 
■*- 126 

India-rubber, core, capacity of per knot, 
electromagnetic, 254 

--electrostatic, 102 

-resistance of, per knot, 253 

— specific inductive capacity of, 97 
-resistance of, 252 

Induced charge, relation of, to difference 
of potential, 35 

— current due to change in neighbouring 
currents, 72 

-reaction of, on inducing current, 73 

Induction, electromagnetic, in broken cir¬ 
cuit, 75 

-in long circuit of considerable capa¬ 
city, 76 

-produces E. M. f., 75 

— magnetic, 113 

— magneto-electric, 279 

— of current on itself, 74 

— of currents by motion of magnet, 69 

— statical, description of, n 

-produces difference of potential, 41 

Inductive capacity of materials, specific, 97 

— circuit in frictional electrical machine, 
271 

— electrostatic machines, 273 
-machine by Holtz, 275 

— retardation, effect of, on duplex sending, 
326 

Inductorium or Ruhmkoffs coil, 287 

— luminous discharges from, 290 

— make and break apparatus for, 289 

— practical construction of, 288 

Inertia, effect of, on moving parts of tele¬ 
graphic instruments, 118 

— of parts, defects in telegraphic appa¬ 
ratus due to, 312 

Influence, name given to electromagnetic 
induction, 72 
Ink-writer, Morse, 301 
Insulating materials, resistance of, com¬ 
pared with conductors, 85 
Insulation ; causes of defective insulation in 
cables and land lines, 349 

— of galvanometer coils, 203 

— resistance, change due to electrification, 
255 

-meaning and calculation of, 252 

-of glass, 257 

-of land lines, 344 

-per knot of cable cores, 346 

— test, by fall of potential, 253 

-by simple galvanometer deflections, 

236 

-by Wheatstone’s bridge, 246 

— tests, precautions to be observed in 
making, 260 


LIG 

Insulators, change of resistance due to 
temperature, 254 

— specific inductive capacity of, 97 

— used for land lines, 341 
Intensity, galvanic cells joined for, 88 

— of magnetisation, definition of, 112 

— galvanometers, 190 

— of magnetic field, in 

-inside circular coil and helix, 

r 4 2 . • , 

-produced by current in straight 

wire, 117 

Interior of bodies, contains no statical 

charge, 16 

Inversions, thermoelectric, 177 
Ions, definition of, 67 

— do not combine during their passage 
through solutions, 173 

— electro-positive and electro-negative, 167 
Iron filings used to show lines of force, 119 

— magnetised by currents, 66 

— soft, meaning of, 114 

— wire, specific resistance of, 252 
Isoclinic lines, definition of, 128 

J OULES, mechanical equivalent of heat, 
41 

T/" ATHODE, definition of, 67 
Key, Morse, 298 
— reversing, 305 

— single needle, or + and —, 305 
Keys for transmitting, magnetoelectric, 286 
Killing iron wire, meaning of, 340 
Kirchhoff's laws, 246 

-applied to Wheatstone’s bridge, 248 

Knot of submarine cable, insulation resist¬ 
ance of, 253 

-capacity of, 253 

-resistance of conductor in, 252 

Kohlrausch’s method of measuring cur¬ 
rents in electromagnetic measure, 140 


T AND lines, contact between wires on, 
■ L ' 343 

-insulation, resistance of, 344 

-insulators for, 341 

-theory of signalling through, 332 

-wire for, 339 

Lead, used as standard thermo-electric 
metal, 176 

Leclanche galvanic cell, 228 
Lenz’s laws, 70 

Leyden jar attached to inductorium, 290 

-either coating may be to earth, 37 

-description of, 18 

— — used in connection with electro¬ 
meters, 206 

— jars, changes of potential due to con 
nection between, 36 

Light, electric, 359 





Index. 


375 


LIG 

Lightning causes death without striking, 
3t>3 

— conductors, action of, 105 

— one form of electric spark, 93 
Lines of force in magnetic field, hi 
-direction of, shown by iron filings, 

TI 9 

-due to thin bar magnet, in 

-used to calculate E. M. F., due to 

motion in magnetic field, 150 

— --indicate direction and intensity 

of magnetic field, 116 

— telegraphic, general description of, 338 
Liquids, electrolysis chiefly confined to, 166 

— form thermo-electric pair, 184 
Local action in galvanic cell, 218 

Loss of charge used as insulation test, 253 

— of insulation, one class of fault, 349 
Luminous currents through rarefied gases, 

290 


M a gne T ; analogy with closed circuit, 

-with solenoid, 60 

— effect of change in dimension on attrac¬ 
tion to armature, 125 

— causes rotation of current, 293 

— made to rotate by current, 293 

— poles, axis, 109 

Magnetic declination, definition of, 127 

— field, at centre of circular current and 
long helix, 142 

-definition of, 111 

-due to earth, description of, 126 

-how to determine intensity of, 

128 

-value of horizontal compo¬ 
nent of force in, 131 

-to electric current, 113 

-e.m.f. produced in conductor moving 

in, 148 

-force experienced by conductor mov¬ 
ing in, 147 
-unit, hi 

— force, earth’s, possible cause of, 367 

— inclination, definition of, 126 

— induction,, 113 
-coefficient of, 123 

— meridian, definition of, 127 

— moment, definition of, 112 

— moments compared by times of oscilla¬ 
tion, 132 

— potential, 115 

— storms, meaning of, 128 
Magnetization by magnetic field, 112 

— increase or decrease of, induces currents, 

7° ... 

— maximum intensity of, in iron, 123 

— of iron by currents, 66 > 

Magneto-electric arrangements, Siemens 

armature for, 285 

-Morse sender, 314 

-induction, 279 


NEG 

Magneto-electric, machine, Clarke’s and 
Pixii’s, 280 

-limit to e.m.f, in, 284 

— --by T. Holmes, 282 

-power required to drive, 284 

— -Wild’s, Siemens’, Ladd’s, Wheat¬ 

stone’s, 285 

-transmitting keys, 286 

Magneto sender for dial instruments, 319 
Magnets, action of currents on, 60 

— adjusting; for galvanometer, 193 

— how made, 119 

— how suspended in galvanometers, 193 

— if broken; pieces are magnets, 119 
Marie Davy’s galvanic cell, 225 
Marine galvanometer, Thomson’s, 199 
Matthiessen; experiments on resistance of 

metals and alloys, 249 
Matthiessen’s thermo-electric series, 176 
Mechanical equivalent of heat, 41 
Medical applications of electricity, 362 
Megavolt, megohm, megafarad, 161 
Melloni; used thermo-electric battery as 
thermometer, 184 
Menotti’s galvanic cell, 224 
Meridian, magnetic, definition of, 127 
Metallurgy, application of electricity to, 357 
Metals and alloys, specific resistance of, 249 
Microfarad ; unit of capacity, 159 
Microvolt, microhm, microfarad, 161 
Mines fired by electricity, 361 
Mirror galvanometer, signalling with, 333 

-formula for speed of signalling by, 338 

Moment, magnetic definition of, 112 

-of long thin bar, 122 

-of sphere, 123 

— of inertia. 129 

-of body, how to find, 131 

— of magnet, experimental determination 
of, 130 

Morse chemical telegraph, Bain’s, 304 

— circuit, 300 

— inkwriter, 301 

— key, 298 

— maximum speed of possible signals, 338 

— signals, 298 

-rate of hand sending, 316 

— sounder, signals received by ear, 305 
Motive power produced by electricity, cost 

of, 295 . 

Moulds for casts, made by deposited metals, 
358 

Multiple arc, cells joined in, 87 
-meaning of, 233 

-resistance between points joined by, 233 


VT EGATIVE and positive currents ; defi- 
^ nition, 298 

-electricity, 7 

-signals, 300 

— ions chemically electro-, 167 
—; list of insulators negative relatively to 
others, 9 






376 


Index. 


RAT 


NEG 

Negative; list of metals electro-negative to 
others, 43 

— metals; thermo-electrically, 175 

— pole of galvanic battery, 220 . 

— thermo-electric power, definition, 179 
Nickel is paramagnetic, 113 

Nitric acid, diluted, specific resistance of, 
260 


QHM name given to unit of resistance, 
Ohm’s law, 82 

-applied to potential at various parts 

of circuit, 241 

-not applicable to brushes or sparks. 


9 2 

Ores, reduction of, by electrolysis, 359 
Oxides when fused are electrolytes, 166 


■pAPER, punched, strips used in auto- 
-*• matic transmitter, 316 
Paraffin, specific inductive capacity of, 97 
Paramagnetism, meaning of; list of para¬ 
magnetic bodies, 113 
Peltier effect, in thermo-electric pair, 185 

— electroscope, 38 

Physiological effects of electricity, 362 
Pile, dry, used with electroscopes, 204 
Pith ball, experiments, with, 4 
Pixii’s magneto-electric machine, 280 
Platinum and platinized silver in galvanic 
cell, 211 

— used for contacts, 314 

Platymeter, used to compare condensers, 
264 

Plucker’s experiments on sparks with 
spectroscope, 290 

Plugs used to make connections, 229 
Points, action of, in electrical machines, 
270 

-in lightning conductors, 105 

— discharge highly charged conductors, 
272 

— discharge positive and negative electri¬ 
city unequally, 106 

Polarization due to electrolysis resembles 
increased resistance, 89 
»— in galvanic cells, 213 

— in insulators, connected with absorption, 
98 

-resembles increased resistance, 90 

— of faults, 354 
Polarized relay, 309 

Pole, strength of magnetic unit, 110 
Poles for land lines, 340 

— magnetic, description of, 109 

— of magnets, not at ends, 119 

— positive and negative of Daniell’s cell, 220 
Porcelain insulators for land lines, 341 
Porous cells, used in two fluid batteries, 219 
Portable electrometer, Thomson’s 207 
Positive and negative currents definition, 298 


Positive and negative electricity, 7 

-signals, 300 

-instruments for, 305 

— ions chemically electro-, 167 

—; list of insulators positive relatively to 
others, 9 

-of metals electropositive to others, 43 

— metals, thermo-electrically; definition, 175 

— pole of galvanic cell, 220 

— thermo-electric power; definition, 179 
Potential, contact series, 43 

— definition of, 26 

— difference of, measurement in units of 
work, 31 

— equality of, 29 

— fall of, used to calculate insulation resist¬ 
ance, 253 

— general conception of, 10 

— magnetic, 1x5 

— of a point, 29 

— of a point in the air, 40 

— of air, how to observe, 366 

— of statically charged conductor is uni¬ 
form, 31 

— on what it depends, 30 

— series ; of metals dipped in solutions, 216 

— unit of, electromagnetic, 134 

-electrostatic, 95 

-practical, 162 

— zero of, 10 

Potentials, practical modes of comparing, 
267 

Power required to drive magneto-electric 
machine, 284 

Pressure, effect of, on insulation resistance, 

253 . . , 

Primary coil in mductorium, 287 

— wire, definition, 155 

Printing, step by step telegraphic instru¬ 
ment, 321 

— telegraph instrument, Hughes’, 321 
Proof plane, 15 

Punched paper used to send signals, 316 


QUADRANT electrometer, Thomson’s, 

Quantity, electromagetic unit (absolute), 134 

— electrostatic unit (absolute), 20 

— force of attraction or repulsion due to, 95 

— galvanic cells joined for, 88 

— galvanometers, 190 

— in a charge depends on difference of 
potential, 96 

— in short current measured by throw of 
galvanometer, 267 

— of electricity measured by measuring 
force, 20 

— practical unit for, 162 


T 3 AREFIED gases, resistance of, 93 

Rate of sending by automatic and 
hand transmitters, 316 






Index. 


3 77 


REC 


SIN 


Recorder, Thomson’s siphon, 334 
Rectangle of wire used to illustrate force 
between currents, 57 

Return currents, in telegraphic circuits, 310 

Relay ; definition, 307 

Relays, diagram of circuit with, 308 

— length of circuit worked by, 309 

— polarized, 309 

— various constructions of, 308 
Replenisher, description of Thomson's in 

ductive, 275 

— used in electrometers, 207 
Repulsion between currents, 56 
-electric charges, 4 

Residual magnetism, effect of, in tele¬ 
graphic apparatus, 312 
-meaning of, 115 

Resistance and potential, relation between, 
in circuit conveying current, 241 

— apparent, various forms of, 89 

— between points joined by multiple arc, 233 

— calculated from loss of charge, 253 

— coils, arrangement of boxes of, 229 
-first description of, 86 

-practical instructions for making, 231 

— electric, definition of, 81 

— insulation, calculation of, 252 
-per knot in submarine cables, 253 

— measured by Wheatstone’s bridge, 244 

— measurement of, by comparison of deflec¬ 
tions, 234 

-by shunted differential galvanome¬ 
ter, 239 

— object of determining, 86 

— of cables, effect of electrification on, 255 

— of copper per knot in submarine cables, 


252 

— of insulators and conductors compared, 
86 

— — — apparently changed by flow of cur¬ 
rent, 90 

-measured as a test, 236 

-effect of age and pressure on, 253 


-temperature on, 254 

-G. P. india-rubber, 252 

— of galvanic battery, how to measure, 


-cell, limits currents, 86 

— of galvanometer, effect of, on current in 
given circuit, 89 

-coils, 202 

— of gases, infinite, 85 

— of graphite and gas coke, tellurium and 

phosphorus, 257 * 

— of large Daniell’s tray cells, 224 

— of liquid electrolytes, 258 

— of metals, effect of temperature on, 251 
-increased by impurities, 251 

— of rarefied gases, 93 

— of shunted galvanometer, 233 

— of vacuum, pj 

— per knot of insulated core, 346 

— precautions to be observed in measuring 
small, 245 


Resistance, relation to length and cross 
section of conductors, 83' 

-to weight, per unit of length, of con¬ 
ductor, 84 

— slide, used to compare condensers, 264 

— specific, definition, 248 
-of metals and alloys, 249 

— unit of, electromagnetic, 134 

-electrostatic, 95 

-practical, 162 

Reverse currents, useful in working land¬ 
lines, 309 

Reversing key for + and — signals, 305 

Rheomotor, definition, 297 

Rotation of one current by another, 291 

— of current by magnet and magnet by 
current, 293 

RuhmkofPs coil or inductorium, 287 i 

-used to send current through rarefied 

gas ; Geissler tubes, 93 


C ALTS, fused, form thermo-electric pairs, 
0 184 

— when fused, are electrolytes, 166 
Sand battery, 211 

Saturation, meaning of, as applied to mag¬ 
nets, 120 

Sawdust galvanic battery, 223 
Screen, metal, between electrified bodies, 
effect of, 24 

Secondary coil in inductorium, 287 

— wire ; definition, 155 
Self-induction in resistance coils, 232 

— of current on itself, 74 

Sensibility of galvanometer, adjusted by 


shunt, 201 

-how adjusted, 192 

Series, electric contact; metals, 42 

— electro-chemical, 168 
-frictional; insulators, 9 

— galvanic cells joined in, 87 

— Matthiessen’s thermo-electric, 176 


— ofinsulators, each positive to successor, 9 

— potential, metals dipped in solutions. 


216 

Shunt, definition of, 201 
— used to adjust sensibility of galvano¬ 


meter, 201 

Shunted galvanometer, resistance of, 233 

Siemens’ and Frischen’s duplex telegraphic 
systems, 326 

— armature for magneto-electric arrange¬ 
ments, 285 

— experiments on effect of temperature on 
resistance of metals, 251 

— polarized relay, 309 

Signalling, theory of, 329 

— with condenserr, 336 

Signals, telegraphic, elements of, 298 

— Morse, 298 

Sine galvanometer, 195 

Single fluid galvanic cells, polarization in, 


215 




373 


Index . 


THO 


SIN 


Single needle instrument, 305 

-key, 305 

-Morse code, 306 

Siphon recorder, Thomson’s, 334 
Smee’s battery, 212 
Soft iron, meaning of, 114 
Solenoid ; analogy with magnet, 60 

— definition of, 60 

— does not in all respects resemble hollow 
magnet, 145 

— effect of introduciiig soft iron into, 146 

— magnetic moment of, 144 

— suction of iron or magnet into, 144 
Sounder, Morse, signals received by ear, 


Source of power in galvanic cell, 54 
Sparks and brushes convey electricity in 
modes not subject to Ohm’s law, 92 

— diminution of air pressure required to 
produce, 104 

— pierce solid insulators, 106 

— weld contacts together, 314 

Specific inductive capacity of dielectrics, 97 

— resistance of a material, definition, 248 

-ot insulators used in cables, 252 

-changed by temperature and 

electrification, 255 

-of electrolytes, 258 

-of glass, 257 

-of graphite, gas coke, tellurium, 

phosphorus, 257 

— resistances of metals and alloys, 249 
Speed of working on land lines, 316 

— of signalling through submarine lines, 


-by min or or siphon, formula for, 

338 

-by Morse, 338 

Spiral coils, flat, attraction and repulsion 
between, 60 

Spirals, conveying currents force, between, 
flat, 141 

Statical induction, description of, ix 
Steam’s duplex telegraphic system, 324 
Steel, coercive force of, 120 
Step by step printing instruments, 321 

-telegraph instruments, 317 

Stoneware insulators for land lines, 341 
Stratified discharge through rarefied gas, 
290 

Street’s fusible alloy, 358 
Strength of a current, 56 

— of constant current equal in all parts of 
circuit, 77 

— of magnetic poles ; definition, no 
Submarine cables, design of, 348 

-practical formulae for speed through, 

338 

-theory of signalling through, 327 

— line, speed of signalling through, 333 
Sulphate of copper in solution, specific 

resistance of, 259 

— of zinc in solution, specific resistance of, 


259 


Sulphuric acid, diluted, specific resistance 
of, 259 

-used in electrometers, 206 

Surface conduction, or creeping on in¬ 
sulators, 260 

Synchronous motion in Hughes’ printing 
instruments, 321 


'"PAIT’S thermo-electric table, 182 

Tangent galvanometer, best construc¬ 
tion of, 194 

— galvanometer, theory of, 135 
Telegraphic apparatus ; classification, 290 
-general remarks on, 311 

— circuit, 297 

Temperature, effect of on resistance, 85 

-insulators, 254 

-metals, 251 

— measured by thermo-electric battery, 184 
Test of copper resistance by Wheatstone’s 

bridge, 246 

— of insulation by measuring resistance ; 
simple galvanometric method, 236 

-by Wheatstone’s bridge, 246 

Tests of iron wire, mechanical, 340 

— for positions of faults, 350 
Thermal equivalent of work, 165 
Thermo-electric bismuth-antimony pair, 

e. m. F. of, 183 

— circuit, absorption and evolution of heat 
in unequally heated portions of, 186 

— current, first notion of, 79 

— currents due to liquids and to fused salts, 
184 

— diagram, 178 

— e. m. f., calculation of from diagram, 180 
-Tait’s table, 181 

— inversions, 177 

— neutral points, 181 

— pair, absorption and evolution of heat at 
junctions of, 185 

-Peltier effect in, 185 

-theory of, in complex circuit, 176 

— pairs in series, 183 

— power, connection between E. M. F. of 
pair and, 179 

-of a pair of metals ; definition, 175 

— powers, influence of mean temperature 
on, 177 

— series, Matthiessen’s, 176 

Thomson s absolute electrometer, principle 
of, 100 

— dead-beat galvanometer, 198 

— graded galvanometer, 197 

— marine galvanometer, 199 

— method of determining resistance in 
electromagnetic measure, 154 

— mirror galvanometer, 62 

— replenisher, and mouse-mill inductive 
machines, 275 

— siphon recorder, 334 

— theory of convection of heat by electri¬ 
city, 186 




Index. 


379 


THO 


ZIN 


Thomson’s theory of signalling, 331 
Throw of galvanometer compares poten¬ 
tials, 267 

— — — gives absolute electro-magnetic 
capacity, 266 

-used to compare capacities, 261 

-measures quantity in transient cur¬ 
rent, 267 
Time-guns, 364 

Time required for any electrical opei'ation 
in signalling, 337 
Torpedos fired by electricity, 362 
Tourmaline, effect of temperature on, 49 
Transmission of signals in two directions on 
one line, 323 

Trembler; one kind of electrtc bell, 327 


TTNIFORM potential throughout con- 
ductors, 31 

Uninsulated bodies, definition of, 10 
Unit electromotive force, how produced by 
motion in magnetic field, 149 

— intensity of magnetic field, in 
•—magnetic pole, no 

— of capacity called microfarad, 159 

— of current electro-magnetic, 117 

— of electromotive force force called a 
volt, 159 

-in terms of Clark’s cell, 159 

-of Daniell’s cell, 159 

— of force and work (absolute), 94 
-of quantity, 20 

-is farad charged to potential of 

one volt, 160 

— of resistance called an ohm, 158 

— of work used to measure potential, 26 

— quantity, resistance andE. M. f., or diff. 
of potential, definition of, electrostatic, 94 

— table of absolute and practical, 162 
Units, British Association, 158 

— dimensions of, 163 

— electro-magnetic, definition of, 133 
-ratio to electrostatic units, 134 

— electrostatic, actual magnitude of, 107 
-equations connecting, 108 


VARIATIONS of magnetic declination 
* and inclination, 127 
Varley’s electrostatic inductive machine, 


— insulators for land lines, 342 

— rule for insulation of land lines, 345 

— system of sending Morse signals with 
reverse currents, 309 

-of signalling with condenser, 336 

Velocity of electricity, 328 


Volt, name given to unit of e. m. f., 159 
Voltaic, arc, meaning of, 360 

— or contact theory of galvanic cell, 4 4 
Voltameter, 166 

Vulcanite insulators for land lines, 343 

— or ebonite used for electrophorus, 268 

— stems, used to insulate, 260 

— used for frictional electrical machines, 
270 

-for mountings of resistance boxes, 229 


VALKER’S graphite battery, 212 
v v Waring’s electric light, 361 
Water and electricity, analogy between, 
used to explain potential, 39 

— electro-chemical equivalent of, 165 

— decomposition of, 67 

Weber, name given by Latimer Clark to 
unit quantity, 160 

Weber’s electro-dynamometer, theory of, 

i ? 8 

Weight of materials required for given 
speed of signalling (submarine lines), 338 
Wheatstone’s automatic transmitter, 316 

— bridge, used to measure resistance, 244 
-theory of, proved by Kirchhoff’s 

laws, 248 

— letter-showing dial telegraphic iAtru- 
ments 320 

Wild’s magneto-electric machine, 285 
Willoughby Smith’s G. P. effect of tem¬ 
perature on resistance of, 256 
-gutta-percha, specific inductive ca¬ 
pacity of, 97 

Wire, sizes used in galvanometers, 63 

-of, used in galvanometer coils, 202 

-of, for telegraphic apparatus, 314 

— iron, employed on land lines, 339 
-weight and mechanical qualities of, 


34 ° 

Wires, spacing of on land lines, 340 
Words per minute through submarine lines, 

33 8 

Work, and force, units of, 94 

-absolute and other units compared; 

British and metrical, 165 

— mechanical, relation to electric poten¬ 
tial, 27 

— positive and negative, 27 

— used to measure difference of potential. 


3 1 


7 INC plates, amalgamation of, 218 
^ -; wire in connection with is 


negative pole of battery 2 


Spottiswoode & Co., Printers, New-street Square, London. 









In 8 vo. Cloth, Plates, 9s. 


IR-IE :p O IR, T S 


OF THE 

COMMITTEE ON ELECTRICAL 
STANDARDS, 

APPOINTED BY THE BRITISH ASSOCIATION FOR 
THE ADVANCEMENT OF SCIENCE, 

REPRINTED BY PERMISSION OF THE COUNCIL. 

REVISED BY 

Sir W. THOMSON, LL.D. F.R.S.; Dr. J. P. JOULE, LL.D. F.R.S.; 
Profs. J. Clerk Maxwell, M.A. F.R.S.; and 
F. JENKIN, F.R.S. 


WITH A REPORT TO THE ROYAL SOCIETY 

ON UNITS OF ELECTRICAL RESISTANCE, 

By Pkof. F. JENKIN, F.R.S. 

AND 

THE CANTOR LECTURES, 

DELIVERED BY PROF. JENKIN BEFORE THE ROYAL 
SOCIETY OF ARTS. 



Prof. FLEEMING JENKIN, F.R.S. 


-- 

London : E. & F. N. SPON, 48 Charing Cross. 




















































































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