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TELEGRAPHY
A DETAILED EXPOSITION OF THE TELEGRAPH SYSTEM OF THE BRITISH POST OFFICE
BY
T. E. HERBERT, A.M.Inst.E.E.
ASSISTANT SUPERINTENDING ENGINEER, POST OFFICE ENGINEERING DEPARTMENT
FOURTH EDITION
(WITH ADDENDUM)
WITH 640 ILLUSTRATIONS
LONDON
SIR ISAAC PITMAN & SONS, LTD. PARKER STREET, KINGSWAY, W.C.2
BATH, MELBOURNE, TORONTO, NEW YORK 1020
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bibliographical note
First edition 1906
Second edition 1907
Reprinted 1008, 1909, 1910 1911
Third edition 1916
Fourth edition 1920
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289058
m 16 19Z5
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■vni * •
^ PREFACE
TO FOURTH EDITION
The rapid exhaustion of the third edition has rendered it necessary to reprint the work, and this opportunity has therefore been taken to make a few additions to the text.
The chapter on Secondary Cells has been reviewed and some additional matter, suggested by Mr. R. G. de Wardt, has been incorporated. A description of the Kleinschmidt Perforator now forms part of Chapter X.
Appendix C on the Gulstad Relay has been re-written in view of the adoption of the G relay on so many long and difficult circuits. I am indebted to Mr. A. H. Roberts, for most of the information now given.
In the Addendum following the Appendix an elementary account of the amplifying valve has been provided, and my thanks are due to Messrs. C. Robinson and R. M. Chamney for checking this section. Whilst it is true that the device is not at present in use on telegraph circuits within t he British Isles, there can be little doubt that its possibilities will not long remain unexploited.
The use of small currents to enable telegraph and telephone circuits to be worked in the same cable has far- reaching consequences. In this connection recent researches show’ that the old empirical rules for finding the working speed of circuits are fallacious. For aerial lines the deter- mining factor is the value of the received current, and I am indebted to Mr. J. L. Taylor for an admirably concise account of his researches.
The vibroplex is described in the final section. Experi- ments are being made to ascertain whether its adoption lessens the strain on the telegraphist, reduces the liability to “ cramp/’ and increases the output of work.
I wish to express my thanks to Major T. F. Purves, O.B.E., Lt.-Col. A. C. Booth, and Mr. Andrew Fraser for the assistance which they have so kindly afforded me.
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PREFACE
During the preparation of the various editions of this work, I have received so much assistance from Mr. 0. P. Moller that I desire to take this opportunity to place on record my appreciation of the help which he has so freely and so willingly rendered me.
T. E. H.
London,
September , 1920.
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EXTRACT FROM PREFACE TO FIRST EDITION
The interdependence of theory and practice cannot be ignored without inflicting injury on both ; and he is but a poor friend to either who undervalues their mutual co-operation.
lit. Hon. A. J. Balfour at the British Association.
The objects of the present volume are to supply the admitted need for an up-to-date and detailed exposition of the telegraph practice of the British Post Office and also to provide for the requirements of the Departmental and City and Guilds* examinations in the subject. With the latter object in view I have furnished a plenitude of fully worked numerical examples and have included elemen- tary accounts of galvanometers, battery testing, and the Wheatstone bridge. After anxious and careful consider- ation in theJight of an extensive teaching experience I have deemed it best to avoid the use of mathematics, and I am satisfied that the more elementary method adopted will make the work accessible to the far larger and wider circle of readers who most need the information I have sought to convey.
The Journal of the Proceedings of the Institution of Electrical Engineers, the Electrical Review and the Elec - trician have naturally been freely consulted during the preparation of the work.
1 beg to acknowledge my indebtedness to : — Sir Samuel Boulton, Messrs. J. E. Kingsbury, E. J. Chambers, A. H. Atkins, D. Murray, W. S. Steljes, and F. Crawter ; also to the following gentlemen of the Post Office Department : — Messrs. M. F. Roberts, J. W. W.illmot, H. R. Kempe, H. Hartnell, T. F. Purves, J. R. M. Elliott, C. C. Vyle, G. F. Mansbridge, W. Moon, H. Wilson, H. A. Miles, W. J. Stubbs, W. E. Twells, R. Ianson, E. I. T. Newton, and A. Q. Ellery.
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VI
PREFACE
The list which follows comprises those firms to whom I desire to acknowledge my obligations either for illustrations taken from their catalogues or for special information relating to the materials which they manufacture or supply:—
Messrs. The British Insulated Wire Co. ; British L. M. Ericsson Manufacturing Co. ; Buck and Hickman ; Bullers ; Burt, Boulton, and Haywood ; Chloride Electrical Storage Co. ; W. F. Dennis ; Electrical Power Storage Co. ; Elliott Bros. ; General Electric Co. ; Hart Accumulator Co. ; India- rubber, Gutta-percha, and Telegraph Works Co. ; London Electric Wire Co. ; Muirheaa and Co. ; Nalder Bros, and Co. ; Siemens Bros, and Co. ; Sterling Telephone and Electric Co.; Typewriting Telegraph Corporation; Western Electric Co.
The material assistance which I have received has been so freely and so willingly given that it seems almost invidious to make distinctions, but owing to the larger demands I have made upon Mr. Hartnell, I feel that it is impossible to allow this opportunity to pass without a definite expression of my warm appreciation of the numerous and valuable suggestions which he has made whilst reading the proof sheets. To Mr. Ianson, also, I desire to express my cordial thanks for the services which he has rendered to me in reading and criticizing both the original manuscript and the proof sheets.
With the exception of the manufacturers* blocks, the drawings for the illustration of the text have been pre- pared by Mr. 0. P. Moller, to whom my thanks are conveyed for the care and thought which he has bestowed upon the work.
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Changes and improvements in detail have likewise been prolific, with the result that a large proportion o^ this work has necessarily been rewritten or rearranged. This task has been vastly facilitated by the advent of the Institution of Post Office Electrical Engineers and the Post Office Electrical Engineers* Journal. The Proceed- ings of this Institution and its Journal have been very freely used, and I am much indebted to the Council Of the Institution and to the Board of Editors for the readily accorded permission to utilize these records. To the Proceedings of the Institution of Electrical Engineers I am likewise under obligation, which I desire here to place on record.
To the Electrical Press I am also under obligation, and my thanks are expressed to Electrical Engineering , the Electrical Review , the Electrician , and to Electricity .
I beg to acknowledge my indebtedness to : Messrs. Martin F. Roberts, H. Hartnell, Donald Murray, H. H. Harrison, F. Crawter, F. G. Creed, J. Gell ; also to the following gentlemen of the Post Office Engineering Depart- ment : Messrs. T. F. Purves, D. H. Kennedy, E. Lack, T. Lakey, S. C. Bartholomew, W. C. Cruickshank, W. A. Hatfield, E. A. Lakey, J. G. Lucas, O. P. Moller, E. I. T. Newton, E. V. Smart, A. E. White, T. Smerdon, and P. D. Moller.
The list which follows comprises those firms to whom I am indebted for illustrations taken from their catalogues or for special information relating to materials which they manufacture or supply —
Messrs. The Automatic Telephone Co.; British Insulated and Helsby Cables ; Elliott Bros.; Evershed and Vignoles ; Nalder Bros. ; New Phonopore Telephone Co. ; R. W. Paul * Peel Connor Telephone Co. ; Siemens Bros* ; and The Western Electric Co.
T. E. H.
London, August , 1916.
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CONTENTS
INTRODUCTION
THE FUNDAMENTAL PRINCIPLES OP MAGNETISM AND ELECTRICITY, AND UNITS
Pa ue
Static electricity — Potential — Calculations in electro-statics — Magnetism — Lines of force — Magnetic induction — Quanti- tive values of magnetic effects — Voltaic electricity — Con- ductors and insulators — Units — Ohm’s law — Other electrical units . - 1 —17
CHAPTER I
PRIMARY CELLS
Simple cell — Internal and external circuit — Local action — Polarization — Elements atad poles of cell — Leclanch^ cells — Lucas’s researches — Chemical action — Dry cells — Clark cell —
Dan kill standard cell — Characteristics of cells used by the Post Office — Tabulated comparison of cells — Ideal cell . 1&-33
CHAPTER II
CALCULATIONS IN CONNECTION WITH CIRCUITS AND CONDUCTORS
Part I. — Arrangement of Cells : —
Size of cells — Ampere-hour capacity — Cells in series — Cells in parallel — Cells in multiple arc — Method in which to join up cells in different circumstances — Cells wrongly joined up and special arrangements — Number of cells required to furnish a given current — Special cases . • . . . 34-47
Part II. — Joint Resistance and Division op Current : — Resistances in series — Conductance — Mho — Several paths in parallel — Two paths in parallel — Several paths of equal resistance in parallel — Complicated circuits — Division of cur- rent between several paths in parallel — Division of current between two paths in parallel — Batteries in multiple are joined to paths in parallel — P.D. and E M. F. A 47-56
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CONTENTS
Part III. — The Resistance of Wires of Varying Dimensions : —
Factors determining the resistance of a conductor — Prob- lems on the resistance of wires of varying length, areas, and diameters — Resistivity — Wires of varying length and weight — Ohm-mile constant — Percentage conductivity — Resistance of one foot grain of wire — Wires of varying weight and diameter — Application of laws to cells — Effect of temperature upon resistance and capacity — Effect of pressure upon resistance 66-68
Part IV. — Electromagnets : —
Law of magnetic circuit — Magneto-motive force, reluctance, and flux — Permeability — Magnetizing force of solenoid — Re- sistance and figure of merit — Problems on the winding of electromagnets 68-73
CHAPTER III the measurement of current
Part I. — Resistance Coius : —
Resistance boxes of various types — Types of wire to be used — Temperature variation of resistance — Gauge of wire — Rheostats — Double winding 74-82
Part II. — Galvanometers : —
Introductory — Tangent galvanometer — Helmholtz galvano- meter— Tangent of an angle — Tangent scale — Theory of tangent galvanometer — Absolute measurement of current —
P.O. tangent galvanometer — Differential winding — Control- ling magnet — Galvanometer constant — Taking constant — Paul’s unipivot instruments — Horizontal galvanometer — Q and I detector — No. 2 detector — Ammeters — Moving iron and hot wire ammeters — Reflecting galvanometers — Lamp And scale — Damping — Kelvin (or moving magnet) reflecting galvanometers — Astatic needles and systems — D’Arsonval (or moving coil) reflecting galvanometers — Ballistic galvano- meter— Figures of merit — Number of convolutions — Sensi tiveness and sensitivity — Galvanometer Shunts : — Principle — Laws — Compensating resistance — Problems — Universal shunt — Constant of reflecting galvanometer . . . 82-126
CHAPTER IV
THE MEASUREMENT OF E.M.F. ANT) BATTERY TESTING
Part I. — Voltmeters: —
Principle — Multipliers — Weston voltmeter — No. 2 de- tector and multiplier — Various types of voltmeter . 126-128
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Part IL — Potentiometer Measurements : —
Principles — Example of test — Rayleigh compensation method-— Crompton potentiometer— balder Bros, potentio- meter 12S-135
Part III. — Battery Testing : —
Measurement of E.M.F. : — Voltmeter test — Post Office standard test — Lucas’s researches — Direct deflection method —Equal current method— Measurement of Internal Re- sistance : — Voltmeter shunt method — Half -deflection method — Diminished deflection direct method — Thomson method — Wheatstone bridge method — M airhead’s method — Resistance secondary cells — Battery testing with detector No. 2 — Rough tests with Q and I detector — Eden battery testing instruments 135-150
CHAPTER V
THE MEASUREMENT OF RESISTANCE
Part I. — The Wheatstone Bridge: —
Theory of Wheatstone bridge — P.O. form — Reversing switch — Practical use of bridge — Measurement of resistances having capacity, inductance, or an E.M.F. — Other patterns of bridge • ......... 151-159
Part II. — The Megger and Bridge Megger : —
Evershed ohm meter — Principle — Description — Range —
Price guard- wire — The bridge megger — Principle — Details 159-166
Part HI. — Various Methods : —
Very low resistances — Rough methods — Voltmeter method — Direct deflection method — Insulation testing set . . 166-171
CHAPTER VI
SINGLE CURRENT SYSTEMS AND RELAY'S
Earth return — Earth connection — Electromagnet — North pole of solenoid — Residual magnetism and retentivity — Sounder — Polarized sounder (original pattern) — Vyle polarized sounder — Theory of polarized sounder — Single current key— Single current galvanometer — Up and down stations — Direct sounder connections — Intermediate stations —Path of current — The direct writer — Polarized direct writer — Open and closed circuit working — Helsby method —
The Single Needle System : — Valley’s coils — Spagnoletti’s coils — Figure of merit — Neale’s coils — Commutator— Skeleton connections of commutator — Connections of single needle circuity — Resistance and battery power — Advantages of
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system— Relays : — Principle — Relaying sounder — P.0, non- polarized relay — Relays used in telephony — D relay — Trans- lating relays — Polarized relay — P.O. standard relay — P.O. standard neutral relay — Resistance and figure of merit — Baudot relay — Test for differentiality — Design of relay — The Double-Plate Sounder : — Plate sounders — Com- mutator— Connections — Up and down offices — Prevention of sparking at relay contacts — Arrangement of apparatus —
Ad j ustinent — Current required — Polarized double-plate sounder — The Single Current Sounder : — Connections — Adjustment — Coils in parallel or series — Direct v. single current sounder— Local inker — Use of D relays — Use of polarized sounder 172-227
CHAPTER VII
CAPACITY, CONDENSERS, AND THE DOUBLE CURRENT SOUNDER
Condensers : — Capacity — Electro-static lines of forco — Electro-static explanation of capacity — Dimensions of con- densers— Specific inductive capacity — Condensers in parallel and series — Dielectric for condensers — Condensers used in telegraphy — Insulation of condensers— Specification of insula- tion and capacity — Condenser discharge — The Double Cur- rent System : — Advantages of double current system — Re- verse current and charge upon the line — Detailed explanation — Other advantages of double current system — Double current key — Connections of double current sounder — Path of current — Use of double current set for single current working — Direct working with polarized sounders — Battery power and current required 228-248
CHAPTER VIII
THE DIFFERENTIAL DJ7PLEX
The Single Current Duplex: — Systems of duplex work- ing— Opposition method — Path of current — Intermediate position of keys — Use of non-polarized relays and direct working- — Differential galvanometer — P.O. or combination method of duplex working — Path of current — Numerical values of current in each part of the circuit — Intermediate position of keys — Skeleton connections required for single current duplex — Duplex switch — Connections of duplex switch — Balancing — Useful facts — Direct working with polar- ized sounders — Difficulty in working very short circuits — Battery power and current required — The Double Current
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PAGE
SomsBML Du plei : — Conditions for duplex working — Skeleton connections — Effect of line capacity— Graphic representation of charge upon a line — Paths of line and compensation circuit charges and discharges — Arrangement of compensation circuit Cor balancing long lines — Effects of defective capacity balance — 'Retardation and condenser coils — Capacity balance may differ at the two stations— Connections of duplex set — Double current duplex with polarized sounders — Resistance balance — Battery power and current required .... 249-284
CHAPTER IX
THE QUADRUPLEX
Principle — Skeleton connections — Value of current under various conditions — Summary of quadruplex conditions — The ** B” kick — The condenser B side arrangement — The A key — The B key — 6-terminal reversing key— Sparking, battery, and earthing resistance coils — Effects of short-circuit in the intermediate position of the keys — Connections — 9- terminal,
2- position switch — Balancing — Adjustment — Decrement working — Use of quadruplex on short circuits — Other quad- ruplex systems — Current required and type of battery used —
The diplex — Wheatstone on the A Bide .... 286-308
CHAPTER X
THE WHEAT8TONE AUTOMATIC SYSTEM
General — Wheatstone Perforator : — Operation of the pouches — Paper-feeding device — Punches — Auxiliary appli- ances— Perforator adjustment— rPneumatie perforators — -The Cell Keyboard Perforator: — Perforator die plate — Punches — Parallel bar and letter combs — Rleinschmidt Keyboard Perforator : — Principle — Guide plate and matrix frame — Spacing and tape feeding device — Connections — Transmitter :
— The divided lever — Motive power — Arrangement of re- ciprocating rods and divided lever — Action of transmitter in signalling a word — Summary of action of transmitter — Magnetic bias transmitter — Transmitter bias — Arrangement for regulating the Bpeed of the transmitter — Action of fan in maintaining uniformity of speed — Stopping and starting lever — “ Bolting ” of transmitter — Speed of slip — Vyle and Smart motor-driven transmitter— The Receiver :— Principled-Ink- ing arrangements — Motive power — Double slip drawer and bell —Motor and train — Winding of coils — Adjustment — Spring receivers, speed of slip, and figures of merit— The Mulligan motor-driven receiver— The Shunted Condenser Self-
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CONTENTS
PAG*
Induction and Time Constant — Use of shunted condenser to balance self-induction — Action of shunted condenser in Wheatstone working — Adjustment of shunted condenser — Action of shunted condenser upon a very short circuit — Resistance of sending circuit — Transmitter switch — Connec- tions of a full Wheatstone set — Adding a transmitter to a key- worked circuit — Substitution of a receiver for a relay — The Wheatstone Duplex : — Principle— Differential duplex with signalling condensers — News circuits and battery power required — The Creed Receiving Perforator : — Principle — Action — The Bille Receiving Perforator: — Principle — Action — The Creed telegraph printer — The Creed translator The Siemens electromagnetic receiving perforator — Siemens automatic Wheatstone transmitter — Siemens automatic Morse transmitter 309-381
CHAPTER XI THE bridge duplex
Use — Advantages of the system — General principle — Inter- mediate position of the key — Resistance of the arms or duplex coils — Double current working — Both keys at rest — One key depressed — Both keys depressed — Intermediate position of keys — Compensation circuit and balancing — General Arrange- ments— The signalling condensers — Summary of the action of the signalling condensers — Reading oondenser — Connections — Calculation of the current in each part of the circuit — Calcu- lation of battery power — Power employed . . . 382-397
CHAPTER XII
THE WHEATSTONE A.B.C., STELJES RECORDER, AND REBESI TYPEWRITING TELEGRAPH
Wheatstone A.B.C. : — Introductory — General principle —
The combined indicator and bell —The generator — The com- municator— Arrangement of the keys and endless chain — Operation of contact maker and pawl arm— Connections for series working — Leak working — Steljes Recorder: — General principle — Type wheel escapement - Printing arrangements — Figure changing cam — General arrangement and slip feeding device — Unison lever — Connections — Rebesi Typewriting Telegraph : — Keyboard transmitter — Steljes relay — Escape- ment— Column printer — Type wheel operating shaft — Type wheel — Printing frame— Paper feed— Battery power . 398-426
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CHAPTER XIII
THE HUGHES
Introductory — Speed of working — General principle — The Hughes electromagnet — Motor and governor — Electrical de- tails— The chariot — The rejector — -Number of characters printed per revolution— The type wheel axle — Change-over from letters to figures — Printing axle entrained — Paper move- ment— Zero-adjusting lever — Connections — Hughes switch — Practical operation — Effects of retardation— -Hughes du- plex — Duplex resistance coils — electromagnetic leak — Connections 427-464
CHAPTER XIV
THE BAUDOT
Multiplex telegraphy — Principle of Baudot — Keyboard — Cadence — Receiver— Selector and combiner wheel — Combiner and type wheel — Retention wheel and figure change mechanism — Type wheel and paper movement mechanism — The distribu- tor— Correction— Baudot quadruple — General arrangement and connections — Baudot duplex — Baudot automatic . 455-479
CHAPTER XV
THE MURRAY AUTOMATIC AND MURRAY MULTIPLEX SYSTEMS
Part I. — The Murray Automatic System : —
Introductory — Alphabet — Murray tape and correction of errors — The perforator — Transmission — Distributing mechan- ism— Method of securing isochronism — The second transla- tion apd printing 480-491
Part TL — The Murray Multiplex : —
✓ Introductory — Principle*— Alphabet — Distributor — Shift- the-hands correction— Phonic wheel motor and vibrator — Electrical details of transmission — Cross-tape keyboard per- forator— Tape transmitter — Method of securing synchronism — Printer — Description and details of action — Cut page feed for the printer — Receiving perforator .... 491-514
Part III. — Murray Modifications : —
General description — Western Electric printer — Western Union multiplex — Western Electric multiplex . . 514-517
Part IV. — The Harrison Printing Telegraph . 618-519
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CONTENTS
CHAPTER XVI
CENTRAL BATTERY TELEGRAPHS AND TELEGRAPH SWITCHING 8Y8TEMS
Central Battery Telegraphs : — Introductory — C.B. om- nibus circuit — Value of feed resistance — Head office special set — Central Battery Duplex : — Purves duplex — Hay duplex — Vyle and Smart duplex — Vyle and Smart duplex for short lines — Wheatstone working on C.B. circuit — Wheatstone ex- tended circuits — Special C.B. circuit giving duplex with Wheatstone working outwards — The Concentrator : — Intro- ductory— 6-point jacks, plugs and cords — Non -polarized indi- cator relay— -Jack, lamp and relay (type 110 AN)— General arrangement of concentrator^— Pilot relay — Electrical details — Electromagnetic indicator key — Time signal — Speaker set testing apparatus — Partial concentration — Working sets — Universal double current circuits — Set for working up, down, or universal D.C. — London Metropolitan Switching System : — Introductory — Number of circuits required — Multiple switch — Need for engaged test — Method of oper- ating— Electrical details — Two circuits connected together — Clearing signal — Speaking apparatus — Collecting offices — Engaged test — Intermediate offices — Other details — Special set for working through the switch 520-566
CHAPTER XVII
SECONDARY CELLS
Introductory — Plants and Faure cells — Chemistry of secondary cells — Double sulphation theory — Hydrometer — Lucsmart hydrometer — Expansion of active material on the positives — Chloride cells — E.P.S. cells — Hart cells — Other types — E.M.F. on charge and discharge — Internal resistance and temperature — Insulators — Electrolyte — First charge — Range of specific gravity and efficiency — Treatment of cells 55^-580
CHAPTER XVIII
SECONDARY CELL WORKING
Introductory — Necessity for separate positive and nega- tive current batteries — Principle of system — Theory of system — Universal working with primary batteries . . . 581-585
Part I. — Power Arrangements : —
Voltages required — 24v sets — Main sets — General scheme of fuses — Battery room — Main fuses at the cells — Switch
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cabinet — Details of positive and negative switches — Main charging switches — Main distributing cabinet — Distribution and fuse case — Original secondary cell installation — Second- ary cell working for small offices— -Charging arrangements — Provision of charging current — Electromagnetic cut-outs —
Size of cells . 586-606
Part II. — Alterations in the Circuit Connections for Universal Battery Working : —
General principle of changes — Protective resistances — Use of resistances between fuses and instruments — Single Cur- rent Working : — Single current sounder — Single current duplex — Double Current Sounder : — Single current key with switch — Double current sounder up and down stations — Intermediate stations — Double current duplex — Wheatstone :
— Wheatstone simplex — Special circuit set — Special circuit set duplex — Wheatstone differential duplex — Wheatstone bridge duplex — Quadruplex : — Principle— -6-terminal revers- ing key — Connections of quadruplex with Wheatstone on A side — Test Box Speaking Set 607-627
CHAPTER XIX
REPEATERS
Working Speed of a Circuit — Skin effect — Battery re- sistance— Kelvin’s law and arrival curve — Silent interval — Insulation resistance — Inductive leaks — Capacity and resist- ance of various types of line — Calculation of speed of working —Theory of Repeater — Principle of simplex repeater — Automatic switch — Simplex repeater — Path of current — Dcplrx Repeater : — Leak circuit — Duplex repeater for cable circuits — Forked Repeaters : — Path of current — External connections of a repeater board — Adjustments — Faults — Loss of speed in repeating — Quadruplex : — Split quadruplex re- peater— Quadruplex A side relayed duplex — Quadruplex A «de relayed C.B. — Forked quadruplex — -Quadruplex repeater — A.T.M. polarized pole-changer — Central battery repeater — Hughes repeater — Inductive leak — Booth’s device for neutralizing inductive interference — Baudot repeater — Silencers: — Sounder silencer — Circuit silencer-— Silencer with condenser and megohm resistance — Hughes silencer 628-676
CHAPTER XX
the test box and protective devices
Part I. — The Test Box : —
Principle and general arrangement — Small office test box —Test box changes — Battery test box — U-link test boards —
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Switch spring test board — Arrangement — Cabling — Cross- connection — Principle — Cross - connection facilities — Test board changes and transfer circuits — Special intermediate set4 — Looping strip ....... 677-688
Part II. — Lightning Protectors : —
Theory — C protector — D protector — G and H protectors — Tablet protector — F protector — Protectors of Saunders and Lodge — Position of protector and inductance spiral . 688-696
Part III. — Protection from Power Circuits : —
Introductory — Guard wires for tramways — Use of covered wire — Guarding electric light and power circuits — Joint pole — Use of india-rubber gloves — Protection applied to circuits — Glass-tube fuse — Heat coils — Protector, heat coil, and fuse fitting — Principles governing the fitting of heat coils and fuses — Fuse insulator — Heat coils, protector, and fuse fittings — Main Distribution Frame : — Use of —Fittings— Cross connecting 695-712
Part IY. — Power Circuit Interference with Tele- graphs : —
Single phase power circuits — Resonant shunts — Application to duplex circuit — Elimination of interference with a trans- former 712-716
Part V.— Precautions against Fire : —
Building— Use of lead-covered cables — Flame-proof wire — Numbered joints — Temporary telegraph office — Open wires — Office Wiring : — Wiring of a large office . . . 716-717
CHAPTER XXI
TELEGRAPH TE8TING AND THE FORMATION OF SPECIAL CIRCUITS
Introductory — Testing points — Organization— Effects of loss of insulation — Apparent and true insulation and con- ductor resistance — Insulation resistance per mile — Extended circuits 718-726
Part I. — The Morning Test: —
Details of test — Working and maintenance standards . 726-727
Part II. — Fault Localization
General — Various types of fault — Earths — Disconnections — Contacts — Intermittent faults — Covered wire faults — Test box detectors — Causes which produce faults — Weather con- tacts 727-740
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Part HI. — Conductor Resistance Tests : —
Effect of earth current — False zero — Balancing out deflec- tion by magnet — Hay method — Individual resistance of a number of circuits between the same two points' — Periodical conductor resistance tests 740-743
Part IV. — Underground Cable Tests : —
Electrification — Grouping wires in an air-space cable for insulation tests — Screened cable 743-746
Part V. — Tests for the Position of a Fault and Resistance of Earth Connection: —
Varley loop test — Murray loop test — Test for position of a contact — Pomeroy's method of testing earths . . . 746-751
Part VI. — Tracing Instrument Faults : —
Introductory — Effect of earth fault — Division of circuits into line, sending, receiving and local — Example of diagnosis — Regulation — Duplex sets — Lack of differentiality — Quad- ruple! circuits — Contacts in coils of apparatus . 751-757
Part VII. — The Making Good of Faulty Circuits, Special Arrangements and Earth Currents : —
Symbols used for lines and apparatus upon plans— Upon maps — The making good of faulty circuits — The formation of special circuits — Resistance and battery power required —
Earth currents — Remedies against — Magnetic storms — Metal- lic circuit working — Interpolation of condenser . . 757-766
CHAPTER XXII
the construction of aerial lines
Introductory— Timber — Preservative processes — Arms — Insulators — Pothead insulators — Bronze wire — Choice of material for line wire — Iron wire — Copper wire — Binding-in — Buller’s clip — Joints — Sleeve joints — Earth wiring— Dimen- sions of poles — Depth to which poles are buried — Stays — Buller’s stay bow — Stay crutch — Pole spur — Struts — A-poles —H -poles— Saddle wire — Pole steps — Buller’s removable pole steps — Iron poles — Erection of a pole — Use of derrick — Wiring — Sags and stresses — Derivation of formulae — Problems —Elasticity — Factors of safety — Elasticity, temperature, sag, and stress — Stresses on stays — Problems — Factor of safety on an open line — Wind pressure — Problems — Renewals and alterations — Wiring arms — Surveying — Longitudinal stays — Terminating brackets — Game guards — Aerial cables — Over- house Construction -Humming of wires — Silencing devices — Brackets — Standards ....... 767-864
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CHAPTER XXIII
THE CONSTRUCTION OP UNDERGROUND LINES
General — Conduits — Iron pipes — Steel pipes — Duct routes — Octagonal earthenware ducts— Single and multiple way earthenware ducts — U-troughing — Cast-iron slide and split pipes — Couplings — Markers and marking posts — Pillar test boxes — Flush boxes and pit channels — Manholes — Cable brackets and bearers — Reinforced concrete — G.P. wires —
Air Space and Paper Core Cables: — Electrolytic damage to sheathing — Bonding— Inductive disturbances — Static and dynamic induction — Variable lay — Screened conductor cable — Air space cable — Twin type — Quadruple pair type — Com- posite cable — Multiple twin cable— Construction : — Cable lengths — Pulling in lead-covered cables — Motor winch — Jointing lead-covered cables — Joint testing and dry -air plant —Electrical tests during construction — Termination of cables — Cable connection boxes — Cable distribution heads — Cable distribution plugs — Parallel joints — Renewal of cables — Surveying — Faults — Pole Test Box (G type): — Fuse U-links — Junction between open and underground route . . 855-913
APPENDICES.
A The Molecular Theory of Magnetism
B Notes on Chemistry
C The Gulstad Belay
D Superposing
E Connections for Creed Working ....
F The Siemens High-Speed Automatic Printing Telegraph G Syllabuses of Examinations .....
H Examples on the Calculation of the Capacity of Circuits
I Useful Numbers
J Standard Wire Gauge
914-018
919-925
926-935
936-947
QU
949-958 959-963 964-967 96* —969 970
ADDENDUMS.
The Thermionic Relay . . .
Week-current Telegraphy .
Working Speed of Cable Circuits
Overhead Telegraphs — Circuit Efficiency and Factors of Safety The Vibroplex .
978
981
983
983
995
INDEX
999-1019
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TELEGRAPHY
INTRODUCTION
THE FUNDAMENTAL PRINCIPLES OF MAGNETISM AND ELECTRICITY, AND UNITS.
STATIC ELECTRICITY.
ELECTRICITY pervades all matter, but it is only when its distribution is altered that its presence is observed by the effects which result. One method of accomplishing this is by rubbing substances together, but the effect is due more to intimacy of contact between every portion of each surface than to actual friction. The result is that the two substances pass from the normal to the electrified condition. The condition of the two sub- stances is different, and one is said to be positively and the other negatively electrified. The terms positive and nega- tive are respectively used to imply a surplus above and a deficiency below the normal amount of electricity present.* If a dry glass rod is rubbed with silk, it will be found that the glass is positively and the silk negatively electri- fied. A list may be prepared (from the results of experi- ments) in which substances are placed in such an order that upon any two substances named being rubbed together the resulting electrical condition of each may be stated according to their relative positions upon the list.
• Recent research shows that the negatively electri6ed body has the exeess of electricity, and that, therefore, the true direction of a current is opposite to that in which it is at present assumed to pass.
I— {506$
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The electrified condition of a body may be imparted to others either by direct contact or by induction. Experi- ment proves that bodies similarly electrified, or charged, repel, and bodies oppositely charged attract each other.
It is vitally important to notice that in every case in which electrification results the values or quantities of positive and negative electrification are equal. This fact may be proved experimentally, or it may be deduced by mathematical analysis. If, therefore, a positive and a negative charge have been produced — suitable conditions being provided — an electric current will flow from the positively to the negatively electrified body until electrical equilibrium has been restored. Where these conditions have not been provided there always exists a force of attraction between the bodies.
Potential.
The term potential implies the power or capacity to do work.* Now a charged body is endowed with the power of attracting light substances — a property which an uncharged body does not possess. The uncharged body is said to be at zero potential, whilst the charged oody has a positive or negative value according to the sign of its electrification. Potential corresponds very closely to level as applied to water, and just as a flow of water takes place from a higher to a lower level, so does a flow of electricity or an electric current take place from a higher to a lower potential in its endeavour to restore electrical equilibrium. The numerical value of potential is defined in terms of the work which a body can do in virtue of its potential. In order to corre- late this definition with what has been said in regard to the identity of potential with electrical pressure, imagine a large tank filled with water and having a small pipe of
* This statement requires some qualification, since the power to do work obviously depends upon the potential of other bodies. No body can be said to have an absolute value of potential, since the conception essentially involves the difference in relative condition of two bodies or noints. For simplicity, the earth is assumed to be at zero potential, and tne potential of auy particular body is given a definite value, but this is merely a method of briefly stating that a difference, equal to that value, exists between the potential of the body and the potential of the earth.
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INTRODUCTION
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considerable length leading from its base along the ground. Consider the difference in the rate at which the water would leave the pipe according to whether the discharging end of the pipe was just below the level of the water, or whether the tank was raised high above the ground. The difference in level between the tank and the issuing water could clearly be defined in terms of the rate at which the water issued, or, what is more to the point, in terms of the work which the issuing water, in virtue of its pressure, could perform.
Calculations in Electro-Statics.
The fundamental facts and definitions upon which the numerical aspects of the various effects are dealt with may be briefly stated as follows : —
1 . Force is anything which changes or which tends to change (a) the state of rest , or (b) the uniform motion of a body .
2. The unit of force ( the dyne) is such that acting for one second upon a gramme of matter generates a velocity of 1 centimetre per second.
If a gramme of matter is allowed to fall freely under the force of gravity, its velocity at the end of one second is in London approximately 981 centimetres per second. A force equal to the weight of one gramme is therefore 981 dynes.
3. Work (in ergs) is equal to the force in dynes multi- plied by the distance (in centimetres) through which the force is overcome .
4. Unit quantity of electricity is such that when placed in air at a distance of one centimetre from a similar quantity it is repelled with unit force (one dyne).
5. Unit potential exists at any point when one erg of work is required to bring a unit of electricity of similar sign from an infinite distance up to that point in oppo- sition to the force of repulsion .
6. The potential at any given point due to a charge is equal to the quantity of the charge divided by its distance from the given point.
7. The force of attraction or repulsion between two
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TBLEQRAPHY
charges in air is equal to the product of their quantities divided by the square of the distance separating them .
8. The capacity of a conductor or system of conductors is equal to the quantity of the charge divided by the differ- ence of potential existing . {Vide page 14 also.)
MAGNETISM.
The starting point in magnetic research was the dis- covery of an ore to which pieces of iron and steel would adhere. This ore received the name of “ lodestone ” and is now known to be the black oxide of iron (Fe804). It was next discovered that a piece of steel, after being rubbed with lodestone exhibited the same properties as the lodestone itself, — in fact, became what is now termed a permanent magnet.
The mariners compass and the law governing attraction and repulsion between magnetic poles followed. The com-
?ass suggested that the earth itself is a magnet with its forth and South poles approximately coincident with the North and South geographical poles. The actual position of the North magnetic pole is lat. 70° 5' and long. 96° 46' W., but it is believed that there are two South poles. A compass needle in London points about 16° west of the geographic North, but this value changes from year to year.
A piece of iron rubbed with lodestone exhibits little or no trace of magnetism when the magnet is removed. If, however, the lodestone is held in contact, the iron exhibits the properties of a magnet.*
Lines of Force.
The disturbance created in the region of a magnet is termed a magnetic field and its strength is determined by the value of the force of attraction or repulsion which it exerts upon magnets.
Lines of force are hypothetical lines along which an isolated magnetic pole would move if perfectly free to do
* The molecular theory of magnetism is given in Appendix A (q. v. ).
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80. Such a pole cannot, of course, be obtained, and its existence is only postulated for the simplification of the reasoning. It may, however, be remarked that its use in dealing with the mathematical side of the subject is as frequent as it is valuable, and that the transition from the postulated pole to actual conditions is easily accomplished.
The directions of the lines proceeding from magnets are readily made apparent by sprinkling iron filings upon a sheet of paper or cardboard placed above the magnets. The lines of force in passing through the filings cause each one to become a magnet and to 11 line up ” with its neighbours along the lines of force. It will, however, be noticed that the filings do not collect along the magnet itself, the reason being that iron and steel conduct lines of force far better than air and but few lines stray out of the metal into the surrounding air.
Every line of force is a closed curve, the direction of which is from South to North inside and North to South outside the magnet. Each line may be regarded as tend- ing to repel the lines of force upon either side of it but having a tension along its length. Again, lines of force can never cross each other. Where such a tendency exists the lines repel each other and form separate and distinct curves. Every line of force tends to shorten itself, and where motion of a system is possible, that motion takes place in such a way as to render the lines as short as possible.
Magnetic Induction.
The difference between a magnet and a piece of non magnetic material is, that the magnet possesses lines of force, whereas the non-magnetic material does not ; also, that in the latter case lines passing through it do not render it magnetic, since its molecules are not magnets. If lines pass from right to left through a bar of iron, at the right-hand side of the iron there will be a South, and at the left-hand side a North pole. The statement is identical with that contained in the subsequent paragraph, and if the reader will draw a couple of bars in a straight line with each other — ope representing a magnet and the other
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TELEGRAPHY
a piece of iron — he will, by filling in the directions of the lines of force due to the magnet, observe the direction in which they pass t hrough the iron bar, and thus deduce the direction of the induced polarity of that iron bar.
Induction takes place along the lines of force, and the induced pole is opposite in character to the inducing pole ; or, to give an example, a North pole approached to the right-hand side of an iron bar causes that end to become a South pole, the result being attraction. The attraction between a magnet and a piece of iron is, therefore, the result of previous induction. A line of force passes just as easily through brass, wood, glass, etc., as through air ; hence the interposition of a piece of copper or other non- magnetic substance does not affect the action of the magnet. From that which has been already said on the subject of lines of magnetic force, it will be seen that the molecules of a magnetic substance arrange themselves along the lines, and that to magnetize a piece of steel the magnet should be stroked along in one direction only. The end at which the stroke ceases will be opposite in polarity to the pole with which the steel is rubbed.
Quantitative Values of Magnetic Effects.
The various calculations in regard to magnets are based primarily upon the definition of a unit magnetic pole, and for the use of more advanced students a lew of the more important definitions and experimental facts are succinctly given below.
1. A unit magnetic pole is such that when placed , in air , at a distance of one centimetre from a similar pole it is repelled with unit force ( one dyne),
2. A magnetic field of unit intensity has one line of force per square centimetre passing through it ; it acts on unit pole with unit force.
The intensity of a magnetic field is defined in Gausses, a unit field being a field of 1 Gauss.
From definition 2 it follows that unit magnetic field (1 Gauss) exists at every point one centimetre from a unit magnetic pole of indefinitely minute size. In other
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INTRODUCTION
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words, 4az lines of force proceed from a unit magnetic pole and one of these lines passes through each square centimetre of the area of an imaginary sphere described, with a radius of one centimetre, around the unit pole.
3. The force of attraction or repulsion (in dynes) between two magnetic poles is equal to the product of their strengths divided by the square of the distance separating them .
As an example of the way in which these definitions may be employed, imagine that a magnet having a pole strength of 10 units and length 8 centimetres is placed with its nearer pole 5 centimetres from a magnetic pole of 3 units strength.
Force due to nearer pole =* — dynes.
10 x 3
Force due to more distant pole = — dynes.
Net effect on isolated pole = — — ^— dynes.
= 1*02 dynes approx.
The moment of a magnet is defined as the product of its pole strength and its length. A rough approximation to the result given above is contained in the statement that the force due to a magnet at a given point, in a straight line with it, is directly proportional to its moment and inversely proportional to the cube of the distance of the centre of the magnet from the given point.
VOLTAIC ELECTRICITY.
The arrangement termed a voltaic cell consists essentially of two dissimilar metals immersed in a liquid which will form a chemical compound with one of them, e. g . a piece of copper and a piece of zinc immersed in dilute sulphuric acid. For the present this primitive form of cell will serve the purpose of illustrating one method of producing the effect known as an electric current. The term “ battery *’ will be used to describe a collection of cells properly con- nected together.
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TELEGRAPHY
A copper wire joining the zinc and copper ends of a voltaic cell has properties which are not possessed by an ordinary piece of copper. These properties, which arise from the fact that the wire conveys an electric current,* are thermal and magnetic. If a cell of sufficient dimensions is employed in conjunction with a thin wire, the latter may be made incandescent. In every case heat is generated, but frequently the amount is too small to be measured or observed by any ordinary method. The magnetic effect is, however, far more readily shown.
A magnetic field exists round any wire carrying an electric current, and the lines of force will be found to lie in concentric circles with the wire as centre. This fact can be demonstrated by a current-conveying wire passing through a piece of glass or cardboard upon which iron filings are strewn. The general appearance of the filings, after tapping the glass or cardboard so as to enable tne filings to settle into position, is indicated in Fig. 1.
An electric current has magnitude and direction. Its direction outside the cell is from the copper pole through the wire to the zinc pole, and the magnetic field created is always in strict accordance with the magnitude and direction of the current.
A few of the lines of force generated in a conductor bent into a loop are shown in Fig. 2, in such a manner that the relation between the direction of the current and the direction of the magnetic field produced is at once apparent.
A compass needle or a freely suspended magnet points to the magnetic North and South, and force is required to deflect it from that position. The best position in which the force can be applied so as to produce the maximum deflection is at right angles to the needle. A magnet, placed at right angles to the needle, tends to send lines of force straight across it, thus attracting one pole and
* The discussion as to what electricity may actually bo is far beyond the scope of this work, but a reference to the source from which the trend of modern thought may be gathered will probably be useful to some readers The reference is Journal of the Institution of Electrical En jineers, Vol. XXXII., “ Electrons,” by Sir Oliver J. Lodge. See also Matter and Energy , by F. Soddy, Home University Library.
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INTRODUCTION
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repelling the other. If the earth’s field were absent the compass needle would set itself along the magnet’s lines of force, in precisely the frame way that the compass needle normally sets itself along the earth’s lines of force. When both fields are present the needle is urged by two forces at right angles to each other, and the position which it takes up depends entirely upon their relative magnitudes. If equal, then a deflection of 45° results.
Fxo. 1.— Iron flliogs round a current- conveying wire.
Fxo. 2.— Illustrate* the relation between the direction of a current and its magnetic field.
It has already been pointed out that, round a wire conveying a current, there are lines of force arranged in concentric circles at right angles to its length. Also that the difference between an ordinary piece of wire and one conveying a current is the absence of the magnetic field in the former case. If the current-conveying wire is placed in such a position that its magnetic field acts at right angles to that due to the earth, an alteration in the position of a compass needle placed at that point will result. The position in which the wire should be placed so as to
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TELEGRAPHY
produce the effect described is above or below, but in the same straight line as the needle. The wire’s lines of force pass round the wire in planes at right angles to the length of the wire, thus tending to cut the earth’s lines of force at right angles, and so produce a deflection of the needle.
It has been stated that where two magnetic fields whose directions when separately considered were at right angles to each other, the magnetic fields tended to cross one another. Lines of force can never cross each other, because the magnetic field at the point of intersection would, in that case, have two values, which is manifestly impossible. A current-conveying wire lying in the magnetic meridian directly above a compass needle causes the needle to be deflected. The field due to the earth is altered in its distribution by the field due to the current, and the needle sets itself in the direction in which the re-distributed lines now stand. In other words, a resultant magnetic field is
Sroduced by the action of the two separate fields and its irection and magnitude depend upon the values of the two fields.
By reversing the battery connected to the wire the direction of the lines of force due to the current is changed.
The direction of a line of force above a current-conveying wire is opposite to its direction below the wire (see Fig. 2), and therefore the direction in which a compass needle is deflected is dependent not only upon the direction of the current, but upon whether the wire is held above or below the needle. There are many1 rules for memorizing these effects, but three only will be given.
1. Mnemonic “ SNOW,” a current passing from South to North Over the needle causes the North pole to be deflected to the West.
2. Place the outstretched right hand between the wire and the needle, with the palm of the hand facing the needle, so that were the hand the wire, the current would flow from wrist to fingers. The outstretched thumb will then indicate the direction in which the North pole will turn.
3. Imagine a man swimming in the wire in the direction of the current, and that he turns so as to face the needle,
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INTRODUCTION
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then the North pole of the needle will be deflected towards his left hand.
The converse of these rules, i.e. the determination of the direction of a current from the known direction in which a compass needle is deflected, is sufficiently obvious.
Conductors and Insulators.
If the poles of a voltaic cell are joined by a dry piece of glass it will be found that no current exists. It is there- fore clear that glass is a substance that will not permit the effect termed an electric current to take place along it. Such substances are termed non-conductors, or insulators, in contradistinction to conductors, and of all known sub- stances silver conducts electricity most freely, whilst perfectly dry air is the best insulator. Electrical con- ductivity is, however, a matter of degree, for, whilst no substance conducts perfectly, it is certain that no substance is a perfect insulator. The best conductors are metals in the following order : — Silver, capper, gold, zinc, platinum, iron, tin, lead, and mercury. Next come carbon, acids, salt solutions, and water. Taking insulators in the same way the order is : — Dry air, glass, ebonite, paraffin wax, india- rubber, gutta-percha, silk, wool, porcelain, oils, paper, marble. This order is, however, subject to variations in accordance with the condition of the material.
The path along which a current flows is termed a circuit, and it is said to be completed when the current is passing.
UNITS .
Before electric currents can be compared standards must be defined in just the same way that the units of length, weight, and time, are defined in ordinary commerce.
Electromotive force stands in much the same relation to electricity as pressure does when applied to water. The different degrees to which various substances will permit the passage of a current has already been remarked. Another way of expressing the same fact is to s.iy that some conductors offer more resistance than others.
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TELEGRAPHY
A pipe of fixed size will deliver water at a certain rate when a given pressure is applied. An increase in the
pressure or an increase in the size of the pipe will result in a corresponding increase in the flow of water through it. Similarly in an electrical circuit an increase in the electrical pressure or E.M.F., or a reduction in the resist- ance of the circuit will result in an increased value of current.
The units of current, electromotive force and resistance are as follows : —
Current The ampere.
Electromotive force . . „ volt.
Resistance „ ohm.
The Ohm is represented by the resistance offered to an unvarying electric current by a column of mercury at the temperature of melting ice (0° G. or 32° F.) 14*4521 grammes in mass, of a constant cross sectional area , and of a length of 106*3 centimetres .
This unit represents about the resistance offered by 80 J yards of the gutta-percha covered wire formerly used in joining up the instruments upon the tables in a telegraph office. It is the resistance offered by about 200 yards of 100-lb. copper line wire, or by about 132 yards of 400 lb iron line wire.
The Volt is represented by 6974 (ttttt) of the electrical pressure at a temperature of 15° C, between the poles of the voltaic cell, known as Clark's cell , set up in accordance with a detailed specification.
The E.M.F. of a Daniell cell is rather more than one volt, whilst that of the Clark cell is rather less than 1£ volts (actually 1*434 volts at 15° C ).
The Ampere is the current which will flow through a circuit having a resistance of one ohm when urged by an electromotive force of one voit .
Such a current will deposit silver from a solution of nitrate of silver in water at the rate of *001118 of a gramme per second. This is the legal definition of a current of one ampere, and a specification is appended
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stating the details of the method of carrying out the determination.*
In telegraph practice the ampere is too large a unit, and it is therefore sub-divided into “ milli-amperes/' which, as the name implies, means thousandth parts of one ampere. This is usually denoted by the contraction “ m.a., and 1000 m.a. would therefore mean one thousand milli- amperes, or one ampere.
In order to avoid the constant writing of the words 1 ohm ” or 14 ohms " after numbers the small Greek letter “•’’(omega) is used as an affix. Thus, “ one hundred and fifty ohms " is written “ 150* The capital letter has been similarly employed to represent “ megohms/’ or millions of ohms, thus 10° means 10 megohms or 10,000,000". This convention is extremely useful in stating insulation resistances, which are usually of this order of magnitude.
For extremely small resistances such as the resistance between the opposite faces of a unit cube of metal or other highly conductive substances the “ microhm/' or one millionth of an ohm, is very frequently employed. For instance, the expression “ 165 microhms ” therefore repre- sents -000165- .
OHATS LAW.
Ohm discovered that the following relations existed between these units : The strength of current through any circuit varies directly as the electromotive force and in- versely as the resistance , or, stated in a more definite manner, the number of amperes flowing through a circuit
anal to the number of volts of electromotive force ed by the number of ohms of resistance in the entire circuit, or : —
r* „ ... Electromotive force • ^ n
ClllTent Resistance ^ * JJ*
whence R =~, and E = C x R,
* Tht definitions of the three unite, together with the specifications as to determination, are to be found in the Electrician of August 81, 1894, 1^518.
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TELEGRAPHY
where G, R and E are respectively the current, resistance, and electromotive force in the circuit.
For instance, an E.M.F. of 12 volts applied to a circuit of 6 ohms resistance will produce a current of -6* = 2 amperes. If the E.M.F. in a circuit be 30 volts and tlie current 10 milli-amperes, its resistance must be . (/Y V = 3000 ohms. If the current is 2 amperes and the resist- ance is 10 ohms, then the E.M.F. in the circuit will be 10 X 2 = 20 volts. These quantities should all b© expressed in volts, amperes, and ohms.
OTHER ELECTRICAL UNITS.
From the three units of current, E.M.F., and resistance, the remaining electrical units may readily be derived and, although detailed treatment is scarcely possible in a work of this description, it is undesirable entirely to omit them since there are many cases in which their use is essential.
The Coulomb is the unit of quantity of electricity and may be defined as the quantity of electricity which would pass any given point in a circuit carrying an unvarying current of one ampere in one second.
The Farad is the unit of capacity and represents (he capacity of a condenser which at a pressure of one volt would be charged with one coulomb of electricity.
Relationships analagous to Ohms law exist between E.M.F., quantity, and capacity. They are: —
_ _ . . Quantity
Difference of potential = CapacT^
r ‘t — Quantity apaci y — jj1^*erence 0p p0tentiaI
Quantity = Difference of potential x capacity.
If a condenser of *001 farad capacity has a charge of 2 coulombs the difference of potential across its terminals is
_ = 200 volts.
001
As an example of the second relation, suppose that the quantity of electricity in a condenser is *01 coulomb whilst
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the difference of potential across its terminals is 50 volts. The capacity is then = *0002 farad.
The third form of the relation is illustrated by ascer- taining the charge in a condenser of, say, ’00002 farads capacity due to the application of an E.M.F. of 50 volts. It is 50 x ’00002 = *001 coulomb.
The values of the capacity chosen in these examples have been extremely small fractions of the unit, the farad, but even these fractions are far larger than are met with in the case of long aerial or even short underground telegraph circuits, consequently a subdivision of the farad, the microfarad, is employed in practice. It is equal to one millionth part of one farad and is usually denoted by the affix “ m.£”
An example of a case occurring in telegraph practice is that of a shunted condenser (g. v.). If an E.M.F. of 30 volts is applied to a condenser of 3 A m.f. capacity the value
of the charge will be^^ = 000105 coulomb.
1,000,000
One microfarad is the capacity of about three miles of a telegraph circuit consisting of a gutta-percha covered wire laid in pipes in the earth. It is the average capacity of about 70 miles of 100-lb. copper wire erected upon poles and of 8 miles of 40-lb. conductor screened cable laid underground.
The phenomenon of self-induction is simple and capable of easy explanation, but the complete definition of the value of the inductance of a circuit is somewhat complex.
Wherever a current exists there is a magnetic field. This field is the result of the current, and in coming into existence it cuts through the current-conveying conductors to which it owes its origin. Now wherever a magnetic field cuts a conductor or vice versa an E.M.F. is generated. Imagine a battery or other source of E.M.F. applied to a coil of wire such as that shown in Fig. 48. The current does not instantly attain its full value, since its rise is opposed by the E.M.F. generated by the lines of force cutting through the conductors. This opposing E.M.F. is termed the “ back E.M.F.” of self-induction. If, now, the coil and battery are short-circuited, a current will flow
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through the circuit in the same direction as the original battery current. This is caused by the collapse of the lines of force which, in so doing, cut through the conductors in the opposite direction.
The Henry is the unit of inductance, and represents the inductance of a circuit in which a counter E.M.F. of one volt is generated when the value of the current changes at the rate of one ampere per second.
One or two general remarks may be made upon this definition, but detailed treatment is altogether beyond the scope of the present work.
If a bar magnet is plunged into a coil of wire the magnet's lines of force cut through the windings of the coil and an E.M.F. is thereby generated. The value of this E.M.F. is directly proportional to (i) the strength of the magnetic field, (ii) the rate of motion, and (iii) the number of convolutions.
The magnetic field generated in a coil of wire by passing a given current through it is proportional to the number of convolutions. By doubling the number, the magnetic field is doubled, and this doubled field will, when the current is stopped or started, cut the windings, which are twice as many as in the former case, and thus generate four times the E.M.F. If the convolutions are quadrupled the quadrupled magnetic field cuts the quadrupled turns, so generating sixteen times the E.M.F. It will therefore be apparent that the inductance of a coil of wire is proportional to the square of thfe number of turns of wire.
The inductance of an electromagnet varies somewhat with the value of the current employed, because the magnetic field generated in the core depends upon the degree or intensity of the magnetization of the iron and is not in direct ratio to the magnetizing force. Hence in stating the inductance of a relay, for instance, the value of the current is stated. The inductance of a P.O. standard “ A” relay is 3*55 henrys, and of a “ B ” relay 3*74 henrys with their coils in series for a current of 20 m.a. The inductance when small in value is often expressed in thousandths of a henry or in milli-henrys.
The inductance of a relay with its coils in parallel
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is one-quarter of its value with its coils in series, since the effective number of turns is one-half in the former case.
The units of power and energy may be given to complete the list of practical units. The watt is the rate at which work is done when one ampere flows through a conductor with a difference of potential of one volt across the ends of the conductor .
JP2
Watts = E x C or C2 x R or .
A. Kilowatt is equal to 1000 watts.
A 25 candle power incandescent lamp requiring *13 ampere upon a 230 volt circuit therefore takes 230 x ‘13 = 30 watts. As 746 watts is equal to one horse-power, the lamp is taking approximately of one horse-power.
The commercial unit in which electrical energy is Bold by electrical undertakings is known as the Board of Trade unit and is the practical unit of energy. The Board of Trade unit is equal to 1000 watt-hours , i.e. 1*34 horse power for one hour.
Twenty of the lamps mentioned above would con- sume 600 watts, and if burning for three hours the energy used would be 600 x 3 = 1800 watt-hours or 18B.O.T. units.
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CHAPTER I
PRIMARY CELLS
AN electric current represents a certain amount of energy. It is not in the power of man to crecUe energy, but the energy with whicn the world is endowed may be applied to effect desired ends. A voltaic cell may be defined as a piece of apparatus which converts chemical energy into electrical energy. A cell supplies electrical energy, in the shape of an electric current, by taking an amount of chemical energy, equal to the electrical energy, from the constituent parts of the cell.
In the simple cell previously mentioned the sulphuric acid attacks the zinc, and with it forms a chemical com- pound known as sulphate of zinc. If, however, a cell of this description is put to practical uses, it will be found that the current grows rapidly weaker, until at last it almost ceases. The reason is that the hydrogen, which is liberated in the re-arrangement of the chemical com- pounds. forms a layer of gas over the copper plate. Again, the impurities in the zinc, such as iron, tin, arsenic, etc., combine with the zinc to form little batteries, and waste it away without any equivalent of work done in the external circuit. This evil is known as local action. The words “external circuit0 are used in contradistinc- tion to the “internal circuit,” or path of the current inside the cell itself. The troubles to which the im- purities in the zinc give rise are eliminated by the process known as amalgamation , which consists in coating the zinc with mercury, thus making it behave as though it were chemically pure.
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Although this remedy has been known since 1828 the theory of its action is still undecided. It has been sug- gested that, since zinc amalgamates so readily, the zinc at once passes to the surface of the amalgam, whereas the impurities, being less readily amalgamated, do not pass to the surface. The amalgam would thus act as a filter, but as soon as it became thin the impurities would project and local action result, which is found to be the case.
This view of the matter is satisfactory so far as the impurities are concerned, but it fails to explain the absence of local action between the zinc and the mercury.*
The accumulation of the hydrogen upon the negative element is not so easily remedied! The thin coating of this electro-positive gas gives rise to what is termed ' polarization,” and its effects are most deleterious.
The surface of the plate being covered with hydrogen reduces the area in contact with the liquid, which in- creases the internal resistance of the cell (see Chapter II). Also, and this is by far the more serious aspect of the question, hydrogen is electropositive, and therefore tends to re-combine with the zinc sulphate and so to deposit zinc upon the negative element. The statement of this tendency is another way of saying that an E.M.F. is set up in opposition to the prime E.M.F. of the cell. The E.M.F. of the cell under such conditions is seriously decreased. In a simple cell such as that considered it was found that the E.M.F. fell from ’85 volt to *54 volt in one minute after its terminals were joined through a resistance of 10", and to *355 volt at the end of five minutes. It will therefore be realized how serious a matter polarization becomes, and that its prevention is imperative if anything which even remotely resembles a steady current is to be obtained.
The E.M.F. of any particular type of cell is independent of its dimensions, but its internal resistance is dependent upon them, and generally speaking the larger the cell the lower is its internal resistance, and also the greater is the amount of electrical energy which may be obtained for a
• Primary Batteries , by W. R. Cooper.
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20
TELEGRAPHY
single charge. These points are, however, reverted to in Chapter II.*
Although it has been noted that the hydrogen liberated during the action of the cell is deposited upon the negative element, the way in which this occurs has not yet been dealt with. The hydrogen does not pass from the positive element through the electrolyte in the form of bubbles. Upon being liberated by the combination of zinc with the sulphuric acid it immediately combines with the SO4 of an adjacent molecule of HtS04, thus liberating the hydrogen from this molecule. The action is repeated across the liquid until the negative element is reached, when the hydrogen comes off in the form of visible bubbles. No sign of the action is to be seen in the liauid which intervenes between the two elements of the cell.
It has already been stated that zinc is the negative and copper the positive terminal of the cell under consideration. In the external circuit the current flows from copper to zinc, but in order that the circuit may be complete (with- out which there can be no current) the current must flow from zinc to copper inside the cell, hence to express both facts the zinc is termed the 'positive element , but the negative pole or terminal of the cell. Similarly the copper is the negative element , but the positive pole .
The positive metal or element is always the one which is acted on or consumed by the liquid. The liquid which consumes the zinc, when the circuit is completed, is called the excitanty as opposed to the liauid or substance taking up the hydrogen, which is called the depolarizer. The hydrogen causes polarization unless means are employed to get rid of it, or, in other words, to depolarize the cell.
Leclanch£ Cellr
The containing vessel of this cell (Fig. 3) consists of a square glass jar, ending in an almost circular collar, shaped to admit the zinc rod which forms the positive element. The rod is cast on to a copper wire, which is usually
* At this point readers who have little or no knowledge of chemistry are advised to read carefully Appendix R on chemistiy.
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PRIMARY CELLS 21
insulated where it emerges from the zinc and forms one terminal of the cell. The collar and a portion of the jar itself are usually very heavily coated with ozokerit to arrest the creeping of the salt. Inside the jar is placed a circular porous pot containing the negative element, a carbon plate, and the depolarizer, manganese dioxide.
Hitherto, it has been laid down as an essential con- dition that the form of the manganese dioxide termed “pebble * should be used, and that it should be free from
Fig. 3. — Porous pot form of Leclanch* cell. Fig. 4.— No. 0 “ Sack *’ Leclanch*
Element.
dust But it has been discovered by J. G. Lucas * and proved by exhaustive researches that the best results are obtained by using powdered commercial manganese dioxide which will pass through a sieve 50, but not through a sieve of 60, meshes to the inch.
The top of the carbon plate is capped with a heavy lead lug carrying a brass terminal. In order to arrest injurious affection of the lead lug and its terminal, the lug and a small part of the upper portion of the plate are thickly
* “ Life and Behaviour of Primary Batteries used for Telephone Pur- poses,” by J. G. Lucas. Paper read before the Institution of Post Oflke Electrical Engineers on December 12, 1910.
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22 TELEGRAPHY
noated with paint. The top of the porous pot is sealed over with the carbon plate in position.
The exciting fluid is a saturated solution of salammoniac (ammonium chloride) contained in the outer jar.
As will be seen when considering the chemical actions which take place during the discharge of a Leclanche cell, free ammonia gas (NHS) is generated, and this has a deleterious effect upon metal work and upon the acid solution in adjacent secondary cells in the battery room. The evolution of this gas necessitates free ventilation in
any battery com- partment which may be used, and evaporation of the solution is there- fore facilitated. In order to permit a cell to be sealed, with the object of thereby retarding evaporation of the sol u tion , manganese chloride is substi-
tuted for ammon-
Fio. 5. — shallow circular rfnc. ium chloride in the
case of batteries where the time of discharge extends over several months. With the manganese chloride excitant no free gases appear to be evolved. The effect of using manganese chloride is to produce a slightly higher E.M.F.
It is essential that the porous pot shall be wet, in order to permit the passage of the current through the cell. Therefore a certain amount of water or a weak salam- moniac solution is added to the porous pot. The latter is a much better conductor than the former.
The cells are usually made in four sizes, known as No. 0, No. 1, No. 2, and No. 3 sizes. The sizes employed by the Department are Nos. 0, 1, and 3, i. e. the four- pint, three-pint, and one-pint sizes respectively.
A large circular zinc plate surrounding the porous pot
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was formerly employed with the No. 1 size, but gave place to the shallow circular zinc illustrated in Fig. 5. The large zinc plate was found to be very wasteful, as the current is not equally distributed throughout the area of the zinc, the result being that it is worn away very unevenly. A hole occurs about an inch and a half from the bottom, and also at the top of the liquid. By experiment it was found that the zinc could be reduced to the form mentioned without any undue increase in the resistance of the cell.
Further, J. G. Lucas has, in his historic paper, called attention to the fact that the resistance of a Leclanch^ cell does not vary in proportion to the size of the zinc used. In a typical ex- periment it was found that a Leclancbe cell with a circular zinc having an area of 30 square inches immersed in the solution gave an internal resist- ance of *86*, and with a rod zinc with an im- mersed area of 8 square inches an internal resistance of but *96“, whilst on reducing the immersed area to 4 square inches the resistance was raised only to 105“ The explanation of these results lies in the fact that the major part of the internal resistance of the cell lies between the outside of the porous pot and the carbon.
In the case cited this would amount to about '75**, ami it will therefore be recognized it would not be possible solely by increasing the size or area of the zinc to reduce the resistance of the cell below this figure. For No. 0 cells two rods are used.
A typical zinc rod is shown in Fig. 6. It has l^t?c!7c been found that a tapered zinc of this shape is cell taper more economical than the ordinary type of rod. (aYemeni?.)
In making up the cell with powdered man- ganese dioxide, the latter should be moistened with water or with a weak solution of salammoniac, and tamped as firmly as possible in position in the porous pot so as to form, practically, a solid mass around the carbon plate. When this is done there is no difficulty in obtaining as
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TELEGRAPHY
low an internal resistance as 5“ with the No. 1 size of cell equipped with a rod zinc. It need only be added that in no type of Leclanche cell is there any appreciable local action.
The powdered manganese cell is far more efficient .than the agglomerate types of cell in which the porous pot is dispensed with by making up the depolarizer in slabs or rods secured to the carbon. In the Sack form of cell the porous pot, the only function of which is to maintain the depolarizer in intimate contact with the carbon, is replaced by a wrapping of textile fabric reinforced by a string lapping (Fig. 4).*
Chemical Action . — When the cell is thus made up there will be no action whatever, as the salammoniac will not attack the zinc, in fact will not have the slightest effect on it when the circuit is not closed. When the circuit is closed, the chemical compounds are entirely altered in their distribution. Salammoniac is a com-
S>und of ammonium and chlorine, and is represented by H4C1 (one atom each of nitrogen and chlorine, together with four atoms of hydrogen). When the circuit is closed, the zinc and the ammonium in the salammoniac change places, and thus part of the zinc will be consumed to form zinc chloride (a substance that readily dissolves in the salammoniac solution), ammonia gas (which combines with water to form ammonium hydrate NH4HO) and hydrogen which is set free. This hydrogen, which appears at the carbon plate, must be removed in order that it may not give rise to polarization. The depolarizer used in the Leclanche cell is, as previously stated, the manganese dioxide packed round the carbon plate. Im- mediately the hydrogen is liberated it combines with the
|
oxygen of the manganese to form water. The action may be stated thus : — |
||
|
Outer cell : — |
||
|
Zn |
+ |
2NH4C1 |
|
One molecule of zinc |
together with |
two molecules of salammoniac |
|
= Zn Cl, |
4* |
2NH, + H, |
|
form one molecule of due chloride |
together with |
two molecules of and two atoms of ammonia gas hydrogen. |
* The Danicll, Bichromate, and Agglomerate cells, which are now obsolete, arc deocribed in the earlier editions of this work.
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Inner Cell : —
H, + 2MnOa = MngOg + H20
Two atoms of and two molecules of form one molecule of and \pne molecule
hydrogen manganese manganese of water,
dioxide sesquioxide
In the inner cell it will be seen that the two molecules of manganese dioxide taking part in the reaction have between them given up one atom of oxygen to the hydrogen, thus forming water. On the other hand, the two molecules of manganese dioxide have become one molecule of a lower oxide, namely, Mn2Os, the sesquioxide of manganese.
Dry Cells.
A dry cell may be defined as a cell in which the exciting and depolarizing materials are applied in the form of thick damp pastes, which in comparison with the fluid electro- lyte of an ordinary cell perhaps justifies, or, at all events, extenuates, the generic title given to this class of cell. If, however, the pastes were actually dry the cell would, by reason of its enormously high internal resistance, be in- capable of supplying a current. As a matter of fact cells frequently fail after some little service because they dry up — a condition indicated by a rapid rise in internal resistance.
Every dry cell is a modification of the Leclanch^ cell and has precisely the same electro-chemical reactions, a fact which is definitely established by the equality of the E.M.F.S of the Leclanch^ and dry cells.
All cells consist of a zinc containing vessel from 13£ to 22 mils, in thickness, with a carbon plate or rod, either cylindrical or fluted, to give greater area of contact with the depolarizer. The carbon is either insulated by a layer of paper or given a half-inch clearance from the bottom of the zinc vessel. The general composition of the two pastes is 10 lbs. of Mn02, 10 lbs. of carbon or graphite or both, 2 lbs. of NH4C1, 1 lb. of ZnCl2, and sufficient water to give the proper amount of electrolyte to the cell Various additions are made by the manufacturers, such as starch or other forms of paste, with a view to improving the contact between the zinc and the white or exciting paste, and to
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promote action throughout the charge. The efficiency of the cell depends very largely upon the purity of the charg- ing materials and upon its contact with the conductive carbon.*
The Siemens Dry Cell { Figs. 7 and 8). This cell has been chosen for detailed description as typical. It consists of a zinc cylinder of a thickness suitable to the size of the cell, with a connection wire attached to the inside of the
Fio. 7.— Siemens dry cell.
Fio. 8.— Section of a Siemens dry cell
VENT
VENT
BITUMEN
-PAPER
CORK
-CANVAS
- WHITE PASTE -BLACK PASTE
cylinder. This latter contains a carbon rod, surrounded by a depolarizer, composed of a mixture of powdered peroxide of manganese and carbon intimately mixed and pressed into close contact with the carbon rod. A brass terminal is fixed into the top of the carbon in the following manner : — A vertical hole is provided in the rod into which the pin of the terminal is inserted, and a molten alloy, composed of bismuth, lead and tin, is poured around the pin. As this alloy expands slightly in cooling, it establishes a per-
* American Electrochemical Society, paper “Certain characteristics of dry cells” hy C. F. Burgess and C. Hambuechen: Electrician , August 12, 1910, p. 743.
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PRIMARY CELLS
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feet contact between the pin and the carbon. An exciting paste composed of plaster of Paris and flour mixed with a solution of ammonium chloride surrounds the depolarizer. A space is provided in the upper part of the cell to receive the gases and water which are formed during the working of the cell, and this space is filled with ground cork as an absorbent for the moisture. The cell is sealed at the top with a layer of bitumen. Small holes are provided for the escape of the gases ; their utility is somewhat doubtful since, if effective, they would carry off the moisture and so cause the cell to dry up earlier than it does. The cell is contained in a strong cardboard box impregnated with paraffin wax, which makes it damp-proof, and thus insn lates the cell.
Other Dry Cells. The E.C.C. cell has a flat carbon plate, and contact between the carbon and the bottom of the container is averted by covering the bottom with a layer of insulating material. In the Hellesen cell the negative element is a hollow circular carbon, the interior of which is filled with silicated cotton.
Dry cells in two sizes are in general use by the Post Office, viz. “Y,” the circular cell of about 40 ampere- hours capacity, and the large square “ Z ” cell with a capacity of 140 ampere-hours. A very small square cell is employed for testing purposes and for the speaking battery on portable telephones.
Standard Cells.
A particular combination of materials in a cell will always produce the same E.M.F. provided the materials are exactly alike. In the form of cell invented by Latimer Clark it is a sine qua non that all the materials employed shall be chemically pure. Under these conditions the E.M.F. of the cell in 1434 volts at 15° C. The cell is usually very small, and is often made in a short wide test tube. Into the bottom of the test tube a short piece of platinum wire is fused. The outer part of this wire forms the positive terminal and the inner serves to make con- nection with the negative element, metallic mercury, which
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TELEGRAPHY
covers it. Above the mercury a thick paste of mercurous sulphate is spread, and above this is a paste of zinc sul- phate into which the zinc rod dips. The zinc rod passes through the cork or bung, and the whole arrangement is sealed up.
The chemical action of the cell is due to the S04 of the exciting fluid (zinc sulphate) combining with the positive element to form zinc sulphate and liberate zinc which com- bines with the mercurous sulphate to form zinc sulphate and mercury. The mercury so formed merely adds to the
Fio. 9.— Clark standard cell (fall size). Fia. 10.— Pafr of Clark cells
and thermometer.
quantity already present. There is a very large number of modifications of the Clark cell in existence, but' in principle they do not vary at all. The final form given to such a cell is illustrated in Fig. 10, and it will be noticed that a thermometer has been added for ascertaining the temperature of the cells, since this has an important influence upon the value of the E.M.F.
A full size section of a cell is shown in Fig. 9, whilst the subsequent figure shows the general appearance of a pair of cells mounted in the usual way with a thermometer.
The Board of Trade specification for the preparation of the cell details the manner in which the materials of
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the cell shall be prepared. It directs that the zinc and mercurous sulphates shall be mixed together in the form of a paste and ensures the formation of saturated solutions of zinc and mercurous sulphates in water.
Daniell Standard Cells.
Modifications of the Daniell cell have been used by some physicists with excellent results, but its use has not been very extensive.
A standard cell which is required for accurate work should only be used to produce a current through very high re- sistances, i. e. resistances of the order of 100,000 “.
Even then the current should only be main- tained for the shortest possible time. Neglect of these precautions en- tails inaccuracy in the value of the assumed E.M.F.
Where the highest accuracy is not essential less delicate apparatus Flo. ll.— P.O. form of standtrU Danioll cell, may be employed. For
example, the P.O. tangent galvanometer requires far too large a current to produce a satisfactory deflection with such a cell as Clark’s. To provide a standard E.M.F. and one capable of supplying a current of a milli-ampere the P.O. standard Daniell was designed and for many years was extensively employed by the Department. This cell, though far less accurate than a Clark cell used under the best conditions, was sufficiently so for its purpose. The zinc and its porous pot (Fig. 11) were kept in one com- partment and the copper in another, and the parts of the cell were only assembled when the cell was actually in use. The lid carried a projection which made it im-
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TELEGRAPHY
90
jH>$sible to close the cell until the porous pot containing the zinc and the copper plate had been replaced in their receptacles.
Special care was taken that the constituent parts of the cell and the chemicals employed were as pure as possible. The exciting fluid was a saturated solution of zinc sul- phate. This cell was replaced by a dry cell whose E.M.F. was periodically measured by accurate apparatus. (See Chapter III).
Characteristics of Cells used by the Post Office.
The E.M.F. of a cell decreases and the internal resistance rises as the cell becomes exhausted, and it is therefore necessary to define the point at which the cell should be considered faulty. Again, bad materials or defective porous pots adversely affect the E.M.F. and internal resist- ance. A pot which is of a too porous character permits the excitant and depolarizer rapidly to commingle. This does not apply in the case of Leclanche cells, and a minimum resistance is not specified. A very hard one, on the other hand, unduly increases the internal resistance of the cell. Cells are considered faulty if their E.M.F.s fall below the minimum value given in the table upon page 32. They are also considered faulty if their internal resistances rise above the maximum or fall below the minimum value ; the latter is usually due to the porous pots being too soft.
Leclanche cells with granular manganese dioxide polarize if heavily worked, since the hydrogen appears at the carbon plate more rapidly than the manganese can dispose of it. With intervals of rest or for small currents the cell pos- sesses many advantages, notably the entire absence* of local action when not in use, and the very small amount of attention necessary.
On the other hand, Leclanche cells charged with
fowdered manganese dioxide are comparatively steady.
n this connection some extraordinary results are given by J. G. Lucas; for example, a Leclanche cell made up with granular manganese dioxide was discharged for
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PRIMARY CELLS
31
five hours per day, six days per week, at a mean current of 41-6 m.a. until the voltage had fallen to lv, by which time 7 watt-hours were obtained. A similar cell, except- ing that it was charged with 'powdered manganese dioxide, was discharged under the same conditions and gave 77*5 watt-hours before the voltage had fallen to lv. At higher current discharge rates the disparity between the two types is shown to be even greater. At a discharge rate of 100 ma. the powdered manganese dioxide cell gave an output 15 times greater than the granular dioxide cell, and at *5 ampere, 30 times greater.
Two cells with granular dioxide were discharged at a mean rate of 41*6 m.a., and 7 watt-hours were obtained by the time the voltage had fallen 33%. The manganese dioxide in both cells was emptied from the porous pots and the contents of one of them was ground to powder. The materials were then restored to their original porous pots and the cells again discharged separately at approxi- mately the same discharge rates as originally. The cell in which the granular contents had been restored gave a further 1*155 watt-hours by the time the voltage had fallen to *95v, whilst the cell in which the manganese dioxide had been restored in a powdered condition gave a further 56 watt-hours before the voltage had fallen to the same value.
The Daniell cell is remarkable for the very small amount of polarization which occurs, even when heavily worked. It is also notorious for the very considerable amount of local action which always occurs. Its comparatively low E.M.F. and high internal resistance render it unfitted for purposes where heavy currents are necessary. The small size was formerly employed for simplex sounder circuits, whilst the large size was used for ordinary duplex circuits and for local batteries generally. Owing to its local action and the more frequent attention required it would not be as satisfactory as the Leclanche cell for single-needle and double- plate sounder stations.
The Bichromate cell was used wherever large currents, sustained for considerable periods, were required. It is Most efficient when it is heavily worked, but owing to the
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TELEGRAPHY
frequent and skilled attention required it is unsuitable for general use. It also suffers from local action, as a result of diffusion of the solution through the porous pot.
|
Type of Cell. |
E.M.F. (volts). |
Internal resistance (Ohms). |
Purpose for which used. |
||
|
Max. |
Min. |
Max. |
Min. |
||
|
Bichromate |
216 |
1*836 |
4 |
2 |
) Superseded by modified Leclanche |
|
Daniell |
1-08 |
•972 |
4 |
2 |
/ types. |
|
New Leclanch6 No. 0 (with two zinc rods) |
1*55 |
1*0 |
2 |
Quadruplex, High speed. Long duplex, Universal, and Central battery telegraph systems. |
|
|
f« i , No. 1 |
1-55 |
1-0 |
2 |
“ |
8ounders simplex and duplex. Local batteries generally. |
|
.» ,» No. 3 |
1*35 |
1-0 |
8 |
Telephone speaking batteries, D. P.8., Single needle and for minor purposes generally. |
|
|
Dry cells . |
1*55 |
1-0 |
3 |
Special arrangements. |
It may be remarked that the internal resistance of a battery affects the speed of working of a circuit (vide Chapter XIX). If too low the transmitter sparks, whilst too high a value reduces the working speed. To obtain an E.M.F. of 100v, 105 Daniell cells would be required as against 55 Bichromate cells. The internal resistances in the two cases would be from 110“ to 220" with Bichromates, and from 210“ to 420“ with Daniells.
Dry cells possess the advantage of portability and are eminently suitable for special arrangements. Indeed, the} may be employed for almost any purpose. Since the internal resistance is very low a 10“ resistance coil is placed in every 10-cell box, so that excessive currents may not be produced. If the 10“ coils were omitted when the cells were used in conjunction with a Wheatstone transmitter, the excessive sparking would at once put the transmitter out of action.
Ideal Cell.
There is no form of primary battery which fulfils all the conditions one would desire from an ideal point of view, and therefore it happens that the choice of a battery
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PRIMARY CELLS
33
largely depends upon the uses to whieh it is to be put. An ideal cell should possess the following characteristics : —
1. High E.M.F.
2. Low internal resistance.
3. Absence of polarization.
4. Absence of local action.
5. Cost of the cell small.
6. Cost of charging small.
7. Amount of energy per charge should be large.
8. Attention required should be little.
9. No injurious fumes should be given off.
10. The materials should be easily and safely handled.
11. Dimensions as small as possible.
Conditions 6 and 7 mean that the cost of a given quantity of electrical energy should be as low as possible, and conditions 7 and 8 specify that the labour cost of maintenance shall be small.
Leclanch6 cells charged with powdered manganese dioxide more nearly approach these ideal conditions than either the Daniell or the Bichromate cells. Moreover, owing to the low internal resistance of the modified cell the more costly agglomerate cells are likewise being super- seded. Indeed, the only types of cell which are now used for general purposes will be (i) the modified Leclanch^ with rod zincs, in three sizes, viz., the No. 0, No. 1 and No. 3, (ii) the dry cell in two sizes, viz , Y and Z, and (iii) secondary cells.
The No. 3 size will be used for (i) telephone speaking batteries — it having been found that an internal resist- ance not exceeding 3" per cell makes no appreciable difference in the speaking efficiency — and, (ii) for all minor telegraph, and telephone signalling, purposes. No. 1 cells will be used for sounder circuits, simplex, duplex and local batteries generally. The No. 0 size, provided with two zinc rods, will be used for high-speed Wheatstone, quadruplex, and long duplex, circuits, universal and small central battery telegraph systems. Dry cells will only be employed in lieu of porous pot cells when the latter cannot be used for reasons affecting portability or accommodation in exceptional circumstances.
*—<5066)
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CHAPTER II
CALCULATIONS IN CONNECTION WITH CIRCUITS AND CONDUCTORS .
PART I. —ARRANGEMENT OF CELLS.
Size of Cells.
TI1HE E.M.F. of a cell is entirely independent of its JL dimensions, so that a cell consisting of a grain of zinc and a percussion cap would have just the same E.M.F. as a cell composed of the same materials, but as large as a Lancashire boiler. The internal resistances in these two cases would differ very widely, as also would the amount of electrical energy obtainable from each. The quantity of energy obtainable from any cell is the product of its average E.M.F., its average current, and the time that it supplies that current. The actual value obtained will differ considerably according to the conditions chosen.
The method adopted by the Post Office takes account of the differences in the dimensions of the various cells tested. It will be obvious that, given two cells of similar type but of different size, the larger cell will furnish a given current for a longer period than the smaller one. Not only so, but, at any period during the discharge, the larger cell is subjected to a less severe test, since its resources, i.e. the quantities of active material, are much greater.
The capacity of the various sizes of modified Leclanch^ cell in ampere-hours decreases, as with every other type of cell, as the current discharge rate is increased. The extent of the variation is indicated in the table in the case of the No. 1 cell.
The method of testing consists in discharging the cell
34
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36
for 5 hours per day, 6 days per week, through a CuS04 electrolytic cell at a mean rate corresponding to the size of the cell ( e.g . 50 m.a. for a No. 1 or a Y dry cell). The ampere hours are computed from the increase in the weight of the copper cathode of the electrolytic cell.
Contrary to the behaviour of Leclanch6 and other wet cells, however, the tendency of the ampere-hour capacity of the dry cell is to decrease as the discharge rate is decreased owing to the fact that with a small discharge rate the period of discharge must necessarily extend over long periods. The cells therefore tend to dry out, and this entails their rejection owing to high internal resist- ance before the elements can be fully utilized. There is therefore a discharge rate for dry cells at which they give maximum output. For, if the current be increased the output is decreased owing to polarization effects. This is indicated by the two results given in the case of each size of dry cell used by the Post Office.
Ampere-Hour Capacity of Cells.
(Cells discharged at rates given for 5 hours per day, six days per week, until E.M.F. has fallen to lv.)
|
Tyi« of <*11. |
Capacity in ampere-hours. , |
Discharge rate m.a. |
Type of cell. |
Capacity in ampere-hours. |
Discharge rate m.a. |
|
No. 0 |
120 |
100 |
No. 3 |
20 |
20 |
|
H 1 |
80 |
20 |
Dry Y |
40 |
60 |
|
” 1 |
76 |
40 |
Y |
42 |
42 |
|
» i ! |
66 |
80 |
Z |
140 |
100 |
|
„ i |
48 |
160 |
Z |
148 |
90 |
|
» i |
36 |
320 |
The internal resistance of a cell is only roughly pro- portionate to its size when the cell is of homogenous construction. In the case of the simple zinc-copper-dilute sulphuric acid cell, for example, the rule holds good, but in case of the Leclanche and dry cells an increase in the size of the cell means that, although the areas of the conduct- ing surfaces are increased, the distance between the zinc Md carbon plates is also increased, and the resistance
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36
TELEGRAPHY
therefore tends to remain uniform. The relationship between area and distance will be fully understood after consideration of the principles enunciated upon page 56.
The Post Office standard of maintenance is (i) a maximum resistance of 3« per cell for the No. 3 size, and 2" for other sizes and types inclusive of the Y to Z sizes of dry cell, and (ii) a minimum unit of 1 volt at any period of the normal discharge.
Three Methods of Joining-up Cells.
There are three ways in which cells may be arranged, firstly in series, secondly in parallel, and thirdly in parallel- series or multiple arc, this method being a combination of the first and second methods.
Cells in Series.
The series method consists in connecting the copper of the first cell to the zinc of the second cell, and connecting
iHHn
Fio. 12.— Cell* in aeriei
the copper of the second to the zinc of the third, leaving the latter’s copper pole free. The zinc of the first cell and the copper of the last cell form the poles of the battery. The conventional symbol universally employed to denote a battery consists of a long thin stroke to represent the positive pole of a cell and a short thick line or a short outlined oblong to represent the negative pole. Three cells, illustrated in Fig. 12, are joined up in series, and it will be observed that in this case the cells all tend to send their current in the same direction. Each cell
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37
therefore adds its pressure to that of the others, but, in so doing, also adds its own internal resistance. The total E.M.F. produced by a battery, consisting of a number of cells joined in series, is equal to the E.M.F. of one cell multiplied by the number of cells in series, whilst the total internal resistance is equal to the internal resistance of one cell multiplied by the number in series.
If the E.M.F. and internal resistance of each of the three cells shown in Fig. 12 is respectively 1 volt and 6 ohms the total E.M.F. of the battery will be 1x3 = 3 volts, and its internal resistance will be 6x3= 18".
Cells in Parallel.
The parallel method consists in joining all the positive poles together and similarly connecting all the negative poles. The circuit to be energized is then joined between the grouped positive and negative poles of the cells. In this case the pressures are not cumulative as in the series method. The total E.M.F. of the arrangement is the E.M.F. of one cell, but the total internal resistance is the internal resistance of one cell divided by the number in parallel. For instance, if the three cells shown in Fig. 13 each have
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TELEGRAPH r
an E.M.F. of one volt and an internal resistance of six ohms, the total E.M.F. and internal resistance of the arrangement will be respectively 1 volt and i. e. 2 ohms.
Cells in Multiple Arc.
The parallel-series or multiple-arc method of joining up cells consists in putting in parallel two or more batteries,
rnA/WW'^/W^ — I
Fia. 14. — Cell* in multiple arc.
each consisting of an equal number of cells joined in series. In Fig. 1 4 six cells have been connected up in multiple arc. The arrangement obviously consists of two batteries, each of three cells in series, connected in parallel. Using the same values as before for the E.M.F. and internal resist- ance ner cell, it will be seen that the total E.M.F. and total internal resistance of either of the three-cell batteries separately considered will be as before (Fig. 12), 3 volts and 18" respectively. The question now becomes — what will be the effect of putting two such batteries in parallel ? The rule given for cells in parallel may be applied to batteries in parallel, and the answer is therefore : —
Total E.M.F. = that of one battery, viz. 3 volts.
Total Internal resistance = that of one battery divided by the number of similar batteries in parallel, i.e.
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In all examples of the parallel-series type the total E. M.F. is equal to the E.M.F. per cell multiplied by the number in series, and the total internal resistance is equal to the internal resistance per cell multiplied by the number of cells in series and divided by the number of similar sets or rows in parallel. Had there been six rows in the above example then the E.M.F. would have been 3 volts as before, but the internal resistance would have been reduced to 3".
In practical telegraphy there are but few cases where it is necessary to join batteries in parallel, and the term battery is usually employed to denote cells in series. For instance a “ 5-cell Daniell ” means five cells joined up in series, and “ two 5-cell Daniells in parallel ” would there- fore mean two batteries, consisting of five cells in series each, connected in parallel, i. e . 2 rows in parallel, each row consisting of five cells in series.
Method in which to join up Cells in different
CIRCUMSTANCES.*
The three methods of joining up cells each have their par- ticular utility, and although the parallel method is never, and the parallel series method but seldom, used in practical telegraphy, it is still desirable to state briefly the conditions under which each arrangement should be employed.
The maximum current which can be obtained from any particular cell is reached when the cell is short-circuited and is equal to its E.M.F. divided by its internal resistance. Similarly if a thousand cells be placed in series and short- circuited the maximum current will be the same, for whilst the E.M.F. has been increased a thousand-fold the internal resistance has been similarly increased.
If it is required to obtain a larger current from the cells they must be placed in parallel. Every cell which is added increases the current, for although the E.M.F. remains the same, the internal resistance is reduced by every fresh cell. If, now, the current produced by a number of cells joined up in series and flowing through a circuit
* This snMect is dealt with exhaustively in Dunton’s Treatise on the grouping of Electric Cells (Spon).
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TELEGRAPHY
of enormously high resistance is considered it will at once be seen that the internal resistance of the cells is insig- nificant in comparison with the enormous external resist- ance. Each cell added in series will therefore increase the current flowing in the circuit. Upon the other hand, the only effect of joining cells in parallel is to reduce the total internal resistance, and this is of no consequence in comparison with the external resistance. The E.M.F. re- mains the same, and consequently the addition of cells in parallel means no practical increase in the current available.
It will now be clear that, for external resistances large in comparison with that of the cell, the cells should be joined in series, whilst for a low resistance the cells should be joined in parallel, i. e. in order to obtain the maximum current from the minimum number of cells.
Between the extremes already discussed come the cases where parallel series arrangements are necessary. The rule, which may be deduced from Ohm’s law, relating to this case is that the arrangement of cells which gives an internal resistance most nearly approximating to the ex- ternal resistance will furnish the maximum current.* To give a numerical example : — Suppose that it is desired to know how best to join up forty cells, each having an E.M.F. of 2 volts and an internal resistance of 12*5" to a circuit having a resistance of 20".
The forty cells may be joined up in the following ways : — (a) all in parallel, (6) all in series, (c) two rows in parallel each of 20 in series, (d) four rows in parallel each of 10 in series, (e) five rows in parallel each of 8 in series, (/) eight rows in parallel each of 5 in series.
With the arrangement (e) the internal resistance of the battery is the same as the external resistance, viz. 20", and this gives the maximum current, viz. 400 m.a. The currents for each of the arrangements are (a) 98 5 m.a., (6) 153*8 m.a., (c) 275*8, (d) 390*2, (e) 400 m.a., (/) 359*6 m.a.
* The arrangement which produces the maximum current is that in which the internal resistance is geometrically ( not arithmetically) nearest to the external resistance. For example, two arrangements having internal resistances of 10<*> and 40« respectively would produce equal currents through an external resistance of 20«>, because 10« : 20*» :: 20« : 40*.
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From that which has been said it follows that the maximum amount of power obtainable from any battery is greatest when the external resistance is equal to the internal resistance. When this is the case the efficiency is 50 °/0> because there is as much energy lost in overcoming the internal resistance of the battery as is available in the external circuit.
With a given number of cells the maximum current is obtained through a given external resistance when the number of cells in series (n) is equal to the square root of the total number of cells (. N ) multiplied by the external resistance ( R ) divided by the internal resistance per cell (r).
The result obtained in the previous example may be found by application of this formula thus : —
/ 40 X 20 . — >77 — q .
a/ — r r ~ — = J 64 = 8 in senes.
y l zo
The number of rows is obtained by dividing the total number of cells by the number per row, i . e. by the number in series.
When a fractional answer is obtained the nearest whole number which will give a whole number when divided into the total number of cells must be chosen.
Example. — How should sixty cells, having an E.M.F. of l '5 volts and an internal resistance of 2" per cell be arranged so as to provide the maximum possible current through an external resistance of *55" ?
<J — 60Xj5o = ^^5 = 4.06
The whole number which will divide into 60 and give a whole number as quotient are 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60. 4*06 is nearer to 4 than to any other of
these numbers, and the best arrangement is therefore fifteen rows each of four cells in series.
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TELEGRAPHY
Cells wrongly joined up and Special Arrangements.
In each of the foregoing cases the cells have been cor- rectly joined up. It will now be well to consider one or two simple cases of wrong connection. If, in joining a number of cells in series, some of the cells are reversed, the total E.M.F. will be reduced whilst the total internal resistance will be unaffected. The E.M.F. will be equal to the E.M.F. of the larger number acting in one direction, less the E.M.F. of the smaller number acting in the oppo- site direction. Where the numbers are equal the E.M.F.s will balance and no current will result ; that is, of course, supposing that the E.M.F.s per cell are equal.
Example. — Ten cells joined in series, E.M.F. 1 volt and internal resistance 5" per cell, are connected to a resistance of 50". What current will be produced if two of the cells are reversed ?
E.M.F. of larger number of cells = 8T
„ of lesser „ „ = 2^
Total E.M.F. of combination = 6T
6V ~~
Current = ■ , ^ = *06 ampere.
5U + 5U
In certain cases a combination of parallel and series methods of joining up might be adopted, as, for instance, where a number of small cells are used in conjunction with a number of cells of larger size.
Example . — What will be the total E.M.F. and internal resistance produced by joining two 5-cell Large Daniells in series with two 10-cell Small Daniell batteries placed in parallel? E.M.F. 1 volt per cell. Internal resistance Large 5" Small 10" per cell.
Total E.M.F. of two 10-cell Small Daniells in parallel = 10*
„ „ of two 5-cell Large Daniells in series = 10v
Total E.M.F. of above in series = 20v Internal resistance of Large Daniells = 5" X 10 = 50“
„ „ Small Daniells = 10“ * 10=50.
Total internal resistance of above in series = 100".
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In other words this combination is equivalent to four 5-cell Large Daniell batteries joined in series.
In the above case the batteries placed in parallel had ( the same E.M.F. Where this is not the case, the battery of higher E.M.F. drives a current through the battery of lower E.M.F. Such an arrangement is most inefficient and is never intentionally used in practice, although it occasionally occurs by accident.
A simple rule for calculating the current due to such an arrangement is that the two batteries are equivalent, as regards the external circuit, to a new battery whose E.M.F. equals the E.M.F. of one of them multiplied by the resist- ance of the other plus the E.M.F. of the latter multiplied by the resistance of the former, the sum being divided by the sum of their internal resistances, whilst the internal resistance of this new battery is equal to the joint resistance of the two batteries.*
Number of Cells Required to Furnish a Given Current.
It is frequently necessary to find the number of cells which will be required to furnish a given current through a certain external resistance. If the internal resistance of the cells required is negligible — as in the case of secondary cells— the required number of cells is obtained by ascer- taining the voltage necessary and then dividing it by the B.M.F. per cell.
* The value of the current C in the external circuit is also given by the following equation : —
C= fl *2 ±_«2*1
n *2 + r, rs -f r2 rB
*here = E.M.F. of first cell.
= „ second cell
rx — Internal resistance of first cell. r2= „ ,, second cell,
r, = External resistance.
If the two cells are joined up so that the cells combine together in serie* the numerator of the equation should be altered to ex r2 — e% rv From this, it follows that when no current flows through the external circuit the ratio of the E.M.F.S of the two cells is equal to the ratio of tkir internal resistances.
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TELEGRAPHY
Example. — How many secondary cells will be required to furnish a current of 20 m.a. through a circuit of 1536«? Note. — E.M F. per cell should be taken as 2 volts.
Current X resistance = E.M.F. required 02 x 1536 = 30*72 volts.
Total E.M.F. XT , r „
n = Number of cells
E.M.F. per cell
Q0*72
— 2 = 15*36, i. e. 16 cells.
The answer 15*36 is not practical because a special cell having an E M.F. of *36 of the E.M.F, of 2 volts would have to be designed, and therefore the smallest whole number in excess of the result is taken.
In the case of primary cells the internal resistance cannot usually be ignored and the procedure shown above cannot be followed, because the total resistance of the circuit is not known until the number of cells in circuit is ascertained. The calculation of the current through a circuit connected to a battery consisting of a number of cells in series has been shown on page 40. By the aid of a little elementary algebra the following rule can be readily obtained :* —
N umber of cells =
External resistance
E.M.F. per cell T . i n
, — Internal res.percell, Current required r
i. e. divide the E.M.F. per cell by the current required (in amperes), and from this deduct the internal resistance per cell. The number of cells required is then equal to the ex- ternal resistance divided by the result of the first operation.
Example. — How many cells E.M.F. lv per cell and in- ternal resistance 10" per cell will be required to provide a current of 15 m.a. through a resistance of 1200*. ?
1200_ = 21.lg) { c 22 cella> •0I5-10
ns
* nr -\-R
= C
n
R
e
C~
r
where n = number oi cells in series,
r = internal res. per cell, R = external res., and C = current in amperes.
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The result obtained from wrongly using the simplified formula applicable to cases where the internal resistance is negligible would have been 18 cells. The same remarks apply to the fractional result as before, save that in this case the internal resistance of the special cell would also have to be proportionally less. The current produced by 22 cells will be slightly in excess of 15 m.a., whilst that supplied by 21 cells would be very slightly less than the specified value.
A minimum value for the E.M.F. and a maximum value for the internal resistance of each type of cell was given in Chapter I. A cell having these values is not considered to be faulty, and although the average values given by an efficiently maintained battery would be far better than these, it is clearly necessary to recognize that the worst values may obtain. In order that the specified current shall always be produced upon a telegraph circuit, the minimum value of the E.M.F. per cell and the maximum value of the internal resistance per cell are always taken in working out the batteiy power.
Example. — What power will be required to work a double current set through a line 100 miles of 100-lb. copper line?
Resistance of wire = 878“
„ „ the two earths = 20*
„ „ two galvanometers = 60*
„ „ one relay = 200“
Total external resistance = 1158*
Leclanche No. 1 cells, E.M.F. 1T, internal resistance 2* per cell, are employed. 14 m.a. required.
1158
Number of cells required = = 16*7
— 1 2
•014
or 17 cells.
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46
Special Cases.
The internal resistance of the battery employed upon telegraph circuits is nearly always much less than that of the external circuit, and therefore the cells are generally arranged in simple series. In such cases the formula just given is always applicable, and the result obtained may be accepted without question. Where, however, the internal resistance approaches or approximates to that of the external circuit a certain amount of caution is necessary. This condition is fortunately indicated by the formula. If the E.M.F. per cell divided by the current is not at least twice the value of the internal resistance per cell, then a multiple-series arrangement is necessary. If the internal resistance is greater than the first-named quantity, the current cannot be provided by cells in simple series. The maximum current is obtained from a cell when it is short- circuited, and this current is the same as that obtained from, say, a thousand cells placed in series and short- circuited.
The internal resistance of a number of cells in multiple arc is : —
Internal resistance per cell Number of rows
X Number in series.
(This is identically the same as the statement on page 39.)
A battery consisting of two rows of cells in parallel is equivalent to one battery (in simple series), having the same number of cells as one row of the former, but having an internal resistance equal to half that of the former per cell.
This forms the key to the solution of such a problem as the following : —
Example. — How many cells having an E.M.F. of two volts and an internal resistance of 10" per cell will be required to furnish a current of 400 m.a. through an external resistance of 18" ?
Simple series : —
18 18
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Denominator negative, therefore simple series will not meet the case.
Two rows : —
g ^ = Infinity.
Three rows : —
1 8
-= = 10*8, i.e. 11 cells.
5 — 3$
Note . — E.M.F.-r current is less than twice the internal resistance.
Four rows : —
1 ft
= x-r = 7’2, i. e. 8 cells.
5 — 2$
Five rows : —
= 6 cells.
O A
Six rows : —
18
-= 5*4, i. e. 6 cells.
5 — If
The total number of cells required is as follows : —
Three rows .... 33
Four rows .... 32
Five rows .... 30 Six rows .... 36
The arrangement with five rows gives the smallest num- ber of cells, and is therefore to be preferred. Where two different arrangements give the same result it is well to remember that the resistance of a primary battery will rise towards the end of its discharge, and therefore the arrange- ment with the lower value of internal resistance should be chosen. It may also be noted that the larger the number of rows the smaller is the current provided by each cell.
PART II.— JOINT RESISTANCE AND DIVISION OF CURRENT.
The total resistance offered by circuits or conductors placed in series is equal to the sum of their separate
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TELEGRAPHY
resistances. For instance, the total resistance of the conductors depicted in Fig. 15 is 1G23".
£0" IJ7J* 3<T
. -VWWVW
Fio. 16. — Resistances in series.
Before dealing with resistances in parallel it is necessary to define some of the important terms which are commonly employed.
Conductance has exactly the opposite meaning to resist- ance, and may be defined as the inverse of resistance. From this definition it follows that
Conductance = =r — —
Resistance
1
and Resistance =
Conductance
The unit of resistance is the “ ohm,” and that of con- ductance is the “mho,” which is “ohm” written back- wards. A circuit having a resistance of one ohm has a conductance of one mho, so that the two units themselves have the same numerical value in this case. A circuit having a resistance of 10" has a conductance of TV mho, whilst a circuit having a resistance of -jV" would have a conductance of 10 mhos.
This definition of conductance is extremely useful in making clear the methods of finding the resistance of a number of paths in parallel and the proportion in which a given value of current will divide amongst them.
It has been found that the total conductance of a number of paths in parallel is equal to the sum of their separate conductances. The joint resistance or total resistance offered by the combination of paths is therefore the re- ciprocal of their total conductance, which latter is obtained by adding together the conductance of each path.
An example of the applicat ion of these rules is appended :
What is the joint resistance of four paths having resistances of respectively 2", 3", 4", and 5" placed in parallel {
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Total conductance = sum of separate conductances
i* n =l + J + i+ i mh°*
1
Resistance
Joint resistance =
Conductance
1
Total conductance
1
. 60 ,
= ^ = *-=r ohm. 77
l
77
60
i+i+i+i
ohm
In the case of a number of paths of equal resistance placed in parallel inspection of the previous example will at once reveal the fact that their joint resistance is equal to the resistance of one of them divided by the number of paths in parallel. For instance the joint resistance of ten 1000"
paths placed in parallel is -yjj- = 100".
Another very useful rule may, with the aid of a little simple algebra, be deduced from the rule on p. 48. It is that the resistance of two 'paths in parallel is equal to their product divided by their sum . An example of its application is given below : —
What is the joint resistance of a 50" path in parallel with a 150" path ?
T . Product 50 X 150 7500
Joint res. = gum = goTTsO = 200
= 37*5".
A formula may be deduced for three, four, five, or any number of paths.*
h problem which occasionally crops up in practice is
* The joint resist a nee of n paths a«, &«, . . .* in parallel
__axbxcxd (n — 1 ) X n
a+ 6+ c + d n-1 n
vhere S i> the product of the resistances of the n paths and foims the uioeratoi of the formula.
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20 X 30
Joint resistance of 20" and 30" paths = 20 + 30 =
Total resistance of upper path = 18 + 12 + 70 = 100" Resistance of whole combination = ^
= 66§".
From the extensions of Ohm’s law known as KirchhofTs laws it can readily be shown that a current divides between a number of paths in parallel in direct proportion to their respective conductances . An example of the application of this rule is given below : —
A current of 10 amperes divides between four paths in parallel whose resistances are respectively 3", 4", 5" and 6". What is the value of the current in each path ?
10 AMPERES
10 AMPERES
B
1 - ■ 1 ■rmywTvy" “ " ^ J
'
Fio. 17.— Division of current between paths in parallel.
The conditions of the problem are shown in Fig. 17. Resistances of paths 3“ 4" 5" 6"
Conductances of paths i i i i
The 10 amperes divide as f : | : £ : &
Bringing to common denominator £# : w : ^ :
The 10 amperes divide as 20 : 15 : 12 : 10
if the total current splits into 20+15 + 12 + 10 = 57 parts,
the current through each path is respectively \h n of 10 amperes.
i. c. 3|+ 2ff, 2^, l£f amperes.
Obviously if this result is correct the sum of the currents should be 10 amperes, and by trial it will be found to be sa The current in the 6" path should be half that in
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the 3" path. These points enable one rapidly to test the accuracy of the arithmetic involved.
A useful rule, the accuracy of which may readily be checked by the above methods, is that by which the current through two paths A and B in parallel may be at once written down without calculation. The current through A B
is ^ g of the total current, and that through B is A
^ g of the total current, e. g.
A current of 10 amperes divides between two paths of 2" and 3" placed in parallel. What is the current in each ?
o
In the 2" path — r
It -f- o
2
In the 3" path 0 --a
I o
of 10 amps = 6 amperes, of 10 amps = 4 amperes.
It is sometimes necessary to deduce the resistance of a path of unknown resistance, placed in parallel with another of known resistance, from a knowledge of the proportion in which a current divides between them. It has been previously pointed out that the current splits in direct proportion to the conductances of the paths. The converse of this is obviously true, viz. that the conductances of paths in parallel are proportional to the currents in each. An example is given below : —
The currents in two paths in parallel are respectively 10 amperes and 8 amperes. If the resistance of the higher path is 40", what is the resistance of the other ?
Currents in the paths respectively 10 and 8 amperes Conductances of the paths 10 : 8
The conductance of the better path = ~ Conductance of other path = Conductance of better path =
1
“ 32
of the other.
mho
Resistance of better path = 32".
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Another method of working this problem is given in order to clearly demonstrate a useful fact in connection with circuits in parallel. Referring again to Fig. 17 ; the difference of potential between A and B can have but one value, since were this not the case either the point A or the point B w'ould have two different potentials at one time. This is clearly impossible, hence the current in each path multiplied by its resistance gives the difference of potential between its ends, and this is the same for all the paths. Practically, this statement means that Ohm’s law may be applied to a part of a circuit. Had there been batteries inserted in the pat 1 is the question would have been a little more complicated.
The working of the previous example by means of the facts stated above is appended.
Resistance of highest path 40"
Current in „ „ 8 amperes.
Difference of potential between its ends 40 x 8 = 320 volts.
R =
E . C ’ *
320
Resistance of other path = 32".
The current sent through any circuit by a battery is equal to its E.M.F. divided by ti e total resistance of the circuit. This total resistance is made up of the internal resistance of the battery and the external resistance. For instance, a battery having an E.M.F. of 20v and an internal resistance of 100" applied to a circuit of 400"
20
will produce a current of |qq _|_ ^qq or 40 m.a. Where
two or more paths are joined in parallel to a battery the external resistance is equal to their joint resistance, as in the following example : —
Example, — What current will be produced in each of four circuits of respectively 20", 30", 100" and 150" resist- ance joined in parallel to three five-cell Large Daniell batteries also joined in parallel ? E.M.F. per cell one volt. Internal resistance 6" per cell.
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E.M.F. of battery =1T x 5 = 5 volts.
6x5
Internal resistance = — Q — = 10**
o
Resistances of paths 20" 30" 100" 150"
Conductances of paths ^ rh
Bringing to common denominator ± ™ 3 2
111 1
11517 T5U
Total conductance =
3U0 300 300 300 15 + 10 + 3 + 2_ 30 300 “ 300
Joint resistance
= ^=10- 30
5 5
Total current = ^ = 9q = 250 m.a.
The current splits as 15 : 10 : 3 : 2 if 250 m.a. splits into 15 + 10 + 3 + 2 = 30 parts
the current through each path is respectively J*-,
oU oO oO
i. e. 125 m.a., 83 3 m.a., 25 m.a., 16*7 m.a.
Whilst dealing with batteries and circuits it will perhaps be well to deduce the relations which exist between the E.M.F. of a battery and the difference of potential between its terminals when connected to a completed circuit. This may best be done by considering a definite case. A bat- tery having an E.M.F. of 2 volts and an internal resistance of 12" is connected to a circuit having a resistance of 8"
2
(Fig. 18). The current through the circuit is =
ampere The difference of potential between the ends of the external resistance is, by Ohm’s law, *1x8" = *8 volt. This is a difference of potential observable at the terminals of the cell when the circuit is closed. The difference between this value and that of the E.M.F. of the battery on open circuit is the E.M.F. which is lost in traversing the resistance of the battery. The current inside the battery is obviously the same as that in the external circuit, viz. T ampere. Hence the value of the E.M.F.
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taken up in the battery itself is *1 x 12" = 12 volts, which is the value deduced from the difference between the E.M.F. on open and closed circuit. In any case of this character the whole of the E.M.F. of the cell must be accounted for.
From a knowledge of the E.M.F. of a battery upon open circuit and the differences of potential across its terminal
5*
when connected by a known resistance, the value of its internal resistance can readily be calculated. This is the principle employed in one method of measuring internal resistance. A numerical example is appended : —
Example. — The E.M.F. of a battery upon open circuit is 30 volts, but when the circuit is closed through an external resistance of 70" the difference of potential falls to 23 volts. What is its internal resistance ?
Method I.
E.M.F. of battery = 30v
P.D. across 70" = 23v
E.M.F. lost in battery itself = 30 — 23 = 7T Current in battery and in 70" circuit is the same.
By Ohm’s law 23 : 7 : : 70 : Internal res.
Internal res.= x 70
213" = approx.
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Method II.
E.M.F. of battery = 30v
P.D. across 70" = 23v
E.M.F. lost in battery itself = 30 — 23 = 7T
PD 23
Current through 70" = ^ ampere
Internal resistance of battery =
E.M.F. lost Current
7
23
70
= 21*3" approx.
PART III.— THE RESISTANCE OF WIRES OF VARYING DIMENSIONS.
It has been found by experiment that the resistance which any conductor offers to an electric current depends upon three factors, viz. : —
1. Its dimensions.
2. Its composition.
3. Its temperature.
If the resistance of any material of known dimensions has a certain value at a particular temperature, then it is a matter of ease to deduce the value of the resistance which will be offered by that material when given different di- mensions at the same temperature. The changes produced by altering the temperature have been carefully determined for all the substances in common use for electrical purposes. It will therefore be seen that if the resistance of any substance of known dimensions is stated for any given temperature the determination of its resistance when made into any particular form is merely a matter of arithmetic.
Experiment proves that the resistance of a conductor of uniform gauge is directly proportional to its length and inversely proportional to its sectional area . It is, of course, assumed that the temperature and composition do not vary. This condition will apply to all the problems given unless otherwise specified.
In order to shorten and simplify the various proportions
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stated the following letters will be employed to denote the values of the resistances and dimensions stated opposite them —
i, to represent the length of the first wire.
^ „ „ „ „ second wire.
|
<*1 |
n |
99 |
sectional area of the first wire. |
||
|
a. |
>9 |
99 |
>» 99 |
99 |
second wire. |
|
<*; |
99 |
99 |
diameter „ |
99 |
first wire. |
|
d* |
99 |
99 |
99 99 |
99 |
second wire. |
|
99 |
99 |
total weight |
99 |
first wire. |
|
|
U?. |
»» |
99 |
99 99 |
99 |
second wire. |
|
99 |
99 |
resistance |
99 |
first wire. |
|
|
Rt |
99 |
99 |
99 |
99 |
second wire. |
Example 1. — If the resistance of 10 miles of wire is 89", what is the resistance of 7 miles of similar wire?
t. e.
h
10
R.
7 x 10
89
89 = 62-3“.
R,
Example 2. — Two wires of similar gauge and material offer resistances of 40" and 28". If the former is 360 yards long, what is the length of the second wire ?
i. e.
R,
40
h =
Xt
28
28 x 360 40
360
h
= 252 yards.
Example 3. — Two wires of equal length have sectional areas of '12 square inch and '15 square inch respectively. If the resistance of the smaller wire is 10“ what is the resistance of the larger ?
*. e.
a 2 •15
•12
12 x 15
10
10
X,
= 8".
Given both resistances and the area of one wire the area of the second would be found in similar fashion.
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TELEGRAPHY
Example 4. — A wire 12 miles long having a sectional area of *021 square inch has a resistance of 7*5 ohms. What will be the resistance of a similar wire 18 miles long having a sectional area of *023 square inch ?
also
i. c.
h : h : : R,
a2 : al : : Rx IjXfl, : l2 x al
12 x 023 : 18 x 021
18 x *021 x 7*5 12 x *023
R»
b:
7-5
= 10 27“.
The sectional area of a round wire is equal to the square of its diameter multiplied by *7854, hence it will be obvious that the resistance of a conductor of uniform gauge is proportional to its length and inversely proportional to the square of its diameter.
Examples of the application of this rule are appended.
Example 5. — What will be the resistance of a wire 26 yards long having a diameter of 33 mils if the resistance of a wire of the same material 52 miles long with a diameter of *01 inch has a resistance of 32“ ?
Note. — In comparing either two lengths or two diameters the units of each dimension chosen should be the same, but it is not necessary that all four quantities should be in the same unit. A mil is one-thousandth of one inch.
*01 inch = 10 mils. l2 i lx : : R2 • R\ and (dxf : (rf,)2 : : R> : Rx
U x (dxf : lx x\d2)2 : : R2 : Rx
(52 x 17C0) x S3*2 : 26 x 102 : : 32 : Rx
P 26 x 102 x J12
•* Kl~ 52' x 1760 X 332
= *0008348 or 834*8 microhms.
In problems where the lengths of the two wires are equal the proportion reduces to: —
W2 : W : : R, : Rr
Example 6. — A wire 30 miles long, 40 mils in diameter has a resistance of 1000*. What is the length of a wire
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69
of the same material having a resistance of 200" and a diameter of 25 mils ?
».e.
1000
200
la X 402 =
: lx x ( (l>) 2 : l2 X
: 30 x 252 : l2 x 200 x 30 X 252 1000
. 200 X 30 X 25*
<2 — 1000 X 40-
= 2'344 miles approx.
(<*,>*
40*
20 miles What is
Example 7. — The resistance of an iron wire long, having a diameter of 171 mils is 266-4". the diameter of a wire 3 miles long having a resistance of 79-92- ?
: : l2 X (dxf : lx
: 3 X 17 l2 : 20 266 4 X 3 X 171-
i.e. 7992
R,
: Rx 266-4
(d,)-
(d,r2
20 X (d2f
79-92 _ 266-4 x 3 X 1712 W — 79-92 x 20
d2 = s/ 14620 = 121 mils approx.
Example 8. — What is the diameter of a wire 7 miles long having the same resistance as a wire 20 miles long which has a diameter of 60 mils ?
f
rI
|
and |
(41 |
: h : W* |
Rx : Rx : |
|
Since |
h x w |
: l2 x (dxf : |
Rx : |
|
i?i = R9 |
|||
|
then |
K |
x (d2y = i2 x (dxf |
i. e.
W =
7 x 60* = 20 X (dx)* 7 x 60*
and
20
xW
20
= 35 *5 mils approx.
Where the diameter of one wire and the sectional area of another is given it is obviously necessary to reduce both to the same dimension. It has been previously stated that
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60
TELEGRAPHY
the area of a circle is equal to *7854 times the square of its diameter. An example in which these complications arise is given below : —
Example 9. — A wire 17 miles long, diameter 171 mils has a resistance of 230®. What is the resistance of a similar wire 152 yards long having a sectional area of *02 square inch ?
Note. — As in the previous problem both lengths must be in the same units. A similar remark also applies to the diameters. #
Preliminary calculations .
The area of a circle = |x (diameter)*
n = 31416 /. x= '7864.
4
Diameter of wire = 171 mils = *171 inch.
Area of wire *171 inch in diameter = *7854 X *171* = *023 square inch.
As in example 4.
lY X a0 : l2X al : : : R»
i. e. 17 X 1760 x 02 : 152 X 023 : : 230 : R2 _ 152 X 023 X 230 * • 2 “ 17 X 1760" x 02
The rules given for the comparison of the resistances of wires of differing dimensions are merely deductions from the experimentally determined equation : —
a
where l = length of conductor (inches or cms.).
a = sectional area of conductor (inches or cms.).
S = specific resistance or resistivity, as it is now termed (cubic inches or c. cms.).
R = resistance of conductor in ohms.
If l and a are made unity then R is equal to St hence resistivity of any substance is the resistance between the opposite faces of a unit cube of that material Since both
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CIRCUITS AND CONDUCTORS
61
inches and centimetres are in daily use as units it is necessary to specify the unit employed. The resistivity of a substance is therefore defined as so many microhms per cubic inch or per cubic centimetre, according to the unit chosen. It is scarcely necessary to remark that l, a, and 8 must all be in either centimetres or inches and not a compound of both.
The resistivities of a few materials, taken from the observations of Dewar and Fleming, are given below : —
|
Resistivity at 0* C. |
||
|
Material. |
Microhms per cubic inch. |
Microhms per cubic centimetre. |
|
8ilver (electrolytic) |
•67795 |
1*468 |
|
Copper* „ |
*61457 |
1*561 |
|
*86496 |
2*197 |
|
|
Aluminium |
1*049 |
2*665 |
|
Zinc .... |
2*264*2 |
5*751 |
|
Nickel (electrolytic) . |
2 7303 |
6 935 |
|
Iron ... |
3*5689 |
9*065 |
|
Tin (pressed) |
5*137 |
13*048 |
|
Lead (pressed) . |
8*0236 |
20-38 |
|
Mercury |
37*04 |
94 07 |
|
German silver . |
8 to 12 |
20 to 30 |
|
Graphite Saturated solution of |
118 to 157 |
300 to 400 |
|
sulphate of copper . Saturated solution of |
11*535 X 108 |
29 3 X 108 |
|
sulphate of zinc |
13*268 X 108 |
33 7 X 108 |
Example 10. — What is the resistance of one mile of
* Modern tables of copper resistance are based on the following values — Rea. of metre-gramme of hard copper at 60° F = -1539"
,, ,, ,, soft „ = T508»
1 cubic foot of copper weighs 655 lbs. or 8*89 grammes per cubic centi- metre at 60° F. Specific gravity 8*90.
The resistance of soft copper is *66783 microhm per cubic inch, and 1*6963 microhm per cubic centimetre, whilst the corresponding values for hard copper are respectively *68154 and 1*73116 microhms.
The resistivity of pure iron is 10 616 microhms j>er cubic centimetre. One mile of pure iron wire having a resistance of one ohm weighs 4656 lbs., whilst an on m -mile of commercial wire should not weigh more than 5328 lbs. (See page 64.)
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TELEGRAPHY
copper wire 112 mils in diameter, given the resistivity as •681327 microhms per cubic inch ?
R =
(1760 X 36) X *681327 . ,
•' /.i Vfuo microhms
•7854 X (112)2 = 4,382,000 microhms approx. = 4-382“.
It may also be well to note that the statement upon page 60 may be written in the following form : —
Specific resistance (per cubic __ Res . in ohms x area (inches orcms.) inch or per cubic era.) Length (inches or cms.)
All quantities must be in inches or all in centimetres.
An example of the application of these facts is appended.
Example 1 1 . — Compare the specific resistances of iron and copper, given that 1 mile of iron wire 171 mils in diameter has a resistance of 13*32 ohms, whilst a mile of copper wire having a diameter of 97 mils has a resistance of 5*855 ohms.
Specific res. of iron per cub. in. =
13 32 X ( 1712 x 7854)
1760 x 36 = 4 829 microhms approx. 5 855 x (0972 X 7854) Specific res. of copper per cub. in. = 1760 x_36 ~~
= *6829 microhms approx.
Answer.
or
4-828
7*07
•6829
This may also be expressed by the statement that the iron has a conductivity equal to 14*14% of that of the copper.
There is still another way in which the gauge of a wire may be specified, and this is by stating its weight per unit length. This method is adopted by the Department, and it will therefore be necessary to consider the relations between the length, weight and resistance of a wire.
The weight of a wire of uniform section is directly proportional to its cubic contents, i.e. to its length multiplied by its sectional area. It has already been stated that the resistance of a wire is directly propor-
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CIRCUITS AND CONDUCTORS
63
tional to its length divided by the square of its diameter. If both the numerator and denominator of a fraction are multiplied by the same quantity the value of the fraction is unaltered, therefore the relation may be re-stated thus : — the resistance of a wire varies directly as the square of its length, and inversely as the product of its length and its diameter squared. The latter quantity is directly pro- portional to its weight, hence the rule becomes: — the resistance of a conductor of uniform gauge is directly proportional to the square of its length and inversely as its total weight .
If two wires of the same total weight are respectively one and two yards long, then their resistances will be as one is to four. Not only is the length of wire greater in the second case, but its gauge is less since it is obvious that the same quantity of metal is spread over two yards instead of one.
An example of the application of the above rule is appended : —
Example 12. — A wire 80 yards long weighing 30 lbs. has a resistance of 2". What will be the resistance of a similar wire 60 yards long weighing only 12 lbs. ?
When applying these rules care must be taken to express the weights of both wires as total weights. As will be shown later, the weight per mile specifies the gauge of the conductor, and its resistance is therefore proportional to the simple length.
Example 13. — A wire 1500 yards long weighing 300 lbs. per mile has a resistance of 3". What resistance will be offered by a wire of similar material 80 yards long having a total weight of 1 cwt. ?
Total weight of 1500 yards of wire weighing 300 lbs.
per mile
1500 X 300 1760
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64
TELEGRAPHY
(lx? : (l2f :: R x and w2 : wx : : Rx
(Zj)2 X w2 : (/2)2 X Wj :
15002 X 112 : 802 X
802 X
1500 X 300 1760
1500 X 300 1760
15002 X 112
R2
Rx :
: : 3 : R2
= *01948"
The weight of a wire of given length and material is proportional to its sectional area. It will therefore be evident that the rule given upon page 56 may also be written “ the resistance of a conductor of uniform gauge varies directly as its length and inversely as its weight per mile .” The application of the rule is so obvious in view of examples 1 to 4 that no illustrations should be necessary.
In practice the various sizes of wire are named by their weights per mile. For instance, an iron wire weighing 400 lbs. per mile is termed a “ 400-lb. iron wire.” As the resistance per mile of any particular kind of wire is inversely proportional to its weight per mile it will there- fore seem that the two quantities when multiplied together will always give the same result. Hence by remembering this number for iron and for copper the resistance of all the various sizes of wire used by the Department may be memorized. The number is 5328 for iron and 878*73 for copper wire.
The resistance per mile of a 400-lb. iron wire is there- ^Ore"400_== a 200-lb. iron wire similarly ls~2oo =
26*64", i. e. twice the resistance of the former.
87873
The resistance of a 100-lb. copper wire is =878*73"
per mile, and of a 150-lb. wire
878*73
150
= 5 8582" per mile.
The copper wire of commerce is not chemically pure, and the presence of impurities increases its resistance. Instead of defining the specific resistance per cubic inch, a con-
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CIRCUITS AND CONDUCTORS
66
ductivity of 99 °/ of that of pure copper is often specified.
From either the specific resistance per cubic centimetre or per cubic inch the resistance of any wire of that material may be calculated. In the same way, from the resistance of a foot of wire weighing one grain similar information may be deduced. This latter value is perhaps more useful in the case of conductors whose gauges are specified by their weights per mile.
The resistance of a foot-grain of pure hard-drawn copper wire is *22064“ and of pure iron 1169“ at 60° F.
The corresponding resistivity formula is : —
W
where l = length in feet
W = resistance of one foot of wire weighing one grain (7000 grains = 1 lb.) w = total weight in grains.
Example 14. — Find the resistance of a copper wire 1 mile long weighing 100 lbs.
R (1760 X 3)2 X 22064
K ~ 100 X 7000
= 8 7873 ohms.
There is one other class of problem which is occasionally met with. In this the weight and diameter of a wire are specified. The relation is that the resistance varies directly fl# die total weight , and inversely as the fourth power of the diameter *
* w is proportional to l X a
.* . I is proportional to —
A
Sow R is proportional to
Substituting for 2,
w
R is proportional to ~ = ~i * iectional area ia proportional to d2,
.*. £ is proportional to -g- •
Hso M)
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TELEGRAPHY
00
Example 15. — Two wires weighing 80 lbs. and 60 lbs. have diameters respectively 100 and 40 mils. If the resistance of the thicker wire is 10“ what is the resistance of the other ?
i.e
w\
w*
wl X (dj)4
80 X 404
• R - 60 X
• • —
Wo
w
W.2 X (rf,)4
4
4
Bi
10
60 x 1004 1004 x 10
= 293“ approx.
80 X 404
R
Example 16. — Two wires having resistances of 256“ and 81“ weigh respectively 10 lbs. and 25 lbs. If the diameter of the first wire is 30 mils, what is the diameter of the second ?
k
R2
81
4
256
10 x (di)*=~'J~
w2 : to,
W : (e**)4
w2 X (d,)4 :
25 X 304 :
256 X 25 x
304
(d2)* =
81
256 X 25 x 81 x 10
304
w, x (d2)* 10 X (rf2)4
d _ v/256 x 25 x 304 81 X 10
= 50*3 mils approx.
Application of Laws to Cells.
A consideration of the laws governing the resistance of wires of varying dimensions makes it obvious why a large cell has a lower internal resistance than a smaller one of the same type. The larger the plates the broader is the liquid between them as compared with the intervening distance. The former corresponds to the sectional area of the wire.
Effect of Temperature upon Resistance.
The temperature was assumed to be the same in all the problems dealt with, and it is therefore necessary that the
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C1RCU1T8 AND CONDUCTORS
67
effect of varying the temperature should now be considered. In the case of all metals the resistance rises as the tempera- ture is increased. In the case of copper wire the resistance increases about *428 per cent, per degree for each degree Centigrade, or *238 per cent, for each degree Fahrenheit. A more accurate formula is : —
Ri = + 0023708 X (t - 32) + 00000034548 X (t - 32)*}
where Rt = Resistance at 41 1° ” F.
*» = „ , , 32° F .
(The numerical coefficients were determined experi- mentally.)
Example 17. — What is the resistance of a copper con- ductor at 52° F. if its resistance is 1000" at 32° F. ?
R,= 1000 (l + -0023708 x 20 + 00000034548 x 20s} = 1047-554102-
By approximate rule (*238 °/0 per degree F.)
Increase = X *238 X 20 100
= 47 6"
Rt = 1047*6"
In the case of carbon the resistance decreases with increase of temperature, and a similar remark applies to most liquid conductors, mercury being excepted. The warming of most insulators decreases their insulating power, i.e. lowers their specific resistances.
The effect of changes of temperature is far more marked with insulators than with conductors, for whilst an increase of 15° F. would raise the resistance of a 1000" copper con- ductor to 1036", a gutta-percha core would decrease from 9000 to 1000 megohms with the same rise in temperature. The equation connecting the resistances of insulators is of the exponential type, and varies largely with the quality as well as with the kind of material.*
In the case of gutta-percha the effect of pressure is very great. The insulation of a submerged submarine cable greatly exceeds that observed at the factory. The deeper
* Handbook of Electrical Testing , by H. R. Kempe, 6th edition, p. 470.
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TELEGRAPHY
as
tlie cable is laid the higher is its insulation resistance. This effect is due solely to the pressure exerted by the water, and amounts to 61 J% per 1000 fathoms depth. Thus a cable having an insulation of 100 megohms at atmospheric pressure would have a resistance 222 J megohms when laid at a depth of 2000 fathoms. India- rubber, on the other hand, decreases in resistance, when subjected to pressure, at the rate of about 16% per 1000 fathoms.
Changes of temperature and pressure are found not to affect the true capacity of a G.P. cable. With india- rubber, a rise in temperature from 100° F. to 212° F. increased the capacity 140% (Kempe).
Experiments carried out on a screened cable (31% air, 69% paper) show that the capacity varies with the insulation of the cable, the capacity falling from T18 mf. at 2,000 megohms, to T08 mf. at 120,000 megohms per mile. The insulation is found to decrease from 20,000 megohms per mile at 16° C. to 2,200 megohms at 44° C., but the capacity rises with the temperature from *1219 mf. at 15° C. to *131 mf. at 43° C. These variations do not, however, follow any simple law.
PART IV.— ELECTROMAGNETS.*
A magnetic field is generated by a loop of wire convey- ing a current. The value of the field produced may be augmented by increasing the number of turns of wire.
It is now necessary also to consider the effect of intro- ducing an iron core into the coil of wire, or solenoid, as it is termed, in this connection. Iron and steel conduct lines of force far better than does air, and a somewhat similar form of law to Ohm’s law for electrical circuits applies to magnetic circuits. A magnetic circuit may be defined as the path of the magnetic lines of force. The law for a magnetic circuit is : —
Magneto-motive force (in Gilberts) Reluctance (in Oersteds)
= Flux (in Maxwells)
* Before reading this part of the chapter the reader should be fhmiliar with the facts illustrated by Fig. 48.
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CIRCUITS AND CONDUCTORS 69
The magneto- motive force corresponds to E.M.F., the reluctance or magnetic resistance to resistance and the flux or number of lines of force flowing through the magnetic circuit to the current. The reluctance of a circuit in Oersteds is equal to its length divided by the product of its sectional area and its permeability. The permeability corresponds roughly to conductivity, and may be dehned as the relative conductivity of the material under con- sideration, and that of vacuum which is taken as unity. There is, however, a most important difference between an electric circuit and a magnetic circuit. The resistance of any particular conductor is the same for any value of current, so long as its temperature remains con- stant. In the case of a magnetic circuit the value varies with the magnetizing force. For instance, with a mag- netizing force of 2, the permeability is 2500, whilst with 350 it has fallen to 54. The reason of these changes in value will be found in the description of the molecular theory of magnetism.
The magnetizing force of a solenoid (in Gilberts) is 1*257 times the total number of ampere-turns, i.e. 1*257 X current in amperes X number of convolutions. Therefore to produce any given value of magnetic flux (in Maxwells) through a given magnetic circuit, a certain number of ampere turns of wire are required. With a sounder of the pattern described later, about 200 ampere- turns are required to work the instrument satisfactorily. This may be provided by a single turn of wire upon each limb of the electromagnet, if a current of 100 amperes is provided. With one ampere 100 turns upon each limb would be needed, whilst with 100 m.a. 1000 turns per limb would be necessary.
From this fact one or two very useful rules may be deduced. One is that the maximum effect is produced by any given type of apparatus when it is wound to a resistance equal to the resistance of the rest of the circuit. The assumption which is made in this statement is that the windings occupy precisely the same space and that the wire is of the same material but of different gauge in the two instances. The relation is a trifle more complex whep
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TELEGRAPHY
the thickness of the insulating covering upon the wire is taken into account, but the approximate rules which will be indicated are sufficiently near to the true results to be of considerable value.
The length of wire, and hence the number of turns of wire, which can be wound upon a bobbin of given dimen- sions is inversely proportional to the square of the total diameter of the wire. Thus
also
*. : k
Th : na
w
w
w
(d,y
where lx and l2% dx and d2, nx and n2 represent respectively the lengths, diameters, and number of turns of wire in each case.
But the relative resistances of the windings Rx and R2 in the two cases may be expressed thus : —
s h X (d,)2 : l2 X (d,)2
Substituting for lx and l2 the relative values in terms of the diameter of the wire which can be wound upon the bobbin,
Rx : Rz . ; (d2f X (d2)2 : (dj2 X
». e. Rx : R2 : : d24 : dx4
but nf : rij2 : : d24 : d24
• . Wj i 712 i j \/ R\ • \/ R%’
The last relation states that the number of turns of wire wound upon an electromagnet is directly, and hence its figure of merit is inversely, proportional to the square root of the resistance of the windings.
The application of these principles may best be shown by a series of numerical examples.
Example 1. — The coils of a trembler bell (50" per coil) can be joined up in series or in parallel. Which method is preferable when the bell is directly connected to two cells in series, having an E.M.F. of 1T and an internal resistance of 5" per cell ?
The magnetic effects, Mx and M2, are proportional to the amperes turns ( A X T) in each case.
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71
Mx : M2 :: Ax X T : A2 X T.
_ 2
In senes, current = ~ ^ = ’0182 amperes
2
In parallel, current = 25 .Ijl iq = 057 amperes.
The current in each coil in the latter case is *0285 amp. since they are in parallel.
Mx : M2 : : 0182 X T : 0285 X T. i.e. Mx : M% : : *0182 : *0285.
Hence the coils should be placed in parallel.
Example 2. — An electromagnet is wound with two eaual wires each having a resistance of 10", and is connected to a battery having an E.M.F. of 20T, and an internal resist- ance of 10". Should the coils be connected in parallel or in series ?
i. e.
In series, current =
In parallel, current =
£ amp. in each wire.
Mx : M2 : : £ : £.
20
20 + 10 20
5 + 10 =
The magnetic effects are equal in the two cases. Since the value of the current in the first case is half that in the second and the energy expended is also half as much, the series arrangement is to be preferred. Moreover, the internal resistance of the battery is likely to rise.
Example 3. — An electromagnet is wound with wire having a diameter of 20 mils to a resistance of 320". With what diameter of wire must it be re-wound in order that its resistance may be 20" ?
Rx :: df : d2\
320 : : 204 : d2\
r2
t. e. 20
. . 320 X 204 ..
20 mi 8
^a2 = */l6 X 204 mils = 1600 mils d% = 40 mils.
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n
TELEGRAPHY
Example 4. — An instrument wound to a resistance of 1000" requires a current of 7 m.a. to satisfactorily work it. What current will be required to produce the same effect if it is re-wound to a resistance of 100" ?
•JR i • JR% : : ;
J 1000 : J100 : : nx : n2 <• e. 31*62 : 10 : : : Wg
Since the effects are equal,
x *007 = n2 X (7 i. e. 3162 X 007 = 10 xC
. ~ 007 X 31*62
. . C = jQ = 22 m.a. approx.
Example 5. — Two electromagnets of precisely equal dimensions are wound with the same volume of wire, but the first is wound with 14 mils wire, and the second with 4*5 mils wire. What current will be needed to produce the same effect with the second electromagnet that 200 m.a. produces with the first ?
dy2 : : : nx : n2
t. e. 4*52 : 142 : : nx : rij Since the effects are equal.
rij x -2 = Wj x C i.e. 4-52 x 2 = 142 x C . n ‘2 x 4 52
. . C = — = 207 m.a. approx.
Example 6. — How would you join up sixty cells, each having an E.M.F. of 2 volts and an internal resistance of 4" per cell, to an electromagnet having a resistance of 15" in order to produce the largest possible effect with the means at disposal ?
This is only another way of setting the type of question shown on page 39, since the effect is greatest when the current is greatest.
„ /(50 X 15 1E „ •
n = ^ ^ = 15 cells in senes
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CIRCUITS AND CONDUCTORS
73
t. e. 4 rows in parallel, each row consisting of 15 cells in
Series-
Current =
30
15 +
15 x 4
= 1 ampere.
Example 7. — Seventeen cells E.M.F. *96 volt and 4" internal resistance per cell are used to work a circuit having a resistance of 132“, of which 36“ is the resistance of the sounder. If the sounder is re-wound to a resistance of 144“, what economy in battery power will result ?
with 36“ sounder, current =
17 X *96
17 x 4 + 132
= 82 m.a. approx. 7144 : 736 : : 82 : C.
current required with 144“ sounder = — ~ ^ m,a* Resistance of circuit = 96 + 144 = 240“ number of cells = — = 13 cells.
*96
*041
-4
Hence four cells are saved.
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CHAPTER in
THE MEASUREMENT OF CURRENT.
PART I.— RESISTANCE COILS.
ASET of resistance coils or a resistance box is perhaps one of the most useful and necessary adjuncts in electrical testing. These boxes contain coils of wire of definite resistance, which can be thrown into circuit or cut out at will. The wire forming the resistance coil is wound upon a bobbin in a special manner — the reason for which will receive consideration later — and is well insulated with one or two layers of silk covering wound spirally upon the conductor.
The coils are connected between a series of brass blocks cut to receive a circular peg between each block and its neighbour (Fig. 19). With all the plugs in position, the brass block forms a continuous conductor of negligible resistance between the two terminals. The removal of any plug inserts a resistance coil between the terminals of the instrument of the value marked near the two brass blocks. In the case illustrated (Fig. 19) the 2W, 3W, and 4" coils are in circuit, that is to say a resistance of 9W is introduced between the terminals. The 1" coil in this case is short- circuited by the plug.
The brass blocks are fitted upon a slab of ebonite, a material possessing very high insulating qualities. The brass blocks are recessed upon either side, beneath the plug holes, in order to provide facilities for cleaning the ebonite and removing all dust, dirt, or metallic filings, due to the continual twisting of the plugs in their holes.
The brass plugs usually take one of two forms — either a turned plug of brass or a plug of brass with an ebonite
74
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THE MEASUREMENT OF CURRENT
75
handle. The latter is the preferable form on account of the superior grip which can be obtained upon it. It is a matter of considerable importance that the plugs should fit accurately and tightly, and that the contact surfaces should be kept bright and clean. Where accuracy is required, these points must receive very careful attention, for it will be obvious that even four bad contacts in series will pro- duce a considerable amount of resistance which should not be present. Again, this resistance will vary with the
IBONITt
Fio. 19. — Connections and windings of a set of resistance coils.
manner in which the plug is inserted. A plug should be put in firmly with a twisting motion in order to ensure a good contact. Neglect of this simple and obvious pre- caution often produces somewhat serious errors. Upon the other hand, resistance boxes must be handled carefully, and the use of considerable force in putting in the plugs is strongly deprecated.
The values given to the coils usually take the following • form: 1, 2, 3, 4; 10, 20, 30, 40; 100, 200, 300, 400, etc. The right-hand set of four coils, shown in Fig. 20, has the values 1« 2", 3“ and 4", and it will therefore be seen that any resistance from 1* to 10 by gradations of lw can be
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thrown into circuit. This is termed a set of unit coils. The centre set of coils contains 1, 2, 3, 4 units and tens — and any resistance from 1“ to 110" by gradations of one
Fio. 20. — Resistance coils.
ohm can thus be obtained. The large set upon the left contains a set of four “ units ” coils, four “ tens ” coils.
Fio. 21. — Retards*. on coils.
four “ hundreds ’’ coils, and four “ thousands ” coils, which thus provide for any integral resistance from 1" to 11,110°.
Two forms of resistance box employed in practical telegraphy are illustrated in Figs. 21 and 22. The former,
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known as a set of “ retardation coils,” on account of the purpose to which it is put (see Chapter VIII), has eight coils of the following resistances: 10", 20", 30", 40", 100", 200". 300", 400". This gives 10" to 1100“ by gradations of 10".
Fia. 22.— Cond "riser enil*.
The second form used for a similar purpose is in contra- distinction known as a set of “ condenser coils.” The resistance of its seven coils are respectively 50", 100", 200", 3C0-, 400", 1000", and 2000", i.e. 50- to 4050" by grada- tions of 50". Both these sets of coils are used in cases where the absolute accuracy of the resistance is of very little consequence, and the form chosen is therefore simpler than those pre- viously illustrated.
Another type of resist- ance box, designed to avoid the resistance due to a number of plugs in series, is illustrated in Fig. 23.
This form necessitates a resistance coil for each value of resistance. To obtain 1« to 9- by 1", nine coils are necessary, as against four coils to give 1" to 10" by the previous arrangement. The heavy central brass block forms one terminal, and the block marked 0 the other. A resistance of 1" is connected between the blocks marked 0« and 1", 1" and 2", 2" and
Pio. 23. — Single-plug resistance coils.
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TELEGRAPH r
3", etc. The introduction of the peg at 1* connects the 1" coil and at 4" the four coils between the 0", 1", 2", 3“ and 4" blocks. For any particular resistance, therefore, there is only one plug needed. This presents a consider- able advantage where great accuracy is required. The guaranteed accuracy of this particular type is *02 per cent.
Shunts are usually arranged in this way, ana a con- sideration of Fig. 31, after reading the latter part of this chapter, will make this apparent.
Type of Wire to be Used.
The material of which the wire for a resistance coil is composed is a matter of considerable importance. Copper wire is quite inadmissible on account of its large changes in resistance with changes of temperature. Again, where a large resistance is required, the quantity of wire necessary would render the coils very bulky, or extremely fine wire would have to be employed.
The wire chosen should have a very high resistivity and a small temperature variation of resistance. The wire should not oxidize, or, in fact, be subject to any change of its resistance through age. The three alloys which are most used are German silver,* platinoid, and platinum silver. Their temperature variations of resistance are respectively ‘044%, *021%, and 031% per degree Centi- grade, as against the '428% of copper. German silver is perhaps the oldest and most extensively employed material, whilst platinoid, manganin,and eureka are coming into ever-increasing use. Platinum silver is very expensive and is only employed for important standards. It is known to age very little and to be subject to no oxidation, and has a small and very accurately known temperature variation of resistance.
The resistivities and temperature coefficients of copper and a few well-known and frequently used alloys are given on page 79 for purposes of comparison.
* German silver is composed of 4 parts of copper, 2 of nickel and 1 of zinc. Manganin consists of 84 parts copper, 12 parts manganese and 4 parts nickel. Platinoid is composed of tungsten nickel, copper and zinc. Eureka is a copper nickel alloy
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|
Material. |
Resistivity »per cubic centimetre, in microhms. |
Temperature coefficient X per degree C. |
|
Annealed copper |
1*6963 |
*428 |
|
German silver |
20 to 30 |
*044 |
|
Platinum silver . |
25 to 30 |
*031 |
|
Platinoid . |
40 |
*021 |
|
Eureka |
40 |
Nil |
|
Manganin . . | |
42 to 46 |
Nil |
All resistance coils are marked with the temperature at which they are correct, and this is usually made 15’5° C. or 60° F. In the case of very important standard coils the temperature variation is carefully determined, and a certi- ficate as to this and the resistance of the coil is provided by the makers.
Gauge of Wire.
The gauge of the wire to be employed next requires consideration. Where cost and size are no object the gauge should be large, since this will give great accu- racy of adjustment, and any rise of temperature due to the passage of a current through it will be reduced to the lowest possible value. Naturally a wire with a large surface will radiate any heat generated much faster than a smaller one, and its temperature will consequently be lower. In practice, however, the questions of cost and bulk are distinctly important, and therefore it is that the low resistance coils are made of a thick wire, whilst the high ones are composed of a fine wire. If fine wire were used for the low resistance coils the length of wire neces- sary would be short, and consequently the accurate adjust- ment of the actual length required would be extremely fine, and therefore subject to considerable inaccuracy. Usually, too, the currents flowing through low resistances are larger than those flowing through high resistances, and upon this account also thick wire is desirable.
Rheostats.
A form of resistance box, termed a rheostat, used by the Post Office upon telegraph circuits is illustrated in Fig. 24.
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It consists of two contact arms, each of which is capable of moving over a semicircle of contact points, and three separate resistance coils and plugs. The one set of studs is consecutively marked 0, 40, 80, 120, 160, 200, 240, 280, 320, 360, and 400, whilst the other half is similarly marked, but with values ten times as great, ie. 400 to 4000. By means of the nearer arm any resistance up to 400" by grad- ations of 40" can be inserted. With the other any resist- ance from 400" to 4000", by gradations of 400«, may be
Fio. S4. — RheoaUt “ 0.**
obtained. Using both arms, any resistance from 0 to 4400- by gradations of 40" may be obtained. On the base of the instrument three coils of 10", 20", and 4000" are provided, thus bringing up the maximum resistance obtainable to 8430". The first two coils provide for gradations of 10" instead of 40" ; for instance 3330" would be provided by the 400" coil arm at 3200", the 40" coil arm at 120-, and the 10" coil plug out. 3340" would require the 20" coil, 3350" both 10" and 20", whilst 3360" would be provided by moving the 40- coil arm to 160" and pluggiug up both the base coils. The 4000«*> coil is for use when the resistance required exceeds 4430". The connections are
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shown in Fig. 25, and are so obvious as to require no comment.
There are at present three forms of rheostat in daily use in the Post Office, that illustrated in Fig. 24 being known as the rheostat “ C.” The “ B ” is somewhat shorter than the “ C ” type, and is wound with finer wire. It is never used upon circuits wrorked with bichromate
/0 20 4°°°
Fio. *5. — Connections of rheostat “ C."
batteries, or upon secondary cell worked circuits, on account of the heating which almost inevitably results.
The third, or “ D ” form, illustrated in Fig. 26 is now the standard pattern, and possesses the merits of greater cheapness and superior efficiency of the contacts. The two radial arms each consist of strips of phosphor bronze, bent as shown, bearing down upon the circular brass con- tact blocks, between which the 40" and 400" coils are connected. In addition, 10", 20", and 4000", plug coils »e provided, as in the “ B ” and “ C ” types.
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Double-winding.
All resistance coils are so wound as to have the smallest, possible self-inductance. This is accomplished by doubling the wire and winding it as indicated in Fig. 19. A current traversing the coil does not generate a magnetic field, and the coil has therefore no inductance. Moreover, magnets moved in the vicinity of the coils will not produce induced currents. In considering such instruments as Wheatstone bridges, it will be quite apparent that this method of winding is essential
A resistance with very small inductance may be formed by "winding the coil upon a thin flat strip of insulating material. In this case the two sides of the coil are so close to each other as practically to neutralize each other’s magnetic effect. This plan is very extensively adopted in telephony.
PART II.— GALVANOMETERS.
An electric current can only be measured indirectly by the effects which it produces under given conditions. Its
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principal effects are magnetic, thermal, and chemical, and each of these effects may be employed to detect, to com- pare or to measure currents.
The magnetic field round a current-conveying wire is strictly proportional to the value of the current flowing in the wire, and its direction depends upon the direction of the current producing it. If the relative values of the magnetic field at a given point produced by two successive currents in a particular conductor or series of conductors can be ascertained, then the values of the two currents producing those magnetic fields can be ascertained.
The underlying principle in all galvanometers (with the exception of the D’Arsonval types) is the comparison of the value of the magnetic field produced by a current in its coils with the earth's magnetic field.
Galvanometers may be distinguished as pointer galvanometers and reflecting galvanometers. All the instruments used in Post Office instrument rooms belong to the former class — a pointer or needle being employed to indicate the deflection. The latter class comprises all those instruments in which a mirror is fixed to the moving system to indicate the deflection by a ray of light.
Tangent Galvanometer.
The merit of the tangent galvanometer lies in the fact that its indications bear a definite and simple relation to the current flowing through its coils, viz. that the current is directly proportional to the tangent of the angle of deflection. Essentially, a tangent galvanometer consists of a circular coil of wire the diameter of which is at least ten times the length of the magnetic needle suspended or pivoted at its centre. The coil is placed in the magnetic meridian, and in order to observe the deflections a light pointer of non-magnetic material is fixed at right angles to the magnetic needle. Beneath the pointer is placed a circular scale divided into degrees reading from 0° to 90° on each side of the normal E. and W. position of the pointer. The object gained by fixing the pointer at right
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TELEGRAPHY
angles to, instead of parallel with, the magnetic needle is that the normal position of the pointer at zero or 0°, and the centre of the scale is then outside instead of under the coil.
Consideration of Fig. 2 and Fig. 48, which latter shows the magnetic field due to a current flowing in a coil of wire, or solenoid as it is termed in this connection, gives the direction of the magnetic field through the coil The magnetic needle of a tangent galvanometer lies in the magnetic meridian, i. e. it is held in a N. and S. position by the horizontal component of the earth’s magnetic field, and this provides the controlling force. The magnetic field due to the earth and that due to the current in the coils of a tangent galvanometer are at right angles to each other. It has previously been pointed outthat magnetic fields cannot cross each other (p. 10), and there- fore when a current is passed through the coils of the galvanometer the direction of the resultant field is altered. If the two fields be of equal strength the resultant field lies midway between the two, i. e. 45° from the magnetic meridian and 45° from the direction of the field due to the coil considered by itself. If the deflecting field be less than the controlling field at the point considered the resultant field is less than 45° from the magnetic meridian. If greater, then it is over 45°. A minute magnetic needle placed at the point in question would lie along the resultant field at that point, and therefore in the three cases taken deflections of 45°, less than 45° and over 45° would be indicated by the pointer.
By making the diameter of the coil ten times the length of the magnetic needle it may still be assumed that the needle indicates the direction of the resultant field at the centre of the coil, and that therefore the tangent law still holds. But were the needle a long one its poles would move further and further from the coil as it deflects, and therefore in the case of two unequal deflections the magnetic fields would not be compared at the same point. With a small needle the magnetic field is practically uniform over the area through which the magnetic needle swings. For still greater accuracy the depth of the
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windings of the coil should bear to their width the ratio
of ya : J2.
The error can be reduced to the order of of \0/ by adopting the form of galvanometer devised by Helmholtz (Fig. 27) and referred to variously as the Helmholtz or Gaugain galvanometer. Two equal and parallel coils are employed with the needle lying midway between them in the line joining their cen- tres. The distance from the centre of either coil to the needle is made equal to half the radius of either coil.*
In fine, the deflecting force, which is strictly proportional to the cur- rent, is at right angles Fio. 27.— nelmholtz or Gaugain galvanometer, to the controlling force
(the horizontal component of the earth’s magnetic field) normally holding the needle in the magnetic meridian. These forces are at right angles to each other, and the current producing a deflection is pi oportional to the tangent of the angle of deflection. If therefore a current of 1 0 m.a. produces a deflection of 38°, the current producing a deflection of 65° would be found thus:
tan 38° : tan 65° :: 10 : x i.e. 7813 : 2 1445 :: 10 : x 2T445 X 10
, x =
*7813
= 27*45 m.a.
The values of tan 38° and tan G5C are obtained from a table of tangents.
• The relation given on page 88 for an ordinaiy galvanometer
[C=^^tan a] becomes for the Helmholtz instrument C v tan 2 wn 32ira
• where Ht r, and n have the same meanings as before.
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Tangent of an Angle.
In order to ascertain the value of the tangent of any particular angle, that angle should be marked off from A 0 along the quarter circle 0 G (Fig. 28). A line is then drawn connecting A and 0 B through the point upon the quarter-circle. The tangent of the angle is equal to the length from 0 to the point of intersection along O B , divided by the length of the radius of the circle. This number has only one value for any given angle, but it will be obvious that the larger the circle the greater is the accuracy with which the measurements may be obtained.
O
Fig. 28.— Division of galvanometer scale into tangent divisions, and lllastrating the values of tan O’, tan 80*, tan 45\ tan 60*.
In Fig. 28 the radius of the circle is one inch, and the divisions are one-eighths of an inch, therefore the tangent of any angle drawn from A 0 is equal to the length in inches of the line from 0 to the point of intersection. The tangent of 0° is 0, since the length along O B for angle of 0° is 0. The tangent of 45° is seen to be eight one-eighths of one inch, %. e. one inch. Its tangent is therefore 1 . In the case of 30° it will be seen that the intersection occurs just after £ inch, and making a guess at the point one would say it was about half-way between £ and -£, 1.6.1+^ = TV inch. Accord- ing to this guess its tangent is then ^ or *56 approximately.
Its actual value is - . - n/3
or ‘57735.
The tangent of 60° is
by the same rough-and-ready process found to be or 1*75.
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Its actual value is ^/3 or 1*73205. It will be noticed that tan 60° is exactly three times as large as tan 30°, a fact which may readily be verified by using a pair of dividers upon Fig. 2tf. From 0 to 14 is exactly three times the distance from 0 to the point marked 30°. The tangent of 90° is iufinity, since the lines A C and 0 B , being parallel, never meet. A 0 is of finite length and 0 B infinite.
Having defined the actual values of the tangents of the various angles, it is an easy matter to show the relative values of the divisions. For the purpose of simplifying the previous calculations the divisions bore a simple and direct relation to the radius of the circle, but this is by no means essential. The length of a division upon the line OB may be of any chosen value so long as all the divisions are of equal length.
The tangents of the angles of deflection are in each case the particular length marked off along O 2?, divided by the radius of the circle. The radius of the circle is the same in each case, therefore the tangents of the angles of deflec- tion are directly proportional to the lengths marked off from O along O B. These lengths are, however, divided into equal divisions, consequently the divisions marked off along O B are proportional to the tangents of the angles, and the current producing any deflection on a tangent galvanometer is therefore directly proportional to the number of divisions on the circle indicated by the needle or pointer.
Tangent Scale.
The construction of a tangent scale therefore consists (i) in drawing a straight line at right angles to the line joining the centre and zero of the scale, (ii) in dividing it into equal divisions of any convenient length, and (iii) in marking and numbering consecutively the points at which lines drawn from each division intersect the circle of the scale. In this way, repeated reference to a table of tangents is avoided, since the current is then directly proportional to the number of divisions indicated by the pointer.
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m
Theory of Tangent Galvanometer.
The deflecting force is the magnetic field due to the current in the coils, and the controlling force which tends to hold the needle in the magnetic meridian is the earth's field. These forces are at right angles to each other, and when the needle comes to rest under their combined action : —
Deflecting force ( F ) = Controlling force (H ) x tan a where tan a is the tangent of the angle of deflection.
By definition, unit current flows in an arc of 1 cm. length and radius when the magnetic field generated at its centre is 1 gauss. The magnetic field F at the centre of a coil of r cm. radius with n turns of wire is
F =
length of wire
2irm
(distance of wire from centre)2 2miC
2im
r
with a current of G units F =
When the needle comes to rest F=H tan a, where a is
the angle of deflection from the magnetic meridian.
,7 2irnG TT A
F = = E tan a
r
~ Hr C= x — tan a.
Z7 ra
Absolute Measurement.
The value of H can readily be determined* from the rate of swing of a magnet in the horizontal field, and from its dimensions and the deflection produced on a magnetometer and its distance therefrom.
Having determined H , and knowing “ n” and “r," the value of the current due to a deflection a can be calculated. Such a measurement is termed an absolute determination, since it has been made independently of existing electrical standu.ds or units. A galvanometer used in this way is termed an absolute galvanometer.
It should be added that in all absolute determinations
* Stewart and Gee’s Practical Physics , Vol. II. chap. ii. and chap, yi., or Grays’ Absolute Measurements in Electricity and Magnetism , chap. ii.
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the value of the current is in C.G.S. units which require to be divided by ten to give the current in amperes.
As an example, the current producing a deflection of 45° (tan 45°=1) on a Post Office tangent galvanometer (with the coil in the magnetic meridian and not from the skew scale zero), and taking H as *18, would be —
_ ~-18 X (6|£ X 2*54) = *000361 units
— °2 X 3141 6 x“ 1400 X 1 = 3 61 m.a.
The P.O. Tangent Galvanometer.
The base, frame, and needle box (Fig. 29) are of well lacquered brass. The magnetic needle, provided with a
Fio. 29.— P 0. Tangent gal ranometw.
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central cap of agate, is pivoted upon an upstanding steel point in the centre of the box. The light aluminium pointer is fixed at right angles to the needle and a mirror is fixed close to the scale in order to avoid parallax error, i. e. the possibility that a deflection of, say, 100 divisions is read as 99 or 101, according to the position of the observers eye above the needle. By taking the reading when the pointer and its image in the mirror beneath
N
coincide it is ensured that the eye is directly above the needle and parallax error is thereby avoided.
In order to obtain an extended range and greater accuracy of measurement the coil of the instrument (Fig. 30) is twisted through an angle of 60° from the magnetic meridian. The deflecting force is at right angles to the plane of the coil, and therefore tends to pull the S. pole of the needle to the N.W. and the N. pole to the S.E. If the current is applied in such a direction as to deflect the pointer off the scale, the current must be reversed, whereas with an ordinary tangent galvanometer the deflection may be read upon either side of zero. This
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is, however, of little consequence since the reversal of the current when necessary is readily effected.
The lower half of the scale (Fig. 30) is marked in degrees, whilst the topside of the upper half is marked in divisions representing equal currents. The scale is prepared upon both sides of the ordinary zero in the same manner as in the case of the ordinary patterns, and it will be observed that the divisions are