■^ 
 
 
QfotncU Hniwerattg Siihrara 
 
 Stliatu, N«m ^ortt 
 
 BOUGHT WITH THE INCOME OF THE 
 
 SAGE ENDOWMENT FUND 
 
 THE GIFT OF 
 
 HENRY W. SAGE 
 
 1891 
 
 ENGINEERING LIBRARY 
 
Cornell University Library 
 TK 301.J35 
 
 Electrical meters; 
 
Cornell University 
 Library 
 
 The original of this book is in 
 the Cornell University Library. 
 
 There are no known copyright restrictions in 
 the United States on the use of the text. 
 
 http://www.archive.org/details/cu31924004687525 
 
ELECTRICAL METERS 
 
UNIVERSITY OF WISCONSIN 
 EXTENSION TEXTS 
 
 A series of Industrial and Engineering Education Textbooks, 
 
 developed under the direction of Dean Louis E. Reber, 
 
 University of Wisconsin Extension Division 
 
 Norris and Smith's 
 SHOP ARITHMETIC 
 
 Norris and Craigo's 
 ADVANCED SHOP MATHEMAT- 
 ICS 
 
 Hills' 
 
 MACHINE DRAWING 
 
 George's 
 
 ADVANCED SHOP DRAWING 
 
 Wooley and Meredith's 
 SHOP SKETCHING 
 
 Longfield's 
 
 SHEET METAL DRAFTING 
 
 Hobbs, Elliott, and Consoliver's 
 GASOLINE AUTOMOBILE 
 
 Norris, Winning, and Weaver's 
 GAS ENGINE IGNITION 
 
 Consoliver and Mitchell's 
 AUTOMOTIVE IGNITION 
 SYSTEMS 
 
 Shealy's 
 HEAT 
 
 Shealy's 
 
 STEAM BOILERS 
 
 Shealy's 
 
 STEAM ENGINES 
 
 Jansky's 
 ELECTRICAL METERS 
 
 J Q/yisliv s 
 
 THEORY AND OPERATION OF 
 D.-C. MACHINERY 
 
 ELEMENTARY MAGNETISM AND 
 ELECTRICITY 
 
 OF RADIOTELEG- 
 
 Jansky's 
 PRINCIPLES 
 RAPHY 
 
 Jansky and Paber's 
 
 PRINCIPLES OF THE TELE- 
 PHONE 
 Part I. — Subscribers' Apparatus 
 
 Hool's 
 
 ELEMENTS OF STRUCTURES 
 
 Hool's 
 
 REINFORCED CONCRETE CON- 
 STRUCTION 
 
 Vol. I. — Fundamental Principles 
 Vol. II. — Retaining Walls and 
 
 Buildings 
 Vol. m. — Bridges and Culverts 
 
 Blair's 
 
 SHOW-CARD WRITING 
 
 MATERIALS OF CONSTRUCTION 
 
 Wines' 
 
 STRENGTH OF MATERIALS 
 
 Jansliy's 
 
 ELEMENTS OF STORAGE 
 BATTERIES 
 
 Koehler's 
 
 THE PROPERTIES AND USES OF 
 WOOD 
 
 Sweeney's 
 
 BOOKKEEPING AND INTRODUC- 
 TORY ACCOUNTING 
 
 Gardiner's 
 
 PRACTICAL FOREMANSHIP 
 
 Jamieson's 
 PRACTICAL BANKING 
 
 CrdTu/'tfliBY ? 
 
 MANAGEMENT IN THE FACTORY 
 
 KoeUer and Thelen's 
 
 THE KILN DRYING OF LUMBER 
 
 Felz's 
 
 SELLING AT RETAIL 
 
ENGINEERING EDUCATION SERIES 
 
 ELECTEICAL METERS 
 
 PREPARED IN THE 
 
 EXTENSION DIVISION OP 
 THE UNIVERSITY OF WISCONSIN 
 
 BY 
 CYRIL M. JANSKY, B. S., B. A. 
 
 ABBOCIATB PBOFEBSOR OF BLBCTBICAIi ENGINEERING 
 THE TJNIVER8ITT OF 'WZBCONSIN 
 
 Second Edition 
 
 ReVIBED and ENIiARGED 
 
 Sixth Impression 
 
 McGRAW-HILL BOOK COMPANY, Inc. 
 NEW YORK: 370 SEVENTH AVENUE 
 
 LONDON: 6 & 8 BOUVERIE ST., E. C. 4 
 1917 
 
Copyright, 1913, 1917, by the 
 McGraw-Hill Book Company, Inc. 
 
 PHINTED IN THE UNITED STATES OF AMERICA 
 
 THE MAPLE PRESS COMPANY, YORK, PA. 
 
PREFACE TO SECOND EDITION 
 
 The many new developments in electrical meter design, since 
 the publication of the first edition of this text, has necessitated 
 the omission of some and the addition of much new material in 
 the revised edition. 
 
 The description of most obsolete meters has been omitted and 
 several new designs are explained. The chapter on Instrument 
 Errors has been almost entirely rewritten and expanded so as to 
 include many experimental results. The influence of frequency 
 and wave form in producing errors in different classes of meters 
 has been added. There has also been added a chapter on In- 
 strument Transformers. Only so much of the theory of instru- 
 ment transformers is given as is necessary for an understanding 
 of their function in connection with meters and their testing. 
 
 C. M. J. 
 
 Universitt op Wisconsin, 
 
 Madison, Wisconsin, 
 
 AprU, 26, 1917. 
 
PREFACE TO FIRST EDITION 
 
 Efficiency is the shibboleth of the modern industrial world. 
 From a physical viewpoint the efficient operation of any plant 
 is mainly a correct application of the laws of conservation and 
 transformation of energy, and hence, the operation of an in- 
 dustrial plant cannot be efficient unless data are available for 
 determining the relation between energy generated or delivered 
 and energy utilized in any manufacturing process. 
 
 The data necessary for efficient operation cannot be had 
 unless proper and accurate instruments are used to determine 
 the various quantities that enter into the operation. In any 
 industry where electrical energy is generated or utilized, elec- 
 trical measuring instruments are necessary for efficient operation. 
 
 When the author decided to offer a course treating of Electrical 
 Measuring Instruments, he was surprised to discover that no 
 suitable text was available, and in fact in this country very 
 little had been published treating, in a comprehensive and 
 systematic way, of the various kinds of electrical measuring 
 instruments. The articles in the technical journals and pro- 
 ceedings of technical societies are, of course, numerous and 
 valuable, but they are inaccessible to the average man who may 
 want information concerning the characteristics and principles 
 of operation of some type of measuring instrument. 
 
 This text is written primarily to supply the author's needs in 
 correspondence instruction, although it is hoped that others also 
 may find it useful. 
 
 Since, in this country, instruments of foreign make are used 
 to such a limited extent, this work is confined almost entirely 
 to instruments made in the United States, and to American 
 practice. 
 
 In classifying electrical measuring instruments, the main divi- 
 sions have been made in accordance with the quantities to be 
 measured, and minor subdivisions according to the principles of 
 operation. Although such a classification necessitates some repe- 
 tition in describing different instruments whose operation is based 
 on the same principles, nevertheless, for the sake of clearness and 
 simplicity such a classification appears justifiable 
 
 vii 
 
viii PREFACE 
 
 The attempt has been made to explain the fundamental prin- 
 ciples in an elementary way, and for this reason many line draw- 
 ings and vector diagrams are used. The manner in which these 
 fundamental principles are applied in practice is usually exem- 
 plified by means of cuts of actual instruments. The illustra- 
 tions used were selected not because the author considers the 
 instruments better than others not shown, but because they are 
 typical, and used quite extensively. 
 
 Great care has been taken to eliminate all errors, yet it is 
 too much to expect that no mistakes will be found. The author 
 will be very grateful to anyone who may discover and report 
 any error. 
 
 The author is under great obligations to Dr. M. G. Lloyd, 
 of Chicago; Professor J. P. Jackson of the Pennsylvania State 
 College, and Professor R. C. Disque of The University of Wis- 
 consin for reading the manuscript and for many valuable sug- 
 gestions. Thanks are also due to Mr. F. C. Thiessen and Mr. G. 
 R. Wells for making the line drawings and vector diagrams; to 
 the several manufacturers of electrical measuring instruments 
 for their kindness in supplying information and electrotypes of 
 their instruments. 
 
 C. M. J. 
 
 The UNrvEESiTT of Wisconsin, 
 
 Madison, Wisconsin, 
 
 November 26, 1912. 
 
CONTENTS 
 
 Page 
 Preface y 
 
 CHAPTER I 
 
 Fundamental Electric al Principles 1 
 
 Energy — Forms of Energy — Conservation of Energy — Electricity 
 and Electrical Energy — Analogies — Magnetism — Properties of 
 Magnetic Fields— Strength of Magnetic Field— Relation between 
 Tension and Flux Density — Magnetic Field Surrounding an 
 Electric Wire— Field of a Circular Coil— Solenoids— Law of the 
 Magnetic Circuit — Force Exerted upon a Wire in a Magnetic 
 Field — Force between Parallel Wires Carrying Currents — Electro- 
 lytic Conductors — Faraday's Laws — Heat Effect — Practical Elec- 
 trical Units — Resistance — Change of Resistance with Tempera- 
 ture — Electric Current — Electromotive Force — Quantity — Energy 
 — Power — Inductance — Capacity — Ohm's Law — Pressure Drop in 
 D.-C. Circuits — Energy Loss. 
 
 CHAPTER II 
 
 Classification of Instruments 26 
 
 Classes of Meters — Groups of Instruments — Electromagnetic 
 Instruments — Electrodynamic Instruments — Electrostatic Instru- 
 ments — Thermal Instruments — Controlling Forces — Magnetic 
 Shielding — Friction of Supports. 
 
 CHAPTER III 
 
 Current and Pressurb-measurinq Instruments 32 
 
 Ammeters and Voltmeters — Uses of Ammeters and Voltmeters — 
 Range of Instruments — Ammeter Shunts — Range of Voltmeters — 
 Voltmeter Multipliers— The Movable Core Type — Approximate 
 Equation for Pull on Iron Core — Movable Coil Permanent Magnet 
 Type — Damping — Torque Exerted by a Magnetic Field upon a 
 Rectangular Coil. 
 
 ' CHAPTER IV 
 
 Fundamental Principles of Alternating Currents 47 
 
 Introduction — Alternating Current — Generation of an Alternating 
 Pressure — ^Law of Fluctuation of Alternating Pressure and Current 
 — Cycle, Frequency, Period, Alternation — Instantaneous Value — 
 Maximum Value — Average Value — Effective Value or Root-mean 
 Square Value — Effect of Capacity — Phase Difference — Power in 
 Alternating-current Circuits — Phase Angle. 
 
X CONTENTS 
 
 CHAPTER V 
 
 Page 
 
 Alternating-current Circuits 61 
 
 Single-phase circuits — Polyphase Circuits — Three-phase Circuits 
 — Current and Voltage Relations in Three-phase Circuits. 
 
 CHAPTER VI 
 
 Induction Principle 67 
 
 Introduction — Rotating and Revolving Magnetic Fields — Pro- 
 duction of Rotating Field — Rotating Field Produced by Unequal 
 Component Fields — Production of a Revolving IMagnetic Field — 
 Speed of Revolving Field. 
 
 CHAPTER VII 
 
 Induction Type Ammeters and Voltmeters 75 
 
 Application of Induction Principles to Meters — Induction Am- 
 meters and Voltmeters — Series Transformer Principle — Relation 
 between Current and Torque — Influence of Frequency — Influence 
 of Temperature — Scale — Damping. 
 
 CHAPTER VIII 
 
 Elbctrodynamic Ammeters and Voltmeters 83 
 
 Introduction — Electrodynamometer Type — Operation of Electro- 
 dynamometer Ammeter — Voltmeters — Effect of Inductance Upon 
 Reading of Electrodynamometer Voltmeter — Construction — -Am- 
 pere Balance — Uses of Kelvin Balance as a Voltmeter — Westing- 
 house Dynamometer Ammeter and Voltmeter — Influence of 
 Earth's Magnetic Field — Advantages— Disadvantages. 
 
 CHAPTER IX 
 
 Miscellaneous Ammeters and Voltmeters 97 
 
 Electrostatic Voltmeter — Westinghouse Electrostatic Voltmeter — 
 Operation — -Insulation — Damping — Advantages — Hot-wire In- 
 struments — Hot-wire Voltmeter — Hot-wire Ammeter — Damping 
 — Thermoammeter. 
 
 CHAPTER X 
 
 Power Measuring Instruments 109 
 
 Wattmeters — Electrodynamometer Type — Theory of Electrodyna- 
 mometer Wattmeter — Compensation for Power Consumed in 
 Instrument — Influence of the Inductance of the Voltage Coil- 
 Correction Factor— Range of Wattmeters — Induction Type Watt- 
 meters — Westinghouse Induction Wattmeter — Lagging Induction 
 Wattmeters — Scale — Mercury Wattmeter. 
 
CONTENTS xi 
 
 CHAPTER XI 
 
 Page 
 
 Phase Relation and Frequency Instruments 127 
 
 Introduction — Power-factor — Power-factor Meter — Analytical 
 Proof of Principles— Polyphase Power-factor Meter — Westing- 
 house Power-factor Meter — Frequency Meters — Resonance Fre- 
 quency Indicator — Campbell Frequency Meter — Hartmann and 
 Braun Frequency Meter — Induction Type Frequency Meter — 
 Weston Frequency Meter — Synchronizing Devices — Weston Syn- 
 chroscope — Westinghouse Synchroscope— Lincoln Type Syn- 
 chroscope. 
 
 CHAPTER XII 
 
 Recording or Graphic Meters 148 
 
 Introduction — Direct Acting — Bristol Recording Instruments — 
 General Electric Recording Meters — General Electric Recording 
 Voltmeters and Wattmeters — Esterline Graphic Meters — Relay 
 Type of Recording Meters — Principles of Operation — Construction 
 — Operation — Damping — Sensibility — Westinghouse Recording 
 Ammeters, Voltmeters, and Wattmeters — Westinghouse Recording 
 Frequency Meters — Westinghouse Recording Power-factor Meter 
 — Operation — Sangamo Graphic Meters — Right Line Pen Move- 
 ment — Advantages and Disadvantages. 
 
 CHAPTER XIII 
 
 Integrating Meters, Watt-hour Meters ... 168 
 
 Introduction — Watt-hour Meters — Electrodynamometer Type 
 (without iron) — Countet-torque — Summation of Power — ^Large 
 Current Capacity Watt-hour Meters — Electro-dynamometer Type 
 (with iron)— Friction Compensation — Creeping — Brushes — The 
 Commutator — Armature — Bearings — Jewels — Magnets — Register- 
 ing Mechanism — Electrodynamometer Type on Alternating-current 
 Circuits^-Lagging — -Value of Shunt Circuit Resistance — Three-wire 
 Direct-current Meters — Mercury Watt-hour Meter — Operation — 
 Compensation for Friction — Full-load Adjustment — Induction 
 Type Watt-hour Meters — Operation — Shifting Magnetic Field — 
 Practical Construction — Sangamo Induction Meter — Balance of 
 Elements — Duncan Induction Watt-hour Meter — Full-load Adjust- 
 nent — Relation between Torque and Power — ^Lagging Induction 
 Watt-hour Meters — The Effect of Over and Under Lagging — Light 
 Load Compensation^Flux Shunting Method — Influence of Fre- 
 quency — Double Lagging — Single-phase Watt-hour Meters on Poly- 
 phase Circuits — Three-wire Single-phase Induction Watt-hour 
 Meters — Voltage Coil Connected Across Outside Wires — Load Un- 
 balanced — Voltage Coil Connected between One Outside Wire and 
 Neutral — Polyphase Watt-hour Meters — Watt-hour Meters for 
 Two-phase and Three-wire Three-phase Circuits — Relation of 
 
xii CONTENTS 
 
 Paob 
 
 Power to Torque in a F-connected System — Relations between 
 Power and Torque in a A-connected System — Polyphase Meters 
 for Four-wire Three-phase Systems — Balance of Metering Ele- 
 ments — Interference of Elements — Effect of Power-factor on 
 Operation — Effect of Improper Connections — Prepayment Watt- 
 hour Meters — Prepayment Device — Operation — Bases of Energy 
 Rates — Two-rate Meters. 
 
 CHAPTER XIV 
 
 Integrating Meters, Ampere-hour Meters 241 
 
 Introduction — Electromagnetic Type Ampere-hour Meter — 
 Accuracy Characteristics — Electrolytic Ampere-hour Meters — 
 Edison Electrolytic Ampere-hour Meter — The Bastian Ampere- 
 hour Meter. 
 
 CHAPTER XV 
 
 Demand Indicators 247 
 
 Introduction — Thermal Type — Induction Type — Time Lag — 
 Westinghouse Demand Indicator, Mechanical Type — Operation — 
 Graphic Demand Meter, Type G — General. 
 
 CHAPTER XVI 
 
 Instrument Testing 263 
 
 Introduction — General Precautions — Kinds of Tests — Apparatus 
 for Instrument Testing — The Standard Cell — Galvanometer — 
 Potentiometers — Slide-wire Type — Operation^ — ^Leeds & Northrup 
 Potentiometer — Operation — Deflection Type Potentiometer — 
 Theory and Operation — Standard Resistances or Shunts — Vari- 
 able Resistance Rheostat — ^Lamp Bank — Water Rheostat. 
 
 . CHAPTER XVII 
 
 Testing Ammeters 278 
 
 Introduction — Comparison of Ammeters — Calibration Curve — 
 Calibration of D. C. Ammeters by Means of Standard Resistance 
 and Voltmeter — Deflection Potentiometer Method — Difference 
 between D. C. and A. C. Ammeters and Voltmeters — Calibration 
 of A. C. Ammeters. 
 
 CHAPTER XVIII 
 
 Testing Voltmeters, Wattmeters, Power-factor, and Frequency 
 
 Meters 290 
 
 Introduction — Comparison of D. C. Voltmeters — Potentiometer 
 Method — Testing A. C. Voltmeters — Calibration Curves — Test of 
 Electrodynamometer Type Wattmeter — Testing Single-phase 
 
CONTENTS xiii 
 
 Paqb 
 
 Power-factor Meters — Testing Polyphase Power-factor Meters — 
 Testing Frequency Meters — Testing Recording Meters. 
 
 CHAPTER XIX 
 
 Testing Watt-hour Meters 303 
 
 Introduction — Rotating Standard Watt-hour Meter — Meter 
 Timing Device — Kinds of Tests — Shop Tests — Installation Tests — 
 Periodic Tests — Complaint Tests — Inquiry Tests — Retests — Re- 
 pair Tests — Special Tests — Meter Constants — Dial Constant — 
 Test Constant — Watt-hour Constant — Watt-minute or Watt- 
 second Constant — Use of Constant in Testing — Methods of Loading 
 — The Consumer's Load — Portable Lamp Bank Method — Special 
 Load Box Method — Portable Storage Battery Method — ^Low Volt- 
 age Transformer Method— Determination of Watt-hour Constant, 
 Experimentally — Method of Procedure — Test for Percentage of 
 Accuracy — Test of a D. C. Three-wire Meter — Test for Balance — 
 Test of Ampere-hour Meters. 
 
 CHAPTER XX 
 
 Methods op Obtaining Different Power-factors 325 
 
 Introduction — Reactance Coil Method — Two Transformer Method 
 — Two Resistance Method — Two Generator Method — Phase-shift- 
 ing Transformer — Ammeter Method of Measuring Power-factors 
 — Ammeter Method on Two-phase Circuits — Ammeter Method on 
 Three-phase Circuits. 
 
 CHAPTER XXI 
 
 Special Tests op A. C. Watt-hour Meters 338 
 
 Test for Quarter-phasing — Test of Single-phase Mster on Non- 
 inductive Load — Test of Single-phase Watt-hour Meter on Induc- 
 tive Load — Testing with Standard Test Meter — Testing of Poly- 
 phase Meters — Test for Interference of the Two Metering Elements 
 — Test to Determine Torque — Test of Influence of Friction — 
 Test to Determine Influence of Stray Field— Test to Determine 
 Loss in Potential Coil — Test for Proper Connections. 
 
 -■ CHAPTER XXII 
 
 Instrument Errors 365 
 
 Sources of Error- Inherent Errors— Inherent Temperature Errors 
 
 Inherent Errors Due to Time and Use — Inherent Mechanical 
 
 Errors — Defective Performance of Springs — Errors Due to Balanc- 
 ing—Errors of Use— Electrostatic Effect— Contact Errors— Errors 
 Due to Thermo-electromotive Forces — Errors Due to Combina- 
 tion of Instruments— Errors Due to Voltage and Current Trans- 
 formers—Errors Due to Frequency and Wave Form— Errors of 
 Observation. 
 
xiv CONTENTS 
 
 CHAPTER XXIII 
 
 Page 
 
 Instrument Transformers 385 
 
 Definitions — Reasons for Use — General Theory — Current Trans- 
 former — Potential or Voltage Transformer — Influence of Trans- 
 former Constants in Power Measurements — Variation of Error 
 with Power-factor — Variation of Error with Phase Angle — Testing 
 Instrument Transformers — Watt-hour Meter and Standard Trans- 
 former Method — Test for Ratio of Transformation, Watt-hour 
 Meter Method — Test for Phase Angle, Watt-hour Meter Method 
 — Ratio by Wattmeter and Standard Transformer Method — Phase 
 Angle by Wattmeter Method — Potential Transformer Comparator 
 Voltmeter. 
 
 Index 405 
 
ELECTRICAL METERS 
 
 CHAPTER I 
 FUNDAMENTAL ELECTRICAL PRINCIPLES 
 
 Before taking up in detail the discussion of electrical measur- 
 ing instruments and their application, it will be well to review 
 some fundamental electrical principles with special reference to 
 their application. 
 
 1. Energy. — The industrial application of electricity is mainly 
 a process of utilizing energy, and the industrial use of electrical 
 measuring instruments is primarily to secure efficient genera- 
 tion, distribution, and conversion of energy. Energy is thus the 
 important entity in all industrial operations. In fact, the whole 
 series of physical phenomena consists in the transfer and trans- 
 formation of this entity. 
 
 Physicists define energy as the ability of a body or a system 
 of bodies to do work; and work is defined as overcoming resist- 
 ance through space, or in other words, the motion of a body 
 against a force. Every moving body possesses the ability of 
 doing work, because by virtue of its motion it can set other 
 bodies into motion. 
 
 2. Forms of Energy. — For purposes of clearness in discussion 
 and calculation, energy is usually considered under two heads 
 which are determined by the manner in which energy manifests 
 itself. As pointed out, a body in motion is capable of causing 
 motion in another body and hence, a body possesses energy by 
 virtue of its motion. Such energy is called kinetic. 
 
 Again, energy may also be possessed by a body in such a 
 position, or condition, that it is capable of motion and ready to 
 do work when the occasion arises. Such energy is called 
 potential. 
 
 These two forms are not distinct in kind, and one form may 
 readily be converted into the other. Perhaps the simplest 
 illustration of the two kinds of energy and the conversion of one 
 form into the other is a vibrating pendulum. At the extreme 
 
 ' 1 
 
2 ELECTRICAL METERS 
 
 positions of its swing the pendulum comes momentarily to rest, 
 hence, its energy of motion, or kinetic energy, is zero. All of 
 the energy is in the potential form. At the lowest or middle 
 point of its swing the energy of the pendulum is wholly kinetic, 
 and at intervening points it is partly kinetic and partly potential. 
 
 3. Conservation of Energy. — Throughout all transformations of 
 energy no body or system of bodies can acquire energy except 
 at the expense of energy possessed by some other system. Hence, 
 to do work is to transfer energy from one system to another, and 
 the amount of energy lost by one system is the exact equivalent 
 of that acquired by the other. This means that no electric 
 generator can ever be made to give out more energy than it 
 receives. Some energy is always dissipated in every trans- 
 formation, and hence, no machine can have an efficiency of 100 
 per cent. 
 
 4. Electricity and Electrical Energy. — We know not what 
 electricity fundamentally is, we know it only through its mani- 
 festations or effects. It matters not, so far as practical results 
 are concerned, whether electricity is a form of energy, or only a 
 vehicle of energy. The fact is that energy always is manifest in 
 connection with the electrical current, and that this energy can 
 be transformed into other forms of energy. It may also be trans- 
 ferred from point to point without the necessity of mass motion. 
 It is this ability to transfer energy without mass motion that 
 makes electricity the only successful medium for transferring 
 energy over long distances. 
 
 The transformation of electrical energy is electrical work and 
 is accomplished in many ways. The rate of transformation is 
 power just as in the case of an expenditure of mechanical energy. 
 
 5. Analogies. — The kinetic energy of a body in motion is pro- 
 portional to the square of its speed. If m represents the mass 
 of the body and Vi its speed, its kinetic energy is given by 
 
 Kinetic energy = }/^m Vi^ 
 
 When a force acts upon a body in motion, its effect is to acceler- 
 ate the speed of the body, that is, to change its speed from Vi 
 to Vi. The kinetic energy then is equal to ^^mFz^, jf the 
 action of the force is such as to increase the speed there is an 
 accumulation or storage of energy equal to }^m{'Vi^ — Vx^). 
 In an analogous way whenever a current in a circuit is increased, 
 the energy in the magnetic field is increased. The mechanical 
 
FUNDAMENTAL ELECTRICAL PRINCIPLES 3 
 
 energy is recovered when the body slows down to its former 
 speed, and the electrical energy is returned to the circuit when 
 the current decreases to its former value. 
 
 Another similarity between mechanical and electrical energy 
 is found in their conversion from kinetic into potential form and 
 vice versa. Mechanical energy can be changed to the potential 
 form by compressing a spring. Electrical energy becomes 
 potential when a condenser is charged. 
 
 This similarity or analogy is brought out more forcibly by 
 writing the expressions for energy in the following algebraic 
 forms : 
 
 J f Mechanical energy of rotation = i^ Kca^ 
 
 \ Energy of magnetic field = 3^ LI^ 
 
 Potential energy in compressed spring = J-^ Px 
 Potential energy in charged condenser = J^ QE 
 
 The letters in the above expressions . have the following sig- 
 nificance: 
 
 K is the moment of inertia, u the angular velocity, L the coef- 
 ficient of induction and I the current strength. In the second 
 set of expressions P is the maximum pressure to which the 
 spring is subjected, x the distance through which the spring 
 has been compressed, Q the quantity of electricity in condenser, 
 and E the difference of electrical pressure between the terminals 
 of the condenser. The terms here used will be explained more 
 fully later. 
 
 6. Magnetism. — Magnetic bodies, or magnets, are bodies which 
 attract or repel each other with a force other than gravitation and 
 which tend to set themselves in a definite direction with reference 
 to the earth's surface. The most obvious property of a magnet 
 is its power to attract iron at a distance. A permanent magnet 
 may be made by placing a bar of hardened steel within a solenoid 
 and sending a current of electricity through the solenoid. The 
 immediate space or region surrounding the magnet possesses 
 unique properties. Some of these may be conveniently shown 
 by placing a sheet of paper over a bar magnet and sprinkling 
 iron filings on the paper. On examining the pattern produced 
 on the paper by the fiHngs, it will be discovered that they are 
 arranged in lines radiating from one end of the magnet and con- 
 verging at the other end, Fig. 1. Another method of exploring 
 the field surrounding a bar magnet is by the aid of a small pocket 
 
4 ELECTRICAL METERS 
 
 compass. When a small pocket compass is placed near one end 
 of a magnet, the needle of the compass will point toward the 
 magnet. When the compass is moved along one of the magnetic 
 lines, it will remain parallel to the line. When the compass is 
 brought near the other end of the magnet, the compass needle 
 will be reversed, showing that the properties of the two ends are 
 different at least in one respect. This experimental fact has led 
 to a conventional statement that the magnetic lines leave the 
 north-seeking pole of the bar magnet and reenter the South- 
 seeking pole. According to this explanation the magnetic 
 lines are closed curves leaving the north pole, curving through 
 
 Fig. 1. 
 
 the air, reentering the south pole, and completing the circuit 
 through the metal. The magnetism about the bar is said to be 
 due to a magnetomotive force analogous to electromotive force. 
 The magnetomotive force sets up a difference of magnetic pres- 
 sure between the two ends of the bar, which causes magnetism or 
 magnetic flux from one end of the bar to the other. 
 
 7. Properties of Magnetic Fields. — When unlike poles of two 
 magnets are placed near each other the arrangement of the mag- 
 netic lines will be as shown in Fig. 2. The lines pass directly 
 from the pole of one to the unlike pole of the other magnet. 
 The attraction between unlike poles may, therefore, be considered 
 as due to a tendency of the lines to shorten. 
 
 When two like poles are brought near each other the resulting 
 field is shown by Fig. 3. An inspection of this figure will show 
 
FUNDAMENTAL ELECTRICAL PRINCIPLES 5 
 
 that the lines from one pole do not connect with those of the 
 other pole. The repulsion between unlike poles is, therefore, due 
 
 Fig. 2. 
 
 to a tendency of the lines to repel each other. These figures show 
 that a tension or stress exists in a magnetic field parallel to the 
 
 Fig. 3. 
 
 lines, and a pressure at right angles to their direction. Further- 
 more, the force of attraction and repulsion has its seat outside 
 
6 ELECTRICAL METERS 
 
 of the iron bar, and within the space surrounding it. This 
 principle should be kept in mind. 
 
 8. Strength of Magnetic Field. — The strength of a magnetic 
 field is measured by the force it exerts upon a unit magnet pole. 
 When this force is 1 dyne the field is said to have unit strength. 
 Since iron filings arrange themselves in lines when subjected to 
 the influence of a magnetic field, it is customary to express the 
 field strength in lines per square centimeter; that is, graphically 
 the density of lines is a measure of the field strength. A field of 
 unit strength is represented by one line per square centimeter 
 in a plane perpendicular to the lines. A field of 10 units would 
 then be represented by 10 lines per square centimeter, etc. 
 
 If the cross-sectional area of the field be S sq. cm. and if the 
 field strength or densitj'^ be represented by B, the total number 
 of magnetic lines is equal to SB. The total number of lines 
 through a given area is called the magnetic flux. Algebraically 
 
 *(flux) = SB 
 
 9. Relation between Tension and Flux Density, — When a mag- 
 netic circuit is made of iron, only a small magnetomotive force 
 is necessary to maintain the magnetic flux. When one or more 
 air gaps intervene, most of the magnetomotive force is utilized 
 in forcing the flux through or across the air gap. As a result, 
 there is manifest a force of attraction between any two parts of a 
 magnetic circuit which are separated by an air gap. Both from 
 experimental and theoretical considerations, it has been deter- 
 mined that this force is proportional to the square of magnetic 
 flux per unit cross-section, or put in algebraic form the tension 
 may be expressed as follows : 
 
 F = KSB^ 
 
 where F is the force, B the flux density, S the area, and K a 
 constant. If F is to be expressed in dynes per square centimeter, 
 the expression becomes 
 
 B^ 
 
 F (dynes) = ^ 
 
 In pounds per square inch 
 
 P/ J ^ (2.54)252 
 
 F (pounds) = 4^5 000 X ^ 
 
 10. Magnetic Field Surrounding an Electric Wire. — The be- 
 havior of a compass needle near a wire through which a current 
 
FUNDAMENTAL ELECTRICAL PRINCIPLES 
 
 
 7^'^-i^cjsSSEi 
 
 
 
 is flowing is much the same as when near a magnet. This 
 shows that the space surrounding a current carrying wire is a 
 magnetic field. 
 
 The magnetic lines surround the wire in concentric circles as 
 shown in Fig. 4. The dark spot in the center of the figure repre- 
 sents a cross-section of the wire. The 
 direction of the magnetic lines is de- 
 termined in accordance with the ex- 
 periment shown in Fig. 5. If a cur- 
 rent passes from south to north along 
 a wire held above a pivoted magnetic 
 needle, the Ai'-end of the needle will be 
 deflected westward. 
 
 The north-seeking end of the mag- 
 netic needle is pushed aside by the 
 field surrounding the wire. The direc- 
 tion of the lines below the wire must 
 
 then be westward. In any given case the direction of the lines 
 may be determined by the following rule: 
 
 Gra.sp the wire with the right hand, the thumb pointing in the 
 direction of the current, the fingers will then point in the direc- 
 
 >%fe;^^ ?<;; -^^ J-'-T- -:H.v ^-'-li -^S 
 
 
 
 4?i 
 
 Fig. 4. 
 
 Fio. 5. 
 
 tion of the magnetic lines. The magnetic field surrounding a 
 
 straight wire may be considered as a series of concentric cyhnders. 
 
 11. Field of a Circular Coil. — When the wire is coiled into a 
 
 circular loop, the magnetic lines enter one side of the loop, pass 
 
8 
 
 ELECTRICAL METERS 
 
 through, and spread out at the other side, Fig. 6. The loop of 
 wire thus has the properties of a magnet; the north-seeking pole 
 being where the lines leave, and the south pole where the lines 
 enter the coil. A magnet brought near the loop will be attracted 
 or repelled, depending on whether unlike or like poles are brought 
 near each other. 
 
 12. Solenoids. — It has already been pointed out that, when an 
 electric wire is wound into a coil, all or nearly all the magnetic 
 lines pass in at one end and out at the other. Many types of 
 instruments make use of some form of a solenoid. When the 
 solenoid possesses an iron core, the combination is called an 
 electromagnet. Figs. 7 and 8 show the general distribution of 
 
 1-it 
 
 the magnetic lines in both a solenoid and electromagnet. Upon 
 referring to the figures in question, it will be noticed that the 
 lines do not all go the whole length of the solenoid, but some 
 escape between the convolutions. The magnetic field is thus not 
 uniform throughout the length of the solenoid. In fact, the 
 coil has to be of considerable length to get a uniform field of 
 10 cm. length. 
 
 When the solenoid has an iron core, fewer magnetic lines take 
 "short cuts" between the convolutions of the coil, but more lines 
 continue throughout the whole length of the solenoid. This is 
 due to the fact that the iron offers less opposition or reluctance, 
 as it is called, to the establishment of the magnetic lines, than air. 
 It requires less magnetomotive force to establish a given number 
 of magnetic lines in iron than in air, so when a definite magnetic 
 
FUNDAMENTAL ELECTRICAL PRINCIPLES 
 
 9 
 
 field is established within a solenoid, the introduction of an iron 
 core will greatly increase its strength. 
 
 The strength of magnetic field within a solenoid is given by the 
 formula 
 
 4 
 
 H 
 
 10 
 
 irni 
 
 
 Sa»(Jj>..Vi;,.-4/,i.-; 
 
 
 Fig. 7. 
 
 where n is the number of turns per unit length — 1 cm. — of 
 solenoid, and I is the current in amperes. This formula applies 
 only to the middle portion of the solenoid where the field is 
 uniform. Toward the ends the value falls off rapidly. When 
 
 an iron core is placed within the solenoid, the flux density within 
 
 the iron is 
 
 4 
 ■B = yq TriJ.nl 
 
 /I is a quantity depending upon the quality of the iron and may 
 
10 ELECTRICAL METERS 
 
 have many values under different conditions. It is always 
 greater than one and may be as large as 10,000. 
 
 The cores of electromagnets should be made of the softest and 
 purest iron, but for alternating currents the core must be made of 
 laminated iron or iron wire. The laminations prevent the forma- 
 tion of eddy currents which tend to flow at right angles to the 
 direction of the magnetic lines. The elimination of eddy currents 
 prevents excessive heating of the core. 
 
 13. Law of the Magnetic Circuit. — The relation between the 
 magnetizing force of a solenoid and the resulting magnetic flux 
 may be conveniently expressed in the form of Ohm's law. 
 
 Analogous to resistance in an electrical circuit there is a quan- 
 tity called reluctance in the magnetic circuit. The readiness 
 with which any given magnetizing force will build up a magnetic 
 field depends upon the permeability, length, and cross-section 
 of the circuit. 
 
 The higher the permeability and the greater the cross-sectional 
 area of the circuit the more readily will the magnetic field be 
 established. On the other hand, the longer the circuit the 
 stronger will the magnetizing force have to be to establish a 
 given field. The effect of these physical properties of a magnetic 
 circuit is called reluctance and is equal to 
 
 fiA 
 
 Where L is the length of circuit, n the permeability, and A the 
 cross-section. 
 
 The magnetomotive force due to a solenoid carrying a current 
 lis 
 
 4 
 m.m.f. = YTj '"'^I 
 
 Where N is the total number of turns on solenoid. 
 
 Analogously to Ohm's law the flux f> = — '-z=^ = — = 
 
 When the magnetic circuit is not uniform, the reluctance of 
 each part must be determined separately. The reluctance of 
 the whole circuit is the sum of the reluctances of its parts. 
 
 14. Force Exerted upon a Wire in a Magnetic Field. — Since a 
 wire carrying a current is surrounded by a magnetic field, a force 
 
FUNDAMENTAL ELECTRICAL PRINCIPLES 11 
 
 of attraction or repulsion will be experienced when the wire is 
 introduced into a field due to a magnet; this force will act at 
 right angles to the wire, and to the field of the magnet, Fig. 9. 
 
 If I represents the current flowing in the wire, H the strength 
 of magnetic field, and I the length of wire at right angles to field, 
 the force is given hy F = IIH. 
 
 The direction of the force, as indicated by the arrow, may be 
 determined by the following rule : 
 
 If the thumb, index, and middle fingers of the left hand be held 
 at right angles to each other, the thumb pointing in the direction 
 of the field, the index finger in the direction of the current, the 
 middle finger will point in the direction of the force acting upon 
 
 
 Fig. 9. 
 
 the conductor. If this conductor is free to move it will move in 
 the direction of the force. Thus in Fig. 9 the direction of the 
 field is from N to S, and if the current flows up through the paper 
 the force will be in difection indicated. 
 
 15. Force between Parallel Wires Carrying Currents. — Two 
 parallel wires carrying electric currents will be either attracted 
 or repelled depending upon whether the currents are flowing in 
 the same or opposite directions. 
 
 If the currents flow in the same direction the magnetic lines 
 will combine so as to encircle both conductors. Fig. 10. The 
 tension along the lines will be manifest as a force tending to 
 draw the wires together. 
 
 When the currents are in opposite directions, the direction of 
 the fields between the conductors is the same, and hence, the 
 pressure at right angles to the lines will tend to force the wires 
 farther apart. 
 
12 ELECTRICAL METERS 
 
 The intensity of the force in either case is proportional to the 
 product of the currents in the two wires. This relation is derived 
 as follows: 
 
 At a distance x from a wire carrying a current I, the strength 
 of field is 
 
 X 
 
 The force between a field H and a current per unit length of 
 conductor is 
 
 F = HI', r is the current in the second conductor 
 
 Since H = — 
 
 X 
 
 27 X /' 
 
 F = , per unit length of conductor. 
 
 When / and I' are in absolute units, x in centimeters, the 
 force is in dynes. 
 
 //■^ ^---" ^^ 
 ! ; o o ) ) 
 
 Fia. 10. 
 When the two currents are equal, I = /', the expression becomes 
 
 F = KP . 
 
 where X is a proportionahty factor. 
 
 These relations are very important as they have numerous 
 applications in electrical measuring instruments. 
 
 16. Electrolytic Conductors. — The passage of an electric cur- 
 rent through some liquids is accomplished by different phenomena 
 from its passage through solids. In fact, in regard to their 
 conductivity, liquids may be divided into three groups, viz. : 
 
 1. Those which make fairly good insulators, or which are non- 
 conductors for practical purposes such as paraffin, mineral oil, 
 etc. 
 
 Note. — The student can find the derivations of the two assumed equa- 
 27 
 tions, H = — and F = HI' in books on Physiea. 
 
FUNDAMENTAL ELECTRICAL PRINCIPLES 13 
 
 2. Those which conduct like soUds without undergoing any 
 chemical change, such as molten metal, mercury, etc. 
 
 3. Those in which the passage of the current is accompanied 
 by chemical decomposition, such as solutions of acids, salts of 
 the metals, and some other chemical compounds. 
 
 Liquids of the latter class are called electrolytes. The process 
 of their decomposition by the passage of the electric current is 
 called electrolysis, and the cell in which electrolysis is carried 
 on is called an electrolytic cell. 
 
 17. Faraday's Laws. — During the years 1833 and 1834 Faraday 
 investigated the relation between the quantity of electrolyte 
 decomposed by an electric current, and the strength of the current. 
 The result of his investigations he expressed as follows: 
 
 1. The mass of the solution decomposed is proportional to the 
 quantity of electricity which passes through it. 
 
 2. The mass of any substance liberated by a given quantity of 
 electricity is proportional to the chemical equivalent of the 
 substance. 
 
 The first law means that a given current of electricity flowing 
 for a given time will deposit the same mass or weight of a given 
 element from a solution, irrespective of the concentration of the 
 solution that contains the element, or of other conditions. 
 
 According to the second law, the mass of substance deposited 
 will depend upon its combining weight, which is called chemical 
 equivalent. Thus, when a solution of copper salt is used as the 
 electrolyte, the mass of copper deposited will depend on whether 
 a cupric or cuprous salt is used. The chemical symbol for cupric 
 chloride is CuCU, and for cuprous chloride CuCl. From this it 
 will be seen that two atoms of copper in the cuprous compound 
 take the place of one atom in the cupric compound. The com- 
 bining weight is twice as great, and twice as much copper will be 
 deposited by a given current from a cuprous solution as from the 
 cupric solution. The law also states that if solutions of different 
 compounds be decomposed, the weight of material deposited by 
 a given current is proportional to the combining weight of the 
 materials or elements forming the compounds. Thus, 1 ampere 
 sent through a solution of silver nitrate for 1 hr. will deposit 
 4.025 grams of silver. The same current sent through a solu- 
 tion of copper sulphate will deposit only 1.184 grams of copper 
 in 1 hr. These laws are the fundamental principles of the 
 operation of electrochemical measuring instruments. The elec- 
 
14 
 
 ELECTRICAL METERS 
 
 trochemical equivalents of some metals are given in the following 
 table: 
 
 Table I 
 
 Metal 
 
 Electrochemical equivalent in 
 milligrams per coulomb 
 
 
 0.0936 
 
 
 0.6588 
 
 CoDDer 
 
 0.3290 
 
 Gold.. 
 
 0.6818 
 
 Iron. 
 
 0.2894 
 
 Iron. . 
 
 . 1929 
 
 Lead 
 
 1.0731 
 
 
 0.3040 
 
 Silver 
 
 1.1180 
 
 
 0.3385 
 
 
 
 It is noticed that two values are given in the table for copper 
 and iron. This is because each of these has different valencies 
 as explained above. The value 0.3290 for copper usually applies 
 when copper is deposited in an electrolytic cell. The table may 
 be reduced to English units by remembering that 1 gram is 
 equal to 0.0353 oz. avoirdupois. 
 
 18. Heat Effect. — The physical principle made use of in some 
 instruments is the expansion of the metals by heat. When the 
 temperature of a wire is raised, it expands; and since some of the 
 energy of a current is always converted into heat, the strength 
 of current may be measured by means of the expansion of a 
 wire suitably arranged. Hot-wire instruments are due to an 
 adaptation of this principle. 
 
 19. Practical Electrical Units. — In the application of electricity 
 many terms are constantly met, and a clear comprehension of the 
 meaning of these terms will aid materially in understanding their 
 industrial application. Among the most important terms are 
 the names of the fundamental electrical units: ohm, ampere, 
 volt, coulomb, watt, joule, henry, and farad. 
 
 20. Resistance. — Every electrical conductor offers a resistance 
 to the flow of electricity. This resistance depends upon the 
 material of which the conductor is made, the length of the con- 
 ductor, and its cross-sectional area. The resistance of a con- 
 ductor is analogous to the resistance a water pipe offers to the 
 flow of water. This resistance will depend upon the roughness 
 
FUNDAMENTAL ELECTRICAL PRINCIPLES 15 
 
 of its surface, or upon the material of which it is made. A long 
 pipe will offer more resistance than a short pipe of same diameter, 
 and a pipe of large diameter will offer less resistance than one of 
 same length but of smaller diameter. It must be remembered, 
 however, that the cause of the resistance of a conductor to the 
 flow of electrical current is not the same as the cause of the resist- 
 ance of a water pipe to the flow of water. They are analogous 
 only. 
 
 The resistance of any conductor can then be written in the 
 following form : 
 
 ^'A 
 
 where R is the total resistance, r, the resistance of a piece of 
 the conductor of unit length and of unit cross-section, A its cross- 
 sectional area, and I its length. 
 
 The ohm is the unit of resistance and is defined as the resistance 
 offered to an unvarying electric current by a column of mercury 
 at the temperature of melting ice, 14.4521 grams mass, of a 
 constant cross-sectional area and of a length of 106.3 cm. 
 
 The ohm is thus a definite quantity and the resistance of any 
 
 rl 
 conductor is expressed in terms of it. In the formula R = -rt 
 
 I and A may be expressed in any units, provided r expresses a 
 resistance based on these units. The definition given for the 
 ohm assumes I to be in centimeters and A in square centimeters. 
 In this country the Brown and Sharpe, or American wire gage 
 has been generally adopted where a gage is to be used. In 
 many cases it is better to specify the actual diameter or cross- 
 section of a wire, and for this purpose the "mil system" has been 
 introduced. In this system the mil is the unit of length and is 
 equal to 0.001 in. 
 
 Since the areas of any two circles are proportional to the squares 
 of their diameters, if the area of a circle 1 mil in diameter be 
 taken as the unit area, the area of any other circle may be ex- 
 pressed as the square of its diameter in mils. The unit area is 
 called the circular mil (circ. mil) and is, as above expressed, the 
 area of a circle 0.001 in. in diameter. Area in circular mils is 
 equal to diameter squared, and the area expressed in square 
 measure is equal to 0.7854 X d^ (diameter squared). The 
 circular mil is, therefore, equal to 0.7854 sq. mil. 
 
 It is seldom necessary to convert the area of round conductors 
 
16 ELECTRICAL METERS 
 
 into square measure. The wire tables which are in common use 
 usually give the sizes in the American wire gage, its diameter 
 in mils, its area in circular mils, and various other properties of 
 wire depending on the completeness of the tables. 
 
 Wires larger than 0000 A.W.G,, that is, of a greater diameter 
 than 0.46 in., are usually designated by their diameters in mils 
 or their cross-sectional area in circular mils. 
 
 The unit of a conductor most commonly used is a conductor 
 1 ft. long and 1 mil in diameter called the mil-foot. The resist- 
 ance of a mil-foot of copper of 98 per cent, conductivity is 9.61 
 ohms at 0°C. or 32°F. This value may be used in our resistance 
 formula, which then becomes 
 
 A 
 
 I being expressed in feet and A in circular mils. 
 
 21. Change of Resistance with Temperature. — The resistance 
 of most conductors changes with the temperature. The resist- 
 ance of pure metallic conductors increases with increase in 
 temperature For pure metals the increase per ohm per degree 
 is practically the same for all. This increase per ohm per degree 
 change in temperature is called temperature coefficient of resist- 
 ance, and for pure metals is nearly 0.00393 per degree Centigrade. 
 The resistance of a conductor at any temperature t°Q. is given 
 by the following: 
 
 Rt = Ro{l + at) 
 
 R„ is the resistance of conductor in ohms at 0°C., a the tempera- 
 ture coefficient, and t the temperature. The resistance of most 
 alloys also increases with increase in temperature, but to a much 
 smaller extent than pure metals. Thus an alloy of 84 parts by 
 weight of copper, 12 parts by weight of nickel, and 4 parts by 
 weight of manganese, called manganin, has a temperature coeffi- 
 cient of resistance which is negligible for practical purposes. 
 Although the temperature coefficient of manganin is very slight, 
 it is positive between 0° and about 50°C. When the temperature 
 is increased above 50°C. the resistance of manganin slightly 
 decreases. 
 
 Carbon and all acid salt solutions have negative tempera- 
 ture coefficients of resistance. That is, the resistance of these 
 decreases as the temperature increases. 
 
FUNDAMENTAL ELECTRICAL PRINCIPLES 17 
 
 22. Electric Current. — The term "electric current" has already- 
 been used several times without explanation, and perhaps an 
 explanation will not aid much in giving a clear understanding of 
 the quantity. 
 
 Since the transfer of energy by water through pipes is in many 
 ways analogous to the transfer of energy by electrical means, 
 the terminology in one case is used to some extent in the other. 
 
 When water flows through pipes the energy transferred by it 
 in a given time depends upon the current and head, or pressure. 
 The current is the number of gallons or cubic feet of water per 
 second, or some other unit of time. The current is then the rate 
 of flow of water. 
 
 Electrical energy may be transferred along a conductor, and 
 while the energy is being transferred the conductor is surrounded 
 by a magnetic field. The transfer of energy is said to be by 
 means of a current of electricity. Thus, the rate of flow of 
 electricity is also called a current. The two cases are evidently 
 analogous. 
 
 In measuring a water current it is possible to measure the 
 quantity of water discharged and thus, the rate of flow. It is 
 not practical to measure an electric current in this way. The 
 electric current is measured by means of its effect, and any effect 
 which is proportional to some power of the current strength 
 may be used for determining unit current, and hence, for measur- 
 ing the current. The practical unit current has been defined in 
 accordance with Faraday's first law as follows: 
 
 The Ampere is the unvarying electric current which, when 
 passed through a standard solution of nitrate of silver- in water, 
 deposits silver at the rate of 0.00111800 gram per second. An 
 ampere will thus deposit 4.025 grams of silver per hour. 
 
 Absolute Unit of Current. — Another definition of unit current 
 rests upon the fundamental principle that about every electric 
 current there is a magnetic field. The intensity of this magnetic 
 field at any point varies directly as the current strength and 
 inversely as the distance of the point from the conductor (see 
 Article 15). 
 
 If a magnet be introduced into such a field, a force will be 
 exerted upon it. The unit current is defined in terms of this 
 force. According to these principles, unit current is defined as 
 that current which, when flowing through a conductor 1 cm. long, 
 bent into an arc with 1 cm. radius, will exert a force of 1 dyne 
 
18 ELECTRICAL METERS 
 
 on unit magnet pole placed at the center of the circle of which 
 the arc is a part. The ampere is one-tenth of this absolute unit. 
 
 23. Electromotive Force. — The real cause of an electric current 
 is called electromotive force. Without going into details, we 
 may say that electromotive force can be generated in three ways: 
 
 1. Chemically, as in voltaic cell. 
 
 2. Thermally, as when the junction of two metals is heated. 
 
 3. Mechanically, as in the case of the static induction machine 
 or when a wire is moved across a magnetic field. 
 
 Of these three methods the last is the all-important one in 
 industrial practice. It consists in the application of the principle 
 that a wire moved in a magnetic field in such a direction as to 
 cut across the magnetic lines has an electromotive force induced 
 in it. That is, the reaction between the magnetic field and the 
 mechanical force causing the motion is manifest as an electro- 
 motive force between the terminals of the wire. The value of 
 this electromotive force will depend upon the strength of the 
 magnetic field, the length of wire, and the speed with which it 
 is moving across the field. This principle is used in the con- 
 struction of all dynamo-electric machines, which form the main 
 means for the conversion of mechanical into electrical energy 
 and vice versa. 
 
 Volt. — Since the resistance of a conductor is comparable 
 to the resistance offered by a pipe to the flow of water, and the 
 electrical current is comparable to the current of water, we may 
 compare the electromotive force or electrical pressure to the 
 water pressure causing a flow of water. Although this com- 
 parison is not exact, it still serves to give a better understanding 
 of the relation of the electrical quantities involved. Water 
 pressure can be measured in terms of pounds per square inch, 
 but usually it is expressed as a head of so many feet. In the 
 same way, the difference of electrical pressure between the termi- 
 nals of a battery may be considered as a difference of electrical 
 level. The current will then flow from a point of higher to a 
 point of lower electrical level, when the circuit is closed. This 
 difference of electrical pressure or electromotive force, is ex- 
 pressed in volts, and the volt is defined as that difference of pres- 
 sure which will cause a current of 1 amp. to flow through a 
 resistance of 1 ohm. 
 
 24. Quantity. — The quantity of water flowing through any 
 given pipe in a given time may be expressed as the strength of 
 
FUNDAMENTAL ELECTRICAL PRINCIPLES 19 
 
 current multiplied by the time. That is, if a unit current gives 
 a cubic foot of water per second, a two-unit current would give 
 2 cu. ft. per second, or 4 cu. ft. in 2 sec. 
 
 Similarly, a unit current of electricity flowing for 1 sec. givea 
 a definite quantity of electricity. This quantity is called 
 the coulomb and is defined as the quantity of electricity conveyed 
 by a current of 1 amp. in 1 sec. of time. The total quantity 
 convej^ed by a current of I amp. in t sec. is then given by 
 
 Q = It, assuming I to be constant. 
 
 25. Energy. — Referring again to our analogy we may consider 
 unit work to be done when a cubic foot of water is delivered 
 under a head of 1 ft. The amount of work done by a head of h 
 ft. delivering q cu. ft. of water will then be hq. 
 
 In our electrical analogy, the head was analogous to electrical 
 pressure, and the number of cubic feet of water is analogous to 
 the number of coulombs. A current delivering Q coulombs of 
 electricity under a pressure of E volts will then do EQ units of 
 work. The unit of electrical work is the joule and is defined as 
 the work expended in a circuit when 1 coulomb is transferred 
 under a pressure of 1 volt. Since the number of coulombs 
 delivered by a current of I amperes in the time t is It, the amount 
 of work expended by a current of I amperes in the time t and under 
 a pressure of E volts is 
 
 Work = Elt joules. 
 
 Watt-hour. — One watt-hour equals 3,600 joules. 
 
 26. Power. — The watt is the unit of power and is equal to 
 
 1 joule per second. The watt is also equal to ^^^ hp. The 
 
 number of joules of work expended by a current of I amperes in t 
 sec, as above expressed, is Elt; the number of joules per second 
 will then be Elt t- t or EI. That is, the power of a current of 
 I amperes flowing under a pressure of E volts is EI watts. 
 
 27. Inductance. — It was briefly pointed out in Article 23 that 
 when a conductor moves across a magnetic field an electro- 
 motive force is induced in the conductor. Evidently it is im- 
 material whether the field is stationary and the conductor moves, 
 or the conductor is stationary and the magnetic field moves; the 
 necessary condition is relative motion between conductor and 
 field. 
 
 3 
 
20 
 
 ELECTRICAL METERS 
 
 This relative motion may be secured in several ways; the one 
 in which we are at present interested consists in changing the 
 magnetic flux around a conductor by means of the current in 
 the conductor. 
 
 Consider the case represented by Fig. 11 where a battery B 
 supplies current through a variable resistance R to an electro- 
 magnet M. Let us suppose the circuit open and no initial or 
 residual magnetism in the core. Upon closing the circuit a 
 current will begin to flow through the electromagnet coil. This 
 
 I '^^ 
 
 <Ey 
 
 
 
 m^ 
 
 
 m^ 
 
 
 ■wrr 
 
 M 
 
 FlQ. 11. 
 
 current will magnetize the core and thus cause a number of 
 magnetic lines to thread through the coil. If the resistance R 
 is varied, the current will change and consequently the number 
 of magnetic lines threading through the coil is either increased or 
 decreased. In other words, any change in the current is accom- 
 panied by a change in the magnetic flux passing through the 
 coil. 
 
 According to the principle of electromagnetic induction, when- 
 ever the number of magnetic lines linked with a circuit is changed 
 an electromotive force is induced in the circuit. Consequently, 
 every time the current in the coil changes, an electromotive 
 force is induced in it. The electromotive force induced by the 
 building up or decay of the magnetic field within the coil, due 
 
FUNDAMENTAL ELECTRICAL PRINCIPLES 21 
 
 to the variation of current in the coil, is called self-induction. 
 The induced electromotive force is in such a direction as to 
 oppose the applied electromotive force. In other words, while 
 the current is changing the electromotive force of self-induc- 
 tion opposes any change. If the magnetic lines threading 
 through the coil are due to a current in an adjacent coil, the 
 phenomenon is the same, but it is called mutual induction. 
 
 From Fig. 6 it is evident that each magnetic line through the 
 center of the coil is linked with each turn; or what amounts to 
 the same thing, the lines due to each turn are linked with every 
 other turn as well. The electromotive force of self-induction then 
 depends not only upon the current but also upon the arrangement 
 of conductors in the coil. If $ is the total flux due to one turn 
 through the coil, and if n is the number of turns, the total flux 
 is n^. This total flux is proportional to the current and hence 
 we may write 
 
 n$ = LI 
 
 The constant L is called the coefficient of self-induction, or 
 simply the self-inductance of the coil. 
 
 The electromotive force of self-induction depends upon the 
 rate of change of magnetic field. This may be expressed by 
 
 d^ jdl 
 
 dl at 
 
 Where ^r represents the rate of change of current. 
 
 According to this expression the inductance L is defined as 
 the ratio of the induced counter electromotive force to the time 
 rate of change of current. 
 
 Henry. — Self- and mutual-inductances are physical quantities 
 of the same nature, and hence the same unit must be used for 
 both. This unit is called the henry and is defined as the induct- 
 ance in a circuit in which the induced electromotive force is 1 
 volt, when the current changes at the rate of 1 amp. per second. 
 
 28. Capacity. — If two metal plates be separated by a good 
 insulator and the two plates be connected to a source of electrical 
 pressure, a momentary current will flow into the plates. The 
 intensity of the current will depend upon the ability of the plates 
 to hold a charge of electricity. This ability of a conductor or a 
 system of conductors, to store electricity is called electrical 
 capacity. The capacity of a system of conductors is determined 
 
22 ELECTRICAL METERS 
 
 by their arrangement, number, and material separating them. 
 The quantity of electricity that a condenser will hold is deter- 
 mined by the capacity of the condenser and by the electrical 
 pressure applied. Algebraically this is expressed by 
 
 Q=^EC 
 
 Where Q is the quantity of electricity, E the pressure, and Cthe 
 capacity. 
 
 Farad. — The unit of capacity is called the farad and is that 
 capacity which is charged to a difference of pressure of 1 volt 
 by 1 coulomb. 
 
 The effect of inductance and capacity in alternating-current 
 circuits will be given later. 
 
 29. Ohm's Law. — The relation between current and electro- 
 motive force in a circuit was first enunciated by Dr. G. S. Ohm 
 in 1827, and is known as Ohm's law. It may be stated as 
 follows: 
 
 The current strength in any circuit is directly proportional 
 to the sum of all the electromotive forces in the circuit. This 
 relation expressed algebraically is 
 
 E = KI 
 
 or 
 
 E 
 
 Y = K, a, constant. 
 
 This holds for both direct- and alternating-current circuits so long 
 as the physical conditions surrounding the circuit remain un- 
 changed. For direct-current circuits K is equal to what is 
 called the resistance of the circuit, and under these conditions 
 
 E = RI 
 or 
 
 j-R 
 
 Thus the ratio of the electromotive force to current is constant 
 so long as physical conditions remain constant. If, for instance, 
 the temperature changes, this ratio will change. This is ex- 
 plained by saying that the resistance changes. 
 
 In alternating-current circuits the total electromotive force 
 must include the electromotive forces of mutual induction, 
 self-induction, and capacity. When these are considered. Ohm's 
 
FUNDAMENTAL ELECTRICAL PRINCIPLES 23 
 
 law, as stated, still holds. What quantities enter into the ex- 
 pression 
 
 when alternating currents are considered is explained in Chapter 
 IV. 
 
 30. Pressure Drop m Direct-current Circuits. — If a current I 
 flows through a circuit, the electromotive force necessary to force 
 it through a resistance R is, by Ohm's law, 
 
 E„ = IR 
 
 Thus the product of current by resistance is equal to the difference 
 in electrical pressure between two points. This quantity IR is 
 called pressure or voltage drop. 
 
 31. Energy Loss. — The flow of electric current through a con- 
 ductor is analogous to the flow of water through a pipe. The 
 pressure forcing the water through the pipe is analogous to the 
 electrical pressure which maintains the electrical current. Work 
 is defined as force times distance through which it acts. Evi- 
 dently, if the water pipe is closed and no water flows, considerable 
 pressure can be exerted and still no work be done. If, however, 
 the water is flowing under a given pressure a certain amount of 
 work will be done which is proportional to the quantity of water 
 times the pressure. This is seen to be true, if the pipe be vertical, 
 in that case, the height of the pipe is proportional to the pressure 
 and the height in feet times the weight of water delivered at the 
 top equals foot-pounds of work. 
 
 Similarly, the work done in transferring a certain quantity of 
 electricity through a conductor is proportional to the pressure 
 times the quantity of electricity. 
 
 If we define our unit of work as the product of unit quantity 
 times unit difference of pressure, the total amount of work will 
 then be represented by the total difference of potential times 
 the current times the time, or 
 W = Elt, since It is the total quantity of electricity delivered. 
 
 Power is the rate of doing work, or is the work done per second, 
 
 hence, 
 
 W Elt 
 Power, or P = — = -r— = EI 
 
 If the difference in pressure between any two points, as A and B 
 
24 ELECTRICAL METERS 
 
 of a conductor, is E and the current is I, the energy spent per 
 second in that portion of the circuit is IE. But, as has been 
 shown, 
 
 E = IR, 
 Hence, P = IE = I X I X R = PR 
 
 This is known as power loss or energy loss per second due to 
 resistance. 
 
 The effects of both the voltage drop and loss of energy due to 
 resistance, are objectionable. The voltage drop produces a dif- 
 ference of pressure between the generator and receiving circuit. 
 The PR losses cause heating of the conductors, thus increasing 
 the fire hazard. They also cause a deterioration of the insulation 
 and lessen the efficiency of the distributing systems. 
 
 SUMMARY 
 
 The Ohm is the unit of resistance. It is the resistance offered 
 by a column of mercury of uniform cross-section, 106.3 cm. in 
 length, weighing 14.4521 grams at 0°C. 
 
 The Ampere is the practical unit of current, and is that current 
 which, when passing through a standard solution of silver nitrate, 
 deposits silver at the rate of 1.118 mg. per second. 
 
 The Volt is the practical unit of electrical pressure and is the 
 electromotive force which will produce a current of 1 amp. 
 through a resistance of 1 ohm. It may also be defined as 
 
 -.J-joo of the electromotive force of the Weston standard cell 
 
 at'20°C. 
 
 The Coulomb is the unit of quantity of electricity and is the 
 quantity of electricity conveyed by 1 amp. in 1 sec. 
 
 The Joule is the unit of work, and is represented by the work 
 expended in 1 sec. by a current of 1 amp. under an electrical 
 pressure of 1 volt. 
 
 Joules = k X volts X amperes X time. 
 
 The Watt is the unit of power and is equal to 1 joule per 
 second. The watt is also equal to }/j46 hp. 
 
 Watts = A; X volts X amperes. In direct-current circuits 
 fc = 1. 
 
 The Kilowatt is the practical unit of power and is equal to 
 1,000 watts. 
 
FUNDAMENTAL ELECTRICAL PRINCIPLES 25 
 
 The Kilowatt-hour is the practical unit of work and represent? 
 1,000 watts supphed for a period of 1 hr. It is equal to 3,600,000 
 joules. 
 
 The Henry is the unit of inductance and is defined as the 
 inductance of a circuit in which the induced electromotive force 
 is 1 volt when the inducing current changes at the rate of 1 amp. 
 per second. 
 
 The Farad is the unit of capacity and is that capacity which is 
 charged to a difference of pressure of 1 volt by 1 coulomb. 
 The farad is too large for practical use, hence, the microfarad 
 
 ( i nno nnn ^^r^*^) i^ commonly used. 
 
CHAPTER II 
 CLASSIFICATION OF INSTRUMENTS 
 
 32. Classes of Meters. — The discriminating characteristic of 
 a classification of electrical measuring instruments may be the 
 quantity to be measured, or the principle upon which the instru- 
 ments operate. The plan here followed bases the main divi- 
 sions of measuring instruments upon the quantities to be 
 measured, while minor subdivisions are according to the principles 
 of operation. The quantities measured by electrical instru- 
 ments are: current, electromotive force, quantity, power, energy, 
 frequency, power-factor, and phase. Frequency, power-factor, 
 and phase will be explained later. 
 
 The instruments for measuring these quantities are ammeters, 
 voltmeters, coulometers or ampere-hour meters, wattmeters, 
 watt-hour meters, frequency meters, power-factor meters, and 
 synchroscopes. 
 
 33. Groups of Instruments. — As already stated, the minor 
 subdivisions of instruments will be based on the principles of 
 their operations. Accordingly, we have electromagnetic, electro- 
 dynamic, electrostatic, and thermal groups. 
 
 34. Electromagnetic Instruments. — Any instrument that makes 
 use of the interaction between the magnetic field surrounding 
 an electric conductor and the magnetic field around an iron 
 core, belongs to the electromagnetic group. The application of 
 the principle is made in various ways and accordingly we have 
 the following types of electromagnetic instruments : 
 
 1. The movable-core type. 
 
 2. The movable-coil permanent-magnet type. 
 
 3. The induction type. 
 
 35. Electrodynamic Instnxments. — The force between two 
 conductors carrying electric currents is called electrodynamic 
 attraction or repulsion. Hence, electrodynamic instruments 
 are those whose actuating forces are due to currents flowing 
 through coils without iron cores. 
 
 36. Electrostatic Instruments. — Electrostatic instruments are 
 4 27 
 
28 ELECTRICAL METERS 
 
 actuated by forces of attraction and repulsion between electric 
 charges. Their action is independent of magnetic forces. 
 
 37. Thermal Instruments. — The actuating forces of the thermal 
 group are due to the expansion of a wire by the heat generated in 
 it when an electric current is flowing.- These are usually called 
 hot-wire instruments. 
 
 38. Controlling Forces. — Where any physical quantity is 
 measured in terms of the force it exerts, provision must be made 
 for the application of some counterforce whose intensity will 
 increase in proportion to the actuating force. Since the common 
 methods of measuring electrical quantities are in terms of their 
 force effects, the moving system of every meter must be counter- 
 balanced in some way. This counterbalancing force must be 
 so adjusted that the deflection or speed of the moving part, as 
 the case may be, is always proportional to the actuating force. 
 If this were not done, the movable system would deflect to the 
 extreme position, or would race, upon the application of a force 
 sufficient to overcome the friction of the movable parts. The 
 controlling forces employed for this purpose are: 
 
 1. The resisting force of a spring. 
 
 2. The torsion of some filament. 
 
 3. The attraction of gravity. 
 
 4. The attraction of permanent magnets. 
 
 5. The attraction of induced and inducing currents. 
 
 6. The mechanical friction of a rotating fan. 
 
 The first four of these controlling forces are utihzed in am- 
 meters, voltmeters, and wattmeters of both the indicating and 
 recording forms, while the fifth and sixth are applied in watt- 
 hour meters of various types. When a spring is used it may be 
 one of two forms, i.e., it may be helical in form, or in the form 
 of a spiral. The helical form is used to control both in torsion 
 and by axial extension. The fundamental law of the relation 
 of the actuating force and distortion of spring within the limits 
 of elasticity is: the actuating force is proportional to the dis- 
 tortion produced. The strength of either form of spring will 
 be increased by decreasing the number of turns, or by increasing 
 the sectional area of the spring. Springs are usually made of 
 some elastic nonmagnetic material. In most cases the material 
 used is phosphor-bronze. 
 
 The use of the torsion of a metal or silk fiber suspension is 
 limited almost wholly to laboratory instruments. The same 
 
CLASSIFICATION OF INSTRUMENTS 
 
 29 
 
 relation between the actuating force and the resulting deflection 
 holds as in the case of spring control. 
 
 The third form of control is very satisfactory, when it can be 
 applied. The application of this method of control permits the 
 construction of comparatively cheap and relatively accurate 
 instruments. In this method the law, mentioned above, con- 
 necting the actuating force with the distortion does not hold. 
 This will be made clear by referring to Figs. 12 and 13. Fig. 12 
 shows a typical arrangement for gravity control. P, the pointer, 
 is balanced by the weights B and C. When the pointer moves 
 to the right, C rises and B falls so that the moment of the two 
 
 cil-= 
 
 Fia. 12. 
 
 FiQ. 13. 
 
 about the point of suspension is zero. The controUing force is 
 furnished by the weight A, which moves to the left and up as 
 the pointer moves to the right. The moment of the force tend- 
 ing to bring the weight back to its vertical position or the pointer 
 to its zero position, will vary with the position of A. The 
 moment of A around the point of suspension 0, Fig. 13, is equal to 
 
 w X bb' at b 
 w X cc' at c 
 w X dd' at d, etc. 
 
 If we call od = ob, etc. = r and if the angle through which the 
 pointer has been deflected be represented by 6, then bb' = rsind; 
 cc' = r sin 6, etc., and thus the moment tending to bring pointer 
 back to zero is in general, 
 
 moment = wr sin 6. 
 Since w and r are constants, the resisting moment varies as the 
 
30 ELECTRICAL METERS 
 
 sine of the angle of deflection. The graduations of the scale on 
 such an instrument are not uniform, being close together at the 
 beginning and end of the scale, and relatively far apart in the 
 middle. 
 
 The fourth method of control is used only to a slight extent. 
 The objection to this method is that in the presence of a magnetic 
 field the indications are likely to be in error without the knowledge 
 of the user. This error in the reading of the instrument is due to 
 the influence of the outside field upon the permanent magnet 
 of the instrument. 
 
 39. Magnetic Shielding. — It is a well-known principle that the 
 reluctance of iron is much less than that of air. Thus, when a 
 piece of iron is introduced into a magnetic field, the magnetic lines 
 will be concentrated in the iron. The lines will deviate from a 
 straight line and pass through the iron instead of through the 
 air. 
 
 The movable or working systems of some meters are quite 
 readily affected by a magnetic field and, to eliminate this in- 
 fluence, they are enclosed in an iron case. When this is done, the 
 external field does not penetrate the instrument, and thus the 
 readings are unaffected unless the external field is very strong. 
 
 40. Friction of Supports. — Several ways have been tried to 
 support the moving system with varying degrees of success. 
 The usual way of supporting the moving coil is to mount it upon 
 two hardened steel pivots with sharpened points resting in 
 sapphire, or diamond jewel bearings. Although the movable 
 system is made as light as possible, the pressure per unit area is 
 considerable on account of the small area of contact between 
 pivot and bearing. Owing to this small contact, the wear and 
 friction on the pivot increase with time, especially in portable 
 instruments, unless some provision is made for relieving this 
 pressure, when the instrument is not in use. 
 
 One method of securing a resilient support for jewels is shown 
 in Fig. 14. In this figure DD is a two-piece shaft fitted at top and 
 bottom with cup-shaped jewels. In the middle or at the junction 
 of the two halves of the shaft is a collar C which carries a small- 
 diameter screw over which the halves of shaft DD are threaded. 
 The distance between the jewels can thus be adjusted by screwing 
 or unscrewing the collar C. Surrounding each half of the shaft 
 is a spiral spring F, one extremity of which bears against the 
 collar and the other against a cup-shaped guide bushing at the end 
 
CLASSIFICATION OF INSTRUMENTS 
 
 31 
 
 of the shaft. This structure permits of longitudinal motion of the 
 shaft against the tension of the spiral springs, and, consequently, 
 in case of a sudden jar the coil G with its attached pointer will 
 
 Fig. 14 
 
 transmit the pressure of the pivot E, until the lower surface G 
 comes into contact with the upper surface of the stationary core 
 H, thus preventing damage to jewels. 
 
CHAPTER III 
 CURRENT AND PRESSURE-MEASURING INSTRUMENTS 
 
 41. Ammeters and Voltmeters. — These two classes of instru- 
 ments will be discussed together since, with the exception of 
 the electrostatic voltmeter, they are alike in most respects. 
 The names ammeter and voltmeter are clearly derived from 
 ampere and volt, the units of current and pressure respectively. 
 
 42. Uses of Ammeters and Voltmeters. — The main difference 
 between ammeters and voltmeters lies in their use. Ammeters 
 are connected in series with the circuit in which the current is 
 to be measured. That is, they are connected in such a way 
 that the total or proportional part of the total current passes 
 through the instrument. Voltmeters, on the other hand, are 
 connected in parallel. That is, the terminals of the voltmeter 
 
 are connected to two points, between which 
 
 0the difference of pressure is to be measured. 
 Fig. 15 shows a standard connection for a 
 Voltmeter Voltmeter and an ammeter. In so far as 
 
 construction is concerned, ammeters and 
 
 ( X) voltmeters are similar. With the exception 
 
 V_-^ of the electrostatic voltmeters, all volt- 
 
 Ammeter meters are ammeters graduated in volts. 
 
 Fia. 15. The moving system is actuated by the cur- 
 
 rent passing through the instrument, and in 
 each instrument the deflection depends upon the strength of this 
 current. 
 
 The pressure drop due to resistance between any two points 
 of a conductor is IR, as already shown. Hence, if B is constant, 
 the pressure drop varies with the current. 
 
 In ammeters with shunts this pressure drop along a resistance 
 is utilized for sending a current through the movable system. 
 The resistance of the movable system being constant, the current 
 through it is directly proportional to the pressure drop and thus 
 to the main current. Since the current through the movable 
 system is proportional to pressure drop, it is evident that the in- 
 
 32 
 
MEASURING INSTRUMENTS 33 
 
 strument may indicate the voltage or current. Thus, if £J is the 
 difference of pressure between the voltmeter terminals, Fig. 15, 
 and if iJ is the resistance of voltmeter coils, the current through 
 
 E 
 the voltmeter is ■? = p- Since R is practically constant, I 
 
 varies as E. The current which causes a deflection of the mov- 
 able system thus varies as the pressure between voltmeter 
 terminals. In place of graduating the instrument in terms of the 
 current passing through it, it is graduated in terms of the dif- 
 ference of pressure between terminals. The action in every 
 respect is the same as that of an ammeter. The current through 
 the ammeter is limited by the circuit to which the ammeter is 
 connected. The current through the voltmeter is limited by the 
 resistance of the instrument itself. 
 
 In order that the energy lost in each instrument may be as 
 small as possible, there is a great difference in the resistances of 
 the two kinds of instruments. Since the load current or a certain 
 per cent of it passes through the ammeter, its resistance must 
 be very low in order that the PR loss may be small. 
 Since the voltmeter is connected as a shunt to the main circuit, 
 its resistance must be very large in order that the current may 
 be small. Thus, voltmeters have coils of relatively high re- 
 sistance — several thousand ohms — while ammeters have low 
 resistance coils — only a few thousandths of an ohm. 
 
 43. Range of Instruments.^ — The current intensity that an 
 ammeter can indicate is mainly determined by the resistance 
 of the movable coil. In practice two methods are used for 
 increasing the range, viz., shunts for direct-current and trans- 
 formers for alternating-current ammeters. 
 
 44. Ammeter Shunts. — There arc so many types of ammeters 
 that it is practically impossible to make a general statement of 
 principles. The following will be found to apply mainly to 
 ammeters whose movable system is actuated by current passing 
 through it. The movable coil carries only a small part of the 
 current so that, when the instrument is made to be used, as an 
 ammeter, a shunt for the main current must be provided. This 
 shunt is nothing more than a low resistance which bears a 
 constant ratio to the resistance of the movable coil. For small 
 currents the shunt is mounted within or as a part of the instru- 
 ment. For measuring large currents, however, the shunt is 
 mounted separately, and the instrument is connected to the 
 
34 
 
 ELECTRICAL METERS 
 
 terminals of the shunt as shown in Fig. 16. The instrument 
 used in this way is in reality a millivoltmeter which measures the 
 voltage drop across the shunt. The current strength is obtained 
 in accordance with Ohm's law. This may be made clear by 
 considering the following example: Assume that the shunt has 
 a resistance of 0.001 ohm and that the instrument reads 40 milli- 
 volts. According to Ohm's law the drop across the shunt is 
 
 IR = E 
 or 7 X 0.001 = 0.040 
 0.040 
 
 hence I = 
 
 0.001 
 
 = 40 amp. 
 
 If the shunt and instrument are to be used together constantly 
 the shunt and millivoltmeter are calibrated together and the 
 scale is graduated in amperes. 
 
 Fio. 16. 
 
 Since the shunts carry the main current and become heated, 
 they must be made of some material whose temperature coeffi- 
 cient is very small. An alloy of copper, manganese, and nickel 
 called manganin, fulfills this requirement more fully than any 
 other, and for that reason is almost universally used for ammeter 
 shunts. Fig. 17 shows some standard Weston shunts. 
 
 45. Range of Voltmeters.— Two methods are also in general 
 use for increasing the range of voltmeters. One is by means of 
 resistance coils connected in series with the instrument and the 
 other by what are called potential transformers. 
 
 46. Voltmeter Multipliers. — It would be very inconvenient to 
 make a movable coil of sufficient resistance to measure high 
 differences of potential. To do this economically would necessi- 
 tate large coils. The same thing can be accomplished in another 
 
MEASURING INSTRUMENTS 
 
 35 
 
 way; that is, by mounting in series with the movable coil of the 
 instrument a resistance sufficiently large to reduce the current 
 to the desired value. By providing different resistances, or 
 
 Fig. 17. 
 
 multipliers as these are commonly called, the range of instrument 
 can be varied considerably. In some cases these multipliers 
 are mounted inside of the instrument case, and the circuit is 
 
 Fig. 18. 
 
 connected to the proper multiplier by means of a push button, 
 separate binding post, plug switches, or some other simple 
 device. 
 
36 ELECTRICAL METERS 
 
 The current in the multiplier is relatively small, so its resistance 
 must be comparatively high. Manganin, constantan, or some 
 other alloy of high specific resistance and low temperature 
 coefficient, is used. Multipliers for Weston voltmeters are 
 shown in Fig. 18. 
 
 47. The Movable-core Type. — To this type of instruments 
 belong all those in which a piece of soft iron is acted upon by 
 an electromagnetic field. The electromagnetic field is formed 
 by an electric current flowing in a stationary solenoid, while the 
 soft iron is pivoted and attached to a pointer which moves 
 over a graduated dial. 
 
 One of the oldest and simplest instruments of this type is 
 shown in Fig. 19. C is the stationary solenoid, P is the soft- 
 iron core pivoted at so that it can move freely up and down. 
 
 To the arbor are also attached the 
 pointer N and the counterweight Q. 
 By referring to the discussion on 
 controlling forces it will be seen that 
 gravity is the controlling force in the 
 plunger type of instrument, as that 
 shown in Fig. 19 is usually called. 
 
 In ammeters of this type the main 
 current flows through the solenoid C, 
 and the core P is drawn into the 
 Fig. 19. solenoid against the force of gravity 
 
 on Q. The coil C, as shown, usually 
 consists of a few turns of heavy wire. In voltmeters, however, 
 the solenoid is made of many turns of fine wire. It is customary 
 to place an additional resistance in series with the voltmeter coil 
 of this type in order to reduce the current sufficiently when used 
 to measure high voltage. By changing the resistance of the 
 multiplier, the range of the instrument can be varied through 
 wide limits. Fig. 20 shows the main features of a Westinghouse 
 plunger-type ammeter. 
 
 Another form of this type of instrument is the Thomson 
 inclined-coil ammeter. The essential features of this instrument 
 are shown in Fig. 21, and the complete instrument is shown in 
 Fig. 22. As shown in the diagram of Fig. 21, the stationary coil 
 makes approximately an angle of 45° with the shaft upon which 
 is mounted a soft-iron vane, also making approximately an angle 
 of 45°, 
 
MEASURING INSTRUMENTS 
 
 37 
 
 The operation of the instrument is as follows: The current 
 flowing through the stationary coil, sets up a magnetic field, as 
 
 Fig. 20. 
 
 shown in Fig. 21. When the pointer is at zero of the scale the 
 plane of the vane is nearly at right angles to the magnetic lines. 
 When the magnetic field is set up, the vane moves so as to become 
 
 11 ^^Spring 
 
 q piEEr Pointer 
 
 Scale 
 
 FlQ. 22. 
 
 parallel to the magnetic field. Opposing this motion is the 
 spiral spring at the upper end of the shaft. Since the pointer is 
 
38 
 
 ELECTRICAL METERS 
 
 also rigidly attached to the shaft it moves over the scale, coming 
 to rest when the torque due to the controlling spring is equal to 
 the torque due to the action of the magnetic field on the vane. 
 The counterweight balances the moving parts. 
 
 The inclined-coil movable-vane instrument is much more com- 
 pact than the plunger type; the movable parts are lighter, 
 reducing friction and making the instrument much more sensitive. 
 
 .^ 
 
 Fig. 23. 
 
 The gravity control of the plunger type is replaced by the spiral- 
 spring control. As has been already shown, the counterforce 
 in the gravity-control method is proportional to the sine of the 
 angle of deflection, while the counterforce of the spring is directly 
 proportional to the deflection. This permits the use of a more 
 uniform scale, although the graduations cannot be made exactly 
 uniform on account of the fact that the deflecting force acting 
 on the vane is not directly proportional to the current. 
 
MEASURING INSTRUMENTS 39 
 
 Another method of applying the principle of reaction between 
 magnetic fields is utilized by the Weston Electrical Instrument 
 Co. in their so-called "soft-iron" instruments. The essential 
 parts of an instrument of this type are shown in Fig. 23. Refer- 
 ring to the diagram, £ is a fixed piece of iron of nearly triangular 
 shape, bent into cylindrical form. Concentric with this is a 
 movable piece of similarly shaped iron D which is secured to the 
 staff F, which carries the pointer P. The movable element is 
 mounted on a support G and inserted in the field coil C, which 
 for the voltmeter is connected in series with a noninductive 
 resistance. Under the magnetizing action of the field coil the 
 two iron pieces tend to separate and thus produce a torque 
 which is opposed and controlled by the spring S. The torque 
 for any deflection is approximately proportional to the square 
 of the current in the field coil. The two iron pieces D and E are 
 shaped so as to give a nearly uniform scale. 
 
 The movable-core or soft-iron instruments may be used on 
 both direct and alternating circuits. This is due to the fact that 
 the iron core of the plunger type, and the vane of the inclined- 
 coil type are attracted by a magnetic field no matter what its 
 direction. When the instrument is to be used on alternating 
 current, the core must be of laminated iron or of a bundle of 
 soft-iron wire; this is done to prevent the flow of eddy currents 
 and consequent alteration of the force. 
 
 48. Approximate Equation for Pull on Iron Core. — -The mag- 
 netic field H within a solenoid is equal to H = 1.257 nl, where 
 n is the number of turns per centimeter length, and I is current 
 in amperes. When an iron core is introduced into the solenoid, 
 the number of magnetic lines is greatly increased. 
 
 Although the permeability of the iron core is not constant but 
 varies with the intensity of magnetization, nevertheless it may 
 be assumed that the flux density is approximately proportional 
 to the current. This may be written 
 
 B = KI 
 
 The pull exerted by the solenoid upon the iron core is propor- 
 tional to the product of the strength of magnetic flux and current, 
 
 or 
 
 Pull = K'BI 
 
 But as has already been shown, B is proportional to /, so by 
 
40 ELECTRICAL METERS 
 
 replacing B by 7 we get pull = K'lP. That is, the pull on the 
 plunger is proportional to the square of the current flowing 
 through the solenoid. When the instrument is used to measure 
 alternating current, the value B is at each instant proportional 
 to the current. Since the current varies, B will vary, but at each 
 instant the pull will be proportional to the square of the current 
 at that instant. We may thus write instantaneous pull = M'^, 
 where i is the instantaneous current. The direction of the pull 
 does not change, for as the current reverses the magnetic field 
 due to the current reverses, or the field and current change their 
 signs together. The inertia of the movable system does not per- 
 mit it to follow the instantaneous fluctuations of the pull; the 
 plunger will assume a position determined by the average pull. 
 By higher mathematics it can be shown that the average pull is 
 proportional to the mean square of the instantaneous values of 
 the current. The square root of the mean-square value is called 
 the effective value, and is the value given by all alternating- 
 current instruments. 
 
 The movable-core type of instrument, when calibrated with 
 direct current, should then give exact effective values of alternat- 
 ing currents. In practice this is not quite true. The magnetic 
 field does not increase uniformly with the current, and also the 
 effect of eddy currents and hysteresis is appreciable. The dif- 
 ference, however, is not great; the readings differing only slightly. 
 
 49. Movable-coil Permanent-magnet Type. — In this type of 
 meter the magnetic field remains constant and is due to a 
 permanent magnet of the horseshoe form. Between the poles 
 of the magnet is mounted a rectangular coil in such a way that 
 it can revolve through a considerable arc within a specially 
 designed magnetic field. When in use, the current flowing 
 through the coil tends to set up a magnetic field at an angle 
 to the field of the permanent magnet. The reaction between 
 the two fields causes a deflection of the pointer which is rigidly 
 attached to the shaft of the moving coih 
 
 The general principles of this type of instrument are well 
 shown in Fig. 24. The permanent magnet is shown in the diagram 
 by NS, N being the north and (S the south pole. The rectangular 
 coil C carries the current causing the deflection. Usually this is 
 only a small per cent, of the total current to be measured. The 
 controlling force is furnished by two spiral springs, one at the 
 upper, the other at the lower end of the shaft. The springs are 
 
MEASURING INSTRUMENTS 
 
 41 
 
 coiled in opposite directions so that when the pointer is deflected, 
 one of the springs is coiled up, while the other is uncoiled. This 
 scheme compensates for any inequalities that may exist in the 
 springs. In most cases the springs also serve to make connection 
 between the coil C and the external circuit. 
 
 Fia. 24. 
 
 Fig. 25. 
 
 In this type of instrument the direction of the main field 
 remains constant. The deflection of the pointer will be in one 
 direction when the current flows from t to t' and in the opposite 
 direction when the current is reversed. This being the fact, it is 
 evident that instruments of this type cannot be used to measure 
 
 FiQ. 25a. 
 
 alternating current. They are, however, very eflacient and con- 
 venient direct-current instruments. The instruments of the 
 Weston Electrical Instrument Co., made in accordance with the 
 foregoing principles, have practically been the standard direct- 
 current instruments for years. 
 
42 ELECTRICAL METERS 
 
 The cross-section of the movable coil is usually rectangular 
 and it usually surrounds a soft-iron cylindrical core. The 
 function of the core is twofold; to concentrate the field and to 
 secure a distribution of flux in the air gap such that uniform 
 graduations are possible. 
 
 A modified form of magnet core is employed by the Westing- 
 house Co. in its movable-coil permanent-magnet type of meters. 
 This is shown in Fig. 25. The two C-shaped magnets, A and 
 A', are attached to two soft-iron pole pieces B and C. Instead of 
 having a central core of soft iron, the pole piece B is shaped to 
 conform to the semicircular cavity cut in the pole piece C. A 
 small air gap G is left between them. The movable coil is wound 
 upon a light aluminum frame to which is attached the pointer and 
 hardened steel pivot, Fig. 25a. The coil is mounted eccentrically, 
 that is, the staff is at one side of the coil. The advantage claimed 
 for this form of construction is that the coil to a certain extent 
 counterbalances the pointer, thus reducing the amount of 
 additional counterweight required and making the weight carried 
 by the pivots a miminum. 
 
 50. Damping. — By damping is meant the checking or impeding 
 the freedom of motion of the movable element. A properly 
 damped instrument will deflect promptly, but not too quickly 
 through the correct angle and no farther. The movement of an 
 undamped instrument is liable to be oscillatory — the movable 
 element will vibrate above and below the correct indication. 
 Good damping is thus necessary, not only on account of the 
 convenience and accuracy of making readings, but also because 
 it reduces the wear on the pivots and lessens the danger of injury 
 in case of overload. 
 
 There are two general methods of damping in use in com- 
 mercial electrical measuring instruments, mechanical and 
 electromagnetic. 
 
 In mechanical damping a vane or plunger is caused to move 
 through a more or less resisting material such as oil or air. The 
 use of oil for damping is restricted to instruments which remain in 
 a fixed position such as on switchboards. In the Westinghouse 
 plunger-type instrument. Fig. 20, the lower end of the plunger is 
 immersed in oil which dampens any sudden movement of the 
 pointer. 
 
 In air damping a vane moves within a chamber which is con- 
 structed with just the desired amount of air leakage. This 
 
MEASURING INSTRUMENTS 
 
 43 
 
44 ELECTRICAL METERS 
 
 leakage may be into or out of the chamber, or it may be from one 
 side of the vane to the other. As the vane moves, it compresses 
 the air in front and rarefies it behind. 
 
 The amount of damping necessary depends upon the weight 
 and moment of inertia of the moving element, and hence if air 
 damping is to be efficient the vane must be Ught and have a small 
 moment of inertia. In this respect the best made instruments 
 meet all reasonable requirements. Fig. 23 shows one method of 
 applying air damping. The vane B is attached to the movable 
 element, and as this is deflected the vane moves in the air damper 
 box A. 
 
 The electromagnetic method of damping is employed in all 
 permanent-magnet movable-coil instruments. The movable 
 coil of these instruments is wound upon an aluminum or copper 
 frame which has eddy currents induced in it as it moves in the 
 field of the permanent magnet. The reaction between these 
 eddy currents and the magnetic field retards or dampens the mo- 
 tion quite satisfactorily. The reaction between the movable 
 coil and the magnetic field may also cause damping. In volt- 
 meters this is not appreciable on account of the large resistance 
 of the voltmeter circuit; but in ammeters it may be appreciable. 
 The theory of electromagnetic damping is quite complicated, 
 but a good discussion can be found in certain texts. ^ In Fig. 
 26 are shown the movable elements of eight different makes of 
 ammeters, while in Fig. 27 the same movable elements and 
 naagnets are assembled.^ The instruments represented in these 
 figures are all of American make. 
 
 51. Torque Exerted by a Magnetic Field upon a Rectangular 
 Coil. — ^Let Fig. 28 represent both a side and a top view of a rec- 
 tangular coil in a permanent magnetic field of uniform distribu- 
 tion and strength H. Assume the plane of the coil to lie parallel 
 to the field. When a current fiows through the coil, a turning 
 moment or torque will be manifest due to the interaction of 
 current and magnetic field. This torque will tend to turn the 
 coil ill such a way that its plane will be at right angles to the 
 permanent magnetic field. The force per unit length of con- 
 ductor carrying a current Z in a field of strength H, is HL If 
 a be the breadth and b the height of coil the force on one side 
 per turn is bHI, and for N turns it is NbHI. For both sides of 
 
 1 Murdoch and Oschwald, "Electrical Insruments." 
 
 2 Fitch and Huber, Bullelin Bureau of Standards, vol. 7, No. 3. 
 
MEASURING INSTRUMENTS 
 
 45 
 
46 
 
 ELECTRICAL METERS 
 
 the coil it will be twice this, or 2NbHL If the coil is pivoted at 
 the middle point of a the torque is 
 
 T = 2NbHI X a/2 
 = NabHI 
 
 T is the torque in dyne-centimeters tending to turn the coil when 
 a and h are in centimeters and I in absolute units. 
 
 When the coil is turned through an angle 6 about the axis of 
 rotation, the component, or one may say, the intensity of the field 
 producing torque, will be different. This component is equal to 
 H cos B. Hence, if the field is uniform as assumed, the torque 
 becomes 
 
 T = ahNIH cos 0. 
 
 
 
 i 
 
 
 
 W^^\ 
 
 : 
 
 N 2 
 
 
 : S 
 
 -3 
 
 
 : 
 
 
 ■<-■ 
 
 a> 
 
 
 Fig. 28. 
 
 In well-designed instruments the pole pieces of the permanent 
 magnet are shaped so that H cos 6 is practically constant within 
 the limits of motion of the coil. The quantities a, b, and N are 
 constant for any given coil, and if H cos 9 is constant, we may 
 replace abNH cos 9 by a constant K, the expression for torque 
 then becomes 
 
 T = KL 
 
 This shows that in well-designed instruments of the movable-coil, 
 permanent-magnet type, the torque is proportional to the first 
 power of current. Since the opposing torque of a spring is pro- 
 portional to the angle of twist, the coiled-spring method of control 
 is ideal, and is universally used upon this type of instruments. 
 These principles make possible practically uniform graduations. 
 
CHAPTER IV 
 
 FUNDAMENTAL PRINCIPLES OF ALTERNATING 
 CURRENTS 
 
 52. Introduction. — Before discussing induction-type instru- 
 ments, some general principles of alternating currents will first 
 be reviewed. 
 
 In Chapter I were discussed some of the fundamental principles 
 of power and work. It was there shown that the power in a 
 direct-current circuit is given by IE watts, where I is the current 
 in amperes and E the electromotive force in volts impressed upon 
 the circuit. Similarly, the energy consumed or utilized by the 
 circuit in t sec. is Elt joules. 
 
 From this, and from the other considerations discussed in 
 Chapter I, it is evident that the measurement of power in direct- 
 current systems is comparatively a simple operation. All one 
 needs to know is the current in amperes and voltage, when the 
 power is readily obtained as the product of the two. Thus an 
 ammeter and voltmeter suffice for power determination in direct- 
 current circuits. 
 
 When power is to be measured in a circuit in which alternating 
 current is flowing, due to an alternating electromotive force, 
 other considerations enter. These considerations we shall now 
 briefly discuss. 
 
 53. Alternating Current.- — An alternating current or electro- 
 motive force is one which begins at zero, increases to a maximum 
 in one direction, then decreases to zero and again increases to a 
 maximum in the other direction, finally decreasing back to zero 
 again in one cycle. These cycles continue one after another so 
 long as the current is flowing. Thus, in an alternating-current 
 system the terminals of the circuit are alternately positive and 
 negative and the current flows first in one direction and then in an 
 opposite direction. 
 
 54. Generation of an Alternating Pressure. — The simplest 
 method of generating an alternating pressure is that indicated 
 in Fig. 29 Here the rotating armature consists of two conduct- 
 
 47 
 
48 
 
 ELECTRICAL METERS 
 
 ors A and B, connected so as to form a loop. The loop is 
 supported on the shaft D, and centered between the two magnet 
 poles N and S. The ends of the loop are connected to two insul- 
 ated metal slip rings, Ci and d. The circuit is completed 
 through the external circuit R by means of metal contacts or 
 brushes bearing on the rings. Assuming that the magnetic lines 
 pass straight across the armature from the N pole to the S pole, 
 when the loop is rotated the sides A and B of the loop have elec- 
 tric pressures induced in them. Since the conductors are moving 
 across the field in opposite directions, the pressures in the conduct- 
 ors will be oppositely directed with reference to the plane of the 
 paper. But the two conductors are so connected that the two 
 pressures act together around the loop; therefore, the pressure 
 
 Iwwwvv""^ 
 
 Fig. 29. 
 
 between the brushes will be twice that developed in either 
 conductor. 
 
 Starting with the plane of the loop in a vertical position, the 
 conductors are moving para,llel to the magnetic lines and, conse- 
 quently, no lines are being cut and no pressure is induced in the 
 loop. As the loop revolves from its vertical position, the angle 
 at which the lines are cut approaches a right angle until the loop 
 has turned through 90°, when the conductors A and B will be 
 passing under the centers of the poles N and S respectively. At 
 this instant they are cutting the lines at right angles, and conse- 
 quently the maximum pressure will be induced in each conductor. 
 As the coil or loop rotates beyond this point, the number of lines 
 cut by the conductor in unit time decreases. When the loop has 
 advanced another 90° it wUl again be in a vertical position, but 
 
PRINCIPLES OF ALTERNATING CURRENTS 49 
 
 A will be at the bottom and B at the top. At this instant the 
 pressure is again zero. During this half rotation the current in 
 external circuit will pass through exactly similar changes in 
 strength. 
 
 Duringthenext half revolution, conductor A will pass up in front 
 of the S pole, and B down in front of the N pole; consequently, 
 the pressure will go through the same changes that it went 
 through the first half revolution, but the pressure will be directed 
 in the opposite direction. The current through external circuit 
 will flow in the opposite direction also, and its changes in value 
 will follow those of the pressure. 
 
 The pressure and current, therefore, pass through a complete 
 cycle of changes; starting from zero they increase to a maximum, 
 then decrease to zero ; reverse in direc- 
 tion, increase to a negative maximum, ' 1 I i I iDi 
 then again decrease to zero, after | M '^ ^ '^ 
 which the same cycle of changes is 
 repeated. 
 
 55. Law of Fluctuation of Alternat- 
 ing Pressure and Cvirrent. — In Fig. 
 30 let C and Ci represent the cross- 
 sections of the two conductors of a 
 loop, as in Fig. 29, revolving about 
 an axis perpendicular to the plane of 
 the paper at 0. Since the pressure 
 induced in one conductor is equal to 
 that induced in the other, it will be sufficient to consider the 
 variation of pressure in one conductor only. Assume the con- 
 ductor to be revolving counter-clockwise as indicated by the ar- 
 row, and let <l> be the angle made by the plane of the coil with 
 the line OA ; OA is taken as the reference line. If the coil rotates 
 with uniform speed, C wiU move around a circle with uniform 
 speed, V, and <j) will be a uniformly increasing angle. Assume 
 that the coil has turned through the angle (j) and reached the 
 position shown in the figure. 
 
 By many experiments it has been determined that whenever a 
 wire is moved across a magnetic field an electromotive force is 
 developed. The intensity of the electromotive force will depend 
 upon three quantities: the strength of the magnetic field, the 
 length of the wire within the field, and the speed with which it is 
 moving. No electromotive force is induced when the wire 
 
50 ELECTRICAL METERS 
 
 moves along the direction of the field; hence, it is evident that 
 the intensity of the pressure will also be influenced by the direc- 
 tion of motion of the wire. Expressing these experimental facts 
 in a mathematical equation we get e = HlVo in absolute units. 
 If we wish to get e in volts, the above expression must be divided 
 by 10*, or 100,000,000, since 10* absolute units equal 1 volt. The 
 expression becomes 
 
 e(volts) = -j^ 
 
 where 
 
 H = strength of field in lines per square centimeter. 
 
 I — total cutting length in centimeters of all conductors in 
 series. 
 
 Yo = the velocity at right angles to the magnetic lines in centi- 
 meters per second. 
 
 Let CD, Fig. 30, perpendicular to OC represent graphically to 
 scale the direction and magnitude of the constant velocity F, 
 with which C is moving around the circle. 
 
 Let DB. be a line drawn through D parallel to the magnetic 
 lines, and CR a line drawn through C perpendicular to the mag- 
 netic lines. It is evident that at this instant the same number of 
 magnetic lines would be cut if the conductor moved horizontally 
 with a velocity Yo, equal to CB. as when it moves around the 
 circle with the velocity Y. Yo is the velocity at right angles to 
 the Unes and it is the velocity which must be used in the formula 
 for e. 
 
 From geometry, the angle made by the lines DC and DB. is 
 
 equal to the angle ^. The ratio of Yo to Y , \-^) , is called the 
 
 sine of the angle 4>; consequently, Yo = V sin <^. Substituting 
 this value for Yo in the formula for e we get 
 
 _ HIY sin (j> 
 
 ^ " To* 
 
 In this expression e is the instantaneous pressure. 
 
 When (^ = 0, sin <^ = and the induced pressure is zero. 
 
 When (j) = 90°, sin <^ = 1 and the induced pressure is a maximum. 
 
 HIY 
 The expression -jTr^ represents the maximum value of the electro- 
 
 HIY 
 motive force. We can then write Em = TTja") ^^'^ ^ ~ ^^ si° *^» 
 
 Em means maximum electromotive force. 
 
PRINCIPLES OF ALTERNATING CURRENTS 51 
 
 The instantaneous value of the pressure is, therefore, propor- 
 tional to the sine of the angle which the plane of the coil makes 
 with a plane at right angles to magnetic field. 
 
 The successive values of the electromotive force, which are 
 induced as the coil passes under the N and 5 poles, can be graph- 
 ically represented, as in Fig. 31. 
 
 Let the base line AB represent 360" and let it be divided into 
 equal parts, each part representing 30°. At points representing 
 0°, 30°, 60°, 90°, etc., draw vertical lines whose lengths represent 
 the maximum value of the alternating quantity times the sin 0°, 
 sin 30°, etc. Between 180° and 360° the sine is negative and the 
 
 Fig. 31. 
 
 values are drawn below the base line. This is in agreement with 
 the fact already mentioned that the pressure changes in direction 
 as the conductors pass from under one pole beneath another pole. 
 
 A curve drawn through the extremities of the vertical lines is 
 called a sine curve. If the maximum ordinate is Em, then the 
 sine curve will be the sine curve of the pressure. If the maximum 
 ordinate represents the maximum value of the current, the sine 
 curve will be a sine wave of current. 
 
 Another method of graphically constructing a sine curve is 
 shown in Fig. 32. The radius of the circle, to the left, is made 
 equal to, the maximum value of the sine curve. Let OM be an 
 extension of the line of reference AB and draw radial lines 
 ON, OP, OQ, etc., making angles of 30°, 60°, etc., with the base 
 line OM. From the extremities of these radii draw horizontal 
 lines intersecting the vertical lines erected at points on AB repre- 
 
52 
 
 ELECTRICAL METERS 
 
 senting the corresponding angles. The points of intersection will 
 be points on the sine curve. Between 0° and 180° the ordinates 
 are above the axis and from 180° to 360° they are below. A curve 
 drawn through all the points of intersection will be a sine curve. 
 At the point on AB representing 30°, the ordinate equals RN. 
 But from trigonometry RN equals ON X sin 30°. If ON were 
 drawn to represent E„ then RN equals E„, sin 30°. In general 
 the curve shows graphically the value of y in 
 
 or 
 
 = A sin a; 
 
 e = Em sin (t>. 
 
 Deqrees or+ime 
 .oi Sec — ■ — >- oaSec 
 
 a40 270 300 330 3&0 
 
 B 
 
 K- Oris cycle 
 
 Fig. 32. 
 
 If w represents the angle described by ON in unit time, 1 sec, 
 in t sec. it will describe an angle equal to wt, and if t is the 
 time required to describe angle <t>, then (j> = coi. The expression 
 for induced pressure then becomes 
 
 e = E„ sin ut. 
 
 There is some advantage in considering AB, Fig. 31, as an axis of 
 time, and plotting successive values of t horizontally rather than 
 the angle <j> or «i. For instance, if ON makes 50 complete 
 revolutions per second, it will make one revolution in }4o oi" 
 0.02 sec. The time required to describe an angle of 30° is one- 
 twelfth of 0.02 sec. Thus the intervals A to 30°, etc., can just as 
 readily be used to represent intervals of time. The significance 
 of this will be seen when we consider phase difference. 
 
 Although the positive and negative loops of an alternating 
 current or pressure curve are nearly always aUke, in general the 
 fluctuations do not follow a simple law. Since any complex wave 
 whose alternate loops are alike may be represented by the sum of 
 
COS 
 
 PRINCIPLES OF ALTERNATING CURRENTS 53 
 
 a series of sine and cosine curves having different amplitudes 
 and frequencies, an alternating-current wave may be represented 
 thus: 
 
 i = 7i sin X + I3 sin 3a; + lb sin 5x + etc. + h cos x + I3 
 3x + /5 cos 5x + , etc. 
 
 An analysis of such a representation of current or pressure is 
 beyond the limits of this text. The following discussion is based 
 on the assumption that the current or pressure curve may be 
 represented by the first term on the right-hand side of the equa- 
 tion; thus i = Im sin x = I„ sin at. 
 
 56. Cycle, Frequency, Period, Alternation. — Referring to Fig. 
 32, we may assume that the electromotive force induced within 
 one coil of an armature, while under a north pole, is represented 
 by the ordinates above the horizontal axis. Similarly, the ordi- 
 nates under the horizontal axis represent the electromotive force 
 induced in coil when under the south pole. These two sets of 
 values are called a cycle. The number of cycles per second is 
 called the frequency. The time required for the electromotive 
 force to change through one cycle is called a period. 
 
 Since the pressure and current pass through a complete cycle 
 of values when the coil or conductor passes under a north and 
 south pole, the number of cycles per revolution of an armature 
 is equal to the number of pairs of poles. The frequency will then 
 be equal to the number of cycles in one revolution multiplied by 
 the number of revolutions per second, or 
 
 /=|xn 
 
 where p is the number of poles and n the number of revolutions 
 per second. If the revolutions per minute are given, as is 
 usually the case, this number must first be divided by 60 to get 
 the revolutions per second. 
 
 There are always two alternations for each cycle, hence the 
 number of alternations in any unit of time will be two times the 
 number of cycles in the same unit of time. 
 
 57. Instantaneous Value. — Representing the fluctuations of an 
 electromotive force or current by a sine curve, the instantaneous 
 value is represented by the distance from the horizontal axis to 
 the curve, at that particular instant. Thus in Fig. 32 the verti- 
 cal lines y, yi, yz, etc., represent the instantaneous values at the 
 
54 ELECTRICAL METERS 
 
 ends of the intervals of — , — , — , etc., sec. after the point 
 
 N has passed through M. 
 
 58. Maximum Value. — The instantaneous value at the point 
 
 marked 90°, or at the end of — sec, is greater than that at 
 
 any other point between 0° and 180°, and is consequently a 
 maximum value. The numerical value at the point marked 
 270° is equal to that at 90°; its direction, however, is downward 
 and is, therefore, a negative maximum value. In alternating- 
 current problems the term maximum has reference to only the 
 numerical value and not to its direction. 
 
 59. Average Value. — The average value of an alternating 
 electromotive force or current is the average of all the instan- 
 taneous values for half a cycle, or the average of all the instan- 
 taneous values for a complete cycle, irrespective of sign. The 
 average or mean value of a series of quantities is, in general, 
 
 , . ai + 02 + as + • . • Ot. 
 average (a) = 
 
 where ai, 02, fls . . • On represent the successive values and n 
 
 is their number. 
 
 Assuming that the instantaneous values of an alternating 
 
 electromotive force vary according to a sine law, or that the 
 
 alternating quantity is harmonic, the average value will be equal 
 
 to the sum of the instantaneous values divided by their number. 
 
 In other words, it will be eqUal to the area between the curve and 
 
 base line divided by the base line. It can be shown by calculus 
 
 . . 2 . 
 
 that this is equal to - X maximum value = 0.636 X maximum 
 
 value. The average value is used in some calculations. 
 
 60. Effective Value or Root-mean-square Value. — The effect- 
 ive value is very important in alternating-current problems. 
 
 When a direct current is sent through a resistance, the energy 
 converted into heat per second is 
 
 Heat = PR joules. 
 
 An alternating current varies in intensity from instant to instant; 
 its heating value is, however, at each instant equal to i^R, where 
 t is the current at the instant considered. The heat developed per 
 cycle will then be the average of PR for the cycle. Since the 
 resistance R remains constant^ the heat developed per cycle 
 
PRINCIPLES OF ALTERNATING CURRENTS 55 
 
 must be equal to R times the average of i^. Thus an alternating 
 current, whose average square is P, will develop the same amount 
 of heat per second in a resistance R as a direct current whose 
 value is I. 
 
 If a direct current I be sent through an ammeter of the electro- 
 dynamometer type, a torque proportional to P will be developed. 
 If the same ammeter is used to measure an alternating current, 
 the torque at each instant. will be proportional to i^. This torque 
 is always exerted in the same direction irrespective of the direc- 
 tion of the current. The resulting torque will be proportional to 
 the average of i^, and if the deflection with direct current is equal 
 to that with alternating current, we may write 
 
 KP — K average i^ 
 
 and I — "s/ average P 
 
 That is, when the deflection is the same, the value of the direct 
 current must be equal to the square root of the average of the 
 squares of the instantaneous values of the alternating current. 
 This square root of the mean-square value is called the effective 
 value, or "root-mean-square value," of an alternating current or 
 pressure. It can easily be shown that for a harmonic current 
 the effective value is 3^\/2 times the maximum value; that is 
 
 1= 0.707 7„ 
 
 and E = 0.707 E^ 
 
 61. Effect of Inductance. — We learned in Article 10 that the 
 wire along which an electric current is flowing is surrounded by a 
 magnetic field. In a direct-current system this magnetic field 
 remains constant, both in intensity and direction, so long as the 
 current remains constant. The building up of the magnetic 
 field requires energy which must be furnished by the initial cur- 
 rent. Since no energy can be stored in any system unless that 
 system reacts upon the source of energy or working substance, 
 it follows that the magnetic field reacts upon the current to which 
 it is due. This reaction prevents the sudden rise of current 
 within a circuit to the maximum value, as indicated by Ohm's 
 law. 
 
 Again, when the circuit is opened and the current ceases, the 
 energy that has been stored in the magnetic field is returned to 
 the circuit and attempts to keep the current flowing. This 
 
56 ELECTRICAL METERS 
 
 energy manifests itself as a spark at the terminals of the circuit. 
 Since the current cannot rise to a maximum value immediately 
 upon closing the circuit, neither can it immediately fall to zero 
 when the circuit is opened. This reaction of magnetic field upon 
 the current is known as induction. 
 
 The effect of induction may be considered as analogous to the 
 action of a flywheel on a steam engine. When first the steam 
 is turned on, some of the energy of the steam is converted into 
 energy of motion, or kinetic energy of the flywheel. The fly- 
 wheel reacts upon the engine until steady speed is reached. 
 When steady speed is reached, no more energy is given to the 
 flywheel, but all of it goes toward running the machinery. 
 When the steam is shut off, the engine does not at once come to 
 a dead stop; the flywheel keeps it in motion for some time until 
 its kinetic energy has all been given back to the engine and 
 machinery. 
 
 62. Effect of Capacity. — In addition to inductance every 
 circuit possesses some capacity, that is, the ability to become 
 charged, or to store up electricity. One conductor alone has very 
 little, but more than one, arranged in suitable ways, may possess 
 considerable capacity. When so arranged, the device is called a 
 condenser. 
 
 An electrical condenser may be considered analogous to an air 
 tank. Suppose we have an air tank that under one atmospheric 
 pressure holds a certain definite quantity of air, say 5 lb. We 
 can define the capacity of the vessel in terms of the number of 
 pounds of air it holds, and call it a 5-lb. tank. 
 
 If the pressure is doubled, the tank will hold 10 lb. of air. 
 Since we have defined the capacity of the tank in terms of unit 
 (one atmosphere) pressure, we cannot call it a 10-lb. tank. A 
 10-lb. tank under the same conditions will hold 20 lb. of air. 
 
 Furthermore, suppose the tank to be exhausted, evidently no 
 back pressure will be exerted when air is first admitted to the tank. 
 As soon as some air is admitted to the tank, back pressure begins 
 to manifest itself, and when the back pressure equals the applied 
 pressure, no more air enters the tank. We thus see that the 
 amount of air entering per unit time depends upon the back 
 pressure, and this back pressure will depend upon the capacity 
 of the tank. For instance, if we put 5 lb. of air in a 10-lb. tank, 
 the back pressure will be one-half as great as when 5 lb. of air 
 are put into a 5-lb. tank. We can then say that unit capacity of 
 
PRINCIPLES OF ALTERNATING CURRENTS 57 
 
 a tank is such that when 1 lb. of air is forced into it the pressure 
 will be equal to one atmosphere. Evidently, a certain amount of 
 work will be done in forcing the air into the tank, and we could 
 define unit capacity in terms of the work expended. 
 
 The capacity of electrical conductors is analogous to the ca- 
 pacity of the air tank discussed above. The capacity of a con- 
 denser or system of conductors is usually defined in terms of the 
 quantity of electricity required to raise the difference of pressure 
 between the terminals by 1 volt. In accordance with this defi- 
 nition the quantity of electricity that a condenser will contain is 
 equal to the product of the capacity and pressure, or Q = EC. 
 The flow of an alternating current within any circuit depends not 
 only upon the resistance of the circuit, but also upon any induc- 
 tance and capacity that may be contained in or connected with 
 the circuit. 
 
 The continual surging back and forth of the current in an 
 alternating circuit gives rise to very important inductance and 
 capacity effects in certain parts of the circuit, and the resulting 
 peculiarities that distinguish the alternating from the direct- 
 current circuit. The two factors mentioned above may be far 
 more important than resistance, and in some cases may entirely 
 control the flow of the current. 
 
 63. Phase Difference. — It has been pointed out that the cur- 
 rent wave is in form much the same as the electromotive-force 
 wave in an alternating-current circuit. The constants of the 
 circuit — that is, resistance, inductance, and capacity — will, 
 however, influence the time at which the current will reach a 
 maximum. 
 
 This fact will probably be understood from the analogy of the 
 flywheel as already given. If the pressure applied to the fly- 
 wheel is constant it may be considered as analogous to the electro- 
 motive force applied to a circuit possessing inductance. The 
 speed of the flywheel may be considered as analogous to the 
 current flowing. The pressure applied to the flywheel is maxi- 
 mum at the start, while its speed does not reach a maximum 
 until later. We can say that the speed lags behind the pressure. 
 Similarly, the current in an inductive circuit does not reach a 
 maximum until some time after the electromotive force. We 
 thus say that the current lags behind the pressure. The time 
 between the positive or negative maximum values of electro- 
 motive force and current is the phase difference. This phase 
 
58 
 
 ELECTRICAL METERS 
 
 difference depends upon the relative values of resistance and 
 inductance of the circuit. 
 
 When the circuit contains capacity, the analogy of the air 
 tank serves to give an idea of the relations of these quantities. 
 When the air is first admitted into the empty tank the current 
 will be a maximum, and the counterpressure a minimum. The 
 current of air thus leads the pressure. Similarly, when a source 
 of electromotive force is connected to a circuit possessing capacity, 
 
 -Vtoor+e 
 
 Fig. 33. 
 
 the current is a maximum ahead, in time, of the pressure; and 
 we say the current leads. Again, the phase difference is repre- 
 sented as the difference in time between the maximum values of 
 current and electromotive force. 
 
 The relative positions of the electromotive force and current 
 curves are shown in Figs. 33 and 34. Fig. 33 shows the condi- 
 tions in a circuit having resistance and inductance; and Fig. 
 34, the conditions in a circuit having resistance and capacity. 
 6 is the phase difference. 
 
 Fig. 34. 
 
 64. Power in Alternating-current Circuits. — Since in direct- 
 current circuits the power is equal to the product of current and 
 pressure, the instantaneous power in an alternating-current cir- 
 cuit will be equal to the product of the instantaneous values of 
 current and pressure. These, however, vary from time to time, 
 so the average power per cycle will be the average of the instan- 
 taneous values of the product of current and pressure. 
 
PRINCIPLES OF ALTERNATING CURRENTS 59 
 
 When the current and pressure are in phase, that is, pass 
 through their maximum and zero values at the same time, we 
 have conditions as shown in Fig. 35. The power curve is ob- 
 tained by multiplying together the instantaneous values of cur- 
 rent and pressure, and, as the figure shows, the power reaches a 
 maximum at the same time as current and pressure. The power 
 curve is, however, always positive, for the product of two positive 
 
 time 
 -CurrenT 
 
 Fia. 35. 
 
 quantities is positive, and Hkewise the product of two negative 
 quantities is positive. 
 
 In Fig. 36 we have conditions that are somewhat different. 
 Here the current lags behind the electromotive force. The 
 power curve has both positive and negative loops, that is, loops 
 both above and below the horizontal axis. The average power 
 supplied to the circuit will thus be the difference of the average 
 
 \ 4 ■'■''Tie 
 ^-'v^- -Currenr 
 
 of the positive and negative loops. It is thus evident that the 
 average product of current and pressure in an alternating-current 
 circuit does not give the average power unless the current and 
 pressure are in phase as shown in Fig. 35. The power will 
 depend not only upon the current and pressure, but also upon the 
 phase difference between them. Ordinarily, the product of an 
 ammeter reading and voltmeter reading will not give the true 
 
 6 
 
60 ELECTRICAL METERS 
 
 power in an alternating-current circuit. In general, the power is 
 less than this product. 
 
 As has already been shown, the phase difference will depend 
 upon the inductance and capacity of the circuit, and hence the 
 power will depend upon the inductance and capacity. 
 
 65. Phase Angle. — We have defined phase difference as the 
 interval of time that elapses between the maximum values of 
 pressure and current. Physically this is exactly what the phase 
 difference is. For purposes of computation, however, the phase 
 difference is best expressed as an angle and, accordingly, the 
 constant by which we multiply the product of the effective 
 current and effective electromotive force to get the actual power 
 in a circuit is usually written as the cosine of the phase angle, thus 
 
 Power = IE cos d 
 
 where I and E are the effective values of current and pressure, 
 or, in other words, are the values that alternating-current 
 ammeters and voltmeters indicate. Cos 6 is the cosine of 
 the phase angle and is called the power-factor. Another defi- 
 nition of power-factor will be given later. When the current and 
 pressure reach the maximum value at the same time, the difference 
 in phase is zero and cos 6 = 1. When this is the case, the power 
 is a maximum. 
 
 This fact, that the alternating current and pressure causing 
 the current may be out of phase, is fundamental in measuring 
 alternating-current quantities, and should be mastered. As 
 already stated, power computed from ammeter and voltmeter 
 indications may be very much in error in some cases. Watt- 
 meters, however, take account of the power-factor and their 
 indications give correct values. 
 
CHAPTER V 
 ALTERNATING-CURRENT CIRCUITS 
 
 66. Single-phase Circuits. — A single-phase circuit consists of 
 two line wires, and is fed by a single-phase generator. The 
 armature of the single-phase generator contains a single wind- 
 ing, the two ends of which are connected to two collector rings. 
 In the revolving-field type of generator the single-phase genera- 
 tor is provided with two terminals to which the external circuit 
 may be connected. 
 
 The electromotive force of a single-phase generator fluctuates 
 between positive and negative values and is well represented in 
 Figs. 33, 34, and 35. Similarly, the current in a single-phase cir- 
 cuit fluctuates between positive and negative values, as indicated 
 in the figures mentioned above. 
 
 The single-phase circuit is thus similar to a two-wire, direct- 
 current circuit. The flow of power in the circuit is, however, 
 considerably different. It can be shown that the power in a 
 single-phase circuit fluctuates with a frequency double that of 
 the electromotive force or current. A curve showing the fluc- 
 tuations of power in a single-phase circuit is shown in Fig. 36. 
 
 67. Polyphase Circuits. — A polyphase circuit may consist of 
 either two, three, or more phases; the three-phase circuit being 
 the most common. 
 
 The winding of the armature of a quarter-phase, commonly 
 called two-phase, generator consists of two distinct sets of coils. 
 This winding is so arranged that, when the coils of one set are 
 under the field poles, the coils of the other set are midway be- 
 tween the field poles. Thus, when the electromotive force in 
 one set of coils is a maximum, that in the other set is zero. 
 The electromotive-force curves of a quarter-phase generator are 
 shown in Fig. 37. Calling the angular distance between two 
 consecutive poles of an alternator equal to 180°, the difference 
 in phase between the electromotive forces in the two sets of 
 windings is 90°, as indicated in figure. 
 
 A quarter-phase circuit usually contains four wires, each con- 
 
 61 
 
62 
 
 ELECTRICAL METERS 
 
 nected to the terminals of one set of coils on the armature. For 
 simplicity, it may be looked upon as consisting of two single- 
 phase circuits. In some cases two of the return wires are joined 
 and the circuit consists of only three wires. This system is not 
 
 Fig. 37. 
 
 very common. The quarter-phase generator is also being dis- 
 placed by the three-phase machine, which is more eflScient, every- 
 thing considered. 
 
 68. Three-phase Circuits. — The voltage relations in a three- 
 phase system are represented in Fig. 38. The windings on the 
 
 FiQ. 38. 
 
 armature consist of three semi-distinct sets of coils so arranged 
 that each occupies approximately one-third the distance between 
 two field poles of the same polarity. The phase difference 
 between the separate electromotive forces is then 120°, or one- 
 third of 360°, since the distance between two like poles is 360 
 electrical degrees. 
 
ALTERNATING-CURRENT CIRCUITS 
 
 63 
 
 The three-phase system may also be looked upon as three 
 single-phase systems whose voltages are out of phase by 120°. 
 In practice, however, this would necessitate six line wires, which 
 would make the system very compUcated and expensive. The 
 efficiency of the system lies in the fact that three ends of the 
 armature coils may be joined together and the other three ends 
 to the line wires, as shown in Figs. 39 and 40. The lamps, or 
 other receiving circuits, are then connected between the line 
 wires as shown by x, y, and z. The manner of connecting the 
 armature coils, shown in Fig. 39, is known as the Y connection, 
 and that shown in Fig. 40 as the delta connection. A, B, and C 
 in each of these figures represent the separate phase windings. 
 
 Fig. 39. 
 
 FiQ. 40. 
 
 69. Current and Voltage Relations in Three-phase Circuits. — 
 Representing the maximum value of the pressure generated in 
 each phase by a line whose length is proportional to the numerical 
 value of the maximum pressure. Fig. 41, three equal lines, making 
 angles of 120° with each other, will represent, both in magnitude 
 and phase, the maximum three-phase pressures generated in a 
 F-connected armature. The instantaneous values of the sep- 
 arate pressures will then be equal to the projections of Eim, 
 E2m, and E^m upon the vertical line YY'. At the instant repre- 
 sented by the figure these instantaneous values are for Eim, Oei; 
 for Elm, Oe^; and for Eim, Oeg. Representing Oei, Od and Oe^ by 
 01, 62 and 63 respectively the following relations hold: 
 
 ei = Elm sin 6 
 
 62 = E2m sin {8 + 120°) 
 
 63 = Eim sin (e + 240°). 
 
 By rotating Eim, E^m, and E3m counter-clockwise, ei, eg, and 63 
 will fluctuate as the sine of an angle, but differing in phase by 
 120°. Hence, they may be properly represented by the sine 
 curves of Fig. 38. 
 The three lines Eim, Etm, and Ezm, Fig. 41, are called vectors. 
 
64 
 
 ELECTRICAL METERS 
 
 Vectors cannot be added algebraically, that is, the sum of Eim 
 and Eim is not the algebraic sum of their numerical values. Vec- 
 tors are combined geometrically. To get the sum of two vectors, 
 form a parallelogram with the given vectors as sides; the diagonal 
 will then represent the sum, both in magnitude and direction 
 
 Fig. 41. 
 
 The vector difference is obtained in much the same way. The 
 direction of vector to be subtracted is reversed and the two 
 vectors are then added. 
 According to this method of addition and subtraction, the 
 pressure across y, Fig. 39, is equal to the vec- 
 tor difference between the pressures generated 
 in windings A and B respectively. Represent- 
 y «^ ^ ^^^ *^® pressure developed in winding A by 
 
 '^ ^ vector Ea, and that in winding B by Eb, Fig. 
 
 42, the vector difference is equal to E, which 
 is the pressure across y. Numerically 
 
 E = Ej. cos 30° + Eb cos 30° 
 = HV^E^ + ViV^EB 
 = VSEj. = V3Eb 
 
 when Ea = Eb, as is usual in practice. 
 In the foregoing demonstration E, Ea, and Eg represent either 
 maximum or effective values. Hence, we may, in general, 
 say that the pressure between the mains of a y-connected three- 
 phase circuit is equal to\/3 times the pressure developed in each 
 armature winding. 
 
ALTERNATING-CURRENT CIRCUITS 65 
 
 The current in each main must be the same as the armature 
 current, as is evident from the connections. 
 
 In the delta-connected system the conditions are reversed. 
 The connections plainly show that the pressure between mains 
 is the same as that developed in one armature winding. The 
 current in either main, however, is the vector difference between 
 currents in two windings, and hence, according to what has just 
 been said, the current in one main equals s/Z times the current in 
 one armature winding. The power in any polyphase system is not 
 pulsating as in a single-phase system, but is constant or steady. 
 
CHAPTER VI 
 INDUCTION PRINCIPLE 
 
 70. Introduction. — The fundamental principle of induction 
 meters, as well as motors, was discovered by Arago in 1825. He 
 found that if a copper disk is pivoted on the axis of a magnetic 
 needle, its plane being horizontal, and rotated, the needle will be 
 deflected. This principle is illustrated in Fig, 42. Above the 
 copper disk C, but not touching, is a glass plate G. In the middle 
 of the glass plate and directly above the center of the arbor is 
 pivoted a magnetic needle. When the copper disk is rotated, the 
 needle is deflected in the direction of rotation. If the position 
 
 Fia. 43. 
 
 of disk and needle be interchanged, and the needle rotated, the 
 disk will rotate in the same direction as the needle. 
 
 Faraday explained this phenomenon on the supposition that 
 relative motion between needle and disk resulted in producing 
 electric currents in the disk, and that the reaction between the 
 magnetic field produced by these currents and the field due to 
 the magnet caused the rotation of needle in the first case, and 
 of the disk in the second case. This explanation has been veri- 
 fied many times since. Whenever a conductor cuts across a mag- 
 netic field an electromotive force is induced. If the conductor 
 7 67 
 
68 ELECTRICAL METERS 
 
 forms a closed circuit, a current will flow through the circuit and 
 a reaction is set up between the conductor and magnetic field. 
 
 In the experiments of Arago and Faraday the magnetic field 
 was caused to rotate by rotating the magnet to which the field 
 was due. It is evident such a device is not suited for measuring 
 instruments. What is needed is relative motion between the 
 field and conductors, without the corresponding motion of 
 magnets. 
 
 71. Rotating and Revolving Magnetic Fields. — In practice 
 there are two types of moving magnetic fields which may be 
 designated by the two terms, rotating and revolving. In every- 
 day language the two words, rotating and revolving, are used 
 interchangeably, but there is a distinction in their meanings 
 which should be kept in mind. 
 
 Fig. 44. 
 
 A body is said to rotate when it has a circular motion about 
 its own center or axis; to revolve is said of a body that moves in 
 a curved path, as a circle or ellipse, about a center outside of 
 itself. According to this distinction a rotating magnetic field is 
 one that turns about an axis passing through the field; and a 
 revolving magnetic field is one that moves around an axis out- 
 side of itself. 
 
 72. Production of Rotating Field. — To produce a rotating 
 magnetic field of constant intensity, and rotating at a constant 
 speed, necessitates polyphase currents. In Fig. 44 is shown a 
 circular coil carrying a current which sets up a magnetic field at 
 the center of the coil. The curved lines with arrow heads repre- 
 sent magnetic lines in one position. When the current is alter- 
 nating, the field is also alternating, increasing and decreasing 
 with the current and reversing as the current reverses. Repre- 
 senting the current by 
 
 i = Im cos ut 
 
INDUCTION PRINCIPLE 
 
 69 
 
 we may represent the instantaneous value of field strength by 
 
 h = Hm cos <at 
 
 A horizontal section of two such coils with their planes at 
 right angles is shown in Fig. 45. The curved lines represent the 
 magnetic lines of the two coils superposed when the intensities 
 of the two fields are equal. When coil A A' is connected to one 
 phase of a quarter-phase circuit, and BB' to the other phase, 
 the currents will produce alternating fields in the two coils. 
 The direction of each field will always be at right angles to the 
 plane of the coil producing it, but the intensities of the two fields 
 will differ by one-quarter of a period. 
 
 B 
 
 The instantaneous values of the field intensities can be repre- 
 sented by 
 
 hi = Him cos ut 
 and hi = H^m sin cat 
 
 The resulting field will be the vector sum of hi and hi. Since 
 hi and h2 are at right angles to each other the instantaneous 
 value of the resultant is 
 
 h = Vi^iM- h'' 
 
 = VHim^ cos2 ut + HiJ sin ut. 
 When Him = Him, that is, when coils are exactly alike, 
 
70 
 
 or 
 
 ELECTRICAL METERS 
 
 h = VHiJ" (cos^ o}t + sin2 cof) 
 h = Him, a constant. 
 
 The rectangular components are hi and ha, and when Him = ^2m 
 = Hm, that is, when the maximum values of the component 
 fields are equal, we have 
 
 and 
 
 or 
 
 hi = Hm cos ut 
 hi = Hm sin wt 
 hi^ + /i2^ = Hm' the equation of a circle 
 
 Therefore, the resultant field rotates at a constant angular speed 
 which is determined by the frequency. 
 
 In practice the two component fields seldom have equal 
 maximum values, consequently, the following is more important. 
 
 73. Rotating Field Produced by Unequal Component Fields. — 
 Two harmonically alternating fluxes at right angles to each other 
 in space may be replaced by two rotating fluxes of different 
 magnitudes rotating in opposite directions but having the same 
 angular speeds. Thus in Fig. 46, let OA = 2Him and OB = 
 2H277. represent two harmonic fluxes, produced by two circular 
 coils having a common center but having planes at right angles 
 to each other. OA and OB are fixed in direction but vary in 
 magnitude according to the sine law. The flux OA may be con- 
 sidered as being the projection of two equal vectors, each equal 
 
INDUCTION PRINCIPLE 71 
 
 to }4 OA, rotating in opposite directions at a uniform speed so 
 as to make one complete revolution while the values of OA pass 
 through one cycle. 
 
 Let OC and OCi represent the two component vectors at the 
 instant they make an angle di with OA. Evidently, at this 
 instant the intensity of the field along OA is given by 20C cos 61 
 = 20c cos ut 
 where w = 27r X frequency. 
 
 Similarly OB may be considered as the resultant of two vectors 
 OD and ODi, each equal to }>iOB. 
 
 Combining the two components that rotate in the same 
 direction we get the two components OF and OFi, which differ in 
 magnitude, rotate in opposite directions, but have the same 
 angular speeds. 
 
 The numerical value of OF and OFi in terms of OC and OD, 
 and thus in terms of OA and OB, can be obtained analytically as 
 follows: 
 
 OF'' = OC'' + OD^ - 20c X OD cos ODF 
 
 and OFi^ = OCi" + ODi" - 20Ci X ODi cos ODiFi 
 but OC = OCi = Hu. and OD = ODi = H,„. 
 Then OF" = Hi^^+ H2J - 2Hi^H2„, cos ODF 
 and Of 1^ = HiJ + H^J - 2Hi^Hi„ cos ODiF,. 
 
 Z ODF is the supplement of Z COD. 
 
 But ZCOD = ZAOD + ZCOA = '^-62 + 81, and hence, 
 
 ZODF = T - (I - 02 + 6*1) =1+ (62- e,) 
 
 IT 
 
 Similarly ZODiFi can be shown to equal ^ — {B2 — 0i). 
 
 Now ^ is the physical angle between the fluxes OA and OB, but 
 
 02 — 01 is the time-phase difference expressed as an angle between 
 the alternating fluxes of which OA and OB represent the maxi- 
 mum values. Representing this phase difference by So we finally 
 
 get: 
 
 0^2 = Hi„,^ + HiJ" + 2HimH2,n sin do 
 
 OFi" = HiJ + HiJ - 2i?i„ff2^ sin e^. 
 
 That is, in place of one resultant field rotating with a uniform 
 
72 
 
 ELECTRICAL METERS 
 
 speed in one direction there are two fields with different ampli- 
 tudes rotating in opposite directions. This principle has impor- 
 tant application in induction-type instruments. 
 
 74. Production of a Revolving Magnetic Field. — Two quarter- 
 phase currents may also be used for producing a revolving field. 
 The manner in which the stator of a quarter-phase motor is 
 connected is indicated in the diagram of Fig. 47. The short 
 heavy lines represent the conductors in the slots of the stator 
 core, and the light lines represent the end connections. The 
 
 Fig. 47. 
 
 curved lines outside may be considered as representing the front 
 end connections, and, under this assumption, the curved lines 
 within will represent the back connections. An examination of 
 the diagram will show that the current in conductor 1 passes 
 across the iron core from front to back while in conductor 11 it 
 passes from back to front. The two groups of conductors, A and 
 A', together with the connecting wires may thus be considered 
 as forming a coil which surrounds a portion of the iron core. 
 Similarly B and B', which surround another portion of the core, 
 will form another coil. Assuming a direct current to be flowing 
 through phase A while phase B is open, it is evident that a north 
 
INDUCTION PRINCIPLE 
 
 73 
 
 pole will develop between A and A', and a south pole between 
 A' and A", etc. In all there will be four poles. Such an arrange- 
 ment of conductors is called a four-pole winding. 
 
 A simplified diagram of an end view of a four-pole two-phase 
 induction motor is shown in Fig. 47a. In this diagram the con- 
 
 ductors are represented by circles. For clearness the end con- 
 nections are omitted. When current in winding A-A', etc., is 
 maximum that in winding B-B', etc., is zero. The position of 
 the magnetic lines at this instant is indicated by dotted lines with 
 arrow heads. The current in group of conductors A is toward 
 
 Fig. 476. 
 
 the observer, and in group A' away from the observer. Under 
 these conditions a south pole is formed at S under the stator core. 
 One-eighth of a period later the current in winding A-A', etc., 
 will have decreased to 0.707 of its maximum value and that in 
 winding B~B', etc., will have increased to 0.707 of its maximum 
 value. The currents will at this instant be equal and as they will 
 
74 
 
 ELECTRICAL METERS 
 
 be flowing in the same direction, the position of the magnetic field 
 will be as indicated in Fig. 47&. The magnetic fluxes due to the 
 two currents will combine forming a resultant pole halfway 
 between A and B'. The same thing will hold true with reference 
 to the other groups of conductors. Thus during one-eighth of a 
 period of the current, the magnetic poles have shifted one- 
 sixteenth of the circumference of the stator. 
 
 After another one-eighth of a period the conditions will be as 
 lepresented in Fig. 47c. At this instant the current in winding 
 A-A', etc., is zero and that in B-B', etc., is a maximum. The 
 magnetic poles have again shifted one-sixteenth of the stator cir- 
 
 FiG. 47c. 
 
 cumference. The magnetic field which is confined to the outer 
 periphery of the rotor and the inner periphery of the stator 
 revolves independently of the iron core. A revolving magnetic 
 field can be obtained from any polyphase circuit by means of 
 appropriate windings. 
 
 75. Speed of Revolving Field. — The speed with which the 
 polarity will be transferred around the stator core will depend 
 upon the frequency of the alternating current. The number 
 of revolutions per minute will depend upon the number of pairs of 
 poles per phase, and upon the frequency. If the frequency of the 
 supply pressure be /, and if there be p pairs of poles per phase, 
 
 then the field will make one complete revolution in i. sec. It will. 
 
 ./ 
 
 /' 
 
 therefore, make n = 60- complete revolutions per minute. 
 
CHAPTER VII 
 INDUCTION-TYPE AMMETERS AND VOLTMETERS 
 
 76. Application of Induction Principles to Meters.— If a suitably 
 mounted hollow conducting cylinder, or disk, be placed inside a 
 rotating field, currents will be induced in it, due to the relative 
 motion of the two, as in the experiment of Arago. The currents 
 will react with the magnetic field in such a way as to cause 
 rotation of the cylinder or disk. The reaction will be in such a 
 direction as to oppose the motion of the magnetic field in ac- 
 cordance with the general law of induction. The cylinder or 
 disk will thus rotate in the same direction as the magnetic field. 
 
 Induction meters operate in accordance with these principles. 
 For single-phase instruments, the principle of rotating, or revolv- 
 ing, field is obtained in a modified way. 
 
 77. Induction Ammeters and Voltmeters. — One method of pro- 
 ducing a revolving, or in this case what may be called shifting, 
 magnetic field for single-phase instruments is shown in Fig. 48. 
 The current circuit of the meter is represented by the winding 
 ABC. The coil B surrounds the laminated iron core I. In the 
 end of this iron core is a slot through which and around one-half 
 of the core is wound a heavy band of copper as shown at E. The 
 alternating current flowing through coil B induces a flux in the 
 iron core. When the flux is increasing, a part of it will pass 
 through the core of the short-circuited copper band, inducing a 
 current in it. This current is in such a direction that it opposes 
 the building up of the magnetic flux within the space surrounded 
 by the band. While the current is increasing, the magnetic 
 density of that part of the iron core which is not surrounded by 
 the copper band will be greater. On decreasing current, the con- 
 ditions are, however, reversed. The flux density of the unwound 
 part of the core will decrease to zero before that in the other part. 
 The flux thus shifts from the unwound portion to the wound part 
 of the core. 
 
 As this shifting flux penetrates the disk D, currents are induced 
 
 75 
 
76 
 
 ELECTRICAL METERS 
 
 in it which react with the magnetic flux, causing the disk to 
 rotate. The controlhng force is supphed by a coiled spring as in 
 other indicating instruments. 
 
 It is plainly evident that the reaction between shifting field and 
 induced currents in the disk is a function of both the intensity of 
 the shifting field and frequency of current. If no provision were 
 made for correcting the infiuence of frequency, changes in fre- 
 quency would affect its indications. To compensate for fre- 
 quency effects, the main coil B is made of low resistance and high 
 inductance. The terminals of the coil B are connected to a non- 
 inductive shunt, ;Si. The circuit is, therefore, divided into two 
 branches, one containing resistance but no inductance and the 
 other inductance but of negligible resistance. At normal. fre- 
 
 rO 
 
 »i 
 
 D 311 
 
 Fig. 48. 
 
 quency the current will divide in a certain ratio between the two 
 branches. An increase in frequency will cause more of the cur- 
 rent to flow through the shunt, thereby decreasing the current 
 in the meter coil. This reduced current, however, will be more 
 effective in producing torque on account of its higher frequency. 
 By properly adjusting the shunt, the two effects are made to 
 neutralize each other so that the registration is not affected by 
 considerable variation in frequency. 
 
 The principles of the voltmeter are identical with those of the 
 ammeter, with the difference that there is connected in series 
 with coil B a high-resistance, non-inductive coil. This particular 
 form of induction meter is no longer on the market, although it 
 is still used. 
 
AMMETERS AND VOLTMETERS 
 
 77 
 
 78. Series-transformer Principle. — A most ingenious method 
 of producing a rotating magnetic field was invented by Mr. 
 Frank Conrad, and is used by the Westinghouse Electric and 
 Manufacturing Co. in its induction instruments. 
 
 In so far as principles of construction are concerned, a series 
 transformer contains two independent windings the same as a 
 shunt transformer. The difference between the two kinds of 
 transformers lies mainly in their use. The primary winding of 
 a series transformer is connected in series with the line, while the 
 
 Fig. 49. 
 
 other has its primary shunted across the line. Fig. 49 is a dia- 
 gram of a series-transformer winding as applied to an induction 
 meter. It is evident from the diagram that there are two dis- 
 tinct windings; P, the primary winding, carries the line current, 
 and S, the secondary, is short-circuited. The circle represents 
 the cylindrical meter movement. The dotted lines marked <p 
 represent the magnetic fluxes set up by currents in the separate 
 coils. 
 
 The current to be metered develops magnetism in the core; 
 this magnetism in turn induces a current in the secondary 
 winding. This induced or secondary current, according to the 
 principles of induction is nearly 180° out of phase with the 
 primary current. If it were not for the losses and magne- 
 tizing current it would be exactly 180° out of phase. If the 
 
78 
 
 ELECTRICAL METERS 
 
 magnetizing current were negligible, the ampere-turns of the 
 primary current would exactly equal the ampere-turns of the 
 secondary, or algebraically 
 
 That is, the magnetizing effect of primary current would just 
 balance the demagnetizing effect of secondary current. 
 
 A vector diagram for primary and secondary ampere-turns is 
 shown in Fig. 50. OP represents the product of primary current 
 and primary turns, and OS represents the product of secondary 
 current and turns. The magnetizing force, which sets up the 
 flux in the core common to the two coils, is the resultant of the 
 primary and secondary ampere-turns, and will, therefore, be 
 
 represented by OM. OM may be 
 considered as the resultant of two 
 components, ON- in phase and OM' 
 in quadrature with OP. ON will 
 represent the ampere-turns necessary 
 to supply energy for the losses, and 
 OM' will represent the true mag- 
 netizing ampere-turns. This mag- 
 netizing component is primarily re- 
 sponsible for the fact that the phase 
 difference between the primary and 
 secondary currents is not exactly 
 180°. A vector diagram of the elec- 
 tric and magnetic quantities is shown 
 in Fig. 51. 
 The combined primary and sec- 
 ondary ampere-turns produce a flux 0i which in time is nearly 
 one-quarter of a period ahead of the flux 02 due to the auxiliary 
 secondary winding. In space the two fluxes are at right angles 
 to each other as shown in Fig. 49. These are plainly the condi- 
 tions necessary for producing a rotating magnetic field. 
 
 Fio. 51. 
 
AMMETERS AND VOLTMETERS 
 
 79 
 
 Within the rotating magnetic field is placed the movable 
 element, which consists of a light aluminum cylinder mounted on 
 
 ^%!r*»^ . 
 
 Fig. 52a. 
 
 FiQ. 526. 
 
 Fio. 52c. 
 
 a shaft. The shaft is supported between jewels as in other types 
 of meters. The rotating field induces eddy currents in the cup- 
 shaped movable element, Fig. 52c, and thus 
 creates a torque which is balanced by a coiled 
 spring exactly as in other types of meters. The 
 structural features of a portable ammeter are 
 shown in Figs. 52a and 52&, and of a switch 
 board voltmeter in Fig. 52d. The principles of 
 
 construction of ammeters and 
 
 voltmeters are exactly alike, with 
 the exception that in the volt- 
 meter the primary coil is wound 
 with fine instead of coarse wire, 
 and an external non-inductive 
 series resistor of zero temperature 
 coefficient is used. 
 
 79. Relation Between Current 
 and Torque. — There are so many 
 varying quantities involved that 
 no exact expression for the torque 
 or deflecting force with refer- 
 ence to the current can be given. 
 A general relation can be deter- 
 mined as follows: 
 The flux in the iron core is proportional to the current to be 
 measured and the induced currents in the rotating disk are pro- 
 
 FiG. 52(1. 
 
80 ELECTRICAL METERS 
 
 portional to the flux. The deflecting or rotating force is propor- 
 tional to the product of flux and eddy currents, hence, the de- 
 flecting force is proportional to the square of the flux, which in 
 turn is roughly proportional to the square of the current in the 
 main coil. The motion is usually opposed by spiral springs and 
 thus the angle of deflection is roughly proportional to the square 
 of the current. 
 
 According to the principles of Article 73, if Hi = <^i, H2 = <t>2, 
 OFi = $1 and OF = $2 the two fields rotating in opposite direc- 
 tions are given by 
 
 *i^ = <l?i^ + W - 24>i^2 sin e 
 
 and $2^ = <i>i^ + (t>2^ + 20102 sin 6 
 
 6 is the time-phase difference between 4>i and <t>2 as represented 
 in Fig. 51. 
 
 Since the cylinder turns only until the driving torque equals 
 the counter torque of spring, the speed of the drum is zero. The 
 actuating torque is due to the cutting of the cylinder by the two 
 fluxes $1 and #2 in opposite directions. The deflection will be 
 in the direction of the greater torque. 
 
 The eddy currents in the drum due to *i and $2 are propor- 
 tional to $1 and $2 and to the speed of these which is 27r/. If the 
 eddy currents lag 7 degrees behind the induced voltage the torque 
 due to $1 is 
 
 Ti = fKi^i^cosy 
 
 and that due to $2 is likewise given by 
 
 T2 = fKi^i'' cos y 
 
 The driving torque is equal to 
 
 Ti- T2= fKi cos 7 («>i2 - $2=) = 4/A:i0i02 sin 6 cos 7 
 
 K T 
 but 01 = —J — ) and 02 = K3I1, where h is the primary 
 
 current. 
 
 inen 1 — ii — I2 — j sm 6 cos 7 
 
 = iKiKiKih'^ sin 6 cos 7 
 
 Ki depends mainly upon the impedance of the drum and varies 
 
 inversely with it. In place of Ki we may write Ki = ■=» 
 
 Z 
 
AMMETERS AND VOLTMETERS 
 
 81 
 
 where Z is the impedance of cylinder; then 
 
 T = — ^— sm d cos 7. 
 
 80. Influence of Frequency. — In the expression given above for 
 torque, Z, 6, and 7 are quantities varying with frequency, and in 
 order that the meter may be independent of frequency Z must 
 vary as sin cos 7. This can only be approximated, although 
 the maximum error due to changes of frequency from 25 to 60 
 cycles is not over }4 per cent. 
 
 8L Influence of Temperature. — Variation in temperature will 
 mainly affect the resistance of the movable cylinder. In order 
 to correct for this variation, the secondary coil is arranged to 
 have a temperature coefficient of resistance such as to exactly 
 cancel the effect of the variations of resistance in the cylinder. 
 To do this another series transformed principle is used. If in a 
 
 I 
 
 Is 
 
 /£>^ 
 
 /oo 
 
 96 
 
 96 
 
 a/nt/> 
 
 Loan/' 
 
 
 Conaui ■tai:/aff ul/Loai ' 
 
 Hei /sta/7i CO.//- ' o6m3 
 We/ff/^ of Mitring ^/er7?e}^-' /O^^ns 
 
 '9=/. 4 
 
 ■Cms. 
 
 ZO 
 
 30 40 
 Fig. 53. 
 
 so 
 
 eo 
 
 70 
 
 Cycles, for curve No. 1 which shows the effect of changes in frequency. 
 Minutes in circuit for curve No. 2 which shows the effect of self-heating at 
 two-thirds load. Air temperature in °C. for curve No. 3 which sho\ys the 
 effect of variations in room temperature. 
 
 series transformer the primary current be kept constant, the 
 secondary current will remain nearly constant while the secondary 
 resistance is varied over a considerable range. Thus, any in- 
 crease in the secondary resistance causes a proportional increase 
 in the flux of the core. This is made possible by working the 
 core a.t a low flux density. 
 
 The Westinghouse ammeter described has the secondary cir- 
 cuit wound partly with copper and partly with a wire of low 
 temperature coefficient, the resulting temperature coefficient 
 
82 
 
 ELECTRICAL METERS 
 
 of the secondary circuit being such as to increase the flux in the 
 iron when the temperature rises, thus compensating for rise of 
 temperature of the aluminum cyhnder. Figs. 53 and 53a show 
 the performance curves of ammeters and voltmeters respectively. 
 82. Scale. — A direct reading scale of the induction type of 
 instruments will have the same disadvantages as those whose 
 deflection is proportional to the square of the quantity to be 
 
 \ 
 
 /(ft? 
 
 90 
 
 96 
 
 20 
 
 30 40 
 
 Fig. 63a, 
 
 Cycles, for curve No. 1 which shows the effect of changes in frequency. 
 Minutes in circuit for curve No. 2 which shows the effect of self -heating at 
 two-thirds load. Air temperature in °C. for curve No. 3 which shows the 
 effect of variations in room temperature. 
 
 measured. In practice, this disadvantage is overcome in two 
 ways. One method makes use of a cam-shaped disk, which is 
 mounted so that less and less of it lies between the poles of the 
 iron core as it rotates. A proper shaping of the disk permits the 
 construction of a practically uniform scale for about 300° of 
 arc. A second method, made use of by Siemens and Halske, con- 
 sists in using an auxiliary weight so mounted that it reinforces 
 the tendency of the moving element to rotate at the zero end of 
 the scale, while at the upper end of the scale, it is vertically below 
 the spindle. The instruments manufactured by the above- 
 mentioned firm have nearly a uniform scale extending over an 
 arc of 90°. \ 
 
 82a. Damping.— The electromagnetic method of damping is 
 employed in these instruments. In the earlier instruments an 
 aluminum disk is mounted on the shaft, and as it moves between 
 the poles of two permanent magnets effective damping is secured. 
 The proper damping is now obtained by means of a "C" shaped 
 permanent magnet located very close to the drum of the movable 
 element. 
 
CHAPTER VIII 
 ELECTRODYNAMIC AMMETERS AND VOLTMETERS 
 
 83. Introduction. — The principle upon which the operation 
 
 of these instruments depends is, as its name impUes, the mutual 
 attraction and repulsion between adjacent circuits carrying 
 electric currents. The principle that currents flowing in the 
 same direction in parallel wires attract and when flowing in 
 
 Fig, 54. 
 
 Fig. 55. 
 
 opposite directions repel, is the fundamental principle of the 
 instruments of this class. The repulsion and attraction is due 
 to the interaction of magnetic fields produced by the currents, 
 but as instruments possess no iron core, the interaction is called 
 electrodynamic instead of electromagnetic. 
 
 84. Electrodynamometer Type. — The essential features of an 
 instrument of this type, which for a long time was extensively 
 used for measuring alternating currents, are shown in Fig. 54. 
 The completed instrument is shown in Fig. 55. As shown in 
 Fig. 54, the instrument contains two coils, one fixed, FF' , and 
 8 83 
 
84 ELECTRICAL METERS 
 
 one movable, MM'. The movable coil is placed outside of the 
 fixed coil and is supported by a fiber which offers very slight 
 resistance to motion of the coil. The lower ends of the coil dip into 
 mercury cups which are connected to binding posts. 
 
 The controlling force is furnished by a spiral spring, one end of 
 which is attached to coil MM' and the other to the torsion head 
 H. The index pin P is also rigidly connected to the torsion head, 
 which passes through the fixed graduated plate A, and may be 
 turned by the milled head at the top of the instrument. 
 
 85. Operation of Electrodjmamometer Ammeter. — The cir- 
 cuit within which the current is to be measured is connected in 
 series with T and Ti, or T and T2, depending upon the magnitude 
 of the current. Assuming that direct current is to be measured 
 and that the positive terminal is connected to Ti, it will be 
 noticed that the current flows up the side of the stationary coil 
 marked F and down the side marked F'. After passing through 
 the junction block R and the connecting link RC the current enters 
 the movable coil at C and flows up through the side M and down 
 through the side marked M', finally leaving the instrument 
 through binding post T. 
 
 Keeping in mind the principle of parallel circuits stated in 
 Chapter I, we see that the current flows in the same direction in 
 sides F, M', and F', M. Since the large coil FF' is fixed and can- 
 not move, the coil MM' will be deflected in such a direction that 
 the side M approaches F, and M' approaches F'. The motion of 
 the coil is stopped when the pointer I strikes the pin N. By 
 turning the torsion head G, the pointer I can be brought back to 
 its original or zero position. The force tending to deflect the 
 coil is then measured by the angle through which the torsion head 
 has been turned, for within the limits of elasticity of the helical 
 spring, the force causing a distortion or twist is strictly pro- 
 portional to the angle through which it has been twisted. In 
 order to measure the current, however, it is necessary to get an 
 expression for the force in terms of the current in the coils. 
 Both theory and experiment show that 'the force is proportional 
 to the product of the current in M and F. In the case considered 
 the same current flows through both coils, hence, the force of 
 attraction must be proportional to the square of the current. 
 Now, since the force is proportional to the angle of deflection, 
 and likewise to the square of the current, it is evident that the 
 square of the current must be proportional to the angle of deflec- 
 
AMMETERS AND VOLTMETERS 
 
 85 
 
 tion. Letting I equal current strength, K^ a proportionality- 
 factor, and d the angle of deflection, we may write the foregoing 
 relation as follows: 
 
 Whence 
 
 I = KVl 
 
 This is the fundamental equation for instruments of this type. 
 It will be noticed that the current is proportional to the square 
 root of the angle of deflection, and, hence, the scale of such an 
 instrument, if it were to be direct reading, could not be uniform. 
 In practice, the scale is graduated in degrees, and the current 
 is determined from calibration curves or computed in accord- 
 ance with the above formula after the constant K has been 
 determined. 
 
 It has been assumed that the current to be measured was 
 direct, or continuous. One of the advantages of the electro- 
 
 Mon-induetive Resiatance 
 
 AAAAAAA-i 
 
 I a. 
 
 Shiint 
 
 Movable CJbil 
 , Fixed Coil 
 
 Fia. 56a. 
 
 Fia. 566. 
 
 dynamometer ammeter is that it can also be used on alternating- 
 current circuits. That the deflection is in the same direction on 
 alternating current as on direct current, will be evident on notic- 
 ing that when the current reverses in the stationary coil it likewise 
 reverses in the movable coil. The current will always be in the 
 same direction in F as in M, and in F' as in M', and consequently, 
 the deflection on alternating current is the same as on direct 
 current. Also, both by theory and experiment, it has been shown 
 that the deflecting force on alternating current is proportional 
 to the square of the effective current. Hence, the instrument 
 gives true effective values of alternating currents. 
 
 86. Shunted Electrodynamometer Ammeter. — To increase the 
 range of an ammeter of this type the coils may be shunted in 
 either one of two ways: A shunt may be connected across both 
 coils as indicated in Fig. 56a, or only the movable coil may be 
 shunted as shown in Fig. 566. 
 
86 ELECTRICAL METERS 
 
 When the connections of Fig. 56a are used, an additional non- 
 inductive resistance of low temperature resistance coefficient 
 must be connected in series with the coils of the instrument. As 
 the coils of the instrument are usually made of copper, the instru- 
 ment when so connected will be subject to two sources of error, 
 namely, temperature and frequency. The temperature error 
 will depend upon the ratio of the resistance of the instrument coils 
 to that of the non-inductive resistance in series. If this is small, 
 the temperature error will be small. 
 
 The frequency error upon alternating^current circuits is due 
 to the inductance of the instrument coils. The per cent error due 
 to this cause may be calculated as follows: 
 Let Ri = resistance of instrument circuit, 
 Ro = resistance of shunt, 
 X = reactance of instrument circuit, 
 L — self-inductance of instrument circuit. 
 Ii = current in maiu. 
 7o = current in Ra. 
 I = current in meter circuit. 
 Then, if the ammeter be calibrated on direct current, the cur- 
 rent flowing in the main to which the ammeter is connected is 
 given by 
 
 I (Ri + Ro), 
 
 h = 
 
 Ra 
 
 When an alternating current gives the same deflection, the current 
 
 J D 
 
 through the instrument coils must also be /: but / = — - r- — = 
 
 VRi" + ^' 
 I R 
 = —y—- lo and / will not be in phase; hence 1 2, the current in 
 
 the main, is the vector sum of I and 7o, or 
 
 h = ^l (7 cos 6 + hY + (7 sin d)^ 
 
 = Si +2 Ih cos d + h^ 
 
 But 
 
 and 
 
 Hence 
 
 7 -:^ 
 io — p 
 
 cos 6 = 
 
 R 
 
 z' 
 
 h = ^^yRo"" + 2 RRx + Z^ 
 
AMMETERS AND VOLTMETERS 87 
 
 .+ ^ 
 
 {Ro + Riy 
 
 and per cent error = 100 — 100 \ 1 + 
 
 X^ 
 
 {Ro + Rir 
 X = 2rfL 
 
 EXAMPLE 
 
 A shunted electrodynamometer ammeter has a coil whose resistance is 
 1 ohm. It is shunted by a resistance of J^g ohm. If the inductance of 
 the instrument coil is 0.3 millihenry, what will the error be when the fre- 
 quency is 100 cycles per second? 
 
 Solution. — 
 
 Per cent error = 100 - 100 \/l + 
 
 4^ 
 
 {Ro + Ri)' 
 Given L = 0.3 X 10-^ henrys, 
 Ri = 1 ohm, 
 / = 100. 
 Then X = 27r/L = 27r X 100 X 3 X 10"^ 
 
 Ro + Ri = "53^ ohms. 
 
 and per cent error = 100 — 100 \/l + 
 
 47r2 X 10< X 9 X 10-« X 992 
 
 10* 
 
 = 100 - 100 X 1.0172. 
 
 = 1.72 per cent low. 
 The remedy for this would be to make the shunt inductive, which is difficult 
 to carry out in practice. 
 
 When the movable coil only is shunted as indicated in Fig. 
 
 566, the frequency error will be much smaller. The algebraic 
 
 expression for the per cent error in this case is given by 
 
 X^ /M \ 
 Per cent error = 100 ^^2\W + l).' 
 
 Where X = 2wfL, 
 
 Ri = resistance of shunted coil, 
 Ro = resistance of shunt, 
 
 M = mutual inductance of the instrument coils, 
 L = self-inductance of movable coil. 
 In a particular instrument the per cent error at a frequency 
 of 100 was found to be 0.01 per cent.' 
 
 87. Voltmeters. — The electrodynamic principle can be used to 
 measure difference of pressure as well as current. The arrange- 
 ment of the coils for the dynamometer type voltmeter is shown in 
 
 ' HiSDALB, Journal I.E.E., vol. 48, p. 621. 
 
88 
 
 ELECTRICAL METERS 
 
 Fig. 57. SS are the fixed coils, which are connected in series, and 
 A is the movable coil to which the pointer P is rigidly attached. 
 The movable and fixed coils are also connected in series together 
 with a non-inductive coil of high resistance and low temperature 
 coeflacient. The effect of this series resistance is to reduce the 
 frequency and temperature errors to a negligible amount. 
 
 The commercial instruments of this type are similar in mechan- 
 ical construction to the permanent-magnet, moving-coil type of 
 instrument. The electrical features differ in that the magnetic 
 field in this type of instrument is due to the current flowing in the 
 coils, which is proportional to the voltage to be measured. In the 
 permanent-magnet type of instrument the magnetic field is due to 
 
 Fig. 67. 
 
 the permanent magnets, and the current in the moving coil only 
 is proportional to the difference of pressure. 
 
 88. Effect of Inductance Upon Reading of Electrodynamometer 
 Voltmeter. — In well-designed voltmeters of this type the induc- 
 tance is reduced to a minimum, and the inductance errors are 
 practically negligible; nevertheless, the influence of this quantity 
 may sometimes be appreciable. The relation between a direct 
 electromotive force and an alternating electromotive force caus- 
 ing the same deflection may be determined as follows; 
 
 Let E = direct-current electromotive force causing a given 
 deflection, 
 E'= alternating-current harmonic electromotive force 
 causing same deflection, 
 
AMMETERS AND VOLTMETERS 89 
 
 L = inductance of coils, 
 
 R = resistance of coils. 
 
 E^ 
 Then the deflecting force on direct current is proportional to ^^i 
 
 that is, to the square of current in' coils. 
 
 Since the deflection is assumed to be the same when alternating- 
 curreht electromotive force is measured, the effective current 
 must be equal to the direct current. The effective current 
 
 and 
 
 whence, E' = 
 
 E E' 
 
 R VW+ oj^L^ 
 
 Ey/W+~i^^ 
 R 
 
 E^f^' 
 
 R^ 
 
 When R is large in comparison with Leo, the second term under 
 the radical sign has little effect; when this is not the case the 
 difference between E and E' will be appreciable. 
 
 89. Construction. — The dynamometer type of voltmeter con- 
 tains no iron, and, as the three coils are all connected in series, it 
 is well suited for alternating-current measurements. A phantom 
 view of the essential features of a Weston dynamometer volt- 
 meter is shown in Fig. 58. The Roller Smith Co. apply the 
 same principle in their dynamometer type of voltmeters. In 
 this case, however, the coil is mounted with its plane inclined at 
 an angle to the arbor or shaft which supports it. Fig. 59. Such a 
 construction makes it possible to fasten the coil to the shaft by 
 small projecting lugs which are integral with and project from the 
 sides of the coil frame. By clamping the lugs between appro- 
 priate nuts, the coil is rigidly fastened to the arbor. The 
 inclined-coil voltmeter of the General Electric Co. is also similar 
 in construction. In these instruments both the fixed and mov- 
 able coils are inclined with reference to the shaft carrying the 
 movable coil, Fig. 60. The movement of a Westinghouse volt- 
 meter of this type is shown in Fig. 61. 
 
 The principles of operation are. the same in all cases. In 
 every case the force causing a deflection varies as the product 
 
90 
 
 ELECTRICAL METERS 
 
 of currents in fixed and movable coils. When these currents 
 are the same, the deflecting force depends upon the square of 
 the actuating current. On account of the change in relative 
 position of coils when in use, exact proportionahty does not 
 
 Fig. 59. 
 
 exist between the deflecting force and the square of current. 
 Since in the instruments of the dynamometer type the controlling 
 force is due to a spiral or helical spring whose counterforce 
 
 varies directly with the deflection, such instruments do not have 
 uniform scales when direct reading. The graduations are 
 crowded together at the beginning and end of scale, especially at 
 the beginning, as is shown in Fig. 61a. 
 
AMMETERS AND VOLTMETERS 
 
 91 
 
 90. Ampere Balance. — A standard instrument for measuring 
 current is known as Kelvin's balance, Lord Kelvin being the 
 inventor and designer of the instrument. The operation of the 
 instrument is based on the electrodynamic attraction between 
 stationary and movable coils, in much the same way as the 
 electrodynamometer discussed above. In Fig. 62 are shown the 
 
 Fig. 61o. 
 
 essential features of the instrument. As shown in the figure, 
 the instrument consists of four fixed and two movable coils. 
 The fixed coils are designated by A, A', A", A'", and the 
 movable coils by B, B'. 
 
 The coils are all connected in series by connections as shown in 
 the diagram. The winding of the lower coil A is reversed with 
 
 Suspension 
 strips:- 
 
 Fig. 62. 
 
 reference to the winding of the upper coil. The current thus 
 flows in one direction in one coil and in the opposite direction in 
 the other coil of the couple. In the same way the current flows 
 in opposite directions in the stationary coils. Assuming that 
 the current flows counter-clockwise in coil A, it will flow in a 
 clockwise direction in coil A'. Thus, if coil A attracts coil B, 
 
 9 
 
92 
 
 ELECTRICAL METERS 
 
 coil A' will repel coil B. On the other side the winding of B' 
 being reversed, it will be repelled by A" and attracted by A'". 
 As a result of this attraction and repulsion, the coils BB' will 
 swing around the suspension C, which also serves for conducting 
 the current into the movable coils. 
 
 The controlling force in this case is gravity acting on the rider 
 which slides along a graduated beam fastened to BB' . When 
 no current is flowing through the instrument, a weight is placed 
 in a pan which balances the movable coils and the rider at its 
 extreme left position, which corresponds to the zero position 
 of the scale. When a current is flowing through the coils, the 
 rider is moved to the right along the beam until the coils are 
 again balanced. The value of the current is then indicated by 
 
 Fia. 63. 
 
 the position of the rider. The balance arm is supported by two 
 trunnions, each hung bj^ an elastic ligament of fine wire, through 
 which the current passes into and out of the movable coil at the 
 end of the balance arm. The instrument as manufactured is 
 shown in Fig. 63. 
 
 With ampere balances four pairs of weights (sliding and coun- 
 terpoise) are supplied with each instrument. The carriage and 
 its counterpoise constitute the first pair. These weights are 
 adjusted in the ratios 1, 4, 16, 64, so that each pair gives a whole 
 number of amperes, or half amperes, or quarter amperes, or 
 some decimal subdivisions or multiples of these magnitudes on 
 the upper or inspectional scale. 
 
 For the adjustment of the zero, a small metal flag is provided. 
 The flag is operated by a fork, having a handle outside the case. 
 
AMMETERS AND VOLTMETERS 93 
 
 To adjust the zero reading, the shding weight is placed with its 
 pointer at the zero end of the scale, and the flag is turned to one 
 side or the other, until it is found that with no current passing, 
 the balance rests in its zero position. 
 
 When a current is passed through the instrument, the balance 
 arm is displaced, and to measure the current the rider is slipped 
 along the trough until the balance arm is again brought to its 
 zero position. The strength of current is then indicated on the 
 upper fixed scale by the pointer of the sliding weight. For 
 greater accuracy the reading of the lower scale must be taken. 
 Each number on the upper, or as it is called inspectional, scale 
 is twice the square root of the corresponding number on the fine 
 scale of equal divisions. Thus if the reading on the lower scale 
 is 292. that on the fixed scale will be 34.18 = 2 X \/292. A 
 table of double square roots is furnished with the instrument. The 
 reading, multiplied by the constant of weight used, gives the 
 current. 
 
 EXAMPLE 
 
 A centiampere balance was used to calibrate a milliammeter. The 
 milliammeter reading was 668 milliamp., and balance reading 326.8 on 
 the lower scale. How much is the ammeter in error if the constant for 
 weight used is 2? 
 Solution. — 
 
 2V326.8 = 36.14. 
 
 / = 2 X 36.14 centiamp. = 722.8 milliamp. 
 Error = 722.8 - 668 = 54.8 milliamp. 
 
 91. Uses of Kelvin Balance as a Voltmeter. — In order that the 
 Kelvin balance may be used as a voltmeter it is necessary only 
 to increase its resistance. When so used, the resistance of the 
 operating coils is about 50 ohms, and special coils are provided 
 to be connected in series. The resistance of these coils ranges 
 from 400 to 2000 ohms, and the maximum voltage that can thus 
 be measured is 500 volts. It is evident that the Kelvin balance 
 operates upon the electrodynamometer principle, yet it is usually 
 classed separately because the controlling force is gravity; the 
 planes of the coils are horizontal instead of vertical; and the 
 movable coils do not rotate around a central axis, but revolve 
 about an axis midway between them. 
 
 The relation between the current strength and the force of 
 attraction is the same as that of the electrodynamometer already 
 
 discussed, i.e., 
 
 P = KW 
 
94 
 
 ELECTRICAL METERS 
 
 but when the coil is balanced the force is proportional to the 
 distance of the rider from the extreme left of the scale, hence 
 
 72 = KH 
 
 or 7 = K-\/T, which is of the same form as the equation for the 
 electrodynamometer. 
 
 From this equation we see that the scale which reads in am- 
 peres cannot be uniform. On the other hand, in order to obtain 
 the current from a reading on the uniform scale we must extract 
 the square root of the reading and multiply this square root 
 by the constant of the instrument. 
 
 The commercial instruments are made in seven sizes ranging 
 in capacity from 0.01 to 2,500 amp. Detailed instruction for 
 using the balance is always furnished with the instrument. 
 
 Fig. 64. 
 
 92. Westinghouse Dynamometer Ammeter and Voltmeter. — 
 
 Fig. 64 shows how the Westinghouse Electric and Manufacturing 
 Co. has adapted the Kelvin balance principle to one type of 
 instrument. The figure shows the general arrangement of the 
 measuring elements, the letters referring to the following parts: 
 
 A, A', A^, A', fixed coils. 
 
 C, C^, movable coils. 
 
 B, non-inductive resistance. 
 
 D, controlling spring. 
 
 E, torsional head. 
 
 F, pointer attached to movable element. 
 
 G, pointer attached to torsion head. 
 
AMMETERS AND VOLTMETERS 95 
 
 The four fixed coils and two movable coils are all connected in 
 series, and in series with part or all of the resistance B, depending 
 upon whether small or large electrical quantities are to be meas- 
 ured. Precisely as in the Kelvin balance the meter depends for 
 its operation upon the electr'odynamic action between the fixed 
 and movable coils. The controlling force is, however, a spiral 
 spring instead of gravity. The influence of gravity is eliminated 
 by mounting the coils with their planes vertical instead of hori- 
 zontal. There is considerable similarity between the Westing- 
 house dynamometer type of instrument and the electrodynamom- 
 eter. In both cases the planes of the coils are vertical and the 
 indications of the instruments are obtained in the same way. 
 When a current is sent through either instrument, the movable 
 coil is deflected and, by means of the torsion head, the movable 
 element is brought back to its zero position. The deflection is 
 indicated by the angle between the two pointers. The same 
 law, viz., 
 
 I = KVe holds. 
 
 93. Influence of Earth's Magnetic Field. — Since the earth is 
 surrounded by a magnetic field which has a definite direction 
 and value, there is bound to be a reaction between this field and 
 a coil carrying a current. In some of the types of instruments 
 so far discussed, the influence of the earth's magnetic field must 
 be considered, when measuring direct currents, if accurate results 
 are expected. 
 
 In instruments of the electromagnetic type, the strength of 
 the operating field is usually so great in comparison with the 
 strength of the earth's field that this influence is practically 
 negligible. 
 
 In some of the dynamometer type of instruments this influence 
 may be appreciable. This is true with reference to those instru- 
 ments having only one stationary coil. Instruments employing 
 the Kelvin balance principle are astatic, that is, they are not 
 influenced by the earth's field. This is due to the fact that the 
 movable element of the Kelvin balance type of instrument con- 
 tains two coils wound in opposite directions. The effect of the 
 earth's field upon one coil is thus neutralized by its influence 
 upon the other coil. 
 
 To prevent undue influence of the earth's magnetic field upon 
 the Siemens electrodynamometer, the plane of the movable 
 
 10 
 
96 ELECTRICAL METERS 
 
 coil should be placed at right angles to the magnetic meridian. 
 The direction of the magnetic meridian is indicated by a compass 
 needle when not influenced by iron or adjacent magnets. 
 
 The mechanical method of damping is used in most of the com- 
 mercial instruments of the dynamoineter type. One of the most 
 serious objections to the Siemens form of current meter is the lack 
 of damping device, which necessitates considerable time and skill 
 in making readings. The other forms of dynamometer instru- 
 ments almost invariably make use of some form of air-damping 
 device. In the Weston dynamometer-type instruments, which 
 may be considered typical, damping is secured by two light 
 symmetrical vanes enclosed in chambers made as nearly air- 
 tight as possible. The Westinghouse meters of the type shown 
 in Fig. 61 use the electromagnetic principle of damping. To the 
 movable element is attached a sector which moves between the 
 poles of permanent magnets. 
 
 With the exception of the Siemens dynamometer and Kelvin 
 balance forms, instruments of the types discussed are also made 
 for switchboard use. 
 
 94. Advantages. — Among the main advantages of the dyna- 
 mometer type of instrument are its sensitiveness, accuracy, and 
 adaptability to both direct- and alternating-current measure- 
 ments. It may be calibrated on direct current and used on 
 alternating current. 
 
 95. Disadvantages. — The Siemens dynamometer and Kelvin 
 balance are not direct-reading; they are not "dead beat," and 
 hence require considerable time and skill in making readings. 
 The necessity for accurate leveling is also a disadvantage. 
 
CHAPTER IX 
 MISCELLANEOUS AMMETERS AND VOLTMETERS 
 
 96. Electrostatic Voltmeter. — The measuring instruments so 
 far discussed require an electric current for their operation. 
 Electrostatic instruments utilize the forces of attraction or 
 repulsion between two electric charges. The gold leaf electro- 
 scope is the simplest form of instrument of this type. 
 
 When two plates are insulated and placed near each other, a 
 force of attraction will exist between them if oppositely charged. 
 If one of these plates is movable, but its motion is counteracted 
 by some controlling force, the deviation of the movable plate 
 from its normal position will be a measure of the force of attrac- 
 
 FiG. 65. 
 
 tion. Since the capacities of the two plates are practically 
 constant, the deviation, or force required to prevent deviation, 
 will be a measure of the difference of electrical pressure between 
 the plates. Instruments which make use of this principle of 
 attraction of charges are ordinarily called electrometers. When, 
 however, they are provided with scales graduated in volts they 
 are called electrostatic voltmeters. The adaptation of this 
 principle to commercial instruments is due to Lord Kelvin. 
 The essential elements of an electrostatic voltmeter are shown 
 n 97 
 
98 
 
 ELECTRICAL METERS 
 
 in Fig. 65. The stationary element consists of two parts or 
 quadrants aa. The movable element bb is a very light figure- 
 8-shaped aluminum vane. The vane is suspended by a fine wire 
 whose elasticity supplies the controlling force. The instrument 
 is practically an air condenser with movable plates. When 
 the connections are made as indicated, the quadrants and vane 
 are oppositely charged and attract each other. If the vane 
 remained stationary, the force of attraction would be propor- 
 tional to the square of the potential difference between quadrants 
 and vanes. Algebraically 
 
 F = KE\ 
 
 Fig. 66. 
 
 Fig. 67. 
 
 This relation is not mathematically exact for the reason that a 
 change in the relative position of vane and quadrants slightly 
 changes the capacity. To measure low voltages the capacity of 
 the instrument must be relatively large. To secure this large 
 capacity. Lord Kelvin mounted several quadrants above each 
 other and between them suspended the same number of vanes. 
 The principle of construction will be readily understood from 
 Fig. 66. Such an instrument may be used for measuring voltages 
 down to 50 volts. The suspending wire supplies the controlling 
 force. For voltages ranging from 400 to 100,000 volts, only one 
 set of quadrants and one vane are used, Fig. 67. The vane is 
 
AMMETERS AND VOLTMETERS 
 
 99 
 
 mounted to swing in a vertical plane and the controlling force is 
 due to the action of gravity upon weights which determine its 
 sensibility. In neither case is the scale uniform. A multi- 
 cellular form voltmeter for low voltages is shown in Fig. 68. 
 
 Fig. G8. 
 
 97. Westinghouse Electrostatic Voltmeter. — The ijrinciple of 
 mutual attraction between two electrostatic charges of opposite 
 
 Q 
 
 Fig. 69. 
 
 kind has been adapted by Mr. S. M. Kintner of the Westinghouse 
 Electric and Manufacturing Co., in a novel manner. The essen- 
 tial features of this voltmeter are shown in Fig. 69. The measur- 
 
100 
 
 ELECTRICAL METERS 
 
 ing elements consist of a series of fixed and movable condensers. 
 The movable element to which a pointer is attached is suitably 
 pivoted and provided with spring control. 
 
 As shown in the diagrammatic sketch, the movable part 
 Ml, Mi consists of two hollow cylinders fixed to a pivoted arm. 
 The curved plates Bi and -B2 are metallically connected to the 
 inner condenser plates of condensers Ci and C2. The operating 
 elements of the meter are immersed in a high grade of insulating 
 oil contained in a metal-lined wooden case provided with an 
 insulating cover. 
 
 Fig. 70. 
 
 98. Operation. — When the terminals Ti and T-z are connected 
 to the circuit whose voltage it is desired to measure, the con- 
 densers Ci and C2 become oppositely charged. These charges 
 induce other charges of opposite polarity on cylinders ilf 1 and M^. 
 The consequent attraction between the charges on B\, B^ and 
 Ml, M 2 causes a deflection of the movable elements. This motion 
 is made possible by the shape and relative position of plates B^ 
 and B2 with reference to the axis of the cylinders. As the cylin- 
 
AMMETERS AND VOLTMETERS 
 
 101 
 
 ders revolve they approach the curved plates Bi and B^. In this, 
 as in the Kelvin electrostatic voltmeter, the torque causing a 
 deflection is proportional to the square of the applied pressure. 
 The form and relative position of operating parts is shown in Fig. 
 70. 
 
 In the more recent instrument a condenser terminal is used in 
 place of the plate condensers shown in Fig. 70. The range of the 
 meter may be changed by short-circuiting layers of the terminal, 
 Fig. 71. 
 
 Fia. 71. 
 
 99. Insulation. — To secure proper insulation for measuring 
 very high voltages is not only very important but extremely 
 difficult. In the electrometer, or Kelvin form of instrument, the 
 insulating properties of air are mainly relied upon. The high 
 insulating properties of oil, together with its relatively high 
 inductivity, makes its use advantageous in many respects. The 
 most important advantages are: 
 
 1. Possibility of more compact construction, as the oil permits 
 the placing of the operating elements nearer together. 
 
 2. The force of attraction between stationary and movable 
 elements is greatly increased, both on account of the smaller 
 distance between them and on account of the high inductivity of 
 the oil. 
 
 3. The buoyant effect of oil greatly diminishes the pressure 
 and friction of bearings. 
 
 100. Damping.^ — Both the Kelvin multicellular and Westing- 
 house electrostatic voltmeter use liquid damping. The axis of 
 
102 ELECTRICAL METERS 
 
 the Kelvin instrument projects through the bottom of the casing 
 and is provided with a suitable vane. The cup in which the vane 
 swings is narrow and deep and only about one-third full of liquid. 
 
 In the Westinghouse instrument, the resistance of the insulat- 
 ing oil upon the movable element produces efficient damping. 
 
 An electrostatic voltmeter of the electrometer type, manu- 
 factured by Hartmann and Braun, employs electromagnetic 
 damping. The moving vane moves between the poles of an 
 electromagnet and as it moves the eddy currents induced effec- 
 tively damp the movement of the pointer. 
 
 101. Advantages. — Among the most important advantages of 
 the electrostatic instruments may be mentioned the following: 
 
 They do not consume any electrical current; may be used on 
 either alternating- or direct-current circuits; are entirely un- 
 affected by temperature, external magnetic fields, power-factor, 
 or frequency. In addition to these they may be used on very 
 high-potential circuits. 
 
 102. Hot-wire Instruments. — When a current of electricity 
 passes through a wire whose resistance is R, the energy trans- 
 formed into heat is I^R joules per second, when I, the current in 
 the circuit, is given in amperes. When a stationary condition 
 in the temperature has been reached, the energy converted into 
 heat must be equal to that radiated, and this quantity is propor- 
 tional to the change in temperature. Hence, it follows that the 
 square of the current, which is proportional to the heat developed, 
 is proportional to the expansion of the wire through which the 
 current flows. It must be remembered, however, that the resist- 
 ance R is not independent of the temperature. The wire of most 
 instruments of this type is made of platinum silver whose tem- 
 perature coefficient is about 0.00024. If Ro is the resistance of 
 wire at room temperature to, its resistance at temperature ti°C is 
 given by 
 
 Rt = Ro[l + 0.00024(^1 - to)] 
 
 Thus, a 100-ohm coil will undergo a change of 0.024 ohms per 
 degree Centigrade. This change in resistance modifies, to some 
 extent, the proportionality between square of current and expan- 
 sion. From a practical point of view this is of no great impor- 
 tance, for the scale can be determined by calibration. 
 
 103. Hot-wire Voltmeter. — The principle mentioned above 
 was first made use of in an instrument designed by Major Cardew. 
 
AMMETERS AND VOLTMETERS 
 
 103 
 
 The wire in the Cardew voltmeter was made of platinum silver 
 and was of such a length that it could be connected across a 
 110-volt circuit without any series resistance. The wire ran 
 twice from end to end of a long brass and iron tube, passing over 
 insulated rollers at each end. One extremity was fixed while the 
 other, after passing over a pulley, was attached to a spring which 
 kept it taut. The pointer was attached to the pulley which was 
 rotated by the expansion and contraction of the wire. The 
 tube consisted of brass and iron so proportional that its coefficient 
 of expansion was the same as that of the wire. Hence, so long 
 as the temperature of both was the same, the tension of the wire 
 was constant and the readings were independent of external 
 temperature variations. 
 
 SB4 
 
 .K^ / 
 
 zero adjustment 
 
 Fig. 72. 
 
 The arrangement of the wire was such that the instrument was 
 bulky and very inconvenient to handle. It is no longer in use. 
 
 In the more modern instruments of the hot-wire type, the work- 
 ing length of wire is from 6 to 8 in. In voltmeters this wire is 
 quite fine, and series resistances are provided. Fig. 72 shows 
 the essential features of a Hartmann and Braun voltmeter. The 
 terminals of the circuit, whose difference of potential is to be 
 measured, are connected to A and B. The resulting current heats 
 the platinum-silver wire causing it to expand. As the tension of 
 AB is lessened, the point C is pulled downward by the tension of 
 the spring HK. The silk thread HF being wrapped around the 
 pulley G rotates the pointer as the end H of the spring HK moves 
 to the left. By means of the mechanism CD and FH, the pointer 
 
104 
 
 ELECTRICAL METERS 
 
 P is made to move many times the sag of AB, The tension of the 
 current wire AB is adjusted by means of the screw S. 
 
 When an instrument of this type has been in use for some time, 
 the pointer seldom returns to its zero position, but by means of 
 the screw S the zero adjustment of the pointer can be readily 
 made. 
 
 The instrument is made "dead beat" by means of the vane V 
 rotating between the poles of the permanent magnet M. The 
 vane V is mounted upon the shaft with the pulley G and pointer P, 
 As these rotate, the vane cuts across the magnetic field of the 
 permanent magnet, inducing eddy currents which effectually 
 damp the vibrations of the needle. 
 
 The mechanism, as shown in the diagram, is mounted upon a 
 suitable base plate not shown in the figure. The base plate is- 
 
 divided near the point C, one portion 
 consisting of iron and the other of brass. 
 The relative lengths of the iron and 
 brass parts are so designed that the ex- 
 pansion of the base plate is the same as 
 that of the wire itself. Even such an 
 arrangement does not give correct in- 
 stantaneous readings. This is due to 
 the fact that the wire reaches its maxi- 
 mum temperature almost instantly, 
 whereas the base plate requires consider- 
 able time to do so. 
 Another arrangement of the working 
 wire is found in the Roller and Smith hot-wire meter, the es- 
 sential features of which are shown in the diagram of Fig. 73. 
 The current-carrying wire in this type of instrument is looped 
 around a pulley, and the two ends are fastened to the same plate 
 C, as shown in the figure. One end of the wire is electrically con- 
 nected to the plate, while the other end is insulated from it. The 
 wire is kept in tension by the spring which may be adjusted by 
 the screw /S., 
 
 In voltmeters a non-inductive resistance of very low tempera- 
 ture coefficient is connected in series with the branch A. 
 
 The pulley D is rigidly attached to a shaft E to which is also 
 attached the arm G. This arm is divided at one end and counter- 
 balanced at the other. To the two branches of one end of the arm 
 
 Fig. 73. 
 
AMMETERS AND VOLTMETERS 105 
 
 is attached a silk thread which is passed around a suitable pivoted 
 small pulley H, to which is also attached the pointer I. 
 
 The current to be measured passes only through the branch A 
 of the working wire A-B, thus heating A only. The resulting 
 expansion diminished the tension of A, and equilibrium is re- 
 stored by the spring F pulling B around the pulley D until the 
 strain is equalized. The motion of D carries G with it and the 
 silk fiber rotates the pulley H causing the pointer to move to the 
 right over a properly graduated scale. 
 
 In this type of instrument no special provision need be made 
 for changes in the temperature of surrounding air. When the 
 temperature changes, both branches of the working wire are 
 affected alike, expanding alike. This expansion is taken up by 
 the spring without the rotation of pulley D. 
 
 Since the expansion of the wire A-B is independent of the 
 direction of the current, it is evident that hot-wire meters are 
 suitable for alternating as well as direct current. 
 
 104. Hot-wire Ammeter. — The principle of the hot-wire am- 
 meter is identical with that of the voltmeter. The construction 
 is practically the same, the working wire being of larger diameter. 
 In order to prevent sluggishness of action, a fairly fine wire is 
 essential, and this introduces a difficulty in the case of ammeters. 
 Messrs. Hartmann and Braun usually so arrange matters that 
 the current is passed through the wire with several parallels, by 
 means of thin silver strips making contact at various points 
 along its length. Even by this means, however, it is found im- 
 possible to pass more than a few amperes through the wire, and 
 hence a shunt has to be employed. This entails a considerable 
 loss of energy, since a fall of potential of 0.2 to 0.5 volts is required 
 across the shunt. The large current taken, however, renders the 
 instrument very susceptible to contact errors. In the more re- 
 cent instruments the Hartmann and Braun Co. have substituted 
 platinum-iridium for platinum-silver as the material of the work- 
 ing wire. Platinum-iridium can be operated at a much higher 
 temperature and its coefficient of expansion is considerably less 
 than that of platinum-silver. As a result, the instruments are 
 much less affected by changes of temperature and the zero shift 
 is much smaller. The new instruments are made as ammeters 
 and voltmeters in both switchboard and portable forms. 
 
 105. Damping. — While the moving element is light and there 
 is no great necessity for a damping device, nevertheless, one is 
 
106 ELECTRICAL METERS 
 
 added. This is practically the same as that applied to the Hart- 
 mann and Braun hot-wire instruments. The damper is an 
 aluminum disk swinging between the poles of a stationary per- 
 manent magnet. 
 
 In a bulletin of the Bureau of Standards on "Testing Electrical 
 Measuring Instruments," we find the advantages and disadvan- 
 tages of the hot-wire instrument stated as follows : 
 
 "The hot-wire instrument is not used in this country to any 
 great extent in practical work; its defects are relatively large 
 consumption of energy, uncertainty of zero, errors due to change 
 of surrounding temperature, and to heating when left in the cir- 
 cuit. As the working wire must be run at a fairly elevated tem- 
 perature, to give proper sensibility, it is easily 
 damaged by sudden overloads, which would 
 do little or no damage to other forms, except 
 the possible bending of a pointer." 
 ■'0 The good points of the hot-wire instrument 
 
 ^..-M which cause it to be still used for certain 
 
 T.5 jr classes of work, are its independence of ordi- 
 
 ^=^(\k^ nary frequencies, wave form, and stray mag- 
 
 netic field; the fact that it may be calibrated 
 on direct current, and that shunts may be 
 used with the ammeter for alternating currents. 
 \J 106. Thenno-ammeter. — For the purpose 
 
 of measuring very small currents, there has 
 ^' oil '^....He^.fgp. recently been devised an instrument whose 
 ' f operation depends upon a combination of 
 
 Fia. 74. the electro-magnetic and thermo-electric 
 
 principles. 
 It is well known that if two dissimilar metals, such as iron and 
 copper, are connected so as to form a closed circuit, and if one of 
 the junctions be heated, an electric current will flow through the 
 circuit. The current flowing will be approximately proportional 
 to the difference of temperature between the two junctions. 
 
 The method of applying a combination of this principle with 
 the other two is shown in the diagram of Fig. 74. 
 
 A single loop of silver wire L is suspended by means of a quartz 
 fiber Q between the pole pieces NS of a permanent magnet. The 
 loop is surmounted by a glass stem which carries a mirror M, 
 while its lower ends are connected to a bismuth-antimony thermo- 
 couple {Bi, Sb). The heating resistance or "heater," consisting 
 
 I 
 
AMMETERS AND VOLTMETERS 
 
 107 
 
 of a fine filament of high specific resistance, is fixed immediately 
 under the thermocouple. One end of the heater is connected to 
 the frame of the instrument to avoid electrostatic forces. The 
 current to be measured, or a definite part of it, is sent through the 
 heater. Part of the heat generated in the heater is radiated and 
 carried by convection to the thermo-junction, raising its tempera- 
 
 FiG. 75. 
 
 ture. The resulting current flowing through the loop L causes 
 it to turn in the magnetic field. The resulting deflection can then 
 be read off by means of a lamp and scale. In the Duddell thermo- 
 ammeter, however, the loop L is mounted in jewel bearings and a 
 pointer is substituted for the mirror. In the usual pattern of this 
 instrument the full scale deflection is produced by a current of 10 
 
108 ELECTRICAL METERS 
 
 milliamp. either continuous or alternating, and by constructing 
 heaters of higher or lower resistances the sensibility to current 
 may be increased or reduced as required. The working elements 
 of this ammeter are shown in Fig. 75. 
 
 The instrument as at present constructed is not suited for 
 central-station use. For measuring current in telephone lines, or 
 for other high-frequency currents, it is of considerable importance. 
 
CHAPTER X 
 POWER-MEASURING INSTRUMENTS 
 
 107. Wattmeters. — The instrument most commonly used for 
 measuring power is called a wattmeter. Wattmeters are of 
 four classes, electrostatic, hot-wire, electrodynamic, and elec- 
 tromagnetic. The electrostatic and hot-wire wattmeters are 
 not in common commercial use, and, hence, will not be discussed. 
 
 Fig. 76. 
 
 Wattmeters in common use are of the electrodynamometer and 
 induction types. 
 
 108. Electrodynamometer Type. — The electrotJynamometer 
 type is very common and may be considered the standard 
 indicating wattmeter. The essential features of such an instru- 
 ment are shown in diagram. Fig. 76, and consist of two coils, one 
 fixed and the other movable, as in the electrodynamometer 
 
 109 
 
110 
 
 ELECTRICAL METERS 
 
 ammeter. In fact, the electrodynamometer ammeter can be 
 used as a wattmeter, if suitable resistance is connected in series 
 with one of the coils, preferably the moving one. 
 
 In the diagram shown, the heavy line connected in series with 
 the line is the stationary or current coil and consists of two 
 parts, each of a few turns of heavy wire. The movable coil, 
 which is mounted in the same manner as the movable coil of the 
 electrodynamic voltmeter, consists of many turns of fine wire. 
 
 Fig. 77. 
 
 The manner of connecting such a wattmeter to a circuit is 
 shown in Fig. 77. L represents the lamp, or receiving circuit, 
 whose power consumption it is desired to measure. 
 
 109. Theory of Electrodynamometer Wattmeter. — In discuss- 
 ing the electrodynamometer ammeter, and Kelvin's balance, it 
 was stated that the force of attraction between the fixed and 
 movable coils is proportional to the product of the currents in 
 the two coils. In that case, however, the same current flowed 
 through the two coils. In the wattmeter under discussion the 
 force of attraction is likewise proportional to the product of 
 the currents in the fixed and movable coils, but the currents 
 are not the same. The fixed coil carries the current supplied 
 
POWER-MEASURING INSTRUMENTS 111 
 
 to the load, but the movable coil carries a current which is pro- 
 portional to the electromotive force across the load. 
 
 On direct-current circuits the deflecting force may be repre- 
 sented by 
 
 F = KI Xi 
 where / is the load current, i the current in pressure coil, and K 
 a proportionality constant. 
 
 If R is the resistance of the pressure coil, and E the pressure 
 
 E 
 across the receiving circuit terminals, i = p- Substituting this 
 
 value of i, we get 
 
 Since R is also constant, the expression may be written 
 
 F = KoEI. 
 
 This expression shows that the deflecting force, and hence the 
 torque, is proportional to the product of current and pressure, 
 i.e., to power consumed in the load or receiving circuit. 
 
 Assuming the inductance of the pressure and current coils to 
 be negligible, the electrodynamometer wattmeter also gives the 
 average power on alternating-current circuits. At any instant 
 the torque is proportional to the product of current and pressure 
 at that instant. The average deflecting torque will then be 
 proportional to the average of the product of current and 
 pressure. 
 
 Representing the instantaneous pressure and current by 
 
 e = Em sin cat 
 and i = I m sin (coi ~ 8) 
 
 the torque causing a deflection will be 
 
 Torque = K average oi e X i 
 or T = K average E^Im sin ut X sin (ut — ff) 
 
 = KEmlm X av. [sin ut (sin ut cos 6 — cos ut sin 6)] 
 = KEmlm av. (sin^ ut cos 8 — sin ut cos ut sin 8) 
 = KEmlm (av. sin^ ut cos 8 — av. sin ut cos ut sin 8). 
 The average of sin'' ut is }4> and the average of sin ut cos ut 
 is 0. Hence 
 
 E I 
 T = K — 2^ cos B 
 
 = KEI cos e 
 
112 
 
 ELECTRICAL METERS 
 
 where E and I are effective values. Thus the wattmeter auto- 
 matically corrects for power-factor. The constant K, depends 
 upon the windings of the instrument but, as instruments of this 
 type are direct reading, it need not be considered. 
 
 Since the reaction of a coiled spring furnishes the controlling 
 force in instruments of this type, it would seem that such an 
 instrument would have uniform scale. This may or may not 
 be the case depending upon the operation of the meter. In one 
 form of this type of wattmeter the movable coil is brought 
 back to its zero position by means of a torsion head as in the 
 
 Fig. 78. 
 
 case of the dynamometer ammeter already discussed. Such an 
 instrument will naturally have a uniform scale. 
 
 In the other form, the pointer is attached to the shaft of the 
 movable coil. Under these conditions the scale is no longer 
 uniform. The graduations at the upper end of the scale are 
 crowded together on account of the fact that when the deflection 
 becomes great the deflecting force is not exactly proportional 
 to the deflection, but more nearly to the sine of the angle of 
 deflection. 
 
 The essential parts of two makes of torsion head wattmeters 
 are shown in Figs. 59 and 78. The principles used in the con- 
 struction of the Roller-Smith wattmeter, Fig. 59, are evidently 
 
POWER-MEASURING INSTRUMENTS 
 
 113 
 
 those of the Siemens electrodynamometer, with the exception 
 that the movable coil is mounted on a shaft, thus permitting 
 the omission of mercury cups. Meters constructed in this way 
 are subject to the influence of external magnetic fields. Fig. 
 59 is the mechanism of a voltmeter, but the same principles are 
 applied in the construction of wattmeters. 
 
 The Westinghouse precision wattmeter, shown in Fig. 78, is 
 also of the electrodynamometer type but is constructed according 
 to the principles of the Kelvin balance. The middle, movable 
 coils are mounted on a light framework carrying suitable jewels 
 mounted on ball bearings. 
 
 As has already been pointed out, such instruments are astatic, 
 that is, not subject to the influence of external magnetic fields. 
 
 FiQ. 79. 
 
 Fig. 80. 
 
 Both the General Electric and Weston portable wattmeters 
 belong to the second form, i.e., the shaft of the movable coil 
 carries the pointer. The deflection of the pointer is thus a 
 measure of the angle through which the coil has been turned. 
 
 The General Electric Co. uses the inclined-coil principle, as 
 is shown by Fig. 79. 
 
 The Weston electrodynamometer wattmeter is shown in Fig. 
 77. The principles of construction of this instrument are the 
 same as those for the voltmeter, Fig. 58. Fig. 77 also shows the 
 manner of connecting such a meter to a circuit. The large termi- 
 nals d-d are connected in series with the power line, and the 
 small terminals e-e are connected across the hne to the terminals 
 of the load. The button b, when pressed down, serves to close 
 
 12 
 
114 
 
 ELECTRICAL METERS 
 
 the pressure circuit. This is necessary to prevent heating of the 
 pressure coil when no readings are being talven. The scale is 
 graduated in watts or kilowatts, depending upon the range of 
 the instrument. The instruments are normally made for a 
 maximum of 150 volts, but the range can be varied by the use 
 of suitable multipliers and shunts. 
 
 For switchboard use, instruments are manufactured upon 
 exactly the same principles. Figs. 80 and 81 show the principles 
 
 Fio. 81. 
 
 of construction of Weston single-phase and polyphase switch- 
 board wattmeters. Although these are direct-reading deflection 
 instruments, nevertheless, the refinement of construction and 
 adjustment makes possible the use of uniform scales. 
 
 110. Compensation for Power Consumed in Instrument. — 
 Since both the current and pressure coils of a wattmeter possess 
 resistance, some power will be consumed in the instrument itself. 
 The amount of this power is not large, yet it would be unfair to 
 charge it ujd to the receiving or load circuit. From the diagram 
 of Fig. 7G it is evident that the current through the series coil 
 is the sum of the pressure and load currents. On direct-current 
 circuits this sum is equal to the algebraic sum of the currents, 
 but in alternating-current circuits, the inductance of the potential 
 coil will never or seldom be the same as that of the receiving 
 circuit, and hence, the two currents will not be in phase. In such 
 a case, the current through the series coil will be equal to the 
 vector sum of the pressure and load currents. 
 
POWER-MEASURING INSTRUMENTS 115 
 
 E^ 
 The power consumption of the pressure coil is i^R = -^ , where 
 
 i is the current in the movable coil and R the resistance of the 
 voltage coil. If the load current is I, and the resistance of the 
 series coil r, the power consumption of the series coil will similarly 
 be Pr. It is necessary to make correction for only one of these 
 losses as can easily be shown. The relation between deflection 
 and power, when current and pressure are in phase, is 
 
 D = KXIXE. 
 
 If the wattmeter is connected to the circuit as indicated in Figs. 
 76 and 77, the current I is equal to the load current plus the 
 pressure-circuit current. 
 
 Let II = load-circuit current, 
 and ie = pressure-circuit current. 
 
 Then the line current is equal to the sum of 7t and ie or 
 
 I = h + ie 
 and the deflection is 
 
 D = KE(h + ie) 
 = KEIl + KEie. 
 
 The deflection is thus due to two quantities, one KEIl, which 
 is proportional to the power taken by the load, and the other 
 KEi„ which is proportional to the power spent in the pres- 
 sure coil. The correction must then be made only for the power 
 spent in the movable or pressure coil. On constant-voltage 
 circuits this quantity is constant and corrections can easily be 
 made by measuring the voltage, and movable-coil resistance. 
 
 When the pressure coil is connected across the line side of the 
 circuit, for accurate work correction must be made for the power 
 used in the series coU. 
 
 When such a connection is used, the current through series 
 coils is only that demanded by the load. The pressure at the 
 terminals of the voltage coil is, however, a trifle higher than that 
 at the load terminals, due to the pressure drop, Ir, across the 
 series coil. The correction to be applied is then equal to Pr. 
 The power spent in the series coil is usually less than that spent 
 in the pressure coil and, hence, the second method of connection 
 is to be preferred when non-compensated wattmeters aroused 
 and no corrections are made. When corrections are to be made, 
 the usual method of connecting a wattmeter to a circuit is that 
 
116 
 
 ELECTRICAL METERS 
 
 indicated in Fig. 77, and corrections are made for the power 
 consumed in the voltage coil. The reason for this is that the 
 resistance of the voltage coil can be determined more easily than 
 the resistance of the series coil. The resistance of the series coil 
 is very small, and the resistance of the contacts d-d is an appreci- 
 able part of this resistance. This, of course, is a variable quan- 
 tity; it, therefore, would be extremely difficult to make any 
 correction if that were to be considered. 
 
 The portable wattmeters manufactured by the Weston Electri- 
 cal Instrument Co., are provided with a compensating coil as 
 shown in Fig. 82. It will be observed that the compensating 
 
 B 160 V 
 
 Fig. 82. 
 
 coil is connected in series with the pressure coil, its winding, how- 
 ever, being reversed with reference to the series coil. The num- 
 ber of turns in this compensating coil is carefully adjusted so 
 that the counter torque, due to the pressure-circuit current, is 
 just equal to the direct torque due to this same current when 
 flowing through the series coil. Such a compensation makes 
 automatic correction at all voltages, since the current through 
 the compensating coil is always the same as that through the series 
 coil at no load and the same voltage. The complete pressure circuit 
 thus consists of the voltage coil proper, the compensating coil, 
 and the resistance R, which, in some cases, may be separate from 
 the instrument. Connection is made to the power circuit through 
 binding posts C and B. 
 
 The binding post D is connected to a resistance r of the same 
 
POWER-MEASURING INSTRUMENTS 117 
 
 value as the resistance of the compensating coil, and is to be used 
 in calibrating the instrument by means of two different sources 
 of current. Also, in measuring power in high-potential circuits, 
 when the series coils are connected to a series transformer and the 
 voltage coil to a potential transformer, the independent ter- 
 minal D is to be used. 
 
 111. Influence of the Inductance of the Voltage Coil. — In the 
 previous discussion, we assumed the inductance of the voltage 
 coil to be negligible. While this is accurate enough for practical 
 purposes and on circuits with large power-factors, on circuits 
 of low power-factor the errors introduced may be appreciable, and 
 the inductance of the voltage coil must be considered. 
 
 When the receiving, or load, circuit has considerable induct- 
 ance, the current through the series coil will lag behind the 
 electromotive force. In such a case, the voltage current, when 
 
 Fig. 83. 
 
 the voltage coil is non-inductive, is in phase with the electromotive 
 force, and the deflecting force is proportional to 
 
 IE' cos d, 
 
 where d is the phase angle between electromotive force and load 
 current. 
 
 When, however, the voltage coil has inductance, the current 
 in voltage coil will lag behind the load pressure and thus the 
 angle between load current and voltage current will be less than 
 between the load electromotive force and current. This is 
 shown in the vector diagram. Fig 83, where a represents the 
 difference in phase between the voltage current and load pressure. 
 
 112. Correction Factor. — Electrodynamometer wattmeters are 
 usually calibrated on direct current, and when so calibrated the 
 inductance has no effect. If B is the resistance of the voltage 
 coil and i is the voltage current, the energy spent in the coil wheD 
 used on alternating-current circuits is. 
 
118 ELECTRICAL METERS 
 
 Ri'' = El cos a 
 whence Ri = E cos a 
 
 and ^ ~ p ^^^ "■ 
 
 But W- = EI cos e 
 
 and Torque = Kil cos 7. 
 
 E 
 Substituting -5 cos a for {, we get 
 
 m KEI 
 Torque, T = — p— cos a cos 7 
 
 and 
 
 72 
 
 T _K cos a cos 7 
 F ~ R cosl 
 
 R cos e 
 
 wiience W = T X j. „ „„, 
 
 A cos a cos 7 
 
 If the voltage and current are sine curves, 
 
 7"= 6 — a 
 and cos 7 = cos {d — a) = cos 6 cos a + sin sin a. 
 
 On direct current the watts are directly proportional to torque, 
 
 or to -v^T, hence, the indication of a wattmeter, correct on direct 
 
 ,.,.,, cos d 
 
 current, must be multiplied by to get the correct 
 
 ' '■ cos a cos 7 ° 
 
 power on alternating current, and the correction factor becomes 
 
 cos d 
 
 cos a. (cos d cos a + sin 6 sin a) 
 
 ^ 1 
 
 cos^ a (1 + tan d tan a) 
 
 _ Sec^ a 
 
 1 + tan 6 tan a 
 
 1 + tan^ a 
 
 1 + tan d tan a 
 
 27r/L, 
 tan a = — 5 — 
 iii 
 
 . . 27r/L 
 and tan Q = — 5— 
 
 li 
 
 where Li and Ri are the inductance and resistance respectively 
 of the instrument coil, and L and R are the same quantities of the 
 circuit whose energy consumption is being measured. Li and 
 Ri are constant for any given instrument, hence tan a varies 
 only with the frequency of the circuit while tan d depends upon 
 
POWER-MEASURING INSTRUMENTS 119 
 
 the frequency and constants of the circuit. These constants are, 
 of course, different in different circuits. 
 
 When tan a is positive and less than tan 9, the correction 
 factor is less than unity, and the wattnleter reads too high. 
 
 When a = 0, or 6, the correction factor is unity and the watt- 
 meter indication gives the correct power. 
 
 When tan a is positive and greater than tan 8, the correction 
 factor is greater than unity and the wattmeter reads too low. 
 
 As tan 6 is likely to be unknown and may have any value, it 
 is very evident that the correction factor is unknown and the 
 wattmeter reading is uncertain. The relation between the true 
 power and the wattmeter reading may be written in the form 
 
 Wattmeter reading = true power X — ; — r~z — s . 
 
 1 + tan'' a 
 
 When a is small, this reduces to an approximate expression 
 
 Reading = power (1 + a tan 0). 
 
 The error in the reading is evidently true power X a tan d, and 
 as tan 6 increases with 8, the error increases as the power factor, 
 cos 0, decreases. 
 
 If the phase difference between pressure and load current is 
 due to capacity, the current will lead the pressure in the main cir- 
 cuit. The relation between the angles is then given by 
 
 y = a -\- 8 
 and the correction factor becomes 
 
 1 + tan^ a 
 1 — tan 8 tan a 
 
 and the indication of the wattmeter is correct only when tan a 
 = — tan 8, that is, when a = 0, or — 6. For any other values 
 of 8 and a the wattmeter reading will be inaccurate and hence 
 electrodynamometer wattmeters should be constructed so that 
 a will be negligibly small. This can be done readily by connect- 
 ing a high non-inductive resistance in series with the movable 
 coil. The inductance of the current coils of standard commercial 
 instruments is inappreciable. The effect of wave form upon the 
 accuracy of the wattmeter will be taken up in Chapter XXII. 
 
 113. Range of Wattmeters. — The range of the electrodyna- 
 mometer type of wattmeter may be changed by connecting 
 multipliers in series with the voltage coil, or shunts in parallel 
 with the series coil on direct-current circuits and low-voltage, 
 
120 
 
 ELECTRICAL METERS 
 
 low-frequency, alternating-current circuits. When the wattmeter 
 is to be used on high-voltage alternating-current circuits, trans- 
 formers are used. It is not the practice of American manu- 
 facturers to shunt wattmeters. 
 
 114. Induction-type Wattmeters. — Induction-type wattmeters 
 use in their operation the principles of the rotating and revolving 
 magnetic fields. To understand the general application of these 
 principles, consider the case illustrated in Fig. 84 which is merely 
 illustrative. 
 
 The essential parts of an induction meter are a pivoted disk or 
 drum D, a pressure coil VC, and a current or series coil CC. 
 The copper or aluminum disk, D, is pivoted at its center and 
 
 OJWOT^ 
 
 Vcl 
 
 CC 
 
 FiQ. 84. 
 
 carries a pointer not shown in the figure. The motion of the disk 
 is counteracted by suitable spiral springs. The voltage coil is 
 highly inductive so the current in the coil lags approximately 
 90° or one-quarter of a period behind the pressure. The current 
 in pressure coil produces a magnetic field which is in phase with 
 it. The variation of this flux through the disk induces eddy 
 currents which are one-quarter of a period out of phase with the 
 flux. 
 
 The current coil CC is non-inductive. The flux, due to this 
 current through the disk, is in phase with it. Hence, the eddy 
 currents, due to pressure current, and flux, due to load current, 
 reach maximum values together and the reaction between them 
 
POWER-MEASURING 'INSTRUMENTS 121 
 
 will be a maximum under these conditions. This reaction causes 
 the disk to rotate. 
 
 The eddy currents are proportional to pressure current, which 
 in turn is proportional to the pressure at terminals of load, or 
 algebraically 
 
 i = KiE, 
 
 where i represents the effective eddy currents, and E the effective 
 pressure. Similarly 
 
 $ = KJ 
 
 where $ is the effective fiux due to effective load current I. 
 The torque is proportional to the product of i and $, hence 
 
 Torque = Koi^ = KxK^EI. 
 Or in other words, the torque is proportional to EI, the power. 
 
 It can readily be shown, by the same process of reasoning, that 
 when the current and pressure are not in phase, the torque is 
 proportional to EI cos d, where d is the difference in phase. 
 Hence, the induction wattmeter, when properly adjusted, gives 
 correct indication on circuits whose power-factor is other than 
 unity. 
 
 115. Westinghouse Induction Wattmeter. — A diagrammatic 
 sketch of the magnetic circuit and windings of the Westinghouse 
 induction wattmeter is shown in Fig. 85. It is evident that the 
 magnetic circuit is of the same pattern as that of the induction 
 ammeter manufactured by the same company. The winding is, 
 however, modified to meet conditions of power measurements. 
 
 The windings consist of two principal coils V-C and C-C. 
 The coils V-C are connected through a resistance across the line, 
 and the coils C-C in series with the load. The coils V-C have 
 relatively high inductance and consequently the flux due to the 
 voltage current is nearly in quadrature with the pressure. 
 
 Operation. — The pressure current makes {W-Z) and {X-Y) 
 opposite in polarity. The load current through coils C-G 
 makes {W-X) and (Z-Y) opposite in polarity, and as the flux 
 due to load current is in phase with the current, the resulting 
 field rotates. As already explained this rotating field acting 
 on the drum armature produces a torque which causes a deflec- 
 
 13 
 
122 
 
 ELECTRICAL METERS 
 
 B.c IE^=£ 
 
 Fig. 86. 
 
POWER-MEASURING INSTRUMENTS 123 
 
 tion. The motion of armature is opposed by spiral springs as in 
 the case of the ammeter. The auxiUary coils B-C are used to 
 equalize any difference in the windings of the voltage coils V-C. 
 A complete instrument of this type is shown in Fig. 86. 
 
 In the foregoing discussion the assumption is made that the 
 current in the voltage coil is exactly one-quarter of a period out 
 of phase with the voltage at its terminals. In practice this 
 relation cannot be secured with the arrangements of coils shown. 
 This is due to the fact that the voltage coil possesses resistance 
 as well as inductance, and also that eddy currents and hysteresis 
 losses in the core are inevitable. Likewise, the current in 
 current coil is not exactly in phase with the resulting flux. 
 Hence, it follows that it is not easy to insure that the flux due to 
 the voltage coil shall differ by exactly one-quarter of a period 
 from that due to the current coil. The effect of any such a dis- 
 crepancy upon the indications of induction instruments is similar 
 to the effect of inductance and capacity in the voltage coil of the 
 electrodynamometer type of wattmeter; that is, the error is small 
 when the power-factor of load is high; but it increases as the 
 power-factor decreases. 
 
 116. Lagging Induction Wattmeters. — The term lagging, as 
 here used, means adjusting the meter so that it will read cor- 
 rectly on inductive and non-inductive loads. This is accom- 
 plished by means of auxiliary coils whose effect is to produce exact 
 quarter phasing between fluxes due to voltage and current coils. 
 Usually the coils for making this adjustment are connected in the 
 voltage circuit. 
 
 One method of securing exact quarter phasing is represented 
 diagrammatically in Fig. 87. This represents the voltage circuit 
 as consisting of three parts. A, B, and C. A is a highly inductive 
 coil, B also possesses some inductance but less than A, while C, 
 which is connected in parallel with B, is a pure resistance. The 
 current in the coil B produces the actuating flux. The principles 
 involved are illustrated in Fig. 88. Representing the voltage 
 across coil B, Fig. 87, by Eb, Fig. 88, it is evident that Zp, current 
 in coil C, is in phase with Eb. Owing to the inductance of coil B, 
 Ib will lag behind Eb by an angle less than 90°. Ib may then be 
 drawn in the direction of OY. I a, or current in coil A, is the 
 vector sum of Ic and Ib- Vector I a represents this current. 
 Since coil A is highly inductive Ea will lead I a by nearly 90° and, 
 hence, may be represented by vector Ea- E, the resultant of 
 
124 
 
 ELECTRICAL METERS 
 
 Ea and Eb, will under these conditions be represented by vector 
 E or OX. The phase differences between E, Ea, Eb, I a, Ib and 
 Ic depend upon the relative values of inductances and resist- 
 ances of coils A, B, and C. It is thus evident that by a suitable 
 
 !a a 
 
 Ic 
 
 c 
 
 BIb 
 
 -' OOOOOOO' 
 
 Ea ■>!<■■ 
 
 FiQ. 87. 
 
 Eb -M 
 
 FiQ. 88. 
 
 adjustment of the inductances and resistances of these three 
 coils, Ib can be made to lag exactly 90° behind E. 
 Perhaps the simplest and most commonly used method of 
 
 ^^f:^ 
 
 Fig. 89. 
 
 lagging a meter consists in winding the core of the voltage coil 
 with, or interposing within the path of the voltage flux, a short- 
 circuited coil whose resistance is adjustable. The short-circUited 
 coil acts as the secondary of a transformer, of which the regular 
 voltage coil is the primary. This is the method used in the West- 
 
POWER-MEASURING INSTRUMENTS 125 
 
 inghouse wattmeter shown in Fig. 85 in which L. C. represents the 
 lagging coil. 
 
 The influence of the lagging coil upon the phase relation 
 between pressure coil and current coil fluxes, is much the same as 
 that of the secondary of a transformer. The phase relation is 
 shown in Fig. 89. * represents the magnetic flux linking both the 
 pressure and lag coils. It induces in the lag coil an electromotive 
 force E'i and in the voltage coil an electromotive force in the 
 same direction, but of different magnitude, determined by the 
 number of turns. Representing the exciting current in voltage 
 coil by I, the ampere-turns necessary to produce the flux $ is 
 represented by Nil, and is made up of two components, NJi and 
 iV272. The electromotive force applied to the voltage coil termi- 
 nals may be separated into three components: the first E'l bal- 
 ances the induced electromotive force due to the flux $; the sec- 
 ond, represented by IiXi, balances the electromotive force pro- 
 duced by any leakage flux which links with the voltage coil, but 
 not with the lag coil; the remainder sends current through the 
 voltage coil and is represented by 7iri. The terminal pressure Ei 
 is the vector sum of these three components. If the lag coil be 
 open-circuited, E^ becomes identical with E'^; NJi becomes 
 identical with NJ; hri becomes smaller and farther from E'l in 
 phase. As the current in the lag coil is increased due to a 
 decrease in the resistance in series with it, Ii must increase to 
 maintain I; angle ^ decreases, Ii becoming more nearly in phase 
 with Ei; liTi increases, making Ei more nearly in phase with E'l, 
 the condition desired. An increase in IiXi also aids in bringing 
 about the desired relation. Since E'l is always in quarter-phase 
 relation with $, adjusting the lag coil resistance secures the proper 
 quarter-phase relation between $ and Ei. 
 
 117. Scale. — Since the motion of the movable element is 
 usually controlled by a spiral spring, the scale will be uniform 
 when the torque is exactly proportional to the power in watts. 
 This exact proportionality is not absolutely essential in indicating 
 instruments as the whole scale can be calibrated. The scales 
 of the best instruments are, however, practically uniform and 
 extend over nearly 300°. It is evident that induction instru- 
 ments can be used only on alternating-current circuits. 
 
 118. Mercury Wattmeter. — The principle of operation of 
 this meter, which will undoubtedly soon be placed on the market, 
 is the same as that of the mercury watt-hour meter explained in 
 
 14 
 
126 ELECTRICAL METERS 
 
 Article 172, to which the student is referred. The difference in 
 constmction consists in the substitution of a torsion spring for 
 the damping disk and damping magnets. 
 
 The range of the instrument is varied by shunting the current 
 coil, a method used only on this type of meter. The designers 
 claim that the operation of the meter is entirely satisfactory. 
 
CHAPTER XI 
 PHASE-RELATION AND FREQUENCY INSTRUMENTS 
 
 119. Introduction. — The indications of two classes of instru- 
 ments are determined by the phase difference between current 
 and pressure in the same circuit, or the difference in phase 
 between pressures in different circuits. 
 
 Instruments of the first class are called power-factor meters, 
 or indicators, and of the second class synchroscopes. 
 
 120. Power-factor. — The term power-factor has been defined 
 in two ways. According to one definition, power-factor is the 
 cosine of the phase difference, the phase difference being the 
 angle between the points at which the curves of current and vol- 
 tage cut the axis in the same sense. Thus, in Fig. 32 the cosine 
 of the angle represented by the distance between points where 
 electromotive force and current waves cross axis in the same 
 sense, is called the power-factor. The other definition has no 
 relation to phase difference, but is based upon the relation. 
 
 True power = volts X amperes X K 
 whence, 
 
 „ . ^ watts 
 
 K, or power-iactor, = — r — — 
 
 ' ^ ' volts X amperes 
 
 If the current and pressure curves are true sine waves, the values 
 of the power-factor obtained in accordance with either definition 
 will be the same. When, however, this is not the case, and es- 
 pecially when the current and voltage curves have different forms, 
 the power-factor K, as determined in accordance with the second 
 relation will not be equal to the cosine of the phase difference 
 between the zero points of the electromotive force and current 
 waves. For practical purposes, the power-factor is usually de- 
 termined in accordance with the second relation given above, 
 and is obtained from the indications of an ammeter, voltmeter, 
 and wattmeter. The product of the ammeter and voltmeter 
 readings gives the apparent pOwer; the wattmeter gives the true 
 power, and thus the wattmeter reading divided by the product 
 of the ammeter and voltmeter readings will give the power- 
 is 127 
 
128 
 
 ELECTRICAL METERS 
 
 factor. It is often advisable, however, to have a separate instru- 
 ment for indicating the power-factor, so that no computations 
 need be made. 
 
 121. Power-factor Meter. — The essential features of one type 
 of single-phase power-factor meter are shown in Fig. 90. The 
 principle of this instrument is much the same as that of the 
 dynamometer-type wattmeter. The instrument, however, is 
 provided with two movable coils in place of one. These coils are 
 mounted at right angles to each other, and the controlling spring 
 
 Fig. 90. 
 
 is omittvjd. The current is led into the moving coils by means 
 of two strips which exert practically no torque. The operation 
 of the instrument is then as follows: 
 
 The main or load current passes through the coils CC, while 
 the voltage current is divided, one part passing through resistance 
 R and coU B; and the other part through the inductance L and 
 coil A. The current in resistance R and coil B will be in phase 
 with the voltage across the load terminals, while that through L, 
 which is highly inductive, will be about 90° out of phase with the 
 current in R and B. 
 
 When the load current and voltage are in phase, the reaction 
 between the coils CC and coil B will be a maximum, and that 
 between coils CC and A a minimum. As a consequence, the 
 coil B will set itself in such a position that its plane will be parallel 
 to the plane of the coil CC; or in other words the flux due to 
 the current in coils CC will pass straight through coil B and in 
 the same direction as the flux due to coil B. Under these con- 
 ditions the pointer, which is attached to the shaft of coil B, will 
 indicate unity power-factor. 
 
 When, however, the load current and voltage are out of phase, 
 
FREQUENCY INSTRUMENTS 129 
 
 the reaction between the coils CC and B will be less and there 
 will be an added reaction between the coils CC and A. This 
 added reaction will compel the coils A and B, which are mounted 
 at right angles to each other, to take a new position. This new 
 position is determined by the phase difference between load 
 current and pressure. The deflection of the movable coils is 
 independent of the magnitude of the main current, but it does 
 depend partly upon the ratio of the currents in coils A and B as 
 well as upon the phase difference between load current and 
 pressure. The value of the current in L depends very largely 
 upon the frequency and wave form of the applied voltage, and, 
 consequently, the indications are also modified by the frequency. 
 By carefully designing the coil L, it is possible to keep the ratio 
 
 Fig. 91. 
 
 of currents in coils A and B practically constant for moderate 
 variations in the voltage and frequency. 
 
 The instrument may be calibrated so as to indicate either phase 
 difference in degrees, or power-factor. 
 
 122. Analytical Proof of Principles. — That the foregoing 
 explanation of principles is correct can readily be shown by 
 mathematical analysis. In Fig. 91, let AA', BB', and CC repre- 
 sent the relative positions of the axes of coils A, B, and CC, 
 respectively, at any instant. Furthermore, assume that the 
 current in coils CC is in phase with the voltage. If the current 
 in series coils is represented by 
 
 ic = Im cos (at 
 
 the currents in A and B may be represented by 
 
 , ia = la sin ut 
 
 and 
 
 ib =■ h cos ut. 
 
 The coils A and B are designed so that their magnetic field 
 
130 ELECTRICAL METERS 
 
 strengths are equal, and as the magnetic field will be in phase 
 with the current producing it, we may represent the instantaneous 
 field strengths of coils A and B by 
 
 ha = Hm sin ut 
 hb = Hm cos ut. 
 
 Now the torque or reaction between either coil and coils CC is 
 proportional to the product of this field strength by current in 
 coil CC, and the sine of angle between the axes of the coils. Hence 
 the average torque exerted on coil B is 
 
 Th = average of Khbic sin ^ 
 
 = av. KHmlm cos cat cos cat sin 4> 
 = av. KHmlm cos^ cat sin (i>. 
 
 But the average of cos^ cat is J^, hence the average torque on B is 
 
 „ KHm T ■ , 
 
 Tb = -^— Im sm <t>. 
 
 This is zero when <^ is and maximum when is 90°. That is 
 torque is when the plane of coil B is at right angles to the plane 
 of coil C. Likewise the average of torque on coil A is 
 
 Ta = av. haic sin (90° + <)!>) 
 
 = av. Hmlm sin cat cos ca cos <^. 
 
 But the average of sin cat cos cat is zero, hence the average torque 
 on A is zero. The movable element will thus be deflected so 
 that the reaction between coils CC and B is zero. This means 
 that is zero, or that the plane of coil B is parallel to the plane 
 of coil C. 
 
 When the current and voltage are out of phase, the same 
 method of finding the torque can be used. Let the pressure lead 
 the current by the angle B; then the instantaneous currents in the 
 several coils will be 
 
 ia = la COS {cat - 90°) 
 
 = la sin cat 
 ib = lb COS cat 
 ic = Im COS {cat — ff). 
 
 The instantaneous values of field strengths due to coils A and B 
 are again 
 
 h,a — Hm sin cat 
 and hb = Hm cos cat. 
 
FREQUENCY INSTRUMENTS 131 
 
 The average torque on coil A is 
 
 Ta = av. Kicha cos 4> 
 
 = av. KI„Hm sin wt cos (wt — 6) cos <^ 
 
 = av. Klmlim cos </) (sin coi cos wt cos 6 + sin^ coi sin ^) 
 
 XT' 
 
 = -^ ImHyn cos (^ sin 6, 
 
 since the average of sin u)t cos wi is zero and of sin^ cot is J^ 
 Similarly the average torque on coil B is 
 
 Tb = av. ivi Ji6 sin 8 
 
 = av. KlntHrn cos coi cos (wi — 6) sin </> 
 
 = av. KImH„ sin $ (cos^ u< cos d + cos wi sin oyt sin fl) 
 I'' 
 
 = -KimHm sin <)!) cos S. 
 
 Fig. 92. 
 
 The total torque at any instant will be equal to the sum of Ta 
 and Tb, or 
 
 T = Ta + Tb = ^ ImHm (cos <^ sin 9 + sin cos d) - 
 
 and T = ^ I^H^ sin (4> + e). 
 
 This torque must be zero when the movable system comes tc 
 rest, or when 4> -\- 9 = 0. 
 
 The scale may be graduated either in terms of the angle 6, or 
 cos 6, the power-factor. An instrument in which these principles 
 are practically applied is shown in Fig. 92. The movable coils 
 
132 
 
 ELECTRICAL METERS 
 
 are not visible in this figure but the manner in which they are 
 mounted on the shaft is shown in Fig. 93. 
 
 123. Polyphase Power-factor Meter.— The indications of the 
 single-phase power- factor meter cannot be relied upon when the 
 
 Fia. 9.3. 
 
 meter is used on circuits whose frequency is different from that 
 for which the meter is designed. To obviate this objection to 
 single-phase meters when used on polyphase circuits, a meter has 
 
 FiQ. 94. 
 
 been designed which utilizes the actual phase displacement of a 
 polyphase system to obtain the voltage-coil magnetic field. A 
 diagram showing the connections of a three-phase meter is shown 
 in Fig. 94. The connections, as there shown, are intended for a 
 balanced system. The three coils A, B, and C are mounted 
 
FREQUENCY INSTRUMENTS 
 
 133 
 
 on the same shaft in the same manner as the coils of a single- 
 phase meter. The planes of the three coils are 120° apart, and 
 one end of each is connected, through a suitable resistance, to one 
 of the three mains, the other ends being connected together. 
 
 The principles of operation are exactly the same as those of the 
 single-phase instrument just described, but as there is no induct- 
 ance in the voltage coils, the indications of the meter are inde- 
 pendent of frequency, wave form, or voltage variations. 
 
 For unbalanced three-phase cir- Q 
 
 cuits, the instrument is made with 
 three current coils, which may be 
 connected to the separate circuits. 
 The power-factor of each phase, or 
 the average of the whole system, 
 can thus be obtained. 
 
 124. Westinghouse Power- 
 factor Meter. — The operation of 
 this meter is based on the interac- 
 tion of a rotating and an alter- 
 nating magnetic field. The pper- 
 ating elements of the two-phase 
 and single-phase meters consist of 
 three coils and a pivoted iron vane 
 or armature, Fig. 9.5. Two of 
 these coils, M and N, are fixed in 
 position at right angles to each 
 other with their axes in the same 
 plane. These coils of a two-phase 
 meter are connected to each phase 
 of the line so that the currents in them are in phase with the hne 
 currents. A resistance coil is connected in series with one of 
 these coils, and a high inductance is connected in series with the 
 other coil of the single-phase meter. The currents in the two 
 coils M and N are thus in quadrature and produce a rotating 
 magnetic field. 
 
 The iron vane is magnetized by a current in phase with the 
 voltage and passing through a third coil, Fig. 96. This coil is 
 mounted with its axis coinciding with the shaft of the vane, and 
 at right angles to the plane of the axes of the coils M and N. 
 As the iron vane will be attracted or repelled by the magnetic 
 field of the coils M and N, it takes a position where the zero of 
 
 Fio. 95. 
 
134 
 
 ELECTRICAL METERS 
 
 its alternating field occurs at the same instant as the zero of the 
 rotating field. Thus, if the current magnetizing the vane is in 
 phase with the current in coil A'', it will assume a position parallel 
 to or in the plane of the coil M. If the current in the coil C 
 is in quadrature with that in coil N, the vane will assume a posi- 
 tion parallel to the plane of the coil N. For any other phase 
 relation between the currents in the coils C and A'^, the iron vane 
 will assume a corresponding position. The iron vane thus shifts 
 around to a position determined by the angle between the vol- 
 tage and current in coil N, that is, the angle between the current 
 
 LaminaTed iron ring 
 
 Current coils 
 producing rotating 
 field 
 
 Iron armature 
 
 .-••Fbinter 
 
 Voltage coil mag- 
 netizing armature 
 
 Fig. 96. 
 
 and voltage of the circuit. The laminated iron ring shown in 
 Fig. 96 provides a return circuit for the flux of the pivoted 
 armature. 
 
 The three-phase meter is similar in construction with the 
 exception that it has three current coils spaced 120° apart. 
 These coils are then connected one to each phase of the three- 
 phase circuit. 
 
 An analytical proof almost exactly like that given in Article 
 122 may be applied to the foregoing principles. 
 
 The motion of the pointer is damped by means of an alumi- 
 num disk moving in the field of two permanent magnets. 
 
 125. Frequency Meters. — Frequency of an alternating current 
 has been defined as the number of cycles per second, where a cycle 
 is considered as consisting of a complete set of positive and nega- 
 tive values. If the magnetic field of an alternator consists of p 
 poles, and has a speed of n revolutions per second, the frequency 
 is given by 
 
 pn 
 "2"' 
 
 / = 
 
FREQUENCY INSTRUMENTS 
 
 135 
 
 An instrument designed to indicate the frequency is called a 
 frequency indicator or meter. Frequency indicators are of two 
 types, that is, they make use of two distinct principles in their 
 construction. 
 
 126. Resonance Frequency Indicator. — The resonance principle 
 is of considerable importance, not only in its application to 
 frequency indicators, but in many other ways. The principle 
 can perhaps be understood from the following illustrations. 
 In ringing a large church bell, the pull on the rope must come at 
 regular intervals. A small impulse, if imparted at the right 
 instant, and oft repeated may result in considerable motion. If 
 two tuning forks of the same pitch be placed some distance apart, 
 and one be caused to vibrate, in a short time the other will be 
 sounding. The first fork sends out regular impulses of the 
 
 ...Solder weight 
 
 mi 
 
 .Electro- 
 Li' magnet 
 
 A.C.Suppfy 
 
 Fig. 97. 
 
 same frequency as that of the second fork. These impulses are 
 transmitted through the air, and, coming at regular intervals, 
 cause the second fork to vibrate. The sounding board of a 
 piano, and the column of air in the organ pipes are also set 
 into vibration by resonance, the former by the impulses from 
 the wire, and the latter by air impulses from the lip of the 
 pipe. 
 
 The application of this principle for indicating the frequency is 
 clearly shown by Fig. 97. Steel strips of different lengths are 
 fastened at one end and free at the other end in much the same 
 manner as the reeds of an organ. These strips have different peri- 
 ods of free vibration, and can readily be caused to vibrate by 
 outside impulses whose frequency is the same. The impulses are 
 magnetic and are supplied by the alternating current in the 
 electromagnet which is connected to the circuit whose frequency 
 is to be determined. If the free period of vibration of the reed 
 is equal to half the period of the current, the magnetic impulses 
 
136. ELECTRICAL METERS 
 
 will set the reed into vibration as follows: As the current in the 
 electromagnet increases, the reed is attracted toward the magnet, 
 and springs away as the current falls to zero; as the current in- 
 creases in the opposite direction the reed is again attracted. 
 The ampHtude is thus increased with each alternation of current 
 until the energy dissipated in the reed by molecular and air 
 friction just equals that imparted to it by the electromagnet. 
 If the period of the alternating quantity differs but slightly from 
 this critical value, the impulses due to the electromagnet will not 
 occur at favorable moments. They wUl occur sometimes too 
 early and sometimes too late, so that instead of reinforcing the 
 motion of the reed, some of the impulses will oppose the motion 
 and thus reduce the amplitude. A very slight difference between 
 the frequency of the reed and that of the alternating current is 
 ■very noticeable in a diminution of the amplitude of the reed. 
 127. Campbell Frequency Meter. — One of the earliest instru- 
 
 FiG. 98. 
 
 ments to make use of the foregoing principle was designed by Mr. 
 Albert Campbell. The essential features of such an instrument 
 are shown in Fig. 98. This meter was made with only one reed 
 S, whose free length was variable. One end was fastened rigidly 
 to a sliding rack, while the other or free end projected in front 
 of an electromagnet M. When in use, the rack is moved either 
 to right or left until the maximum amplitude of vibration is 
 obtained. The corresponding frequency is then indicated by 
 the pointer upon a suitable dial. 
 
 128. Hartmann and Braun Frequency Meter. — The essential 
 features of the Hartmann and Braun and Siemens and Halske 
 indicators are the same as those shown in Fig. 97. Instead of one 
 reed whose free length can be varied, these indicators are made 
 with many reeds, one for each frequency. 
 
 In another form the reeds are mounted on the outside of a 
 
FREQUENCY INSTRUMENTS 
 
 137 
 
 cylinder, which can be rotated about a central axis. The electro- 
 magnet is mounted on an arm pivoted at the axis of the cyhnder, 
 and projecting a little beyond or outside of the cylinder. By 
 rotating the cylinder, each reed may be successively brought 
 
 Fig. 99. 
 
 within the influence of the electromagnet. Every reed is tuned 
 to correspond to a different frequency, and, as stated above, its 
 vibration will be reinforced by a current whose frequency is one- 
 
 FiG. 100. 
 
 half that of the reed. Thus, when the electromagnet is brought 
 up to a particular reed, it is set in vibration and emits a distinct 
 sound only if the conditions are as stated. The frequency of the 
 current to which the reed responds can be read on a dial fixed 
 above it. 
 
138 ELECTRICAL METERS 
 
 In still another form of meter, the electromagnet and reeds 
 are both fixed. The electromagnet is oblong in form and extends 
 over several reeds. The reeds have their free ends whitened and 
 their vibration is shown as a white band, Fig. 99. These are 
 suitable for switchboard use. Fig. 100. 
 
 Yet another form is supplied with two pairs of electromagnets, 
 one pair in front and the other back of the reeds. By this 
 means, two frequencies from different sources can be determined 
 at the same time. 
 
 If alternating frequencies higher than those for which the 
 instrument is made are to be measured, a magnetic superposition 
 arrangement is required. This is accomplished by adding a few 
 turns of a second winding upon the electromagnet core. Through 
 this second winding is sent a direct current which, to a certain 
 extent, polarizes the magnetic field due to the alternating current. 
 By this means the scale readings have double values. The 
 explanation of this is as follows: The electromagnet is alternately 
 positive and negative with the fluctuations or alternations of the 
 current in the coil. A non-polarized reed is attracted by both 
 positive and negative magnetism and, hence, the reed will 
 vibrate twice as fast as the frequency of the current. When, 
 however, the reed is polarized, that is, made a permanent magnet, 
 it will be attracted by only one of the magnetic impulses. For 
 instance, if the north pole of the reed is near the electromagnet, 
 it will be attracted when the electromagnet is negative, and 
 repelled when the electromagnet is positive. Since the alter- 
 nating magnetization is superposed upon a permanent magnetiza- 
 tion, the latter is merely increased and decreased, but not 
 reversed. Under these circumstances the frequency of the reed 
 will be the same as that of the current. The same reed may thus 
 be used to measure two frequencies, the lower frequency will be 
 indicated when the reed is unpolarized, and the higher frequency 
 when it is polarized. 
 
 Instruments of this type are very permanent and accurate in 
 their indications. 
 
 129. Induction-type Frequency Meter.— An instrument of this 
 type is manufactured by the Westinghouse Electric and Manu- 
 facturing Co. The essential features of such an instrument 
 are shown in Fig. 101. The instrument may be described 
 as consisting of two induction voltmeters, the electromagnets of 
 which tend to cause the disk to rotate in opposite directions. 
 
FREQUENCY INSTRUMENTS 
 
 139 
 
 The electromagnet B of one of the voltmeter elements is con- 
 nected in series with a non-inductive resistance H, and the 
 electromagnet A of the other voltmeter element is connected in 
 series with a relatively high inductance or a condenser. The 
 current through B is thus independent of frequency while that 
 through A will vary with the frequency, other conditions re- 
 maining constant. The coils are so adjusted that any change 
 in voltage causes the torque due to the two electromagnets to vary 
 in the same ratio. The indications of the instrument are thus 
 independent of voltage variations, but depend solely upon varia- 
 
 FiG. 101. 
 
 tions in frequency. The aluminum disk G consists of two halves 
 of eccentric circles. If the disk were a true circle any change 
 in frequency would produce continuous rotation. The left-hand 
 edge of the disk which moves under A is practically the arc of a 
 circle whose center coincides with the shaft. The right-hand 
 edge, which moves under B is practically the arc of a circle 
 whose center is slightly above the shaft. With this arrangement 
 the amount of metal in the air gap of electromagnet A is prac- 
 tically constant, while the amount of metal in the air gap of 
 electromagnet B varies with the position of the disk. When 
 the frequency decreases, electromagnet B becomes stronger than 
 A and the disk turns counter-clockwise. The part of the disk 
 in the air gap of B decreases until the torques of the two 
 electromagnets balance, when the disk stops; when frequency 
 
140 ELECTRICAL METERS 
 
 increases, the torque of B is decreased and the disk rotates clock- 
 wise; a greater part of the disk gradually enters the air gap until 
 the two torques are again balanced. For every frequency, there 
 is a definite point at which the meter comes to rest. The exact 
 shape of disk is obtained by experiment; such an arrangement 
 avoids the necessity of controlling springs. The mechanism of 
 this meter is shown in Fig. 102. 
 
 Fig. 102. 
 
 • 130. Weston Frequency Meter. — The frequency meter of the 
 Weston Electrical Instrument Co. operates on somewhat the 
 same principle as the movable-core type of ammeter and volt- 
 meter. There is, however, this difference; in the ammeter 
 and voltmeter the magnetic field varies in intensity but not in 
 direction, while in the frequency meter the field remains constant 
 so long as pressure is constant, but its direction varies with the 
 frequency. The direction of the field is determined by the ratio 
 of the currents in two coils which are mounted at right angles to 
 each other. The relative intensities of the currents are deter- 
 mined by an ingenious arrangement of inductance and resistance 
 coils. 
 
 Fig. 103 is a diagram of the internal connections of the instru- 
 ment. The two fixed coils are marked (1-1) and (2-2) respec- 
 tively. As is plainly evident from the diagram, coil (1-1) is 
 connected in series with reactance coil Xi and in parallel with 
 resistance coil Ri; and coil (2-2) is connected in series with re- 
 
FREQUENCY INSTRUMENTS 
 
 141 
 
 sistance coil R^ and reactance coil Xz- The two coils are also con- 
 nected in series. At the center of the two coils mounted on a shaft 
 
 Fig. 103. 
 
 is the movable iron core BC. To the shaft is also attached the 
 pointer. The actual construction of the instrument is shown 
 in Fig. 104. At a particular frequency, the fall of potential along 
 
 Fio. 104. 
 
 Xi and coil (1-1), Fig- 103, to point b is the same as that across Ri 
 to a. Under these conditions the current through coil (1-1) is the 
 
142 
 
 ELECTRICAL METERS 
 
 same as that through (2-2) and in phase with it. The resultant 
 magnetic field in this case will be parallel to CB in the diagram. 
 This position of the magnetic field will remain fixed so long as 
 the frequency remains constant. This is shown in Fig. 105, 
 where Hi represents the position and maximum value of field 
 due to coil (1-1), and Hi represents the maximum field due to 
 coil (2-2). Since the intensities of the two fields change to- 
 gether, the resultant field will be represented by H, both in mag- 
 nitude and direction. The resultant magnetic field will thus 
 coincide in direction with OB, and only its intensity will change 
 when voltage alone changes. The position of the soft-iron core is 
 determined by the position of the resultant magnetic field. 
 
 Fig. 105. 
 
 Fia. 106. 
 
 Any change in frequency will change the ratio of the currents 
 in the two fixed coils. For instance a higher frequency will 
 decrease the current through Xi and also through X^. Part of 
 the current through Ri under this condition passes through A 
 and through coil (2-2) in addition to that which passes through 
 coil (1-1). The magnetic field of coil (2-2) is thus stronger than 
 that of coil (1-1) and the resultant magnetic field is shifted in the 
 direction of Hi, Fig. 105. Thus every change in frequency is 
 accompanied by a shifting of the space position of the resultant 
 field, and this shifting causes a deflection of the pointer. 
 
 131. Synchronizing Devices. — Although instruments that 
 indicate whether two generators are in synchronism are not prop- 
 erly meters, nevertheless their practical importance justifies a 
 discussion of them in this text. 
 
 When two alternators, or two synchronous motors, are to be 
 operated in parallel, some device is necessary to show whether 
 the two machines are in synchronism, that is, whether at the 
 
FREQUENCY INSTRUMENTS 143 
 
 same frequency, and whether the terminals of the separate 
 machines are positive and negative together. The simplest form 
 of a device for this purpose is an incandescent lamp connected 
 across the contacts of a single pole switch as shown in Fig. 106. 
 When the points A and B are at the same potential, no current 
 will flow through the lamp L and, consequently, it will not 
 light up. In order that this condition be fulfilled the electro- 
 motive force of one generator must equal the electromotive force 
 of the other generator and the two electromotive forces must be 
 in phase. Owing to the fact that it requires an appreciable differ- 
 ence of potential to cause an incandescent lamp to light up, 
 there is considerable indefiniteness in the use of such an indicator. 
 In well-appointed central stations the synchronizing lamps are 
 rapidly being displaced by special devices called synchroscopes or 
 synchronism indicators. An indicator of this type should per- 
 form three distinct functions, as follows: 
 
 1. It should indicate the difference in speed between the two 
 generators to be synchronized. 
 
 2. It should indicate which machine is running the faster, and 
 finally, the time of exact synchronism. 
 
 3. It should indicate phase difference when frequencies are 
 equal. Modern synchronism indicators perform these functions 
 well. 
 
 The principles of operation of synchronism indicators are 
 practically the same as those of the power-factor meters already 
 discussed. Thus, in Fig. 90, if the coils CC are wound with fine 
 wire and connected to the terminals of one alternator while the 
 two ends marked a and b are connected to the terminals of the 
 other alternator, the pointer will indicate the phase difference 
 between the electromotive forces of the two machines. 
 
 In practice, the stationary coils CC are connected to the line, 
 or terminals of machine running, while the moving coil is con- 
 nected to the generator to be synchronized. The resistance R 
 is usually an incandescent lamp. The inductance L and resist- 
 ance R are used for "splitting" the phase of the current through 
 the rotating element so as to produce a revolving field. 
 
 The field through the stationary coils pulsates with a frequency 
 equal to that of the "running" generator while the field in rotat- 
 ing coils, due to the incoming generator, revolves. If the fre- 
 quencies of both machines are the same, there is a certain position 
 of the armature where no torque will be exerted upon it. If, 
 
 16 
 
144 
 
 ELECTRICAL METERS 
 
 however, the frequencies are different, the field of one set of coils 
 is constantly changing its phase with reference to the other, and, 
 consequently, there is a torque exerted upon the armature caus- 
 ing it to rotate. The speed of the armature is equal to the dif- 
 ference of the frequencies, the armature making one revolution 
 for each complete cycle gained by one generator over the other. 
 The direction of rotation will also depend upon the relative speeds 
 of the two generators. 
 
 132. Weston Synchroscope.— A synchroscope, working on the 
 foregoing principles, would evidently rotate in one direction if the 
 incoming generator were too fast and in the opposite direction if 
 too slow, and the rotation would be continuous unless some 
 retarding force were used. The Weston synchroscope uses 
 spiral springs to counteract this motion. The movement of 
 the pointer is thus limited. The connections of the various 
 
 Incoming Machine 
 
 4]^ 
 
 Bus Bars 
 
 ^^ 
 
 > — www- 
 
 4 
 
 Lamp 
 
 [—1 Movable Coil ] 
 Fixed 3 
 
 3^ 
 
 T- 
 
 Coils 
 
 —u — 
 Fia. 107. 
 
 operating parts of this synchroscope are shown in the diagram of 
 Fig. 107. The incoming machine is connected to terminals A 
 and B, while the machine with which it is to be synchronized is 
 connected to busbars at C and D. If the two machines are not 
 running at the same frequency, the phase displacement will con- 
 tinuously shift and with it the torque on the movable coil will 
 vary from zero to maximum in one direction back to zero and 
 to maximum in the other direction. This variation in torque 
 will cause the pointer to move back and forth over the dial. If 
 the machines have the same frequency, but are not in phase, 
 the pointer will come to rest at one side or the other of the 
 middle point of the scale, the position being determined by the 
 average of the torque. 
 
 Remembering that the average torque is zero when the current 
 
FREQUENCY INSTRUMENTS 
 
 145 
 
 in the movable coil is 90° out of phase with the current in the 
 stationary coil, it is evident that the pointer will stand in verti- 
 cal position when the two machines are in synchronism; for at 
 that time the current in the movable coil leads the other current 
 by one-quarter of a period. This phase displacement is brought 
 about by the condenser in the movable-coil circuit. 
 
 When the two generator currents are not in phase, the currents 
 in the movable and stationary coils will no longer be in quad- 
 rature. When this is the case, a torque will be exerted upon the 
 movable coil causing a deflection. The direction of the deflection 
 will be to the left when the incoming machine is slow and to the 
 right when it is running too fast. 
 
 Pointer -B 
 
 SL 
 
 iron 
 core"' 
 
 „..•• Shaft- 5 
 
 J A 
 
 T 
 
 CoilC 
 
 40 
 
 Fia. 108. 
 
 The synchronizing lamp which illuminates the dial is con- 
 nected to the low-voltage secondary of the transformer. An 
 examination of the winding on the transformer will show that 
 when A and C are of the same polarity, the flux through the 
 secondary winding is a maximum and the lamp is brightest. 
 That is, the lamp is brightest when the pointer indicates exact 
 synchronism. 
 
 133. Westinghouse Synchroscope. — The essential principles 
 of another form of soft-iron movable-core synchroscope are shown 
 in Fig. 108. As shown, the winding consists of three fixed coils 
 M, N, and C. 
 
 The axis of the coil C coincides with the shaft to which the 
 pointer is attached. Upon this shaft is mounted a cylindrical 
 
146 
 
 ELECTRICAL METERS 
 
 iron core which carries two projections A-A . The other two coils, 
 have their axes 90° apart, but in the same plane; this plane, how- 
 ever, is at right angles to the shaft. The axes of the three coils 
 thus correspond to the three rectangular axes of coordinate 
 geometry. 
 
 In series with coil M is connected an inductive reactance, 
 while in series with N is connected a non-inductive resistance. 
 The two coils are connected in parallel across the busbars. The 
 
 coil C is connected through a non- 
 inductive resistance R2 across the 
 mains of the generator to be syn- 
 chronized. 
 
 Analysis of the principles in- 
 volved will show that the principles 
 of operation are nearly identical 
 with those explained in Article 72. 
 There it was shown that a movable 
 core would rotate when subjected 
 to the influence of two coils which 
 are mounted at right angles to 
 each other and through which cur- 
 rents in quadrature flow. When 
 an alternating current flows through 
 C the projections A-A are alter- 
 nately positive and negative. If 
 at the same time a current be flow- 
 ing through coil N, the movable 
 iron core will be deflected so that 
 the projections A-A are parallel to the field of the coil A''. If 
 the frequencies of the two currents are equal, the current in 
 coil C will reverse with that in A'', and hence the movable core 
 will remain stationary. If, now, a current in quadrature with 
 that in C be passed through coil M, its average torque on the 
 armature will be zero, according to the explanation of Article 
 122. When, however, the frequency or phase of the current 
 in coil C is not the same as that of the current in coil A", the 
 magnetic field in coil M will have some effect in causing a de- 
 flection. The demonstration for this is identical with that given 
 in Article 122 concerning the electrodynamometer type of power- 
 factor meter. That is, the pointer will come to rest when <j) -\- 
 d = 0, where 4> is the deflection and 6 the phase difference. 
 
 FiQ. 100. 
 
FREQUENCY INSTRUMENTS 147 
 
 This expression also shows that <p is constant so long as 6 remains 
 constant, and varies as d varies. Thus, when the frequencies 
 of the two machines are different, d will be a varying quantity, 
 and the pointer will rotate. 
 
 134. Lincoln-type Synchroscope. — The Westinghouse Electric 
 and Manufacturing Co. makes still another form of synchro- 
 scope known as the Lincoln type. A diagram of the internal 
 connections of this type is given in Fig. 109. The essential parts 
 of the Lincoln type of synchroscope are a bipolar laminated field 
 M, the winding of which is connected to the busbars, and thence 
 to the machine in operation. On iron core D, which is mounted 
 on a shaft in such a way that it can rotate freely, are wound two 
 coils, B and C, at right angles to each other. These two coils 
 are connected in a "split-phase" relation through a non-inductive 
 resistance R, and an inductive reactance X to the incoming 
 machine terminals. 
 
 The theory of the operating principles of this form of synchro- 
 scope is identical with that of the power-factor meter, Article 
 122, and hence need not be repeated. Since the relation between 
 the deflection of the pointer and phase difference is given by <t> + 
 = 0, it can easily be shown that the angular speed of the pointer 
 is proportional to the difference in the frequencies of the two 
 machines. If the two currents start in phase but have fre- 
 quencies /i and /2 after an interval of time t, they will be out of 
 phase by 
 
 8 = 2:r/i< - 2tU 
 = 2x<(/, -U). 
 
 Hence <t> = — 2Tt(fi — fi) 
 
 or J = CO = — 2ir(/i — fi) ; - or CO is the speed of rotation of 
 
 t t 
 
 the pointer. 
 
CHAPTER XII 
 RECORDING OR GRAPHIC METERS 
 
 135. Introduction. — By recording meter is meant an instru- 
 ment which makes a continuous record, on a properly ruled chart, 
 showing the instantaneous values as well as fluctuations of a 
 quantity whose magnitude changes with time. Quantities 
 whose instantaneous values as well as fluctuations lend them- 
 selves to such a record are current, voltage, power, power-factor, 
 and frequency, or in fact, any quantity whose instantaneous value 
 may be given by an indicating instrument. 
 
 Nearly all electrically operated apparatus and machinery 
 requires, for efficient operation, either constant potential or 
 constant current. Thus the ordinary carbon filament lamp will 
 change about 25 per cent in candlepower with a 5 per cent 
 fluctuation of voltage. A knowledge of the fluctuations in elec- 
 trical quantities is thus of great importance. This information is 
 most readily obtained by the aid of recording, or graphic meters. 
 These meters may be roughly divided into two general classes — 
 direct-acting, and relay. 
 
 136. Direct-acting. — It is very evident that from purely 
 theoretical considerations a recording meter can be made by 
 attaching a pencil or pen to the pointer of most of the indicating 
 instruments so far discussed, and also attaching a properly 
 graduated chart, moved by clockwork, upon which the pen or 
 pencil can trace a line. 
 
 Simple as such an arrangement appears, it is by no means 
 easily carried out in practice. The chief practical difficulty is 
 the elimination of pen friction. The friction of the pen is con- 
 siderable and, to overcome this, considerable force must be 
 exerted by the movement. This necessitates an expenditure of 
 additional energy, else the accuracy of the instrument is decreased. 
 The pen must also contain a large quantity of ink, enough at 
 least for several days' use. As the ink is used up, the weight at 
 the end of the pen varies. The pen must be so designed as to be 
 filled easily and the ink must not be spilled in the event of sudden 
 movements of the pointer. 
 
 148 
 
RECORDING OR GRAPHIC METERS 
 
 149 
 
 The main difficulties or drawbacks to most of these meters may 
 be classed as follows: 
 
 1. The attention required in winding the clock, changing the 
 paper, and filling the pen. 
 
 2. The inaccuracy in readings occasioned by the friction of 
 the pen. 
 
 Fig. 110. 
 
 3. The increased consumption of energy to overcome the ef- 
 fect of friction. 
 
 4. On account of the friction and weight of pen, the instrument 
 is liable to lack sensitiveness. 
 
 137. Bristol Recording Instruments. — One of the oldest and 
 simplest forms of direct-acting graphic meters is that of the 
 Bristol Co. The ammeters of this company make use of the 
 electromagnetic principle for their operation, while the voltmeters 
 
150 
 
 ELECTRICAL METERS 
 
 and wattmeters operate on the Kelvin balance or electrodyna- 
 mometer principle. Fig. 110 shows the construction of a high- 
 current capacity ammeter. The current coil is stationary, being 
 attached to the back of the instrument. The moving element 
 consists of a combination of disk armature mounted on a non- 
 
 FlG. 111. 
 
 magnetic shaft extending through the current solenoid. Both 
 ends of the shaft are supported upon vertical steel springs. 
 
 When current flows through the current coil the armature is 
 attracted toward the stationarj^ coil. The motion of the arma- 
 ture, which is proportional to the current, is opposed by the 
 vertical knife-edge springs. The pen arm is attached directly 
 to one of these springs. It is clear that the motion of the pen 
 
RECORDING OR GRAPHIC METERS 151 
 
 is many times that of the disk armature. In another form the 
 pen is mounted on a Icnife edge below the axis of the coil. The 
 pen is actuated by the iron core as shown in Fig. 111. By 
 means of such a device the motion of the pen is multiplied. 
 There are no jewels, permanent magnets, make-and-break 
 contacts, or spiral control springs. The sensitiveness of the 
 meter is mainly determined by the friction of the pen on the 
 paper. 
 
 Fig. 112. 
 
 Where current rapidly fluctuates it is advisable to have some 
 damping device. In this particular case this is secured by 
 attaching one end of an arm to the disk armature shown at the 
 left of the coil and the other end to a vane which is submerged in 
 oil in the box above the coil. 
 
 Since the voltmeter and wattmeter both operate on the same 
 principle an explanation of one will be sufficient. 
 
152 
 
 ELECTRICAL METERS 
 
 Fig. Ill shows the construction of a wattmeter. The current 
 coil is stationary, while the voltage coil is mounted upon a shaft 
 the ends of which rest upon the knife edges of the spring supports. 
 The terminals of the voltage coil are connected to the positive 
 and negative conductors, and the magnetic effect of the current 
 through this coil of high resistance will be dependent upon the 
 voltage, while the magnetic effect of the main current through the 
 current coil which is of low resistance, will depend upon the 
 
 Fig. 113. 
 
 number of amperes passing. The mutual attraction of the coils 
 will be the product of these magnetic forces and proportional to 
 the number of watts. The marking arm is attached directly to 
 the knife-edge supports of the movable coil and partakes of its 
 motion. One of the knife-edge supports is made with a double 
 bearing. By this means the motion of the movable coil is 
 multiplied, permitting the location of the voltage coil near the 
 current coil. Such a construction makes it possible to use an 
 evenly divided scale on alternating-current instruments as the 
 
RECORDING OR GRAPHIC METERS 
 
 153 
 
 magnetic field is quite constant over the short distance that the 
 coil moves. 
 
 The construction of the voltmeter is in principle the same as 
 that of the wattmeter. The voltage coil is divided, one part being 
 rigidly attached to the meter frame, and the other part is mounted 
 in the same way as the voltage coil of the wattmeter. The 
 graduations on the dial are, of course, in volts instead of watts. 
 Fig. 112 shows a Bristol recording voltmeter. 
 
 In the beginning of this article it was stated that a recording 
 meter could be made by attaching a pencil or pen to the pointer 
 of an indicating instrument. The serious difficulty encountered 
 
 :=:SR3?r^. 
 
 Pig. 114. 
 
 in making a graphic meter in this way lay in the excessive friction 
 introduced. This difficulty has, however, been overcome by 
 the simple process of having the pointer moved in front of a chart 
 against which it is momentarily pressed by a lever arm actuated 
 by a clock. Between contacts the pointer is free to swing just 
 as in any indicating instrument. The intervals between successive 
 impressions can be made as short or long as desired. 
 
 The instruments of this type as manufactured by the Bristol 
 Co. employ two tj^pes of recording mechanism. In one type 
 the record is made on a smoked surface. Every time the pointer 
 is pressed against the chart a white dot is left. If the intervals 
 
154 
 
 ELECTRICAL METERS 
 
 between the impressions arc brief, and if tlie quantity being re- 
 corded does not fluctuate too rapidly, the dots nialvo a continuous 
 line. To make the record permanent, the charts after use are 
 dipped into a solution of shellac which quickly dries and prevents 
 the rubbing off of the smoke. 
 
 In the other type of recording mechanism, to the end of the 
 pointer is attached a small capillary tube, and the lever arm is a 
 curved ink pad which is supported in front of the chart in a plane 
 parallel to its surface. At regular intervals the ink pad is auto- 
 matically pressed against the capillary tube which is thus forced 
 
 Pig. 115. 
 
 against the chart making an ink mark. The capillary tube is 
 supphed with ink every time it comes into contact with the ink 
 pad. Figs. 113 and 114 show the milliammeter of this type. 
 138. General Electric Recording Meters. — Another form of 
 the direct-acting type of recording meters is that made by the 
 General Electric Co. The appearance of a polyphase watt- 
 meter with cover removed, is shown in Fig. 115. The movable 
 element of an ammeter is shown in Fig. 116, by the aid of which 
 the operation of the instrument will be most readily understood. 
 
RECORDING OR GRAPHIC METERS 
 
 155 
 
 The two fixed coils AA are connected in series with each other 
 and with the line. The current in these coils sets Tip a magnetic 
 field which acting on the iron armature B produces a turning 
 moment on the shaft D. The consequent movement, which is 
 opposed by the spiral springs E, is transmitted through the 
 pen-arm supporting frame G to pen arm H. The resulting mo- 
 tion of the pen K traces on the chart L a curve whose distances 
 from a zero line are proportional to the current. As shown in 
 Fig. 115, the motion of the pen is restricted to a straight line. 
 
 Fig. 116. 
 
 and hence the chart may be ruled in rectangular coordinates, 
 which is an advantage in many respects. 
 
 The movable element is suspended from the top support by 
 means of a steel piano wire. The lower end of the shaft D is 
 accurately centered by a small steel pivot passing through a 
 sapphire jewel. The friction due to supports is thus nearly 
 eliminated. 
 
 The comparatively heavy weight of the movable element, 
 including the pen, necessitates a strong torque to give sufficient 
 sensitiveness. 
 
 The pen, a cut of which is shown in Fig. 117, holds enough ink 
 to operate one week without refilling. The pen depends for 
 its operation upon capillary action. The point consists of an 
 
156 
 
 ELECTRICAL METERS 
 
 iridium tube of very small bore, hard, durable, non-corrosive, 
 and capable of receiving a high polish. This point is sealed 
 into the end of a very small glass tube which in turn is placed 
 inside a larger glass tube. The lower end of the small capillary 
 tube is submerged in ink, which is carried to the point by capillary 
 attraction. 
 
 The record is made on a band of specially ruled paper which 
 is fed at the rate of 3 in. per hour by 
 means of clockwork. 
 
 Damping. — To prevent undue swinging 
 of the pen, its motion is damped by 
 means of an aluminum disk rotating be- 
 tween the poles of permanent magnets. 
 140. General Electric Recording Volt- 
 meters and Wattmeters. — In so far as 
 the recording device is concerned, the 
 voltmeters and wattmeters of the General 
 Electric Co. are practically identical with the ammeter. 
 
 The voltmeters and wattmeters operate on the dynamometer 
 principle, employing fixed and movable coils. This principle has 
 already been fully explained. 
 
 141. Esterline Graphic Meters. — Direct-acting graphic meters 
 are also manufactured by the Esterline Co. The direct-current 
 meters are of the permanent-magnet movable-coil, or as it is 
 
 Pig. 117. 
 
 Fig. 118. 
 
 commonly called, D'Arsonval type. The alternating meters are 
 of the dynamometer type. 
 
 The movement of a direct-current ammeter is shown in Fig. 
 118. The large permanent magnet ensures a strong magnetic 
 field with a consequent heavy torque. 
 
 The writing mechanism consists of a stationary ink reservoir 
 
RECORDING OR GRAPHIC METERS 
 
 157 
 
 attached to the meter element near the upper bearing, and a 
 metal tube fitted with a capillary glass pen at the outer end. One 
 end of the pen is bent down and dips into the ink reservoir. The 
 intake is flexibly supported on pivots carried by another arm 
 attached to the shaft. An adjustable counterweight is fitted 
 to the back end of the tube by means of which the pen can be 
 balanced so as to give a light uniform pressure on the paper. 
 
 Damping. — The movable coil is wound on a metal frame in 
 which eddy currents are induced as it moves in the magnetic 
 
 Pig. 119. 
 
 field. The reaction between these eddy currents and the 
 magnetic field effectively damps the motion of the pen. 
 
 The motion of the pen of the alternating-current meters is 
 damped by a vane which is attached to the lower end of the 
 movable element, Fig. 119, and which moves in a cup of oil. 
 The meter element used in wattmeters and alternating-current 
 ammeters and voltmeters is shown in Fig. 120. 
 
158 ELECTRICAL METERS 
 
 142. Relay Type of Recording Meters. — The objections enumer- 
 ated at the beginning of this chapter against recording meters 
 are, to some extent, eliminated in meters operated on the relay 
 principle. 
 
 In this type of meter, the moving element of the meter proper 
 operates merely a set of contacts, which close an auxihary circuit. 
 This auxiliary circuit energizes the solenoids which operate the 
 pen. A comparatively large amount of energy is not objection- 
 able in this case nor does friction in any way impair the accuracy 
 and sensitiveness of the instrument. 
 
 The clock mechanism which moves the paper is made electric- 
 ally self-winding and does not require attention. The recording 
 pen is made to move across the paper in a straight line, and the 
 record is obtained on a continuous sheet of paper ruled with 
 rectangular coordinates. 
 
 143. Principles of Operation. — A complete set of recording 
 instruments embodying these features is built by the Westing- 
 house Electric and Manufacturing Co. The voltmeters, alter- 
 nating-current ammeters, wattmeters, and frequency meters, 
 operate on the electrodynamometer or Kelvin balance principle. 
 The operating principle of the power-factor meter is that of the 
 magnetic vane or movable iron core. The measuring elements 
 of the direct-current ammeters operate on the principle of the 
 permanent-magnet moving-coil type. In order to diminish the 
 influence of the earth's or other external magnetic field, two coils, 
 astatically arranged, are pivoted within the magnetic fields of 
 two permanent magnets. 
 
 144. Construction. — The Westinghouse recording voltmeter, 
 with cover removed, is shown in Fig. 121. The electrically 
 operated measuring element is shown in the upper part of the 
 cut.. The similarity between the Kelvin balance and this is at 
 once evident. 
 
 A schematic diagram of the connections is shown in Fig. 122, 
 which shows quite clearly the manner in which the meter oper- 
 ates. The fixed coils A, B, C, D, and the two movable coils E 
 and F are connected in series in the same manner as those of the 
 Kelvin balance. The movable coil E is provided with a relay 
 contact J, located between the stationary relay contacts H and 
 I of the solenoid circuits of the recording element. 
 
 The recording element comprises the pen-actuating solenoids 
 K and L, their iron plungers K' and L', which are supported by 
 
RECORDING OR GRAPHIC METERS 
 
 159 
 
 the T-shaped lever arm M, pivoted at N; the pen arm is con- 
 nected to M by pin bearing P and provided at the upper end with 
 a pin R, wlrich moves in the stationary guide slot V] and the 
 recording pen S, arranged to pass across a suitable record paper 
 T moved by clockwork not shown in the diagram. 
 
 The control spring consists of the helical spring U, mechan- 
 ically connecting the movable-coil system of the meter element 
 with the movable pivoted supporting arm M of the recording 
 element. 
 
 The solenoid coils K and L are connected to the stationary 
 relay contacts H and I, respectively, as shown, with their junc- 
 tion brought out to binding post No. 2. The contact J of the 
 movable-coil system of the meter element is connected to binding 
 post No. 1. 
 
 Leads from the control circuit are brought to binding posts 
 Nos. 1 and 2, and leads from the circuit to be metered are brought 
 to binding posts Nos. 3 and 4. 
 
 145. Operation. — The measuring coils are wound in such a 
 direction that when the current in them increases, coils E and 
 F are attracted by coils B and C and repelled by coils A and D 
 
 17 
 
160 
 
 ELECTRICAL METERS 
 
 respectively. This attraction will close the relay contact J 
 on the solenoid terminal I, thus closing the recording circuit 
 through solenoid L, energizing it and causing it to pull the 
 plunger L' downward. The downward motion of L' rotates 
 the T-arm M about the pivot N. This movement of M moves 
 the pen toward the right across the chart. 
 
 The downward motion of L' will continue until the tension of 
 spring U is just suflScient to counteract the attraction and repul- 
 sion between fixed and movable coils. When the torque of the 
 
 Fig. 122. 
 
 movable-coil system is balanced by the controlling spring, the 
 contacts / and J are pulled apart, opening the solenoid circuit. 
 The dimensions and weights of the various parts of the meter 
 and the control spring are so porportioned that the entire moving 
 system, including solenoids, pen-actuating arms, and measuring 
 coils, remains stationary in the position occupied when the sole- 
 noid circuit is broken. In the meantime, the clock continues 
 to move the record paper forward, thereby causing the stationary 
 pen to draw a line lengthwise on the chart. This line represents 
 the quantity which is being metered. 
 
RECORDING OR GRAPHIC METERS 161 
 
 If the quantity being metered rises, the contact J is again 
 forced down against the contact I, and the entire operation 
 already described is repeated until the increased tension of the 
 control spring U again balances the increased torque of the mov- 
 ing coils and opens the solenoid circuit. The recording system 
 will then remain stationary until another change takes place in 
 the current in the measuring coils. 
 
 Where the quantity measured decreases in value, the electro- 
 dynamic torque decreases and control spring U depresses the 
 coil spring F, bringing contact J against contact H. The diagram 
 clearly shows that this operation opens the circuit of solenoid L, 
 but closes the control circuit through K. The electromagnetic 
 effect of the current in K pulls K^ downward, thus turning the sup- 
 porting arm M to the left and causing the pen arm to move the 
 pen toward zero or minimum scale value. This movement con- 
 tinues until the arm M has been sufficiently tilted to relieve the 
 tension in the spring U, thus restoring the balance between the 
 actuating forces of the meter element and the spring, causing the 
 contact J to leave the contact H and breaking the circuit through 
 the solenoid K. Thus any variations in the quantity measured 
 cause the contact J to move up or down, making or breaking the 
 circuit through either one or the other of the pen-actuating sole- 
 noids. The corresponding oscillating motion of the pen, com- 
 bined with the uniform motion of the clock-driven record paper, 
 results in the drawing of a line, the distances of which from the 
 zero line represent the magnitude of the quantity in the metered 
 circuit. 
 
 Damping. — The motions of all the moving parts of the meter 
 and recording elements are rendered dead beat by means of 
 suitably arranged pistons working in glycerine dashpots. The 
 movements of the solenoid plungers are damped by the action 
 of pistons attached to their lower ends and working in dashpots 
 located below and partly within the solenoid coils. One of these 
 is shown at B, Fig. 121. The action of the pistons relieves the 
 plungers of excess momentum, thus preventing them from over- 
 shooting and hunting. The magnitude of this control can be 
 readily varied by changing an adjustable opening in the washers 
 located just below the pistons. Quick pen action is readily 
 obtained by increasing the size of the opening, or by using a light 
 grade of oil, while the use of a heavy grade of oil will give extreme 
 slowness of action on badly fluctuating loads. In general it 
 
162 ELECTRICAL METERS 
 
 will be found most satisfactory to have the pen travel across the 
 paper in from 15 to 20 sec. 
 
 In all meters except power-factor meters, a piston working in 
 the dashpot shown at C, Fig. 121, damps the motion of the mov- 
 able coils of the meter element, thereby preventing the movable 
 contact from vibrating against the stationary relay contacts. 
 
 146. Sensibility. — The sensibility of the meter may be readily 
 controlled by varying the distance between the stationary relay 
 contacts. With the contacts adjusted close together, the line 
 drawn on a rapidly fluctuating load will be very irregular. A 
 more regular curve can be obtained, however, by increasing the 
 distance between the stationary contacts. 
 
 147. Westinghouse Recording Ammeters, Voltmeters, and 
 Wattmeters. — The foregoing principles are applied to both 
 alternating-current and direct-current voltmeters and wattmeters 
 and to alternating-current ammeters. The only difference 
 being in the character of the windings. The fixed and movable 
 windings of the voltmeters and ammeters are connected in series. 
 The voltmeter windings are of fine wire and those of the ammeters 
 are of wire large enough to carry 5 amp. The range of the instru- 
 ments may be changed by the use of multipliers and shunts on 
 direct-current circuits, and voltage and current transformers on 
 alternating-current circuits. The single-phase wattmeters have 
 fixed coils identical with those of alternating-current ammeters, 
 and are operated from current transformers. The movable, or 
 voltage coils, are wound with fine wire and connected in series 
 with each other and in series with an external resistance. The 
 direct-current wattmeters are similar to alternating-current 
 wattmeters, except that the current coils are designed to carry the 
 total current. The direct-current ammeters differ in that no 
 fixed coils are used. In place of fixed coils two permanent mag- 
 nets are used. The movable coils and permanent magnets are 
 arranged astatically. 
 
 148. Westinghouse Recording Frequency Meters. — These 
 meters are of the same type of construction as voltmeters, except 
 that the coils are wound differentially in two circuits, one circuit 
 being connected in series with a non-inductive resistance and the 
 other with an inductive reactance. The two circuits are then 
 connected in parallel across the line, so that any variation in the 
 frequency will change the current in the inductive circuit, and 
 hence the torque on the movable coil will change with the fre- 
 
RECORDING OR GRAPHIC METERS 
 
 163 
 
 quency. The recording element operates in the same manner as 
 that of the other meters. 
 
 149. Westinghouse Recording Power-factor Meter. — The con- 
 struction of the relay type of graphic power-factor meter is 
 shown in Fig. 123. It is plain that the recording element is 
 identical with that of the other meters. The meter element is 
 the same as that of the Westinghouse indicating power-factor 
 meter, explained in the previous chapter. The only novel feature 
 is the manner in which the circuit through the controlling sole- 
 
 FiG. 123. 
 
 noids is closed and opened. This feature can readily be explained 
 by reference to Fig. 124. To the shaft of the iron armature G is 
 connected a light arm which plaj-s between contacts H and I on 
 the slotted arm. The contact arm takes the place of the pointer 
 on the indicating power-factor meter. No controlling springs 
 are emplo3red. 
 
 150. Operation. — The direction in which the light arm moves 
 is determined by the power-factor. If the phase difference 
 between the voltage in coils A-B and current in coil C is such 
 that the light arm makes contact with I the recording circuit is 
 closed through solenoid L. The resultant pull on plunger L' 
 will move pen, pen arm, and arm U to the right. This motion 
 
164 
 
 ELECTRICAL METERS 
 
 will continue until the arm has moved a distance which on the 
 indicating meter would represent the phase difference. The 
 final position of pen S will then be determined by the power- 
 factor, and any change in the power-factor will cause the posi- 
 tion of the pen to change. The line traced will thus represent 
 the power-factor. 
 
 151. Sangamo Graphic Meters. — The operating element of 
 the Sangamo graphic meter consists of two motor movements 
 whose principles of operation are the same as those of the mercury 
 watt-hour meter to be explained in later. As shown in Figs. 
 125 and 126 the movable elements are placed at the back of the 
 instrument and insulated from each other. 
 
 The actuating force is obtained by the reaction of the current 
 flowing through the mercury chamber and the copper-disk 
 
RECORDING OR GRAPHIC METERS 
 
 165 
 
 armature, and the magnetic field produced by a current flowing 
 througli the coils on the magnet yokes, Fig. 126. In the 
 direct-current meter, the yokes carry shunt coils, while in the 
 alternating-current wattmeter, series coils are carried on these 
 yokes. The armature current for the operation of the alternating- 
 current meter is obtained from a suitable transformer whose pri- 
 mary is connected across the line at 100 or 220 volts, and whose 
 secondary, of one or two turns, supplies a comparatively large 
 current to the armature. 
 
 The direct-current meters may be used on either the two- or 
 three-wire circuits without change; while the alternating-current 
 
 "*-««-^ 
 
 
 -<*«^ 
 
 ^m 
 
 k 
 
 ^^ 
 
 ^f^^T^^^St/M 
 
 h8VS 
 
 I^Bt^W ' 
 
 
 ^ 
 
 H-^ ^^ 
 
 EK^S 
 
 K^Mm 
 
 
 m^ 
 
 ^^^ 
 
 
 ^%l 
 
 * IfvP^H 
 
 
 
 Hj 
 
 J 1 1 ^„ 
 
 
 ^^wl 
 
 i |uh^H| 
 
 
 
 ^vr 
 
 _L 
 
 ^ 
 
 
 Hh^^ 
 
 ^^HH| 
 
 
 
 i 
 
 _L+- 
 
 
 3 
 
 Ifl 
 
 ■ 
 
 
 J 1 
 LL 
 
 
 r 
 
 i 
 
 f 
 
 t — "h^ — '- 
 
 
 i 
 
 ^ 
 
 s 
 
 m 
 
 m 
 
 sw 
 
 Fiu. 125. 
 
 instruments may be used on either the two-wire or three-wire 
 single-phase, or polyphase circuits. 
 
 While Figs. 125 and 128 are of the wattmeter, the same gen- 
 eral principles of construction and operation are applied to 
 direct-current and alternating-current ammeters, and to alternat- 
 ing-current voltmeters. The direct-current voltmeter movement 
 consists of two d'Arsonval elements operating on mercury 
 bearings, so that an identical mechanical structure and the same 
 general arrangement of the motor elements are preserved. 
 
 The two movable arms are connected by a cross link as shown 
 in Fig. 125, moving on jewel bearings in each of the arms. On 
 this cross link are mounted the pen and the ink reservoir. The 
 pen is very light and terminates in a capillary tip. As the mov- 
 
166 
 
 ELECTRICAL METERS 
 
 able system passes across the chart, the position of the capillary 
 tube, with respect to the ink well, changes, so that the position 
 of the pen with reference to the chart remains constant. By this 
 construction the pen maintains constant pressure against the 
 chart, irrespective of the amount of ink in the reservoir. The 
 construction also permits the use of rectangularly ruled charts. 
 
 152. Right-line Pen Movement. — To obtain accurate records 
 on charts having rectangular ruling, the pen must move in a 
 straight line at right angles to the motion of the paper. This 
 right-line, or parallel motion, is obtained by making PN = 
 PS = PR, Fig. 122. R is a, pin rigidly attached to the arm 
 and sliding in slot V. 'With such an arrangement, the pen S 
 
 Fig. 126. 
 
 moves in a straight line perpendicular to a line through R and 
 A''. In the older form of these instruments the pin R was fixed 
 and the slot was in the pen arm 0. The arm PR thus varied 
 in length and the motion of the pen was only approximately a 
 straight line. 
 
 152a. Advantages and Disadvantage. The chief advantage of 
 a recording meter lies in the fact that it makes a continuous 
 record of the value of and variations in the electrical quantity. 
 An examination of the record maj^ thus be made at any time. 
 This examination may be the means of detecting faults or dis- 
 closing characteristics which need improvement, and which would 
 otherwise be overlooked. 
 
 The disadvantage in their use is lack of sensitiveness, which 
 
RECORDING OR GRAPHIC METERS 167 
 
 defect is due mainly to the weight and friction of the pen. The 
 objections to the form of pen used on the Bristol meter are the 
 evaporation of the ink due to the exposure of a large surface, and 
 the small capacity of the V-shaped trough. The effect of the pen 
 friction, which is a variable quantity, impairs the accuracy of 
 the record. The weight of the pens on the General Electric and 
 Westinghouse meters makes accurate record impossible when 
 the quantity fluctuates rapidly. Then, since the ink is fed by 
 capillary action, the capillary tube will, sooner or later, become 
 clogged, and it is cleaned with considerable difficulty. 
 
 Recording voltmeters are always more difficult to employ 
 satisfactorily than the other instruments, because they are of 
 very little use unless they are both sensitive to small changes of 
 voltage and also remain in accurate calibration to within 1 volt 
 or less. 
 
 The records of such instruments are often useful not merely 
 for indicating the range of fluctuation of voltage in a distributing 
 system, but also for indicating the nature of the fluctuations, as 
 to suddenness, protractedness, and frequency. The cause of 
 the fluctuations can often be determined from an examination of 
 the charts with reference to these points of behavior, with reason- 
 able expectation either of removing or of minimizing such as may 
 be serious. The degree of damping is an important considera- 
 tion in the operation of the recording instruments. They 
 should be strictly aperiodic as far as possible, neither overshooting 
 the mark on the one hand, nor undershooting and lacking in 
 promptitude on the other. 
 
 18 
 
CHAPTER XIII 
 INTEGRATING METERS, WATT-HOUR METERS 
 
 153. Introduction. — Integrating meters are instruments that 
 register the sum of the electric quantity measured over a period 
 of time. Thus if the intensity or strength of a quantity varies 
 with time, the registration of an integrating meter will be pro- 
 portional to the sum of the several products formed by multi- 
 plying together the quantity at a given time by the time during 
 which it remained constant. For instance, if li, 1 2, and Is are 
 currents in a circuit for times Ti, T2, and T3 respectively, the 
 integrating meter will register a quantity which is proportional 
 to IiTi + liTi + I3T3. It is thus clear that the element of time, 
 as well as the electrical quantity determines the registration of 
 the meter. In practice it is necessary to know the electrical 
 energy and quantity of electricity that has been utilized, and 
 accordingly we have watt-hour meters and ampere-hour meters. 
 
 154. Watt-hour Meters. — The definition of the unit of energy, 
 the watt-hour, is given in Article 25. An instrument whose 
 registration is proportional to the energy impressed or utilized, 
 is called a watt-hour meter, often incorrectly called "recording 
 wattmeter" or simply "wattmeter." It is gratifying to note 
 that makers have recognized this confusion in names and all 
 of them now call the meter by its true name. 
 
 The distinction between a watt-hour meter and other meters 
 such as wattmeters, both indicating and recording, is very clear, 
 and the reader should keep this distinction in mind. The indi- 
 cation or registration of a watt-hour meter is determined by 
 the energy that has passed in a given time, while the indication 
 of a wattmeter is determined by the rate at which that energy is 
 passing. 
 
 An analysis of the principles of operation of watt-hour meters 
 will show that they may be classed as electrodynamometer and 
 induction types. The former type is usually used only on direct- 
 current circuits, although instruments of this type may be used 
 on alternating-current circuits. The induction type can be used 
 on alternating-current circuits only. 
 19 169 
 
170 
 
 ELECTRICAL METERS 
 
 155. Electrodynamometer Type (without iron). — The diagram 
 of Fig. 127 shows the essential features of this type of meter. 
 The similarity between the essential parts of this type of meter 
 and those of an electrodynamometer is very evident. The 
 electrodynamometer contains fixed and movable coils. The 
 watt-hour meter likewise contains fixed and movable coils. 
 The stationary, or series winding, consists of two coils FF 
 through which all or a proportional part of the line current 
 passes. The movable coil, or armature A, consists of several 
 
 Fig. 127. 
 
 coils of fine wire and is connected in shunt with the load through 
 the resistance R, and compensating coil C, whose function will 
 be explained later. The main difference between the electro- 
 dynamometer and this type of watt-hour meter consists in the 
 permissible rotation of the movable coil. The motion of the 
 movable coil of an electrodynamometer is opposed by a spiral 
 spring, and the coil is thus restricted in its rotation. On the 
 other hand, the movable coils of the watt-hour meter are free 
 to rotate continuously. This is accomplished by mounting 
 upon the shaft a commutator to which the ends of the several 
 
WATT-HOUR METERS.- 171 
 
 coils are connected. Current is led into the armature coils by 
 means of brushes which rest upon the commutator. For this 
 reason this type of meter is usually called the commutating type 
 to distinguish it from another form which does not require a 
 commutator. The movable system is then mounted between 
 supports, the ends of the shaft resting on jewels. On account 
 of the manner in which it is connected to the circuit, this type of 
 watt-hour meter is sometimes compared with the shunt motor. 
 This similarity is very evident. There is one distinction, how- 
 ever, and that is the fact that neither the field nor armature of 
 the watt-hour meter contains iron. It has been shown that the 
 attraction between the stationary and movable coils of the 
 electrodynamometer is proportional to the product of the cur- 
 rents in the two coils. The torque causing the deflection is thus 
 proportional to the product of these currents. The torque on 
 the armature of a watt-hour meter 4s likewise proportional to the 
 product of currents in armature and field coils. The current in 
 the armature is proportional to the voltage across load terminals, 
 and the current through field coils is equal, or proportional, to 
 the load current; hence, the torque on the armature is propor- 
 tional to the product of the load voltage and current. That is, 
 the torque is proportional to the power. 
 
 156. Counter-torque. — In order that the driving torque may re- 
 main proportional to the power, there must be present a counter- 
 torque whose value increases and decreases with the load. Such 
 a counter-torque is obtained by mounting upon the armature 
 shaft a disk of aluminum which rotates between the poles of two 
 permanent magnets. These magnets and the disk are shown in 
 Fig. 128, which is a view of the Westinghouse direct-current watt- 
 hour meter. The development of the retarding torque and its 
 relation to the driving torque is as follows : The magnetic flux be- 
 tween the poles of the permanent magnets is constant, and 
 hence the eddy currents induced in the disk, as it rotates, are 
 proportional to the speed of the disk. The counter-torque is 
 proportional to the product of the eddy currents and magnetic 
 flux between the magnet poles. Since the currents are propor- 
 tional to the speed, the counter-torque must be proportional to 
 the speed. The counter-torque thus increases and decreases 
 with the speed, that is, with the direct torque on the armature. 
 When the load increases, the speed increases until the counter- 
 torque just balances the torque on the armature. When the 
 
172 
 
 ELECTRICAL METERS 
 
 load decreases, the speed decreases until the two torques are 
 again equal. Thus, neglecting friction, the speed of the arma- 
 ture is proportional to the load, and the meter should register 
 correctly at all loads. 
 
 Dish 
 
 Rear 
 
 '-ci/iPoiriG 
 
 Armature or Pressuwe 
 Coils 
 
 Fig, 128. 
 
 157. Summation of Power. — The torque acting upon the rotat- 
 ing element at each instant is proportional to the power being 
 consumed by the load at that instant. For simphcity, assume 
 the load to consist of a fixed number of incandescent lamps, 
 and that the voltage E is constant. Under these conditions, the 
 power will be constant and equal to IE. The driving torque is 
 likewise constant and equal to KIE. Since the counter-torque 
 increases with the speed, the driving torque will increase the 
 speed until the two torques just balance each other. When 
 
WATT -HOUR METERS 
 
 173 
 
 this condition is reached, the speed remains constant, that is, 
 the disk makes the same number of rotations each minute. 
 Under these conditions the number of rotations of the disk in a 
 given time is strictly proportional to the time. We may thus 
 write 
 
 Torque X time = work 
 but Torque X time = KIE X time. 
 
 It has already been shown that IE X time is electrical energy, 
 hence the torque X time is proportional to electrical energy pass- 
 ing through the meter. The 
 product of the torque by the 
 time evidently determines the 
 total number of rotations of 
 the disk, hence 
 
 Kn = electrical energy. 
 
 The total number of rotations 
 n of the disk is then a measure 
 of the energy transmitted to 
 the metered circuit. The num- 
 ber of rotations of the disk or 
 armature is transmitted 
 through a suitable train of 
 gears to the dials. The 
 operation of the registering 
 mechanism is quite simple 
 and needs little explanation. 
 The upper end of the shaft is 
 finished with a worm, or small gear wheel, the teeth of which 
 mesh with the first of a train of gears. The number of teeth 
 on the gears is such that when the one operating the pointer 
 on the first dial has made ten revolutions, the one operating the 
 second has made only one revolution, etc. The dials are 
 graduated in units of electrical energy such as the watt-hour or 
 the kilowatt-hour. 
 
 The speed of the meter is usually adjusted so as to make the 
 meter direct-reading. This is taken care of in the design of the 
 instrument and by adjusting the position of the permanent 
 magnets. 
 
 The general principles here explained are applied in the West- 
 inghouse, General Electric and Duncan, Columbia, and other 
 
 FiQ. 129. 
 
174 
 
 ELECTRICAL METERS 
 
 direct-current meters, in- 
 terior views of which are 
 shown in Figs. 128, 129, 
 130 and 131. 
 
 157a. Large Current 
 Capacity Watt-hour Me- 
 ters. — A large-capacity 
 series-type watt-hour me- 
 ter for switchboard 
 mounting is manufactured 
 by the General Electric 
 Co. The movable ele- 
 ment of this meter con- 
 sists of two spherically 
 wound armatures 
 mounted on the same 
 shaft as shown in Figs. 132 and 133. The field winding 
 consists of four circular coils placed as near each other 
 as possible, one on either side of each armature. The 
 armatures and field coils are so connected that the currents 
 
 Fig. 130. 
 
 CYUNOfilCAL eruSHES 
 OF CHEMICALLY PURg 
 SILVER-POSITIVE CON. 
 TACT WITH MINIMUM 
 FRICTION 
 
 SEGMENTS IN PLACE OF, 
 The usual 8. TESTED 
 TO 1200 V0LT3 A. C. 
 
 RELD WINDING OF 
 SIMPLE CIRCULAR SEC- 
 TION, GIVING HIGHEST 
 EFFICIENCY. 
 
 ARMATURE CONSISTS 
 OF BUT THREe INTER- ' 
 LOCKED COILS. TESTED 
 TO 10,000 VOLTS 
 
 5IRECT READING ASSO- 
 :iATION DIAL. TRAI 
 =LY DRIVEN-MISALIGN- 
 MENT CAN CAUSE 
 BINDING. 
 
 MICROMETGH MAG- 
 NETIC SHUNT ADJUST- 
 MENT FOR CONTROL- 
 LING MAIN SPEED. 
 
 ALUMINUM DAMPER' 
 use STIPPLED TO BE 
 PERFECTLY RIGlp, 
 
 MicnoMCTEft scntw 
 
 ADJUSTER FOR REGU- 
 LATING BRUSH 
 TENSION. 
 
 JSH CLAMP ENA- 
 BLING SWINGING 
 (USHES CLEAR OF 
 .1MUTAT0R AND RE- 
 NGAGING WITHOUT 
 TERING TENSION 
 
 RIGID ONE-PIECE CAST 
 
 ALUMINUM BASE WITH, 
 
 STIFFENER RIBS. 
 
 SHORT, STIFF SHAFT 
 WITH PIVOTS FRIC- 
 TION CLAMP AT- 
 TACHED. 
 
 LIGHT LOAD ADJUST- 
 
 MENT OF WIDE 
 
 RANGE. 
 
 ADJUSTS WITHOUT 
 
 TOOLS-CANNOT SLIP 
 
 OR CHANGE- 
 
 IMPORTED STEEL 
 
 DAMPER MAGNETS 
 
 MMOVABLV CLAMPED 
 
 IN PLACE. 
 
 jewel'bearinq 
 instantly remova- 
 ble using no t00l3 
 
 WHATfiOEVFR. 
 
 Fig. 131. 
 
WATT-HOUR METERS 
 
 175 
 
 in one set flow in a direction opposite to that in the other set; 
 that is, they are connected astatically. By such an arrange- 
 ment the effect of a stray niagnetic field upon one armature or 
 
 Fig. 132. 
 
 element is neutralized by its effect upon the other element. 
 The damping magnets are also arranged astatically and for 
 further protection are enclosed in a laminated soft-steel case. 
 
 Fig. 133. 
 
 An interesting feature of the construction shown in Fig. 132 
 is the gravity control for brush tension. A counterweight 
 C composed of two knurled nuts is mounted on a lever to 
 the other end of which the brushes are attached. The use of 
 
176 
 
 ELECTRICAL METERS 
 
 two nuts permits the locking of the counterweight in any de- 
 sired position, obviating any danger of change in tension due to 
 vibration. 
 
 Two types or models of these meters are manufactured. The 
 difference between them consists in the construction of the field 
 coils. In one the field coils are circular and in the other they 
 are of busbar type. The former is made in capacities ranging 
 from 50 to 1,500 amp., while the latter is made in capacities 
 ranging from 2,000 to 10,000 amp. Both are made for two- 
 
 FiQ. 134. 
 
 or three-wire circuits and for potentials ranging from 100 to 
 600 volts. A 2,000-amp. 500-volt meter is shown in Fig. 133. 
 The series watt-hour meter is not well adapted for measuring 
 energy on circuits carrying heavy currents. The main difficulty 
 lies in the construction of the series coils. To meet these diffi- 
 culties, several watt-hour meters of the shunted type have been 
 placed on the market within the past few years. One of the 
 latest forms of the shunted type is shown in Figs. 134 and 135. 
 The construction of the meter is in general very similar to the 
 series form. The field consists of four comparatively large 
 
WATT-HOUR METERS 
 
 177 
 
 coils of large conductors surrounding a rather elongated arma- 
 ture. The conductors have to be very large in order that their 
 resistance may be low enough to permit sufficient current to flow 
 with only a small voltage drop across the shunt. Furthermore, 
 in order that the magnetic field may be strong enough to give a 
 relatively high torque, the field coils must contain many turns. 
 The use of shunts introduces complications which result in 
 variable errors. 
 
 Fia. 135. 
 
 158. Electrodynamometer Type (with iron). — There has lately 
 been placed on the market a watt-hour meter which differs in 
 some respects from those already discussed. This is made by 
 the Columbia Meter Co. 
 
 The main difference between this form of Columbia direct- 
 current watt-hour meter and other direct-current watt-hour 
 meters lies in the design of armature or rotating element. This 
 difference will be brought out more clearly by reference to Fig. 
 136, which shows the rotating clement of the Columbia instrument. 
 
 The armature windings, as shown, are a group of six cylindrical 
 coils arranged between two aluminum disks, close to the central 
 shaft and parallel to it. 
 
 Within each coil is a thin strip of silicon steel whose ends are 
 bent at right angles to the axis of the coil, and extend radially 
 
178 
 
 ELECTRICAL METERS 
 
 along the lower surface of the upper, and upper surface of the 
 lower disk. These radial extensions are split so as to distribute 
 the flux more uniformly around the circumference of the disk. 
 The series winding consists of four coils arranged astatically. 
 That is, the coils are connected in such a way as to cause the 
 magnetic flux to flow through each element of a pair in opposite 
 directions. By such an arrangement, the influence of a stray 
 field on one coil is neutralized by its influence on the other coil of 
 
 the pair. The positions of the 
 various parts of the meter are 
 shown in Fig. 137. 
 
 Another characteristic difference 
 between the Columbia and other 
 direct-current watt-hour meters is 
 the use of shunts, which use is 
 made possible by employing iron 
 in the armature. The use of iron 
 in the armature makes it possible 
 to secure sufficient torque to 
 operate the meter with a much 
 smaller field current. Accordingly, 
 they adjust all their meters so as 
 to take exactly 5 amp. in the cur- 
 rent coils at full load. 
 
 159. Friction Compensation. — 
 No matter how carefully the 
 meter is constructed, all friction 
 cannot be eliminated. Some energy is thus always required 
 for the operation of the meter. In a well-designed meter 
 this amount of energj^ is very small, yet if some means 
 are not provided for overcoming this frictional torque, the 
 meter will not register on a very light load. With the 
 introduction of high-efficiency incandescent lamps, the neces- 
 sity for accurate compensation is much greater than previously. 
 Nevertheless, the compensating torque should not be so great as 
 to overcome excessive or unnecessary friction. It is usual to 
 design the coil so that on about 5 per cent of full load the maxi- 
 mum possible compensating torque will give an excessive speed 
 of about 10 per cent. If the frictional torque is greater than this, 
 the cause should be discovered and removed. 
 
 The compensating torque is obtained by connecting a coil in 
 
 Fig. 136. 
 
WATT-HOUR METERS 
 
 179 
 
 series with the armature or voltage coil, the plane of the coil 
 being parallel to the current, or series coil. Such a coil is shown 
 at C, Fig. 127. The strength of the compensating torque can be 
 adjusted in either one of two ways. In the General Electric, 
 Westinghouse and new Duncan watt-hour meters the position of 
 the compensating coil with reference to the armature is changed 
 until the proper degree of compensation is secured. The arrange- 
 ment of the compensating coil of the Westinghouse meter is shown 
 
 Fia. 137. 
 
 in Fig. 128, where it is called friction compensation. By releasing 
 the clamping screw B, the arm supporting the coil is released and 
 may be moved up or down, nearer to or farther from the arma- 
 ture, thus changing the torque it exerts. In the more recent 
 Duncan model E J-^ watt-hour meter the fixed compensating 
 coil has been replaced by a coil whose position is adjustable. 
 This is shown in Fig. 130. 
 
 The Duncan Electric Manufacturing Co. formerly used a some- 
 what different method of varying the torque. In the older Dun- 
 can meters the compensating coil is firmly fixed within the front 
 
180 ELECTRICAL METERS 
 
 series coil, and the intensitj^ of tlie compensating field is varied by 
 changing the number of active turns on the coil. This is accom- 
 plished by moving a small contact lever either to the right or 
 left, as the case demands, over multipoint contacts. Fig. 138 
 shows this compensating coil with the lever at its middle position. 
 The Columbia Meter Co. uses in principle a like method. 
 The only difference is that the proper adjustment is obtained 
 by changing the position of the hard-rubber plug with its enclosed 
 brass spring bushing along the projecting terminals of a series of 
 small-resistance coils visible to the right of the dial plate, Fig. 131. 
 Changing the position of the plug changes the number of active 
 turns and, hence, the compensating torque. 
 
 Fig. 138. 
 
 160. Creeping. — The armature circuit, when the meter is in 
 service, is connected to the mains all the time. Thus, there is a 
 current at all times through the armature. When the field due 
 to the compensating coil is such as to furnish torque just sufficient 
 to overcome the friction when the meter is installed where there is 
 no vibration, it may creep when installed in a place subject to 
 jar. The jarring reduces the friction of the bearings, and at the 
 same time the armature is partially relieved of its weight while 
 the vibration lasts. Under these circumstances the initial torque 
 may be sufficient to cause the meter to revolve slowly. 
 
 Another cause of a meter's creeping may be due to a higher 
 voltage than that for which the meter was adjusted. If the com- 
 pensating torque on a certain voltage is nearly great enough to 
 
WATT-HOUR METERS 181 
 
 cause the meter to register on no load, an increase in voltage will 
 increase the armature current and, since the compensating coil 
 is in series with the armature, the compensating current will 
 increase. The compensating torque, which is proportional to 
 the product of the armature current and compensating current, 
 will also increase. The two currents being the same, the com- 
 pensating torque is then proportional to the square of the 
 armature current. We may write this 
 
 T = KP 
 
 but 7=1 
 
 K 
 
 where E is the electromotive force between mains and R the 
 
 resistance of armature circuit, including compensating coil. 
 
 Then 
 
 E^ 
 72 = P^ and substituting for P, we get 
 
 T =^„X E' 
 
 K and R both being constant, the expression shows that the 
 compensating torque is proportional to the square of the voltage 
 between mains. It is thus evident that a compensated meter cor- 
 rect on light loads will register on no load when the voltage is 
 raised. The average conditions in practice are met by adjusting 
 the meter so that on light load it is from 1 to 2 per cent slow. 
 
 161. Brushes. — Some of the chief objections to the commutator 
 watt-hour meter are friction of brushes, sparking at the brushes 
 when the commutator becomes oily or dirty, a change in speed 
 due to improper position of brushes, and additional weight of 
 moving parts due to commutator. The use of a commutator 
 thus introduces difficulties which cannot be wholly eliminated, 
 but their effects can only be minimized by careful design and 
 construction. Brushes must therefore be made out of material 
 whose elastic properties do not change with time. To meet this 
 and other requirements, it is common practice to make the 
 stems of the brushes out of phosphor-bronze wire or strips, and 
 to provide the contact ends with silver tips. It has been found 
 that brush friction is considerably reduced by making the tips 
 round instead of flat. 
 
 The pressure of the brushes upon the commutator is governed 
 
182 
 
 ELECTRICAL METERS 
 
 by cither the tension of a spring or the force of gravity. Where 
 spring control is used, the elasticity of the stem of the brush 
 supplies the necessarj' tension. Two typical devices of this kind 
 are shown in Fig. 139 and 140, an examination of which will 
 give an understanding of its operation. 
 
 In the gravity method of control, uniform pressure is secured by 
 attaching the l:)rushes to one end of an arm which is pivoted 
 and carries a counterweight at the other end. The distance of 
 
 the counterweight from the fulcrum 
 may be changed, thus changing the 
 tension. 
 
 162. The Commutator. — In order 
 that the frictional torque may be 
 reduced to a minimum, the commu- 
 tator must be of very small diameter. 
 The smallest diameter that can be 
 
 Pig. 139. 
 
 Fio. 140. 
 
 successfully used on a 110- to 220-volt meter is about Yiq in. 
 For higher voltages the diameter of the commutator must be 
 greater to permit of proper insulation. 
 
 The commutator is usually made by forcing a piece of silver 
 tubing over a fiber bushing on the shaft. The tube is then sawed 
 into the proper number of segments which are held in place by 
 fiber or metal rings. The metal rings are, of course, insulated 
 from the segments. It is customary to use silver for both the 
 commutator segments and brush tips, because it is the cheapest 
 metal that can be used which does not readily oxidize. The com- 
 mutator of the Duncan shunted tj^pe is made of gold. Some 
 makers use fiber to insulate the segments from each other, while 
 others leave merely an air space. 
 
WATT-HOUR METERS 
 
 183 
 
 163. Armature. — The distinctive characteristics of some meter 
 armatures have already been briefly pointed out. The armatures 
 of watt-hour meters without iron in their magnetic circuits are 
 mainly of two forms, spherical and cjdindrical. The spherical 
 form permits of a more compact construction, thus minimizing 
 the magnetic leakage and correspondingly increasing the torque; 
 or, what amounts to the same thing, securing maximum torque 
 with a given weight of armature and given energy consumption 
 in armature and field. For the cylindrical form, the advantage 
 
 Fig. 141. 
 
 Fig. 142. 
 
 is claimed that it can be repaired much more readily. The 
 cylindrical form is shown in Fig. 141. 
 
 The windings of both forms of armature are of the drum type. 
 The coils of the spherical armature are usually wound upon a 
 light fiber shell which is mounted directly upon the shaft, the 
 coils being held in place by grooves pressed in the shell. The 
 supports for the cylindrical armature are two light hardwood 
 spiders firmly fastened to the shaft. This permits of a light and 
 open construction which is conducive to good ventilation. 
 
 The coils of the armature are wound with wire of pure copper 
 and of smallest gage consistent with mechanical strength, 
 
184 
 
 ELECTRICAL METERS 
 
 usually not larger than No. 40 B. & S. gage. Armatures wound 
 for 110 to 220 volts have as a rule eight coils of 1,000 turns each 
 connected to the eight segments of the commutator. The 
 Columbia meter, however, has only three coils which are con- 
 nected to a three-segment commutator, Fig. 142. For voltages 
 above 220 it is common practice to wind the armature with 16 
 coils, and the commutator has a corresponding number of seg- 
 ments. The main reason for this is to reduce the voltage between 
 adjacent coils and commutator segments. 
 
 The resistance of the armature coils and auxiliary resistance is 
 so adjusted that practically the same current flows in the arma- 
 ture of meters for different voltages. The armature resistance 
 is practically the same in each case, but for the higher voltages 
 additional resistance is placed in series. 
 
 Bushing- 
 
 ,-• Discs of 
 Billiard cloth 
 soaked in 
 Jewelers' oil 
 
 -Spiral 
 spring 
 
 ..-Hard fiber 
 bushing 
 
 Shaft 
 
 Fig. 143. 
 
 Fig. 144. 
 
 164. Bearings. — The necessity for a very small frictional 
 torque makes the proper design of the bearings of great impor- 
 tance. The function of the top bearing is merely to hold the 
 movable element centered, and is therefore subject to very little 
 pressure, and, consequently, very little friction. One form of top 
 bearing is shown in Fig. 143. It consists of a steel pin fastened 
 to a removable screw and projecting down into a bushing in a 
 recess drilled in the shaft. The bottom of this recess is filled 
 with billiard cloth, saturated with watch oil. A film of oil is 
 maintained around the pin by capillary action. In another form 
 of bearing the conditions are reversed. The pin is a part of the 
 shaft and the recessed bushing projects from above downward. 
 This form is shown in Fig. 144. 
 
 Owing to its importance, by far the most attention has been 
 devoted to the design of the lower bearing, which has now reached 
 
WATT-HOUR METERS 
 
 185 
 
 a high degree of perfection. There are, in general, two forms of 
 lower bearing. One form may be called pivot bearing and the 
 
 Fig. 145. 
 
 other ball bearing. Details of a typical pivot bearing are shown 
 in Fig. 145. The pivot is not an integral part of the shaft, but 
 is made separately and screwed 
 into the lower end of the shaft or 
 spindle. It will be observed that 
 the bearing consists of a hollow 
 screw with a helical spring. Sur- 
 mounting the spring is a plug 
 within the upper face of which is 
 embedded the cupped jewel. 
 
 The ball bearing is shown in 
 Fig. 146. The lower end of the 
 shaft, instead of ending in a con- oimpinj Nut, 
 ical pivot, has a cup-shaped jewel 
 fixed in it. Another cup-shaped 
 jewel is fixed in the upper face 
 of the plug, and between these 
 jewels is a hardened steel ball. 
 It is claimed that the ball bear- 
 ing has the longer life. In so 
 far as friction is concerned there 
 is perhaps not much choice. 
 
 165. Jewels. — Until recently it has been almost universal 
 practice to use sapphire for the jewels. Experience has demon- 
 
 20 
 
 Pig. 146. 
 
186 ELECTRICAL METERS 
 
 strated the inability of sapphire to withstand, for more than a 
 comparatively short time, the grinding and hammering action 
 of the pivot. The only material that is able to show permanently 
 satisfactory performance is the diamond. The earliest diamond 
 jewels were flat and required a stone ring to maintain the pivot 
 in place, an arrangement which did not give complete satisfaction. 
 Later experiments showed that it was possible to grind the dia- 
 monds in the form of a cup, and jewels of this form require no 
 guiding ring. The cupped diamond jewels are now used exten- 
 sively for meter bearings. Experiments performed on meters 
 with sapphire and diamond jewels show that a higher accuracy 
 on light load was maintained by the meters with diamond 
 bearings. 
 
 166. Magnets. — A most important feature of the watt-hour 
 meter is the permanent magnets, for upon their permanency 
 depends to a great extent the performance of the meter. The 
 necessity for magnets whose strength will remain constant can 
 easily be appreciated when it is remembered that the retarding 
 torque is proportional to the product of eddy currents in the disk 
 by magnetic flux. The eddy currents at any given speed of disk 
 are, however, proportional to magnetic flux, hence the retarding 
 torque is proportional to the square of the magnetic flux, or in 
 algebraic symbols, 
 
 T = K^\ 
 
 It is thus very evident that a small change in $ will have an 
 important effect in changing the counter-torque and, indirectly, 
 the registration of the meter. In this respect the manufacturers 
 of first-class instruments take special precautions, and strive 
 to produce magnets that will retain their strength indefinitely. 
 
 167. Registering Mechanism. — A typical registering mechan- 
 ism is shown in Fig. 147. This consists of dials, dial train, and 
 reducing train. The, dial and dial train of gears are not clearly 
 shown; the reducing train, however, is. Great care is necessary 
 in the manufacture of the various parts in order to eliminate all 
 imperfections. The wheels are usually made of hard brass and 
 gold-plated to prevent corrosion. The entire mechanism is 
 aligned by dowel pins and attached to the frame by screws. 
 
 168. Electrodjmamometer Type on Alternating-current Cir- 
 cuits. — Since the principles of operation of the commutator form 
 of watt-hour meter without iron are the same as those of the elec- 
 
WATT-HOUR METERS 
 
 187 
 
 trodynamometer-type wattmeter, most of the theory of the latter 
 instrument as given in Chapter X will hold with reference to 
 the watt-hour meter. In the discussion referred to, it was shown 
 that the deflecting torque is proportional to the power when the 
 voltage coil is non-inductive. This, however, is seldom the case 
 and, hence, adjustments, termed lagging, must be made before 
 the meter will register accurately on alternating-current circuits. 
 It was shown in Chapter X that a wattmeter with an inductive- 
 voltage circuit gave too high indications on circuits of low power- 
 factor, and that on circuits where the current leads the pressure, 
 
 Pig. 147. 
 
 the deflection under certain conditions would be negative. An 
 electrodynamometer wattmeter which has not been lagged is 
 subject to exactly the same inaccuracies, viz., on inductive load 
 the registration will be too high, and on a load such as an over- 
 excited synchronous motor, it may run backward. This will be 
 the case where a is greater than cos 6, a and 6 having the same 
 significance as in Article 112. 
 
 169. Lagging. — In order to avoid the foregoing errors it is 
 necessary to adjust or modify the series circuit of the meter in 
 such a way that the angle between the series current vector and 
 the voltage vector shall be exactly the same as that between the 
 armature current vector and the voltage vector on non-inductive 
 load. This is accomplished by shunting a part of the series 
 current through a non-inductive resistance. Under these condi- 
 tions, the main current will divide inversely as the impedances of 
 the two parallel circuits. Since the series winding is to some ex- 
 
188 
 
 ELECTRICAL METERS 
 
 tent inductive, the current in this will lag behind the current 
 through the non-inductive shunt. The main current will then be 
 the vector sum of these two components, and its angle of lag will 
 be determined by the ratio of these components. Thus in Fig. 
 148, let 7i be the current through the series winding. Then if R] 
 and Xi are the series-coil resistance and inductance respectively, 
 RJi will be the resistance drop, and Xili the reactance drop. 
 The series current will be in phase with RJi; and the applied 
 voltage and current through non-inductive shunt are in phase 
 with OE. If Oil represents the series-current vector, and Oh 
 the shunt-current vector; then 01 is the resultant, or main- 
 current vector. The angle p by which the series-circuit current 
 lags behind 01 can evidently be changed by changing the ratio 
 of 07) and 01^. These in turn depend upon the resistance of the 
 
 ^z^. 
 
 I ^J coae 
 
 ^^s/n& 
 
 Pig. 148. 
 
 Pig. 149. 
 
 shunt circuit. In a properly lagged meter this angle /3 is made 
 equal to the angle of lag between applied voltage and voltage- 
 circuit current. 
 
 170. Value of Shunt-circuit Resistance. — The value of the 
 shunt-circuit resistance can be calculated if the resistances and 
 inductances of the voltage and series circuits are known. Thus 
 in Fig. 149 let I\ be the series current, and Ii the shunted current. 
 R, R\ and R-i are the resistances of the voltage, series, and shunt 
 circuits respectively, and if X and Xx are the reactances of the 
 voltage and series circuits, we may find R2 in terms of R, Ri, 
 X, and Xi, as follows: 
 
 I2 sin 6 
 
 but 
 and 
 
 tan /3 
 
 cos d = 
 
 sm = 
 
 7i + Ii cos 6 
 
 Ri 
 
 {Ri^ + Xi^)^ 
 
 X^ . 
 
 'Ri' +Xi-')^ 
 
WATT-HOUR METERS 189 
 
 Then 
 
 .tan^ = ^^^ + ^>^)' 
 
 L + ^'^' 
 
 {R,^ + X,^)^ 
 
 72 Xi 
 
 The relation between 7i and I2 is given by 
 
 h : I2 :: R2 : (Ri' + X^^ 
 
 whence I2 = ir (Ri^ + X)^. 
 
 Substituting for I2, we get 
 
 tan /3 = 
 
 7i (i2,2 + Xi2)>^ + ^ (i2,2 ^Xi^)!^ 
 
 This reduces to 
 
 tan fi = 
 
 72i -|- 7^2 
 
 But the angle of lag of current in the voltage circuit is given by 
 the relation 
 
 tan a = p- and if a is to equal /3 
 X Xi 
 
 Whence 72 
 
 R Ri + R2 
 RXi — XRi 
 
 X 
 
 In practice, 72 is large, being about 1,200 ohms, while Ri, X, and 
 Xi are comparatively small. Hence, it is evident that R2 will 
 be large and that only a small per cent, of the line current will 
 pass through the shunt. No account is taken of the capacity 
 of the armature, since the inductance usually predominates. 
 Likewise, the effect of mutual inductance of the coils is so small 
 that in practice it is negligible. 
 
 171. Three-wire Direct-current Meters. — For measuring 
 energy on three-wire direct-current circuits, one three-wire, or 
 two two-wire meters may be used. A three-wire meter differs 
 very little from a two-wire meter in construction, and in principle 
 
190 
 
 ELECTRICAL METERS 
 
 of operation not at all. In meters intended for three-wire cir- 
 cuits the two series coils are distinct; the ends of each being 
 brought out to terminals which, when in service, are connected 
 to the load circuits as indicated in Fig. 150. The voltage coil 
 may be connected across mains 1 and 3, or between either 1 or 3 
 and neutral 2. 
 
 When the connection is as indicated in Fig. 150, the torque 
 exerted upon the armature is equal to the sum of the torques 
 exerted by coils A and B separately. When the voltage between 
 mains 1 and 2 equals that between mains 2 and 3, the torque 
 exerted by coil A is 
 
 Ti = KJiE 
 
 Shunr 
 
 I 
 
 2 
 3 
 Pig. 150. 
 
 and the torque exerted by coil B is 
 
 T2 = K2I2E. 
 
 Since the two current coils for accurate registration should exert 
 the same torque under like conditions, Ki = K2 and the total 
 torque equals 
 
 r = Ti + Ta = K{h + U)E 
 
 which is evidently proportional to the load. 
 
 If, however, the load is unbalanced to such an extent that the 
 voltages are no longer equal, then the torques cease to have the 
 
WATT-HOUR METERS 191 
 
 same ratio to the load. Let Ei, E2, /i and h represent the vol- 
 tages and currents on the two sides. The total load is then 
 
 W = EJi + E-J-, 
 
 The pressure current is, however, due to Ei only, hence the meter 
 registration is equal to 
 
 TFi = (/i + U)Ei 
 
 The difference between W and Wi is the error. This is 
 
 W -Wi = EJi + E2I2 - E2I1 - EJi 
 = IiiEi — E2) 
 
 This is zero only when Ei = E^. When Ei is greater than E^, the 
 meter is slow, and when E^. is greater than Ei, the meter is fast. 
 This error may or may not be appreciable, depending upon the 
 degree of unbalancing. 
 
 When the voltage coil is connected across outside mains, that 
 is, 1 and 3, Fig. 150, the error on unbalanced load will always 
 be of the same sign. Under the previously assumed condition 
 the load is again 
 
 W = £'i7i + E2I2 
 
 but the registration of meter is 
 
 W = yiEih + h) 
 
 where E is the voltage between mains 1 and 3. 
 
 But E = E1 + E2 
 
 hence TFi = M(^i + E2)ili + h) 
 
 and error is 
 
 W -Wi = Eih + E2I2 - }iEiIi - HEJi - YiEJ^ - YiEili 
 = M(^i - E2){Ii - 1 2) 
 
 which is zero only when Ex = E2 or 7i = I2. In general, on un- 
 balanced load the meter will register too high, for when 7i is 
 greater than 1 2, Ex is less than E2 and W — Wi'is negative; also 
 when I2 is greater than Zi, E2 is less than Ei and again W — Wi 
 is negative, that is, the registration is higher than the energy 
 supplied. 
 
 It must also be noted that on unbalanced load the error is in 
 general greater when the voltage coil is connected between neutral 
 
192 ELECTRICAL METERS 
 
 and one outside wire than when it is connected between the two 
 outside wires. 
 
 On circuits that are subject to considerable unbalancing it is 
 preferable to use two-wire meters. 
 
 172. Mercury Watt-hour Meter. — The source, or cause of 
 many commutating type watt-hour meter troubles is the com- 
 mutator. The chief objections to the commutator are: friction 
 of brushes, sparking at brushes when commutator becomes oily 
 or dirty, change in speed due to an improper position of the 
 brushes and additional weight of moving element. Many 
 attempts have been made to lessen the influence of these troubles, 
 but the most radical procedure has been the development of a 
 watt-hour meter which eliminates the commutator entirely. 
 
 The principle of operation of the mercury integrating meter 
 was discovered in 1823 by Barlow. Fig. 151 is a diagram of the 
 
 Fig. 151. 
 
 operating parts of Barlow's invention. As the reader will 
 observe, this consisted of a copper disk D mounted on a horizontal 
 axis so as to rotate freely between the poles of a permanent 
 magnet. When current is passed into the disk through the axle 
 and out at the circumference, the reaction between the current 
 in disk and the permanent-magnet field develops a torque, which 
 causes the disk to rotate in the direction of the arrow head. The 
 rotation is in such a direction as to carry the current out of the 
 magnetic field. This torque will vary with the current strength, 
 for, as has already been shown, the torque is proportional to prod- 
 uct of current strength and field. The field being constant, 
 the torque must vary with the current. 
 
 The adaptation of this principle to integrating meters will be 
 readily understood by reference to Figs. 152, 153 and 154 which 
 show the essential characteristics of the Sangamo direct-current 
 
WATT-HOUR METERS 
 
 193 
 
 iDBulation Around 
 Upper Bearing 
 
 Olamp '. 
 
 MognetHolding Ear 
 
 f oJe Plate 
 
 Fig. 152. 
 
 Pig. 153.. 
 
 Fig. 154. 
 
194 ELECTRICAL METERS 
 
 watt-hour meter. Fig. 152 shows a cross-section of the motor ele- 
 ment with the principal parts designated. The rotating element, 
 or armature, is the copper disk submerged in the mercury. Sur- 
 mounting the disk is a hardwood float whose weight is adjusted 
 so that the buoyant effect of the mercury will relieve the lower 
 bearing of the weight of the entire moving system. By careful 
 adjustment the downward pressure has been entirely ehminated 
 and a small upward thrust has been produced. 
 
 The mercury chamber of the meter is made of insulating 
 material into which have been imbedded two nickel-plated 
 copper terminals and a laminated steel ring. The copper termi- 
 nals serve to lead current into and out of the mercury chamber, 
 and the steel ring reduces the reluctance of the magnetic circuit, 
 thus compelling the magnetic lines to pass through the armature 
 disk. 
 
 173. Operation.— A simplified diagram of the connections and 
 wiring of the meter is shown in Figs. 153 and 154. The current 
 enters the meter at the terminal Ti, passes through the heavy 
 conductor and through copper lug Ei into the mercury and arma- 
 ture disk A ; it leaves the armature disk through the mercury to 
 lug E2, thence through heavy copper conductor to terminal T2 
 and back to hne. The voltage circuit consists of the fine winding 
 surrounding the magnet core Y, and a resistance coil R'. The 
 current in this circuit develops a magnetic field between the ends 
 of core Y and the return steel plate. Fig. 152. The intensity of 
 this field is proportional to the current in coil SC and hence, to 
 the voltage across the main line. The torque on the armature 
 is proportional to the product of armature current and magnetic 
 field, and hence to power, which is the condition necessary for 
 watt-hour meters. This torque is, however, very low, being only 
 about 2 cm.-grams when 5 amp. are flowing through the disk. 
 This low torque is due to the fact that the armature may be con- 
 sidered as consisting of only one turn. Since the pressure of the 
 movable element has been relieved, and the friction reduced to a 
 minimum, a very high torque is not absolutely necessary. It is 
 not practicable to pass more than 10 amp. through the mercury 
 and disk, and hence shunts are used on all meters above 10 amp. 
 capacity. 
 
 The counter-torque is obtained by the aluminum disk D rotat- 
 ing between poles of permanent magnets M exactly as in all 
 motor watt-hour meters. 
 
WATT-HOUR METERS 195 
 
 174. Compensation for Friction. — ^Light-load compensation is 
 secured by sending, in the proper direction, through the mercury 
 chamber a current from a thermocouple. The thermocouple 
 consists of two strips' of dissimilar metal terminating in slotted 
 ends held by screws B and C, Fig. 155. The couple is energized 
 by the coil A which is connected in series with the voltage coil 
 as shown by H in Figs. 153 and 154. The thermocouple is 
 shunted by a variable resistance G, Fig. 155, and the degree of 
 compensation can be varied by changing the position of the slid- 
 ing clamp E. Recently an improvement has been made so that 
 either positive or negative compensation may be obtained. This 
 reversal of compensation is secured by changing the thermocouple 
 connections from under screws B and C to screws C and D. 
 Another modification in construction allows a compensation so 
 that the meter has a range from about 5 per cent slow to 10 
 per cent fast on 10 per cent of full load. This is secured by 
 connecting one end of the thermocouple to a point somewhat 
 remote from the left-end bracket. This point of connection 
 becomes the zero point of adjustment, so that when the clamp 
 is moved to this position there is no compensating effect. When 
 the clamp is moved to the right the desired starting effect may be 
 obtained, but if the meter shows a tendency to creep on light load 
 with the clamp at the zero position, this tendency can be 
 eliminated by moving the clamp slightly to the left. 
 
 The load current through the mercury chamber has a tendency 
 to demagnetize the field magnet. To overcome this, but primarily 
 to compensate for fluid friction on the movable element which 
 increases with load, the load current is passed around the magnet 
 core. As the load increases the demagnetizing and compensating 
 actions increase together. 
 
 These meters are now made for both two- and three-wire 
 circuits. Fig. 154 shows the connections for the three-wire 
 instrument. 
 
 175. Full-load Adjustment. — One other difference between the 
 Sangamo mercury watt-hour meter and the other makes of watt- 
 hour meters is worthy of mention. The retarding effect of the 
 permanent magnets is varied by shunting some of the magnetism 
 through the soft-iron disk, instead of moving the magnets nearer 
 to, or farther from the axis of the disk. The soft-iron disk is 
 threaded and may be screwed up or down, thus changing the 
 reluctance of the magnetic circuit. If the disk is screwed down, 
 
196 ELECTRICAL METERS 
 
 some of the magnetism passes from one magnet through the 
 magnetic shunt to the other, thus weakening that which passes 
 through the copper disk. Under these conditions the meter 
 will run faster. 
 
 176. Induction-type Watt-hour Meters. — Some of the dis- 
 advantages of the electrodynamometer type of watt-hour meter 
 for use on alternating-current circuits have already been men- 
 tioned. The advantages of the induction type of watt-hour 
 meter have relegated the electrodynamometer type to direct- 
 current circuits almost exclusively, and hence, the two types are 
 sometimes classifiod as direct-current and alternating-current 
 watt-hour meters. 
 
 The fundamental advantage of the induction-type watt-hour 
 meter is the absence of commutator, and in fact of all sliding 
 
 Fig. 155. 
 
 electrical contacts. The electrical circuits are all stationary, 
 hence the movable element consists merely of a shaft and disk. 
 The disk performs the functions of both the armature and retard- 
 ing disk in the other type. This great reduction of the number 
 of parts greatly decreases the weight of the movable element, 
 and consequently diminishes the bearing friction and jewel wear. 
 The fact that all windings are stationary permits a much more 
 rugged and cheaper construction, eliminates commutator troubles, 
 decreases the friction, and greatly improves the accuracy of the 
 meter over long periods of time. The induction-type meter 
 can, however, be used on alternating-current circuits only. Fig. 
 156 shows the parts of a General Electric induction-type single- 
 phase watt-hour meter. The essential operating parts are a 
 stationary element comprising the electric and magnetic cir- 
 
WATT-HOUR METERS 
 
 197 
 
 cuits, the rotatable disk, the registering mechanism, and retarding 
 magnets. 
 
 177. Operation. — These meters operate upon the principle of 
 the revolving magnetic field already explained in connection 
 
 t^ 
 
 with the induction-type wattmeters. Although exactly the 
 same general principles apply in the two cases, nevertheless they 
 are applied in a somewhat modified way and hence a more ex- 
 tended discussion is justified. To make clear these principles 
 there is given in Fig. 157 a simphfied diagram of the driving and 
 
198 
 
 ELECTRICAL METERS 
 
 revolving parts. The element consists of two magnetic circuits, 
 M and M', which are built up of laminated steel punchings. 
 Core M carries the voltage coil P and lag coil L. The series 
 coils CC are wound upon the two projections of M'. Imme- 
 
 „ Liqht load 
 
 Pig. 157. 
 
 diately below the central prong of M is a copper stamping F 
 known as the light-load clip. The disk is shown in position 
 between the central prong of M and upward projecting parts of 
 M'; mm are the retarding magnets. 
 
 Pig. 158. 
 
 Fig. 158 shows the distribution of the magnetic lines around 
 the two cores of the series coils. It is very evident that the end 
 of one of these cores is a north pole whiie the other is a south 
 
WATT-HOUR METERS 
 
 199 
 
 pole. The distribution of the magnetic lines due to voltage coil 
 is shown in Fig. 159. It will be seen that these lines radiate in 
 all directions, chiefly to the right and left, some, however, 
 passing downward. 
 
 Pig. 159 
 
 These figures were obtained by sprinkling iron filings upon 
 sensitized paper, which was laid flat upon the stationary element 
 of the meter, while direct current was passed successively through 
 
 Magnetic Irnes,^ 
 
 Fig. 160. 
 
 the series and voltage coils. The figures thus do not accurately 
 show the field within the air gaps, but outside of the cores as the 
 iron filings shunt the magnetic lines. Illustrative diagrams of the 
 distribution of the magnetic lines between the cores correspond- 
 
200 
 
 ELECTRICAL METERS 
 
 ing to Figs. 158 and 159 are shown in Figs. 160, 161, and 164. 
 Fig. 162 shows the relative position of voltage coil core, B, 
 
 Pig. 161. 
 
 series coil cores, A- A, and the disk. It is thus clear that when 
 direct current is used for excitation the lines due to the series 
 
 coil leave the end of one core and 
 enter the other while those due 
 to the voltage coil divide and pass 
 upward through the adjacent iron. 
 When alternating currents are 
 used for excitation, the resultant 
 fields are similar to those pro- 
 duced by direct currents, but, 
 owing to the fact that they are 
 due to alternating currents, they 
 shift either in one direction or the 
 other. 
 
 The coil P, Fig. 157, consists of 
 many turns of fine wire, the coil is highly inductive, and the 
 current flowing in it is almost one-quarter of a period behind 
 the voltage across its terminals. On the other hand, the coils 
 
WATT-HOUR METERS 
 
 201 
 
 CC are nearly non-inductive and the current in them is in 
 phase with the voltage, when the load power-factor is unity. 
 The phase relation of these quantities is shown in Fig. 163. 
 This figure is a tracing of an oscillogram, and curve I represents 
 the series current, E the applied voltage, and i the voltage coil 
 current. It is very evident that although the line voltage and 
 current are in . phase, the voltage coil current lags only about 
 72° behind the voltage. The important thing is that the vol- 
 tage-coil flux and series-coil flux should be in quadrature, and 
 not that the currents should be. How this is secured will be 
 shown later. 
 
 178. Shifting Magnetic Field. — Giving attention to the char- 
 acter and distribution of the magnetic fields only when at their 
 
 3 
 
 FiQ. 164. 
 
 maximum values, it can be shown that the resultant field shifts 
 with reference to the disk, as the currents in the pressure and 
 series circuits fluctuate. 
 
 For the time being, assuming a phase difference of one-quarter 
 of a period between series and voltage currents, at the instant 
 the series current has reached a positive maximum value, the 
 voltage current is zero. At this instant the polarities of the iron 
 cores will be as indicated at A, Fig. 164. 
 
 Considering a north pole -1- and a south pole — , the polarity 
 of 1 is 0; of 2 it is -|- ; of 3 it is zero; of 4 it is — ; and of 5 it is 0. 
 
 21 
 
202 
 
 ELECTRICAL METERS 
 
 A quarter of a period later, the current in the series coils has 
 fallen to zero and that in the voltage coil is a maximum. The 
 polarity of the cores at this instant is indicated in B, Fig. 164. 
 In the same way C shows the direction of flow of magnetic lines 
 at the end of half a cycle and D at the end of three-quarters of a 
 cycle. Arranging a table to show the magnetic condition of 
 cores 2, 3, and 4 at the given instants, we get the following: 
 
 Table II. 
 
 
 Poles 
 
 lnstanl-s 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5+art 
 
 
 
 X 
 
 
 
 - 
 
 )i period 
 
 - 
 
 
 
 \ 
 
 
 
 >2 " 
 
 
 
 - 
 
 
 
 X 
 
 % " 
 
 + 
 
 
 
 - 
 
 
 
 End cff period 
 
 
 
 + 
 
 
 
 - 
 
 Shunt elemenr 
 
 Fig. 165. 
 
 An examination of Fig. 165 shows that, under the conditions 
 assumed, the polarity shifts continuously from left to right. 
 This, of course, is true of the other magnetic conditions. The 
 shifting of the magnetic field induces 
 currents in the disk, as already explained, 
 and the reaction between these currents 
 and magnetic field causes the disk to 
 rotate. 
 
 179. Practical Construction. — In Fig. 
 166 is shown the essential parts of the 
 magnetic circuit of the Westinghouse 
 single-phase induction meter. This 
 shows that the construction differs very 
 little from that of the General Electric 
 meter. The principles of operation are 
 exactly alike in the two instruments. The complete Westing- 
 house type C meter with case removed is shown in Fig. 167. 
 It is very evident that the meter is very compact and rugged. 
 Type Ki induction meter of the Fort Wayne Electric Works 
 applies the same principles in a somewhat modified manner. The 
 
 series 
 elemeriT 
 
 Pig. 166. 
 
WATT-HOUR METERS 
 
 203 
 
 relative position of the series and voltage coils is shown in Fig. 
 168. In actual construction, in the earlier instruments the coils 
 
 Series 
 Coils v 
 
 lOP BEARIhJG 
 
 Screw 
 
 Registering 
 Mechanism 
 
 i Disk, 
 
 Power FACTOf, 
 Adjustment 
 
 Light Load. 
 
 Adjustmei-jt 
 
 Loops 
 
 Shunt 
 Coil 
 
 Retarding 
 /Magnet 
 
 Mou>iting 
 Frame 
 
 -^^. Magnet 
 Clamping 
 ScREvvsA 
 
 Laminated 
 Electro Hagnet 
 Core 
 
 Pig. 167. 
 
 Series coll 
 
 - Shurrt coil 
 
 Fic. 168. 
 
 had only air cores, but the coils of the later forms have laminated 
 iron cores, just as the other makes. In place of a disk, the rotat- 
 able element is an aluminum cylinder. The two figures, 169 and 
 
204 
 
 ELECTRICAL METERS 
 
 170, show clearly the actual construction of one form of this 
 instrument. Since the absorption of the Fort Wayne Electric 
 Co. by the General Electric Co. type Ki has been superseded 
 by the type K^ meter which is exactly the same as the General 
 Electric type 1-14 meters. 
 
 Fig. 169. 
 
 Fig. 170. 
 
 Yet another way of securing a rotating or shifting magnetic 
 field is shown in Fig. 171. The voltage element consists of a 
 pair of fine wire coils. Each of these coils is wound on a lami- 
 nated sheet-steel core of rectangular form as shown. The mag- 
 
 Poten+ial 
 element 
 
 <--Aluminum disk 
 Series elemen-f 
 
 Pig. 171. 
 
 netic circuit is very nearly all confined to the steel core, but at 
 the bottom, near the disk, is a narrow slot where some leakage 
 will naturally occur. This leakage flux must pass through the 
 disk. In doing so it sets up the desired eddy currents. 
 
WATT-HOUR METERS 
 
 205 
 
 The series coils are mounted on short laminated cores which 
 differ from the potential-circuit cores in not forming closed 
 magnetic circuits, but instead present exposed ends to the 
 aluminum disk. The series coils are placed below the disk but 
 displaced with reference to the pressure-circuit windings. A 
 complete view of the Columbia induction meter is shown in 
 Fig. 172. 
 
 180. Sangamo Induction Meter. — Since the expiration of the 
 Tesla patents, more companies have taken up the manufacture 
 
 SOLID MOLDED 
 
 INSULATION 
 TERMINAL BOX 
 SEPARATELY 
 PtRFECTLY SEALED. 
 
 CUSHIONED UPPER *^^ 
 
 BEARING STOPS ALL'- ''^ 
 
 RATTLING NOISE, 'v ■» 
 
 MICROMETER LIGHT 
 LOAD ADJUSTERS. 
 CAN BE WORKED . 
 DIFFERENTIALLY. 
 
 DIRECT READING 
 ASSOCIATION DIAL, 
 
 FLY DRIVEN. INTER- 
 CHANGEABLE WITH 
 
 CYCLOMETER 01AU. 
 
 COMBINATION 
 MOTOR AND DAMP- 
 ER DISC OF RIGID, 
 5TIPLED ALUMINUM. 
 
 JEWEL BEARING 
 
 INSTANTLY REMOV. 
 
 ABLE WITHOUT USE 
 
 OF ANY TOOLS- 
 
 INDUCTIVE LOAD 
 COMPENSATION, 
 EFFECTIVE TO 
 iBELOW 25 = I» POWER 
 FACTOR- 
 ADJUSTMENT 
 INSTANTLY CHANGE- 
 ABLE FROM HIGH TO 
 ORDINARY 
 ' FREQUENCY WITH. 
 OUT NECESSITATING 
 RECHECKING. 
 
 ONE-PIECE MAIN 
 
 SUPPORTING GRID 
 
 GIVES THREE POINT 
 
 ■' SUSPENSION ON 
 
 BASE, 
 
 EFFICIENT MOTOR 
 
 ELEMENT GIVES 
 TORQUE OF HIGH 
 - TORQUE METER 
 WITH ENERGY CON- 
 SUMPTION OF LOW 
 TORQUE METERS. 
 
 SHORT STIFF SHAFT 
 WITH INTEGRAL 
 
 WORM. PIVOT 
 
 FRICTION CLAMP 
 
 ATTACHED, 
 
 IMPORTED STEEL 
 DAMPER MAGNETS 
 
 SOLIDLY 
 SUPPORTED. 
 
 SEAMLESS DRAWN 
 
 STEEL BASE LIGHT 
 
 . AND OF MAXIMUM 
 
 STRENGTH. 
 
 Pig. 172. 
 
 of the induction-type watt-hour meters. The front of the San 
 game single-phase meter with cover removed is shown in Fig. 
 173, and the back of the meter is shown in Fig. 174. 
 
 The operating principle is exactly the same as that already 
 described, but there are some details of construction which 
 distinguish it from the meters of other companies. A front view 
 of the polyphase meter is shown in Fig. 175. 
 
 181. Balance of Elements. — An interesting feature of the 
 Sangamo polyphase meter is the provision for equalizing the 
 torque of the two elements. This equalizing device consists of 
 
206 
 
 ELECTRICAL METERS 
 
 a plate carrying the two scries yokes and coils, arranged so that 
 it may be clamped to the base of the meter by two screws. In 
 the center of the plate is an eccentric stud or screw accessible 
 from the front. Rotation of this stud will cause the plate carry- 
 ing the two yokes to move up or down through a short distance, 
 thus changing the air gaps of the two series magnets until equahty 
 of torque between the two elements is obtained. 
 
 Full Load 
 Adjustment 
 Clamp Screw 
 
 Binding Post- 
 Terminal Box 
 
 Terminal Box 
 Cover 
 
 Type and Number Plate 
 
 Line Wire Bushmgs 
 
 Fio. 173. 
 
 Base 
 
 Recording Train' 
 or Register 
 
 Main Grid" 
 Magnet Clamp 
 
 Micrometer 
 Light Load 
 Adjustment 
 
 Light Load 
 
 Adjustment 
 
 Clamp Screw- 
 
 Lower Bearing 
 Screw 
 
 lealing Lug 
 Sealing Screw 
 
 182. Duncan Induction Watt-hour Meter. — In so far as prin- 
 ciples of operation are concerned, the Duncan meter is the same 
 as those already described. A front view of this meter with 
 cover and dial removed is shown in Fig. 176, and the construction 
 of the series and potential elements is shown in Fig. 177. 
 
 There are some interesting construction features which dis- 
 tinguish this meter from other makes. Thus only one retarding 
 magnet is used, and it is mounted in such a manner that both 
 poles are above the disk. Directly below the poles of the magnet 
 and disk is placed a screw with a large flat head, Fig. 176. 
 
WATT-HOUR METERS 
 
 207 
 
 The head of the screw serves as a magnetic shunt. Some of the 
 magnetic flux passes from one pole of the magnet through the 
 disk to the head of the screw and then through the disk to the 
 opposite pole. To make adjustment for full-load retarding 
 torque, the screw is turned up or down. As it is brought closer 
 to the poles of the permanent magnet, the reluctance of the 
 bypass is decreased and more flux passes through the disk, and 
 
 6t>-2^p 
 
 Fig. 174. 
 
 the retarding torque is consequently increased. The opposite 
 movement of the screw will result in a decreased retarding torque. 
 The light-load compensating device is very similar to those 
 already explained. 
 
 The quarter-phasing or lagging device consists of a heavy 
 one-piece die-made copper plate. By moving this up or down, 
 as required, the proper adjustment is secured. 
 
208 
 
 ELECTRICAL METERS 
 
 183. Full-load Adjustment. — The fundamental principles of 
 
 operation of these various makes of induction meters are all the 
 same. Similarly the full-load adjustment is performed by vary- 
 ing the retarding effect of the permanent magnets. This, in 
 general, is accomplished in two ways, either by changing the 
 position of the magnets with reference to the shaft, or by shunting 
 some of the magnetism. 
 
 The full-load speed of the General Electric and Westinghouse 
 meters is adjusted by moving the permanent magnets either 
 away from, or nearer to, the shaft as the case demands. 
 
 Grid 
 
 Shaft 
 
 Adjustable 
 
 Plate (or 
 
 Balancing 
 
 Element 
 
 Permanent T/lagnet 
 Lower Shunt Magnei 
 
 Connection Box 
 Main Load Adjustment 
 
 Fig. 175. 
 
 The retarding torque is proportional to the product of eddy 
 currents and strength of magnetic field. The eddy currents are 
 proportional to the magnetic field strength and speed of disk, 
 hence the torque is proportional to the product of the square of 
 the magnetic field and speed of disk. Mathematically this can 
 be expressed by T" = k^hw where $ is the flux, r is the mean 
 radial distance from the shaft of the disk to the poles, co is the 
 angular speed, and k a proportionality constant. 
 
 If the magnet is moved outward, the distance r is increased 
 and, hence, the speed must decrease if the torque is to remain 
 
WATT-HOUR METERS 
 
 209 
 
 SUPPORTiriG LUG 
 
 ij- ItirnjCTlVI^. LOAti 
 AQJUSTMENT 
 C L AMP SC^^t^^ 
 
 MlCnQMtTf-"ft 
 PULL LOAD 
 AOJUSTMtM r 
 
 F-FULL LOAD 
 
 CLAMP SCHt-:w 
 
 SvvlriciNG COVER. OF 
 Tkrmimal chamber 
 
 5 f- A L 1 H G LUG 
 
 Pig. 176. 
 
 FiQ. 177. 
 
210 ELECTRICAL METERS 
 
 constant. If the speed does not decrease, the retarding torque 
 increases in proportion to r. 
 
 If the disk is replaced by a cylindrical cup, as in the older Fort 
 Wayne meter, moving the magnets up or down does not change 
 the radial distance. In this case a change in retarding torque is 
 secured by changing the flux that passes through the aluminum, 
 cylinder. By moving the magnets down beyond a certain point, 
 some of the magnetic lines pass below the edge of the cylinder 
 and have no effect in inducing eddy currents. Under this 
 condition, the retarding torque is less and the meter runs faster. 
 Moving the magnets upward will obviously have the opposite 
 effect. 
 
 A change in torque may also be secured by providing for the 
 magnetic lines a bypass or magnetic shunt, whose reluctance 
 may be varied. This is the method used on the Sangamo meters 
 and the Duncan induction-type meter. An adjustable armature 
 bridges the gap between the poles of the magnets, and a change 
 in the position of this armature with reference to the magnet poles 
 diverts a greater or smaller part of the flux around the disk. 
 
 184. Relation between Torque and Power.-^According to the 
 principles just explained, an expression may readily be derived 
 for the driving torque. For, if we represent the mean of the 
 eddy currents by /, and the average flux by $, the driving force 
 at a given position of retarding magnets is given by 
 
 T = MI. 
 
 But the eddy currents are proportional to the product of flux 
 and relative speed of magnetic field and disk. Since r is a con- 
 stant quantity, the driving torque in general is then given by 
 
 T = k"^^i>3r where oir is the relative speed. But in 
 
 Chapter VI it was shown that $ is the equivalent of two magnetic 
 fields rotating in opposite directions at the same angular speed. 
 If then in Fig. 46, OFi and OF represent *i and #2, the two 
 opposite torques due to these rotating fields are 
 
 Tl = fcl*l2 (wi -I- co) 
 
 and Ti = fci4>2^ (wi — u). 
 
 Where wi is the angular speed of rotating fluxes and is equal to 
 2irf, u is the angular speed of disk. 
 
WATT-HOUR METERS 211 
 
 The retarding torque due to the permanent magnets when at 
 a fixed distance from the shaft is likewise given by 
 
 Ts = ki^z^cj} 
 
 where $3 represents the flux of the permanent magnets. 
 
 The retarding torque, due to the permanent magnets, is in 
 the same direction as Ti, hence Ti + T3 retard the disk, while 
 T2 drives it. When constant speed has been reached, the 
 algebraic sum of these torques must be zero, or 
 
 T2= Ti + T,. 
 
 That is, hi<^i^{o3i — w) = fci$i^ (wi + w) + fca^s^w. 
 
 Reducing we get A;i($2^ — ^i'') wi = fci ($2*^ + $1^) w + fca^s'to. 
 
 But #22 = H,^ + i?2^ + 2HJIi sin Bo 
 
 and *i2 = Hi" + Hi" - 2HJIi sin ^o (see Art. 73). 
 
 Hence $2^ — ^i^ = 4:H\Hi sin Bn 
 
 and ^i" + $i2 = 2(ffi2 + Hi"). 
 
 Therefore, ikiHiH^ui sin do = 2fci {Hi^ + Hi^) ca + /ba^s^ co. 
 0)1 is equal to 2irf, and for any given frequency is constant. Re- 
 placing Sirki by if 1, we get, 
 
 KifHiHi sin So = 2fcico(ifi2+fl'22)-f /ba^s'u. 
 
 The term KifHiH^ sin 9o represents the driving torque, and the 
 two right-hand members represent the retarding torque. The 
 term 2kiu {Hi} -f H2'') represents the retarding effect of the 
 rotating fields, and kz^^^oi is the retarding effect of permanent 
 magnets. When w is low, the effect of 2ki {Hi^ + Hi') w is 
 negligible and the retarding effect is wholly due to Ka^a^'co. 
 Under this condition the relation between driving and retarding 
 torque is 
 
 KifHiHi sin do = ks^z^co 
 
 Now Hi is proportional to the voltage, and H2 is proportional 
 to the series current. We may then write 
 
 Hi = k'E 
 and H2 = k"I, which, substituted in the above equation, 
 
 give Kik'k"fEI sin do = kg^z^u 
 
 or EI sin do = Ko^z^co, 
 
 where Ko = ^^^ 
 
212 ELECTRICAL METERS 
 
 That is, the product of current, pressure, and sine of phase dif- 
 ference between the magnetic field due to series and voltage 
 currents respectively is proportional to the speed of the disk. 
 The actual power is, however, equal to EI cos 6, hence if the 
 meter is to register accurately 
 
 sin ^0 = cos 6 
 
 or do = ^± e. 
 
 For correct registration, it is thus imperative that the phase 
 difference between the two magnetic fields be exactly one- 
 quarter of a period when the power-factor of load is unity. 
 
 If 2ki {Hr' + H2^)ui is not negligible in comparison with ka^i^o}, 
 the calibration curve of the meter will not be a straight line. 
 If the meter is correct on light load, it will be slow on full or over- 
 load, and vice versa. On any given voltage and frequency, Hi^ is 
 constant; the inaccuracy in registration is then due to Hi^co, and 
 in order that this may be negligible both H^ and co must be small. 
 This is taken care of in the design of the meter. 
 
 185. Lagging Induction Watt-hour Meters. — As has just been 
 demonstrated, for accurate registration on circuits of low power- 
 factor, the flux due to the pressure coil must be one-quarter of a 
 period out of phase with the flux due to the series current when 
 operating on circuits whose power-factor is unity. Mainly on 
 account of the resistance, eddy currents, and hysteresis of the 
 voltage circuit, this phase difference is not obtained without 
 additional adjustment. 
 
 The methods of lagging used by the General Electric Co. and 
 the Westinghouse Co. are identical in principle. The manner 
 in which this is carried out in practice is shown in Figs. 157 and 
 167. Coil L, Fig. 157, is known as the lag coil, and consists of 
 a few turns of a high-resistance wire wound around the end 
 of the voltage-coil core. A similar coil is shown in Fig. 167 
 where it is labelled "power-factor adjustment." The function 
 and operation of the lag coil is explained in Article 116. As 
 there pointed out, part of the flux due to the voltage coil, passes 
 through the lag coil. The resistance of the lag coil is adjusted, 
 until the phase displacement of the resultant flux is exactly 
 90° in time phase from the flux due to the current coils. The 
 greater part of the pressure-coil flux does not pass through the 
 lag coil, but takes the shorter path as indicated in Fig. 161. 
 
WATT-HOUR METERS 213 
 
 This fact is not shown clearly in Fig. 159, for in that case direct 
 current was used for excitation and the inductance of lag coil 
 had no effect. 
 
 186. The Effect of Over and Underlagging. — The driving 
 torque of an induction meter is given by 
 
 T = KkifoHiHi sin 9o where Hi and H^ are the maximum 
 values of the voltage and current fields respectively, and 6o is 
 the time-phase difference between them. The power in the 
 load circuit is, however, given by 
 
 P = EI cos e. 
 In order that the torque may be proportional to power, Ba must 
 be equal to ^ + ^- In case this relation does not exist, the 
 torque will be either too large or too small and the registration 
 will be in error. For instance, suppose do = -r + a + d, ov that 
 
 the meter is overlagged. Then sin 0o = sin ^ + (" ± ^) = cos 
 
 (a + 6) and the dri-dng torque will be given by T = K'EI cos 
 (a + e). 
 
 When Q is positive, or the current leads the pressure, cos (a + 6) 
 is less than cos 6 and the torque is too small. When 8 is an angle 
 of lag, cos {a — 6) is greater than cos 9, and the torque is too large. 
 Thus, an overlagged meter will under register on leading current, 
 and over register on lagging current. 
 
 It can easily be shown that when the meter is underlagged oi 
 
 TT 
 
 when do = ^ — a ± 6, the meter will be slow on lagging and fast 
 
 on leading current. The demonstration is left for the student. 
 
 187. Light-load Compensation. — Exactly as in the electro- 
 dynamometer type and other types of watt-hour meters, for 
 accurate registration on light load, some means must be provided 
 for overcoming the retarding torque due to friction. Owing to 
 the absence of brushes, and to the fact that the movable elements 
 of induction-type watt-hour meters are much lighter, and have 
 a higher torque per unit weight than commutator meters, there 
 is much less necessity for friction compensation. 
 
 When compensating devices are used, they are operated by the 
 voltage circuit as in other types of watt-hour meters. The 
 compensation remains constant at all loads with a given adjust- 
 ment; it may, however, change with the voltage or frequency. 
 
214 ELECTRICAL METERS 
 
 The general principles upon which the various compensating 
 devices of different makers operate are fundamentally the same 
 although the methods of applying these principles differ con- 
 siderably. The fundamental principle consists in the production 
 of an unbalanced or shifting magnetic field. The compensating 
 device operates so that at any instant the magnetic flux is not 
 uniformly distributed over the pole face of the voltage-coil core. 
 The variation in the distribution of the magnetic flux produces 
 the same effect as a shifting field. 
 
 This non-uniformity in flux distribution may be produced 
 by interposing within the air gap a short-circuited conductor, 
 or by modifying the voltage-coil core in such a way that the flux 
 density will vary in time from one side of the pole face to the 
 other. 
 
 The former method is made use of by the Westinghouse, Gen- 
 eral Electric, Sangamo, and Duncan companies. Fig. 167 shows 
 how this method is applied by the Westinghouse Co. 
 
 As here shown, the light-load compensation is secured by means 
 of two "light-load adjustment loops" which are in reality 
 two copper punchings forming a closed electrical circuit. One 
 side of each loop is in the air gap of the voltage-coil core, and the 
 whole loop is mounted in such a way that it may be turned 
 through a small angle, thus changing its position with reference 
 to the magnet core. This adjustment is accomplished by means 
 of two knurled nuts which are accessible from the front of the 
 meter but not shown in the figure. 
 
 It is clearly shown in Fig. 167 that turning either of these 
 loops down or up permits more or less of the magnetic flux to pass 
 through the loop. This flux as it passes through the loop induces 
 a current therein, and the reaction of this current upon the flux 
 retards its development when increasing, and vice versa. This 
 retardation unbalances the main flux, and produces the same 
 effect as a shifting field. The result is the development of a 
 torque whose value is modified by any change in the position of 
 the short-circuited loop. By carefully adjusting the position of 
 these loops, a torque just sufficient to overcome the retarding 
 torque of friction may be secured. 
 
 A similar method is employed by the General Electric Co., 
 as is evident from Fig. 157. As shown, the light-load compensa- 
 tor F consists of a rectangular copper punching, which is placed 
 under the central prong of the voltage coil core. If this punching 
 
WATT-HOUR METERS 
 
 215 
 
 is not symmetrically placed with reference to the core, the flux 
 through the disk will vary in intensity from one side to the other. 
 
 133 cycle 
 lagging 
 
 resistance 
 
 Reac+ance 
 coil 
 
 m ,60 cycle 
 
 IW" "egging 
 
 resistance 
 
 Open for 133 cycles 
 Closed -for 60 cycles 
 
 Fig. 178. 
 
 This variation, or one may say shifting of flux, will produce 
 enough torque to overcome that due to friction. 
 
 Light-load compensation of the Sangamo induction watt-hour 
 meter is also secured by means of a copper punching within the 
 
216 
 
 ELECTRICAL METERS 
 
 field of the potential coil. This punching is mounted on a staff 
 carried by a brass bracket which is fastened by screws to the 
 back of the grid or frame. To the lower end of the staff is riveted 
 a sector which meshes with a worm screw the head of which is 
 accessible from the front. By turning the screw, the punching 
 is caused to shift within the magnetic field. The amount of the 
 shifting is indicated by a scale on the head of the screw. Close 
 compensation can thus be obtained. 
 
 The second method of applying the general principle is exem- 
 plified in the meter whose connections are shown in Fig. 178, and 
 the induction meter of the Columbia Meter Co. 
 
 In Fig. 178 is shown the auxiliary core (6) which is pivoted in 
 the middle. Loosening screw *Si and tightening Si moves the 
 end that is near the cylinder from left to right. Such a change 
 in the relative positions of the auxiliary and main cores causes a 
 shifting of the magnetic flux. 
 This shifting is similar to that 
 produced by the other com- 
 pensating methods. 
 
 188. Flux-shunting Method. 
 — In the older form of the 
 Columbia induction meter the 
 necessary unbalancing is ob- 
 tained by means of a piece of 
 soft iron adjustably bridging a 
 part of the air gap in the 
 voltage-coil core. The bridg- 
 ing piece of iron is held in 
 place by two screws passing 
 through a slot in the extension 
 arm which carries it. By 
 loosening these screws, the 
 of iron can be varied. In 
 
 Fig. 179. 
 
 position of the bridging piece 
 the more recent designs the 
 shunting of magnetic lines by means of a piece of iron 
 across the air gap is no longer used. The method employed is 
 shown in Fig. 179. As is evident from the figure, a specially 
 designed piece is mounted in an adjustable manner on top of each 
 voltage-coil core. The frame of the meter is made of non-magnetic 
 material and, hence, any leakage flux will follow the path of least 
 reluctance. The case of the meter is of magnetic material, and as 
 it comes near the back of the voltage-coil cores some leakage flux 
 
WATT-HOUR METERS 217 
 
 will pass through the case downward and enter the core again 
 from the bottom through the armature disk. "When the sliding 
 pieces of iron are symmetrically placed with reference to the 
 cores and case, the effect of the leakage flux from one core 
 balances the effect of the leakage flux of the other core. When, 
 however, the reluctance of the leakage-flux path is changed by 
 moving one of the sliding pieces nearer to or farther away from 
 the case, this balancing no longer exists, and the disk will be 
 caused to rotate. If the right-hand piece is nearer the case, the 
 disk rotates from left to right. If the other piece is near the 
 case, the disk rotates from right to left when the voltage circuit 
 alone is closed. Hence, by adjusting the positions of the two 
 sliding pieceSj any necessary degree of compensation can be 
 produced. 
 
 189. Influence of Frequency. — The current through the pres- 
 sure coil of a watt-hour meter is given by 
 
 j = I 
 
 where R is the resistance and X the inductive reactance of the 
 coil. The resistance R changes only with the temperature, the 
 effect of which will be discussed later; but X, which is equal to 
 27r/L, varies with frequency. Hence, I will increase with decrease 
 in frequency and decrease with increase of frequency. This 
 increase or decrease will cause a corresponding increase in the 
 voltage-coil flux, and as the torque is proportional to the product 
 of the maximum value of the voltage-coil and current-coil flux, 
 it will also vary. Again, the angle of lag of voltage-coil current 
 
 ■y O fT 
 
 may be obtained from the expression tan ^ = ^ = —5 — That 
 
 is, the tangent of the angle of lag varies as the frequency. Since 
 without great error, one may assume that the voltage-coil flux 
 is in phase with the voltage-coil current, it is evident that the 
 angle do, in the expression for torque, viz., T = K0H1H2 sin do, 
 depends upon the frequency. Any variation in frequency, thus, 
 produces two effects : first, increases or decreases the voltage-coil 
 flux; and, second, changes the phase relation of the two operat- 
 ing fluxes. 
 
 A decrease in the frequency increases the voltage-coil current, 
 but a lowering of the frequency decreases the value of do, pro- 
 ducing the same result as underlagging. It has been shown 
 that an underlagged meter tends to run slow on lagging cur- 
 22 
 
218 
 
 ELECTRICAL METERS 
 
 rent, hence the increase in torque, due to greater current, will 
 tend to compensate for the phase-difference error. On leading 
 current, however, the error will be increased. 
 
 Similarly, when the frequency increases, the voltage-coil current 
 increases, and the phase difference between the two operating 
 fluxes increases. The effect of the difference in phase is the same 
 as though the meter were overlagged. These two effects tend 
 to neutralize each other on inductive load, but are cumulative 
 when the load current leads the pressure. 
 
 This double effect will be more readily understood from the 
 vector diagram of Fig. 180. In this diagram OE represents 
 
 »E 
 
 Fia. 180. 
 
 both the magnitude and direction of the applied voltage and 
 
 0*1 = voltage-coil flux at normal frequency, 
 
 0$2 = voltage-coil flux at a frequency below normal, 
 
 0^3 = voltage-coil flux at a frequency above normal. 
 
 The corresponding lag-coil fluxes are given by 0$'i, 0^'^, and 
 0<I>'3. The meter is assumed to be properly lagged for normal 
 frequency, i.e., di is 90°. At low frequency the resultant flux 
 $'b makes an angle 62 with the voltage and this angle differs from 
 90° by the angle ai. The phase relations are thus the same as 
 though the meter were underlagged on normal frequency. 
 
 The resultant flux 0$"k, when frequency is above normal, 
 is out of phase by an angle ^3 = 90° -|- 0:2, and plainly the phase 
 effect is the same as though the meter were overlagged on 
 normal frequency. 
 
WATT-HOUR METERS 
 
 219 
 
 The effect of variations in frequency on the accuracy of the 
 meter is shown in Fig. 181. 
 
 The meter for which the curve is given was lagged for accurate 
 registration on 60 cycles. It is seen that there is a falling off 
 in accuracy both with increasing and decreasing frequency. 
 
 190. Double Lagging. — The foregoing discussion shows that 
 when meters are designed for two widely different frequencies, 
 some provisions must be made for changing the effect of the lag 
 coil. Such a device is called double lagging. A good example of 
 
 Fia. 181. 
 
 a double-lagged meter is the 60- or 133-cycle watt-hour meter of 
 the Fort Wayne Electrical Works. The internal connections of 
 this meter are shown in Fig. 178. 
 
 As shown, the voltage-coil core consists of two parts, a and 
 6; the main core (a) forms nearly a closed magnetic circuit, 
 while 6 is a laminated piece of rectangular cross-section pivoted 
 at P. This auxiliary core b is wound with an auxiliary coil, G, 
 which is conected in series with a resistance, H, and shunted 
 across a few turns of reactance coil, I. 
 
 The voltage coil consists of two parts: one D, which is wound 
 around cores a and b, and / which has a separate iron core. 
 The iron core of I forms a closed magnetic circuit and hence its 
 inductance is much higher than the inductance of D whose core 
 has an air gap. 
 
 The lag of voltage current is due to the influence of both coils, 
 but the magnetism developed by D alone is effective in causing 
 rotation of armature, and it alone must be in exact quadrature 
 with flux produced by coils C-C on the load of unity power-factor. 
 To compensate for any discrepancy in the quarter-phase relation 
 mentioned, there are provided two coils, E and G. On circuits of 
 low frequencies, both coils are operative while on circuits of high 
 frequency, coil E is opened and G alone is effective. In general, 
 a change in the frequency adjustment will affect the speed of the 
 
220 ELECTRICAL METERS 
 
 meter. This effect can be corrected by an adjustment of the 
 position of the permanent magnets when the meter is under 
 test. 
 
 191. Single-phase Watt-hour Meters on Polyphase Circuits. — 
 It will be shown later that to measure power on polyphase cir- 
 cuits, by means of single-phase instruments — with the exception 
 of the two-phase system — there are needed as many meters as 
 there are phases less one. That is, on a three-phase circuit two 
 meters are sufficient, and by properly connecting single-phase 
 meters to the polyphase circuits the energy will be equal to the 
 algebraic sum of the meter readings. 
 
 192. Three-wire Single-phase Induction Watt-hour Meters. — 
 The three-wire system of distribution is much more economical 
 than a two-wire system when any considerable amount of energy 
 is to be transmitted. To measure the energy, either two single- 
 phase two-wire meters or one three-wire meter may be used. 
 When discussing three-wire meters of the electrodynamometer 
 type, it was shown that the registration was correct only under 
 certain conditions. Somewhat the same limitations apply to 
 three-wire induction watt-hour meters, with the additional fact 
 that these limitations are complicated by the characteristics of 
 alternating currents. 
 
 The alternating-current three-wire meter differs very little in 
 construction from the two-wire instrument. Like the direct- 
 current three-wire meter the instrument contains two series or 
 current circuits and one voltage circuit. The series circuits are 
 connected, one in each of the outside lines, and the voltage circuit 
 may be connected either across the outside wires or between 
 neutral and either outside wire. Which method of voltage-coil 
 connection is used depends upon the design or make of instru- 
 ment. The former method is perhaps the most common for 
 reasons that will presently appear. 
 
 Assuming the meter to be correctly adjusted, the accuracy of 
 its registration will depend to a considerable extent upon the 
 character of the load and connection of voltage coil. The influ- 
 ence of these different conditions upon the accuracy of the meter 
 may then be considered under the following heads: 
 
 I. Voltage coil connected across outside wires. 
 
 1. Load balanced. 
 
 2. Load unbalanced. 
 
WATT-HOUR METERS 
 
 221 
 
 II. Voltage coil connected between neutral and one outside 
 wire. 
 
 1. Load balanced. 
 
 2. Load unbalanced. 
 
 193. Voltage Coil Connected Across Outside Wires. — Fig. 182 
 is a diagram of an unbalanced single-phase three- wire system. 
 Si and ;S2 represent the series coils and V represents the voltage 
 
 s, 
 
 
 FiG. 182. 
 
 coil of the watt-hour meter. The vector diagram of Fig. 183 
 shows the phase relations of currents and voltages as produced by 
 a most serious case of unbalancing. Very seldom would all the 
 conditions there assumed be met at once. 
 
 Fig. 183. 
 
 If Elm and Ez™ represent the maximum pressures across loads 
 Li and La, then Em will be the maximum pressure between wires 
 1 and 2. The current in load Li is assumed to lag 6 degrees 
 behind Eim, and 0i degrees behind Em. If /o represents the cur- 
 rent in middle wire 0, then 1 2 will represent maximum current 
 in load L2. This current lags 62 degrees behind E2m, and <t>a 
 
222 ELECTRICAL METERS 
 
 degrees behind E„, According to the notation assumed, the 
 instantaneous values of the electrical quantities involved are; 
 
 e = Em sin cot 
 ei = Eim sin (ut — ai) 
 62 = E2m sin (a)i + 0:2) 
 ?i = 7i sin {(nt — (j>i) 
 i% = 1 2 sin {(lit — (^2). 
 
 The instantaneous power being delivered to loads Li and L2 is 
 
 W = Cil'i + 62*2. 
 
 Since the meter is direct-reading, the proportionality factor is 
 taken care of by the calibration of the meter and is omitted. The 
 instantaneous torque on the disk when the meter is properly 
 adjusted is r = J^e(ii + H) 
 
 but e = ei + 62. 
 
 Hence, t = >^(ei + 62) (ii + u). 
 
 If T is equal to w, the registration will be correct. When this 
 is not the case, the error in registration will depend upon the dif- 
 ference between w and t. 
 
 Now w — T = eiH + e^ii — J^ (ei -|- e^) (ii + ij) 
 
 = /-iiieiii + e^ii) — {eiH + eiii)]. 
 But ei = i/im sin {wt — aC) 
 
 and fi = 1 1 sin (cof — <j>^. 
 
 Then eii'i = i^imi^i sin (coi — ai) sin (w< — <^i) 
 
 Expanding sin (oji — on) and sin {oit — <^i) we get, 
 
 ei*i = ^im/i[(sin coi cos ai — cos oit sin o!i)(sin oit cos </>! — cos u>t 
 
 sin <^i)] 
 and the average of eii\ equals the average of the right-hand mem- 
 ber of the equation. 
 
 Performing the multiplication indicated, and remembering 
 that the average of sin^ uit and cos" coi is l^^, and the average of 
 sin co< cos ut is zero, the expression reduces to 
 
 av. ciii = yiEiJLi cos (<^i — ai). 
 By a similar process of analysis the average of 
 62*2 = Eimli cos ((^2 + 0:2). 
 The average of 
 
 62^1 = y^Eimll cos ((^1 + 02) 
 
 and the average of 
 
 eiii = y^Ei^Ii cos {(f>2 — ai). 
 
WATT-HOUR METERS 223 
 
 Substituting these values, the expression for the difference be- 
 tween power and torque becomes 
 
 average of iw — t = 34 [Eimli cos (0i - on) + E2mh cos (<^2 + "2)] 
 
 - HiElmli cos {<t>2 - ai) + Eimh cos (</>! + 0:2)]. 
 
 The accuracy of the meter evidently depends upon the value of 
 this expression. If the conditions are such that the expression 
 reduces to zero, the registration is correct; if the expression is 
 negative, the average torque is higher than the average load and 
 the meter registration is too high, and when the expression is 
 positive, the registration is too low. 
 
 Conditions that are most likely to be met with in practice are 
 Ii = I2, El = E2, ai = ai and <^i = ^2- When this is the case 
 it is evident that the average of w — t = and the meter 
 registers correctly. 
 
 194. Load Unbalanced. — When the load is unbalanced, in 
 general the expression will not reduce to zero, even if the unbal- 
 ancing is not sufficient to make Ei differ materially from E2. 
 
 Let El = E2, Oil = «2 and 4>i = 4>i- Then 
 «)-T = Ji^i„[7iCOs(<^i-ai) — (/i-/2)cos((^i+Q!i) — Z2C0s((^i-q;i)] 
 = ^^1™! (■fi--''2)Lcos((^i-ai) -cos(<^i-l-ai)]} 
 = }4Eim{Ii—l2)sm^i sinai. 
 
 So long as I2 is less than Ii and 0i is less than 5 the meter will 
 
 register too high. In practice ai will never be equal to 90°. 
 If the power-factors of Li and L2 are each unity; then 4>\ = 0, 
 and the meter registers correctly. In general, the meter will 
 register incorrectly on an unbalanced load when the voltage coil is 
 connected across the outside wires. 
 
 195. Voltage Coil Connected between One Outside Wire and 
 Neutral. — Such a connection is indicated by the dotted line ab, 
 Fig. 182. Using the same notation as in Article 193, the power 
 is given by 
 
 w = ei?i -|- 6212 
 but torque r = eiii + 6112 
 
 and w — T = 62^2 — eiii. 
 
 It has been shown that 
 
 aV. 62^2 = yiE2ml2 cos (<^2 + "2) 
 
 and av. eii2 =}4Eimh cos (<^2 — "i) 
 
 Hence average (w—r) = }4l2[EimCOs{(l>2+ 0(2) — i?imCos(^2— «i)]. 
 
224 
 
 ELECTRICAL METERS 
 
 The meter will register accurately only when the average of 
 {w - t) = 0. 
 
 If the load is balanced so that E^m = Eim, and a^ = ai the average 
 value of w; — r = — ^^^nmh 2 sin ^2 sin a^ = — E^mh sin 02 sin a^. 
 
 This expression is zero only when 02 = 0, for only under such a 
 condition will 02 be zero. 
 
 It is perfectly clear, then, that a three-wire induction meter will 
 not register correctly when the voltage coil is connected between 
 one outside wire and neutral even though the load on the three- 
 wire system be balanced. It will register correctly only when the 
 load is balanced and the power factor is unity. When the voltage 
 
 Source 
 
 
 
 Loaef 
 
 NeuZ-ra/ 
 
 
 
 
 
 
 
 
 
 looool 
 
 LJ 
 
 
 
 looool 
 
 LJ 
 
 
 
 Fig. 184. 
 
 coil is connected between neutral and one outside main, the meter 
 in general will be fast if the voltage impressed upon the voltage 
 coil lags behind; and slow when the pressure-coil voltage leads the 
 voltage between outside mains. This answers the question why 
 it is preferable to connect the voltage coil between outside mains, 
 a practice followed by most manufacturers. 
 
 Upon three-wire circuits that are subject to unbalanced loads, 
 two single-phase two-wire meters are preferable. When these 
 are used they are connected as shown in Fig. 184. 
 
 196. Polyphase Watt-hour Meters.- — In metering energy on 
 polyphase circuits, polyphase induction meters are usually 
 employed, although the practice of some companies favors the 
 use of two or of three single-phase meters, on the ground that 
 when this is done the failure of one meter will not cause a com- 
 plete loss of the record. The use of two single-phase meters 
 has the advantage that from their registrations the average 
 power-factor of the load can be computed. 
 
 On the other hand, the use of more than one meter is subject to 
 objection not only on account of the additional expense, but also 
 
WATT-HOUR METERS 
 
 225 
 
 on account of the difficulty of explaining to customers the 
 characteristics of polyphase systems. 
 
 197. Watt-hour Meters for Two-phase and Three-wire Three- 
 phase Circuits. — One make of polyphase watt-hour meter for 
 a two-phase or a three-wire three-phase system is shown in Fig. 
 185. The illustration shows clearly that the instrument is a 
 
 Pig. 185. 
 
 combination of two single-phase metering elements, the armature 
 cylinders of which are mounted on the same shaft or spindle. 
 Only one registering mechanism is thus necessary. The total 
 driving torque is the sum of the torques exerted by the two 
 actuating elements, and the registration is proportional to the 
 energy passing through both. 
 
 It was pointed out that for correct registration on inductive 
 load, the flux due to the load current must be in quadrature with 
 the flux due to the voltage-coil current. Exactly the same con- 
 
226 
 
 ELECTRICAL METERS 
 
 V\iift '70ur Meter 
 
 Phase A 
 
 
 l-Zne 
 
 Fig. 186. 
 S, 
 
 M 
 
 QQQQQ 
 
 a. 
 
 Phase a 
 
 Phase I 
 
 W 
 
 L-ine 
 
 JyOOOv 
 
 Fig. 187. 
 
 Tfe 
 
 Fig. 188. 
 
 Fig. 189. 
 
WATT-HOUR METERS 
 
 227 
 
 ditions must exist in each of the metering elements of polyphase 
 meters. 
 
 The manner in which two-phase and three-wire three-phase 
 meters are connected to circuits is shown in Figs. 186, 187, 188, 
 and 189. 
 
 When used on four-wire two-phase circuits one operating ele- 
 ment is connected in each phase exactly as though it were a 
 single-phase meter and it is evident that under these conditions 
 a meter theoretically correct will register accurately on balanced 
 or unbalanced circuits. 
 
 It is not so evident, however, that two single-phase meter 
 elements combined into one instrument will register all of the 
 
 s. 
 
 
 /v 
 
 
 4 
 
 Fig. 190. 
 
 energy supplied by a three-phase circuit. It is true, nevertheless, 
 as can readily be shown. 
 
 198. Relation of Power to Torque in a Y-connected System. — 
 The two general methods of connecting three-phase receiving 
 circuits are shown in Figs. 190 and 191. In the F-connected 
 system if Bo, ei, d and io, ii, and ii are the instantaneous voltages 
 and currents applied to loads Lo, Li, and Li, the instantaneous 
 power is 
 
 w = Coio + eiH -|- eiii 
 
 but the torque exerted by the two meter elements is 
 
 T = e'iii 4- e'zii when the meter is properly adjusted, 
 
 The difference between w and t is 
 
 w — T = {edo + eiii + eatz) — (e'li'i + e'tii) 
 but e'l = e<, -t- Ci 
 
 and e'2 = 60 + 62 
 
 therefore, 
 
 w — T = {e„io + eiii + 6212) — [ii(e„ -f- ei) -f- iz (eo + 62)] 
 
 = {fioio + Ciii + e^ii} — {fioi\ -h ^\i\ -\- eoii + eiH) 
 
 = eo(i« — ii — is). 
 
228 
 
 ELECTRICAL METERS 
 
 Since the middle wire at each instant may be considered as the 
 return for wires 1 and 2, then to — ii — 12 = under all conditions. 
 Hence 
 
 w — T = eo{io — ii — ii) = 
 
 and the watt-hour meter registers correctly the total energy in 
 a F-connected system no matter whether the load be balanced 
 or unbalanced. 
 
 \SmSLn 
 
 -k.Q.QOQQr-J 
 
 
 -nm^ 
 
 ^z 
 
 Fig. 191. 
 
 199. Relation between Power and Torque in a A (delta) -con- 
 nected System. — Using the same notation in Fig. 191 as in Fig. 
 190 the instantaneous power supplied to loads L„, L\, Li, is 
 
 w = e„to + e-dx + 62^2, and the torque r = exi\ + e^i' 
 but i'l = ix + io 
 
 and i'l, = i^ — i„ 
 
 hence 
 
 w — T = Coio + exix + e%ii — {exi\ + eii„ + dii — eiio) 
 = Coio — exio + Ciio 
 = ioie„ — ei + 62) 
 but e„ — ex + 62 = 
 
 therefore, w — t = 0. 
 
 Again the torque at each instant is just equal to the power, and 
 hence, the average torque must be equal to the average power 
 and the meter registers correctly on both balanced and unbalanced 
 loads. 
 
 It should be noted that no conditions have been imposed upon 
 the character of the electromotive forces or currents and, there- 
 fore, the demonstrations are true no matter what the form of 
 voltage or current wave or what the power-factor may be. 
 When the meter is theoretically correct and properly connected 
 
WATT-HOUR METERS 
 
 229 
 
 to the circuit it will register correctly under all conditions of 
 load. That is, any inaccuracy will not be due to the method of 
 use, but will be due to faulty characteristics of the meter. 
 
 Furthermore, it must be perfectly clear that two separate single- 
 phase meters may be used in place of the polyphase meter and 
 that, the sum of their registration will give the true energy. One 
 single-phase meter alone will not register the correct energy 
 unless the separate phases are accurately balanced. As this is 
 seldom the case it is best to use either two single-phase or one 
 polyphase meter. 
 
 200. Polyphase Meters for Four-wire Three-phase Systems. 
 — In Fig. 192 is shown a Y-connected four-wire three-phase 
 
 / 
 
 
 \- 2 
 
 ?■' «"» /<, ^^^/ 
 
 .3 
 
 6 6 Kn 
 
 2 
 
 ^ ^%. 
 
 ^ 
 
 Fig. 192. 
 
 receiving system. In Article 198 it was shown that a three-wire 
 polyphase meter registered correctly when e„(io — i\ — i^) = 
 and that under the conditions there assumed io — ii — ii always is 
 zero. When, however, another wire is added, as shown in Fig. 
 192, io may no longer be equal to ii + h. When i„ ^ f i -f ii, w is 
 no longer equal to t and the meter registration is in error. Thus 
 it is seen that a three-wire polyphase watt-hour meter cannot be 
 used on four-wire circuits. 
 
 A combined Y and A four-wire receiving system is shown in 
 Fig. 193. Representing the instantaneous currents and pressures 
 by i and e with proper subscripts and primes, the instantaneous 
 value of power consumed in the system is 
 
 w = Biii + eiii + edz + e'li'i + e\i'i. -\- e'zi'z 
 
 but 
 
 e'l = ei 
 
 ea; e'a = 63 — 62) e'3 = 62 — 61 
 
 Substituting these values of e'l, e'2, and e'3 we get 
 
 w = e\i\ -f e^ii -f 6313 + i'\ (ei — 63) -|- i\ (es — 62) -|- i'z (62 — ei) 
 
230 
 
 ELECTRICAL METERS 
 
 or w = ei {ii + i'l — i'd + ez (^2 + i's — ^2) + 63 (is + i'2 — i'l) 
 but 
 
 ii + i'l — i'z = i"i; ii + i's - i\ = ^''z; »3 + i'i — i'x = i"z 
 hence, w = eii"i + e2i"2 + ^"3. 
 
 ei, 62, and 63 are the voltages between neutral iV and mains 
 1, 2, and 3, respectively; and i"\, i'\, and ^"3 are the currents in 
 
 /\f 
 
 J-r 
 
 
 
 
 
 / 
 
 ^/' 
 
 
 
 
 / 
 
 1 
 
 
 
 
 ./ 
 
 ^^ 
 
 
 
 
 ,^ 
 
 eiT 
 
 fc 
 
 z. 
 
 j: 
 
 ^^^ 
 
 :;/9^ 
 
 ^^ 
 
 J,^-^ 
 
 
 
 V 
 
 >v» 
 
 Fig. 193. 
 
 the corresponding mains. To measure the energy, either three 
 single-phase watt-hour meters or a specially designed polyphase 
 meter is necessary. 
 
 A four-wire three-phase meter differs from a three-wire meter 
 mainly in the winding of the current coils. The four-wire meter 
 
 Pig. 194. 
 
 contains four series coils, two of which, one on each element, are 
 connected in series and carry the current in one line wire. The 
 other two series coils, one on each element, are separate, and each 
 carries the current in one of the other line wires. A diagram 
 of such a connection is shown in Fig. 194. 
 
WATT-HOUR METERS 231 
 
 Representing the voltages between mains 1, 2, 3, and neutral 
 by El, Ei, and E3 respectively, then according to Article 200 the 
 total power at any instant is equal to 
 
 w = eiii + eai'a + 6313. 
 
 The methods of connections employed show that the driving 
 torque in terms of electrical quantities must be 
 
 T = fiiii + eiii + €312 + eai-i. 
 
 Hence, w — r = eiii + eiii + eais — eiii — eifa — 6312 — Csis 
 = 6212 — eiii — fiaia. 
 
 M) — T = 12 (62 — Cl — 63) 
 
 but 62 — ei — 63 = 
 
 hence, the total energy will be registered by a four-wire meter 
 when connected as shown in Fig. 194, however unbalanced the 
 circuits may be. 
 
 201. Balance of Metering Elements. — In order that the poly- 
 phase meters may register correctly when the circuits are un- 
 equally loaded, they must be adjusted so that the driving torques 
 of the actuating elements are equal when the same amount of 
 power is passed through each. If these two torques are not equal, 
 the meter will run too fast when one side is carrying most of the 
 load and too slow when the other side is loaded more heavily. 
 
 Since the driving torque is proportional to the product of the 
 maximum values of current and voltage-coil fluxes, it is evident 
 that changing the number of turns on the voltage coil will change 
 the torque. This is the method of balancing used by some 
 makers. Another method based on the same fundamental 
 principle consists in changing the reluctance of the path of the 
 voltage flux. This is accomplished by the use of a short-cir- 
 cuited turn, called "balancing loop," upon the voltage-coil core. 
 Changing the position of this loop changes the reluctance of 
 that part of the magnetic circuit, and causes more or less of the 
 flux to pass through the disk and interact with the flux of the 
 current coils. This again increases or decreases the torque of 
 that element. The method employed in the Sangamo meter is 
 explained in Art. 181. 
 
 202. Interference of Elements. — One source of error to which 
 polyphase meters are liable is due to the electromagnetic inter- 
 
232 ELECTRICAL METERS 
 
 action between the elements. This source of error was investi- 
 gated by the Electrical Testing Laboratories and it was found 
 that different makes differed considerably in this respect. In 
 some makes the effect of interference of the elements was so 
 small that careful tests failed to detect any error due to this 
 cause. In other makes, the interference was such that relatively 
 serious errors might under certain conditions be produced. 
 These facts were brought to the attention of the manufacturers 
 whose meters were defective in this respect, with the result that 
 these defects have been remedied, and polyphase meters now on 
 the market are practically free from errors due to this cause. 
 
 203. Effect of Power-factor on Operation. — In Articles 198 
 and 199 it was shown that a polyphase meter connected as 
 shown in Figs. 190 and 191 will correctly register the total 
 energy transmitted no matter whether the load be balanced or 
 unbalanced. 
 
 The instantaneous torque on each element is 
 Ti = eit'i 
 and T2 = 62^2, where ei, 62, ii, and i^ are the instan- 
 
 taneous line voltages and currents, respectively. In a A-con- 
 nected system e\ and 62 are the instantaneous voltages at load 
 terminals, and z'l and 1% are the differences between currents in 
 mains 1 and and mains 2 and 0, Fig. 191. Thus, in Fig. 195, 
 Tim, hm, and /<,„ are maximum values of currents in branches 
 AO, BO, and AB of Fig. 191. 7i„ is shown as lagging d degrees 
 behind Ei„. The vector difference between 7i„ and /<,„ is 7„ 
 which evidently lags 30° behind 7i„ and (d + 30) degrees behind 
 Elm. The average torque on one element is then Ti = EI 
 cos {d + 30) degrees, and by a similar process of reasoning it 
 can be shown that the average torque on the other element is 
 
 Ti = EI cos (8 - 30) degrees, 
 
 where E is the effective pressure between mains and 7 is the 
 effective value of current in mains. 
 
 When = 0, Ti = T2 = EI cos 30°. 
 
 When d = 30°, Ti = EI cos 60°, 
 and Ti = EI or T2 is twice Ti, 
 
 when e = 60°, Ti = EI cos 90° = 0, 
 and T2 = EI cos 30° = 1^ V3^7. 
 
 That is, the total driving torque is exerted on one element only. 
 
WATT-HOUR METERS 
 When e = 90°, Ti = EI cos 120° = - ^' 
 
 233 
 
 and 
 
 Ti = EI cos 60° = + 
 
 EI 
 
 In this case the two torques are equal and opposite. When d is 
 > 60° and < 90°, Ti is negative while T^ is positive. The 
 effect of Ti is thus to drive the meter in a direction opposite to 
 that of Ti. 
 
 This clearly shows the importance of properly connecting a 
 polyphase meter to a circuit. 
 
 Fig. 195. 
 
 204. Effect of Improper Connections. — A three-wire three 
 phase meter will in general have six free terminals; four for the 
 series coils and one each for the two voltage coils. From Figs. 
 190 and 191 it is evident that the series coils may be connected 
 in any two of the line wires, but that when so connected the 
 free ends of the voltage coils must be connected to the third wire, 
 preferably to the same point. It has already been pointed out 
 that when properly connected, the torque on the two elements 
 
 23 
 
234 ELECTRICAL METERS 
 
 is in opposite directions on loads whose power-factor is less than 
 0.5. It is thus erroneous to assume that the meter will register 
 correctly if the meter disk rotates in the proper direction when 
 either voltage coil is disconnected. Hence, disconnecting the 
 voltage coils in succession and noting the direction of rotation 
 cannot be used as a check upon the correctness of the connections 
 unless the power-factor is known. 
 
 One wrong connection for a three-phase three-wire meter is 
 shown in Fig. 196. The series coils Si and S^ are properly con- 
 
 — r 
 
 eenemtor \ 
 
 a, 
 
 nnnrv 
 
 TfvJ 
 
 - 
 
 & ?o 
 
 -LJ um^ 
 
 ToLooaf 
 
 "5 
 Fig. 196. 
 
 nected but the voltage coil of Fi is connected to main 2 instead 
 of main as it should be. When so connected, the instantaneous 
 torques on the two elements are 
 
 and n = e%i\ 
 
 The average torques on balanced circuits will be 
 
 Tx = average eoi'i 
 and Ti = average e^i'^ 
 
 Now Eom. is (150 -}- Q) degrees out of phase with /„ as shown in 
 Fig. 175. Hence 
 
 Ti = El\ cos (150 + ff) degrees 
 
 = EI cos (150 + e) degrees where E 
 and / are effective voltage and current respectively. It has been 
 shown, Article 203, that 
 
 Ti = EI cos (30 - e) degrees 
 When = 0, Ti = - ^y[sEI, and T^ = }4y[3EI. 
 
 The two torques are thus equal but in opposite directions. 
 Reversing the connection of the pressure coil of Vi, its torque is 
 reversed and the total driving torque is 
 
 T = T, + T2 = ^i^EI + }i yjSEI = V3£/ 
 
WATT-HOUR METERS 235 
 
 and the meter registers correctly. When 8 = 30°, Ti = EI 
 and Ti = EI and T = 2EI. The load, however, is yfSEI cos 
 30° = 1.5^7, and the meter registers 33>^ per cent too high. 
 This shows that although the meter registers correctly on load 
 of unity power-factor, it will not register correctly on loads whose 
 power-factor is less than unity. The registration will also be 
 incorrect when the three-phase system is unbalanced. For cor- 
 rect registration, the four-wire three-phase meter may be con- 
 nected to the circuit in practically one way only. This is due to 
 the fact that there is only one neutral wire, and the voltage coils 
 must both be connected to this neutral conductor. It is very 
 necessary then to know the exact order in which the mains are 
 to be connected, and which is the neutral conductor. Since the 
 voltage between the neutral and any line wire is less than between 
 any two mains, which of the four wires is the neutral conductor 
 can easily be determined by means of a voltmeter. When this 
 is determined, the diagram of connections furnished by the maker 
 must be carefully followed. 
 
 205. Prepayment Watt-hour Meters. — In many instances it is 
 advisable to collect pay for energy in advance of its use. For 
 instance, the use of prepayment watt-hour meters simplifies the 
 station bookkeeping, and relieves the proprietor of all responsi- 
 bility as regards electrical bills when meters are installed in apart- 
 ment buildings whose tenants -frequently change. For such and 
 other service of like nature, prepayment meters have been 
 developed. 
 
 The principles of operation of the meter proper are the same 
 as those already discussed. That is, on the electrical side the 
 instrument is either a direct- or alternating-current watt-hour 
 meter to which has been added a device which by the insertion 
 of a coin and the turning of a knob automatically closes a switch 
 and keeps the circuit closed until the energy paid for has been 
 used, when the circuit is automatically opened. The external 
 appearance of a General Electric prepayment meter is shown in 
 Fig. 197. 
 
 206. Prepayment Device. — One form of prepayment device is 
 shown in Fig. 198. This consists of a drum the front of which 
 is formed by the crediting dial and the back by the double, gear 
 wheel B. The wheel B contains both spur and annular gears, the 
 second are not shown as they are within the drum. Within the 
 drum is also an actuating spiral spring C, and two gear wheels. 
 
236 
 
 ELECTRICAL METERS 
 
 Fig. 197. 
 
 Fig. 198. 
 
WATT-HOUR METERS 237 
 
 One of the gear wheels is mounted on the knob stem to which it 
 is locked by the coin. The other intermediate gear plainly 
 shown, is mounted on a stud which is fastened to the front dial 
 plate. This intermediate gear meshes with the pinion on the 
 knob stem and the annular gear of wheel B. The spur gear of 
 the wheel B meshes with a pinion of the escapement mechanism 
 D. This mechanism is released by the operation of the registering 
 mechanism of the meter proper, one gear of which meshes with 
 pinion E. 
 
 207. Operation. — The prepayment mechanism is operated as 
 follows : The coin that is inserted in the slot in the crediting knob 
 stem acts as a key and locks the stem of the knob to the pinion 
 on its end. On turning the knob one-half turn to the right, the 
 pinion is carried with it, causing the intermediate gear to roll 
 round on the annular gear of the wheel B and to carry with it 
 the crediting dial. This action winds up the springs and at the 
 same time, by the action of a cam, the switch lever F is moved 
 upward, closing the circuit through the meter. This operation 
 of crediting may be repeated until the coin register at the bottom 
 of the meter shows that the full number of coins for which the 
 meter is designed has been inserted. When current is taken 
 the intermediate gear and dial are driven by the main, spring in 
 the opposite direction. The pinion E, which is driven by a gear 
 of the meter registering train, carries a cam G. This cam as it 
 revolves oscillates the bell-crank H, which in turn moves a finger 
 backward and forward across the rim of the release gear I in 
 mesh with the damper fan. 
 
 Pinion E makes one complete rotation during one oscillation 
 of the finger; during the first half of the rotation, the finger dis- 
 places a catch from a pin set in the rim of the gear I, and during 
 the second half of the rotation it is withdrawn from the pin. 
 When the finger K has returned to its outer position, the gears 
 of the escapement mechanism are free to rotate under the action 
 of disk B, which is driven by the main spring. The gear D makes 
 one rotation every time the catch is released^ A pin on this gear 
 pushes the catch back into the path of the stop-pin on gear I 
 and so arrests its motion after it has made the requisite number 
 of rotations to permit the turning back of the crediting dial one 
 place. At every rotation of pinion E this operation is repeated 
 until the purchased energy has been used, when a cam on the 
 dial plate automatically opens the meter circuit. 
 
238 
 
 ELECTRICAL METERS 
 
 It is very evident that since the prepayment device is controlled 
 by the registering mechanism of the watt-hour meter, it can be 
 used on watt-hour meters of any type. In fact, a shght modifi- 
 cation of the device and the meter with which it is to be used, 
 permits the installation of the prepayment mechanism at points 
 distant from the meter. When the device is to be installed 
 separately, the escapement mechanism is controlled by an electro- 
 magnet connected directly into the line. The excitation of the 
 
 electromagnet is governed by 
 suitable gears and the com- 
 mutating device in the regis- 
 tering mechanism of the watt- 
 hour meter. 
 
 There are several other de- 
 signs of prepayment meters 
 manufactured, especially in 
 England. In this country 
 the use of the prepayment 
 meter is quite limited, con- 
 sequently no other forms will 
 be explained. The general 
 appearance of the Westing- 
 house prepayment meter 
 with cover removed is shown 
 in Fig. 199. 
 
 208. Bases of Energy 
 Rates. — The cost of supply- 
 ing electrical energy depends 
 not alone upon the amount supplied but also upon the time 
 and rate of supplying the same. Any equitable method of 
 charging should take these things into consideration. The com- 
 mon method of charging, which allows discounts in proportion 
 to the quantity of energy used, is just in some respects, but it 
 does not take into consideration the time and rate of supply 
 elements as mentioned above. 
 
 In order to take into consideration these two elements, two 
 types of instruments have been devised. One type, known as the 
 two-rate meter, permits the collection of two different rates; a 
 relatively high rate for energy used during the peak of the load, 
 and a relatively low rate during the rest of the day. This method 
 of charging tends to discourage the extravagant use of electrical 
 
 Pig. 199. 
 
WA TT-HO UR- METERS 239 
 
 energy during heavy load, and increase its use during periods of 
 light loads, thus increasing the load factor. The second type of 
 instrument is described in Chapter XV. 
 
 209. Two-rate Meters, — The essential difference between a 
 two-rate or double-tariff meter and a regular watt-hour meter is 
 the addition of an extra registering train and clock. The clock 
 controls a suitable switching-over clutch mechanism for throwing 
 on or off the separate registering mechanisms. One registering 
 mechanism indicates the energy consumed during the time of 
 peak load, and the other during the other hours of the day. The 
 clock automatically, and at the proper time, connects either the 
 high- or low-rate train; a high rate being charged for energy con- 
 sumed during the hours of the peak load. The use of a two-rate 
 meter has not met with great favor in this country. From a 
 mechanical standpoint the two-rate meter is practical and has 
 been successfully carried out in practice. 
 
CHAPTER XIV 
 INTEGRATING METERS, AMPERE-HOUR METERS 
 
 210. Introduction. — In many industries using electric current, 
 it is advisable and often necessary to know the quantity of 
 electricity that has been used within a given time. This is 
 especially true in industries whose operation depends upon 
 electrolytic processes, and in charging storage batteries. 
 
 The unit of quantity of electricity is the coulomb, and a cou- 
 lomb has been defined as the quantity of electricity given by 
 1 amp. in 1 sec. In 1 hr. a constant current of 1 amp. will give 
 3,600 coulombs. For practical purposes, the coulomb is too 
 small a unit, and hence 3,600 coulombs, called the ampere-hour, 
 are used as the unit. Commercial instruments whose registra- 
 tions are proportional to the quantity of electricity passing are 
 called ampere-hour meters, and are of two types : electromagnetic 
 and electrolytic. 
 
 211. Electromagnetic-type Ampere-hour Meter. — In the dis- 
 cussion on watt-hour meters it was shown that the registration is 
 proportional to Elt. Hence, it is evident that if E remain con- 
 stant the registration will be proportional to It. If t is in hours 
 the scale may be graduated in ampere-hours. Thus, a watt-hour 
 meter with constant voltage-coil excitation may be made to 
 register in ampere hours. 
 
 Since alternating currents cannot be used for electrolytic 
 processes, an alternating-current ampere-hour meter would be of 
 little practical use. For direct currents the constant field excita- 
 tion is best obtained by the use of permanent magnets. 
 
 The essential features of the Sangamo ampere-hour meter are 
 shown in Fig. 200. The similarity between the ampere-hour 
 meter and the mercury watt-hour meter is plainly evident. In 
 place of the electromagnet of the voltage field the ampere-hour 
 meter is provided with a permanent magnet. The operation 
 of the ampere-hour meter is in every respect exactly like that of 
 the watt-hour meter. The current flowing from one terminal 
 through the disk to the other terminal reacts with the permanent- 
 magnet field. This reaction produces a torque upon the disk, 
 24 241 
 
242 
 
 ELECTRICAL METERS 
 
 causing it to rotate. Since the field is constant, the torque, 
 and hence speed, is directly proportional to current strength. 
 The counter-torque is obtained by rotating an aluminum disk, 
 which is mounted on the shaft between the poles of permanent 
 magnets exactly as on watt-hour meters. The dial is graduated 
 in ampere-hours instead of watt -hours. 
 
 It is well known that the efficiency of a storage battery varies 
 with the rate of charge and discharge, and that the number of 
 
 ampere-hours required to charge the battery is greater than is 
 given out on discharge. In order that an ampere-hour meter 
 may indicate the condition of the battery with a reasonable 
 degree of accuracy some provision must be made whereby this 
 difference in ampere-hours is automatically corrected. In the 
 Sangamo meter this is accomplished by shunting the movable 
 element by a variable resistance. This variable resistance con- 
 sists of a small copper bar pivoted at the center and immersed in 
 mercury, as shown in Fig. 200. This bar is free to rotate 
 through a small angle from a position directly in line with the 
 
AMPERE-HOUR METERS 
 
 243 
 
 two contact points at the opposite sides of the mercury cham- 
 ber. The movement of the bar is limited by two stops, one of 
 which is adjustable. 
 
 The resistor element is clamped below the main mercury 
 chamber of the meter and there is sufficient magnetic leakage 
 from the poles of the permanent magnet through this mercury 
 chamber so that any current flowing through the copper bar will 
 have the same effect as the current through the meter disk. 
 
 100 
 
 150 
 
 Upper Scale — Percentage of Full I.oad 
 Lower Scaler Ampere Load 
 200 250 300 
 
 360 
 
 102 
 100 
 98 
 
 ■, 94 
 
 -I 
 ^102 
 
 glOO 
 §98 
 
 96 
 
 ol 
 
 
 
 
 5 
 
 
 
 
 
 10 
 
 
 
 
 
 16 
 
 
 
 
 
 20 
 
 
 
 
 
 25 
 
 
 
 
 
 30 
 
 -1 
 
 
 
 
 39 
 
 
 
 
 ^ 
 
 _ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ,A 
 
 
 
 
 
 
 ~ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 _1 
 
 
 
 
 
 
 
 
 
 
 
 
 — 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ' — 
 
 — 
 
 -- 
 
 ^ 
 
 
 
 
 
 
 
 As 
 
 10 
 
 h 
 
 m 
 
 pei-e 
 
 L 
 
 n 
 
 hi 
 
 In 
 
 ed 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 50 
 
 
 
 
 
 no 
 
 
 
 
 
 .■■n 
 
 
 
 
 
 ^ 
 
 
 
 
 
 250 
 
 
 
 
 
 WO 
 
 
 
 
 
 350 
 
 
 
 
 
 10 
 
 
 
 
 
 20 
 
 
 
 
 
 30 
 
 
 
 
 
 40 
 
 
 
 
 
 50 
 
 
 
 
 
 60 
 
 
 
 
 
 70 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 "~- 
 
 *-. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 — 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 — 1 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 2 
 
 OJ 
 
 \.IL 
 
 P< 
 
 re 
 
 , 
 
 r 
 
 an 
 
 te 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Fig. 201. 
 
 When the meter is recording the charge, the copper bar is in the 
 position indicated in Fig. 200, that is, it is in such a position that 
 the resistance of the resistor is a minimum, and thus the meter 
 will register a quantity somewhat less than that required to 
 charge the battery. The meter is slow on charge. When the 
 battery is discharging, the current through the resistor mercury 
 chamber is reversed; the copper bar is deflected through an angle 
 increasing the path of the current through the mercury. As 
 the resistance of mercury is about 60 times that of copper, the 
 current through the resistor is decreased and that through the 
 movable element of the meter is relatively increased with a con- 
 sequent increase in the speed of the meter. The postion of the 
 stop-pins may be adjusted so that the metxsr will operate at any 
 
244 
 
 ELECTRICAL METERS 
 
 percentage of battery overcharge desired between the limits of 
 and 25 per cent. 
 
 212. Accuracy Characteristics. — Two curves showing the per- 
 centage of accuracy of a 10-amp. meter with and without shunt 
 are shown in Fig. 201. It will be observed that on currents below 
 5 and above 15 amp. the accuracy falls off quite rapidly. This 
 falling off is much more rapid at low values of current than at 
 the higher values. The cause of the deviation of the percentage 
 of accuracy curve from a straight line at low values of current is 
 undoubtedly due to the effect of friction, as no compensating 
 
 Pig, 202. 
 
 device is used. The deviation at the higher values is due pri- 
 marily to fluid friction. An external view of a Sangamo am- 
 pere-hour meter is shown in Fig. 202. 
 
 213. Electrolytic Ampere-hour Meters. — The principles ac- 
 cording to which electrolytic or ampere-hour meters operate were 
 discovered by Faraday, and are, therefore, known as Faraday's 
 laws. These were discussed in Article 17. The passage of 
 electricity through an electrolyte decomposes the chemical com- 
 pound, and the mass of the metal deposited is a measure of the 
 ampere-hours. As long as the voltage remains constant, the 
 energy transmitted is proportional to the ampere-hours; hence, on 
 constant-voltage circuits such instruments will indicate a quan- 
 tity proportional to ampere-hours. The name wattmeter com- 
 monly applied to these instruments is plainly a misnomer. 
 
AMPERE-HOUR METERS 245 
 
 214. Edison Electrolytic Ampere-hour Meter. — The Edison 
 electrolytic or chemical meter employed two zinc plates in a solu- 
 tion of zinc sulphate, the bottle containing the plates being placed 
 in the meter at the beginning of the month and replaced by a simi- 
 lar bottle at the beginning of every month. One of the zinc plates 
 (the anode) was carefully weighed before and after this term of 
 service, and from the loss, the current, and hence the monthly 
 bill, was calculated. To pass the whole current through the 
 bottle was impracticable, on account of the large size of plates 
 that would be needed; the bottle was, therefore, put in a shunt 
 circuit, and only about 1/1,000 part of the main current passed 
 through it. This shunting caused a large part of the theoretical 
 accuracy and reliability of the electrolytic meter to disappear; 
 the voltage causing electrolysis being very low at light load, any 
 polarization in the cell, or abnormal resistance due to oxidation 
 of the plates, would make the meter indications too low. 
 
 This meter was used to a considerable extent, and may, perhaps, 
 still be found in some installations. 
 
 215. The Bastian Ampere-hour Meter. — ^An electrolytic meter 
 that is still on the market, and perhaps the simplest in construc- 
 tion, operates by decomposing water. The whole current passes 
 through acidulated water, decomposing it into its constituent 
 gases which are allowed to escape. The drop in the elevation 
 of the liquid is a measure of the ampere-hours supplied to the 
 consumer. 
 
 In the older type, two platinum electrodes are suspended in the 
 liquid at the bottom of a long glass tube open at the top. The 
 bore of the tube is as uniform as possible throughout its length. 
 The suspending leads are enclosed in two vulcanite tubes screwed 
 into a vulcanite frame which forms a protection for the platinum 
 electrodes enclosed by it. A scale graduated in watt-hours or 
 kUowatt-hours at a definite voltage is fixed in front of the tube 
 in such a manner that the level of the electrolyte can be readily 
 read. The glass vessel is enclosed in a cast-iron or sheet-iron 
 case in front of which is a long window. The electrolyte is a 
 dilute solution of sulphuric acid and water. Since only the water 
 is decomposed, it is necessary to refill the tube with water alone. 
 To prevent evaporation, paraffin oil is poured on top. There are 
 several objections to this meter. Among the most important are 
 the following : 
 
246 
 
 ELECTRICAL METERS 
 
 1. Large and variable pressure drop. 
 
 2. Necessity for refilling with water. 
 
 3. If left too long in circuit, all record is lost. 
 
 4. Inaccuracy. 
 
 The pressure drop across the elec- 
 trolyte is never less than 1.5 volts, 
 and in a 5-amp. meter, under full 
 load, may be 3 volts. This drop is 
 variable, depending to some extent 
 upon the height of the column of the 
 liquid in the tube. 
 
 Since different consumers use dif- 
 ferent quantities of energy, the re- 
 filling of the meters becomes quite 
 complicated. If left too long all 
 record is lost, and disputes are liable 
 to arise between the consumers and 
 the supply company. 
 
 The advantages claimed for this 
 meter arc: 
 
 1. Extreme simplicity. 
 
 2. Small chance of getting out of 
 order, when properly cared for. 
 
 3. Low first cost. 
 
 In a later form of meter the 
 platinum electrodes have been re- 
 placed by nickel, and the electrolyte 
 is an alkaline solution which has no 
 action upon the electrodes. The 
 substitution of nickel for platinum permits the use of larger 
 electrodes at a reasonable cost, and the resulting pressure drop 
 is less. Fig. 203 shows the complete instrument. 
 
CHAPTER XV 
 DEMAND INDICATORS 
 
 216. Introduction.— In Article 208 it was mentioned that two 
 types of instruments have been devised for the purpose of making 
 energy rates more equitable. The two-rate meter has been 
 briefly mentioned. With the other type of instrument, known 
 as the maximum demand indicator, the charge is at a rate depend- 
 ing upon the ratio of consumption to the maximum demand. 
 These instruments may be classed under three heads: thermal, 
 induction, and mechanical. 
 
 217. Thermal Type. — The main features of the Wright maxi- 
 mum ampere demand indicator whose operation depends upon 
 the heating effect of the electrical current are shown in Fig. 204. 
 The principle of operation is that of the recording thermometer. 
 That is, the meter does not directly indicate the maximum ampere 
 consumption, but indirectly by heating a column of air whose 
 expansion is proportional to the square of the current passing. 
 As shown in Fig. 204, the instrument consists of a U-shaped 
 tube with a bulb at each end partly filled with sulphuric 
 acid and hermetically sealed. A resistance of platinoid is 
 wound around bulb A and connected in series with the cur- 
 rent or a shunted part of the current. The heat generated by 
 the current flowing through the resistance expands the air in the 
 left bulb, and this expansion forces the liquid into the right hand 
 part of the U. As the liquid rises above a certain height, it flows 
 over into the index tube. The amount of liquid flowing over into 
 this tube is proportional to the expansion of the air in bulb A 
 above that in bulb B. The expansion of the air is proportional 
 to the square of the current flowing through the resistance coil. 
 If the tube has a uniform bore, the height of the liquid in the indi- 
 cator tube will be a measure of the square of the maximum cur- 
 rent. The head generated by a current in a resistance is equal to 
 
 H = PRt 
 
 where / is current, R resistance, and t is the time. It will thus 
 require some time for the air in tube A to reach a maximum 
 
 247 
 
248 
 
 ELECTRICAL METERS 
 
 temperature, or a temperature sufficiently high to indicate 
 maximum current. The manufacturers state that if the load 
 continues for about 40 min. the full 100 per cent, is indicated. 
 Momentary overloads are not recorded. An overload continuing 
 for some time will, however, fill the index tube and make an 
 accurate record impossible. 
 
 Since the indication is proportional to the square of the current, 
 the scale cannot be uniform if the bore of the indicator tube 
 
 is uniform. An examination of the 
 scale will show that the divisions 
 increase from the bottom up. 
 
 After a reading is taken, the 
 instrument is reset by tilting and 
 allowing the liquid to flow back 
 into tube B. To prevent the pas- 
 sage of air from one side of the U 
 to the other, small inverted glass 
 funnels called "traps" are rigidly 
 fastened to the bottom of the U. 
 When the indicator is being reset, 
 -Capif/ary the traps remain covered by the 
 liquid, preventing the passage of 
 air into the wrong side of the tube. 
 Indicators whose maximum 
 capacity is 25 amp. may be used 
 interchangeably on direct- or al- 
 ternating-current circuits without 
 shunts. Indicators of larger than 
 25 amp. and less than 200 amp. 
 are provided with shunts and may 
 be used on either direct or al- 
 ternating currents. Current transformers must be used in all 
 cases on alternating-current circuits where the voltage exceeds 
 1,150 volts, and also where the current capacity is over 200 amp. 
 The fact that the indications of the thermal type of indicator 
 depend upon the square of current only, makes it evident that it 
 will not give correct indications of maximum power on circuits 
 whose power-factor is other than unity, or on circuits of variable 
 voltage. 
 
 218. Induction Type. — The registration of the induction-type 
 maximum-demand indicator is determined by the maximum 
 
 Capillary 
 
 Tyap 
 
 T>ap 
 
 Pig. 204. 
 
DEMAND INDICATORS 
 
 249 
 
 power consumed for a definite time and not upon the maximum 
 current, as in the case of the thermal type. Since the deflection 
 of a wattmeter is determined by the power, it is evident that an 
 ordinary wattmeter could theoretically be used to indicate the 
 maximum watt demand if the meter were provided with another 
 pointer which would remain at the point of maximum deflection. 
 Since it is not desirable to keep records of momentary fluctua- 
 tions, such a scheme is not used. The recording wattmeter 
 records not only the maximum and minimum demand but also 
 the duration of such a demand. 
 
 Since the torque on the movable element of the watt-hour 
 meter varies with the load it too may, with some modifications, 
 be used to indicate the maximum watt 
 demand. The polyphase maximum 
 watt demand indicator of the General 
 Electric Co., shown in Fig. 205, is es- 
 sentially a polyphase induction watt- 
 hour meter with both actuating ele- 
 ments acting upon the top disk. 
 
 To secure the proper time lag, the 
 retarding system consists of several 
 powerful permanent magnets arranged 
 around the periphery of the lower disk. 
 In addition to the retarding effect of the 
 permanent magnets, the motion of the 
 movable element is opposed by three 
 spiral springs connected in series. 
 
 There are enough convolutions in these springs to permit the disks 
 to make three complete rotations. The regular registering mech- 
 anism is replaced by a circular dial with a scale over which move 
 two pointers. One of these pointers is driven by the movable 
 element of the instrument by means of a reducing gear so that 
 it makes only one complete revolution while the movable ele- 
 ment makes three. The second pointer is moved by the first 
 in a forward direction only, and is left at the extreme position 
 reached by it, being held in place by a ratchet. The second 
 pointer indicates, therefore, the maximum energy that has passed 
 through the indicator since it was last set. The second pointer 
 is reset by a thumb nut. Since the driving torque of an induc- 
 tion watt-meter is proportional to the power, and the reaction 
 of the spiral spring is equal to the torque, it follows that the 
 scale of such an indicator is uniform. 
 
 Pig. 205. 
 
250 ELECTRICAL METERS 
 
 219. Time Lag. — As already mentioned, momentary fluctua- 
 tions of load would not be a just basis for rate-making, as they 
 might not indicate a legitimate demand. Hence, some time 
 should elapse before the indicator pointer reaches its extreme 
 position. This time interval is controlled by the amount of 
 magnetic damping of the disk and counter-torque of spiral 
 spring. The following demonstration, which may be omitted 
 by students unacquainted with the calculus, shows this: 
 
 Assuming the change in the load to be instantaneous, the driv- 
 ing torque is proportional to the change in load, and is constant 
 so long as the load is constant. The counter-torque is due to the 
 damping magnets and to the reaction of the spiral controlling 
 spring. The torque due to damping magnets is proportional to 
 the speed of the disk, and the torque due to spring is directly 
 proportional to the deflection. This may be expressed by 
 
 Torque = Kou + Kid 
 
 where oi is the angular speed, and B is the deflection. 
 
 do 
 But '^ ~ dt ~ ^^*^ ^* which deflection is changing. 
 
 d9 
 Then Torque = T = Ko-^ + KiO 
 
 and Tdt = K^de + Kiddt 
 
 , ,, K,dd 
 
 whence dt = rp _ j^ g 
 
 Integrating between t = 0, and t = h, which hmits for time 
 correspond to 6 = 0, and 9 = 0i we get 
 
 '"•l 
 
 " de 
 
 Kid 
 
 -K„. T - Kidi 
 = ^^log y 
 
 This shows that ti is a logarithmic function of 6. 
 Solving the above for Kidi, we get 
 
 KiBi = T (l -e^»'^A 
 
 The time lag is defined as the interval of time taken to record 
 90^ per cent of any change in load, which amounts to the same 
 thing as to say that it is the interval of time required for the 
 
DEMAND INDICATORS 251 
 
 pointer to deflect 90 per cent, of the maximum deflection due to 
 a given change in load. According to the equation for K161, 
 
 when the pointer has deflected ~th of the maximum deflection 
 
 n 
 
 Ki-d, =-T. 
 n n 
 
 Then 
 
 where <2 is the time required for a deflection of - 61 
 
 n 
 
 
 l-i= 1 
 
 
 and e^° 
 
 n-1 
 
 and ^^ ti log e = log - 
 
 1 ^ 
 and f _ ^o n — 1 
 
 ' ~ Kt log e 
 
 If the deflection is to be 90 per cent of the maximum deflection 
 
 ^=0.9 
 
 n 
 
 and n = -^■ 
 
 Then <2 = t?~ ~^ = 2.3 -^^' 
 
 Ki log e Ki 
 
 This shows that the time lag h depends mainly upon the ratio 
 of Ka to Ki. Now Ko is determined by the strength of the field 
 of the permanent magnets and their distance from the shaft. 
 Ki is determined by the physical properties of the controlling 
 spring. Ko is large when the permanent-magnet field is strong, 
 and Ki is small when a spring of many convolutions is used. 
 ti then is large when many permanent magnets and weak con- 
 trol springs are used. It is also clear that changing either one 
 of these factors will change the time lag. Curve of Fig. 206 
 shows the relation between the per cent of deflection and time. 
 
252 
 
 ELECTRICAL METERS 
 
 If Ko and Ki were known, this curve could be plotted from 
 the equation 
 
 KiOx = t(i - e~K7hy 
 
 This instrument has the advantage that the maximum demand 
 can be read at once from the dial, and that it is easy to maintain. 
 The disadvantage is that no record of demand is obtained other 
 than that taken down by the meter reader, and that the time 
 at which the maximum demand occurred is not indicated. 
 
 
 -|— 
 
 /nduaUon/ 
 
 ■y^/>msnr//ne//C3e.or 
 
 
 
 
 _,, 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 — 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^•M 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 V 
 
 If 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^^ 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 f 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 S «^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 _ 
 
 
 
 
 /0 IIS 
 
 ^rne.inWnuteSi. 
 Fig. 206. 
 
 .£'1!' 
 
 The polyphase watt-demand indicator may be used on single- 
 phase as well as polyphase circuits. When it is to be used on 
 single-phase circuits, the current coils are connected in series 
 and the voltage coils in parallel. 
 
 220. "Westinghouse Demand Indicator. — Instead of employing 
 a separate instrument for indicating the maximum demand, the 
 Westinghouse indicator is a combination of a watt-hour meter 
 and a demand indicator. The meter is essentially a watt-hour 
 meter which has been modified by the addition of another disk 
 which is driven by the shifting magnetic field in exactly the same 
 manner as the watt-hour meter disk. The tendency of the 
 auxiliary disk to rotate, however, is counteracted by a spiral 
 spring. The construction and operation will be readily 
 understood from Figs. 207 and 208. The auxiliary disk 2 has 
 its motion counteracted by the coiled or spiral spring 4 at the 
 
DEMAND INDICATORS 
 
 253 
 
 Wheel 
 
 Trip 
 
 Main Pawl--sH- 
 
 Pointer 
 
 & 
 
 ./ 
 
 Spring 
 
 ^ 
 
 Pawl 
 
 ^ Ratchet 
 
 Lleht Spring 
 
 Dog 
 
 Timing^ 
 Gearff 
 
 um ^ 
 
 \Double 
 Pivot 
 Bearing 
 
 Ball Bearlag- 
 
 I ' M I nirrnmii 
 
 .Escapement 
 Wheel 
 \ Escapement 
 Eccentric 
 Claw 
 
 ¥ 
 
 Auxiliary 
 / Disk 
 
 PiQ. 207. 
 
254 ELECTRICAL METERS 
 
 upper end of the shaft. Upon the shaft is mounted a gear 7 
 which meshes with gear 10 on the counter which transmits the 
 motion of the auxiUary disk through a dog drive to the pointer. 
 The pointer is held in its position of maximum deflection by a 
 fine-toothed rachet and pawl. In this respect the demand mech- 
 anism does not differ materially from that of a wattmeter. 
 In order that the pointer be not deflected instantly, further modi- 
 fications are necsssary. The mechanism by which this is accom- 
 plished consists of an escapement wheel 8 which engages with 
 an escapement 13. The other end of the escapement lever is 
 forked, and within this fork rotates an eccentric. This eccentric 
 is rotated by the main disk through gears 11, 12 and 15. The 
 schematic diagram of Fig. 207 shows the connections more 
 clearly. The movement of the pointer is thus controlled by the 
 motions both of the auxiliary and of the main disks. The motion 
 of the auxiliary disk causes the pointer to deflect, and the speed 
 or rate of deflection is governed by the main disk. As soon 
 as energy flows through the meter, the auxiliary disk tends to 
 deflect instantly to indicate the load just as the disk of the in- 
 duction wattmeter, but it cannot do so on account of the action 
 of the escapement. The main disk through the gears and eccen- 
 tric already mentioned oscillates the escapement and thus per- 
 mits the rotation of the escapement wheel one tooth at a time, 
 just as in a clock, until the counter-torque of the control spring 
 just balances the torque developed in the disk. The time lag 
 is thus fixed and depends upon the gear ratio of the gears be- 
 tween the shaft of the main disk and escapement, and the number 
 of teeth on the escapement wheel. It is likewise constant, since 
 the deflection of the pointer and the rate of deflection bear a con- 
 stant relation to each other. 
 
 221. Mechanical Type. — For the want of a better term, we 
 shall call the third form of demand meter the mechanical type, 
 since it is merely an automatic printing attachment to a watt-hour 
 meter. The attachment is operated by clockwork in connection 
 with the registering mechanism of the meter, while the printing 
 device leaves a record of the rate of the use of energy on a moving 
 tape. 
 
 222. Operation. — The mechanical features of one make of the 
 " Printometer, " as this type of demand register is called, is shown 
 in Fig. 209. 
 
 The printometer can be attached to any type of watt-hour 
 
DEMAND INDICATORS 255 
 
 meter, and when so connected the type or recording wheels of the 
 instrument are electrically interlocked with the registering 
 mechanism of the meter. The movement of the recording mech- 
 anism of the printometer is thus in synchronism with the move- 
 ment of the meter register, and hence the record is an indication 
 of the rate at wliich energy is being used. The printometer 
 record is made on a paper tape by means of a copying ribbon 
 which, at regular intervals, is pressed against the type wheels by 
 
 Fig. 209. 
 
 a rubber platen. The rubber platen is actuated by a solenoid 
 whose circuit is closed at regular intervals by a contact-making 
 clock. 
 
 In addition to the energy-recording mechanism, the instru- 
 ment contains an hour wheel containing numbers from 1 to 24. 
 This hour wheel is also automatically advanced so that by every 
 imprint of the energy there is left a record of the time. This 
 hour wheel is connected to the printing platen through a star 
 wheel and pins, which are plainly shown in Fig. 209. By chang- 
 ing the position of the pins, the wheel can be advanced in such a 
 way as to give readings every hour, half hour, 20, 15, 10, or 5 
 min. Fig. 210 shows a record of hourly readings. 
 
 The circuit of the solenoid that advances the type wheels is 
 
256 
 
 ELECTRICAL METERS 
 
 24 I 7 8 
 
 1 I 8 4 
 a I 8 9 
 
 closed through a commutator, which is mounted on one of the 
 spindles of the meter register. This is shown in Fig. 211 and 
 212. On the end of this commutator is a slip ring which is 
 connected to a number of bars across the face. The number of 
 bars depends upon the constant to be used with the 
 attachment. There are three contact brushes, one 
 bearing upon the slip ring, and the other two at op- 
 posite points on the commutator in such relative posi- 
 tions that they alternately close the circuit of the 
 type-wheel actuating solenoid. To prevent the de- 
 struction of the commutator by sparking, the circuit 
 is broken by the forward movement of the plunger 
 of the solenoid. As this moves forward it turns a 
 contact wheel which is made of alternating segments 
 of conducting and non-conducting material joined by 
 a metal slip ring. Three brushes make contact with 
 this wheel; one with the slip ring, and the other two 
 with the segments. The distance between the two 
 brushes is such that when one rests on a conducting 
 segment the other rests on a non-conducting segment. 
 The operation of the commutator and contact wheel 
 in closing and breaking the circuit is much the same 
 as that of two three-way switches. The closing of 
 the circuit by the commutator on the registering 
 mechanism of the meter excites the solenoid and 
 drives the plunger forward. The turning of the contact 
 wheel by the forward movement of the plunger changes the 
 position of the brush on the conducting segment to a non-conduct- 
 ing segment, thus breaking the circuit 
 which again will be closed after the 
 commutator on the meter register has 
 rotated the proper distance. The 
 solenoid circuit is thus closed by the 
 slow-moving commutator and opened 
 by the quickly moving contact wheel. 
 Another form of maximum demand 
 indicator is shown in Fig. 213. This is a device which in conjunc- 
 tion with a watt-hour meter indicates the maximum demand. It 
 consists essentially of a demand-registering and timing mechanism 
 mechanically connected and mounted within the same case. The 
 demand-registering element is driven electrically from the register 
 
 Fig. 210. 
 
 Pig. 211. 
 
DEMAND INDICATORS 
 
 257 
 
 T^ptb-3 Confact on 
 V^af-f hour Meter 
 
 Co/rylnj Pibht 
 
 Contact BreaHing 
 Switch 
 
 Counter advanced one 
 point for each contact 
 Paper roll ot meter register 
 
 /» energized 
 
 Cam on C-z Clock 
 
 for rrxiking contact 
 ct equal consecutive 
 Intervals^ made of 
 inivlatlnj mstfr/al. 
 
 Fig. 213. 
 
 25 5 
 
258 
 
 ELECTRICAL METERS 
 
 of the watt-hour meter, while the timing mechanism is driven by the 
 action of a shifting magnetic field on a separate disk in the alter- 
 nating-current indicator, or a clock in the direct-current indicator. 
 The actual operation will be readily understood from a considera- 
 tion of Fig. 214 which shows diagrammatically the essential 
 parts of the alternating-current indicator. The contact on the 
 
 Operating Coil /^ 
 
 flrmature 
 
 Con fact on 
 IVatthour Meter 
 
 Trip Lever 
 Worm Wheel 
 
 Pig. 214. 
 
 watt-hour meter opens and closes the electromagnet circuit after 
 a definite number of rotations of the watt-hour meter disk, that is, 
 after the passage of a definite number of watt-hours. Every 
 time the electromagnet circuit is closed the armature lever is 
 moved forward and by means of the pawl or dog, ratchet wheel, 
 and train of gears the friction pointer is moved along the dial. 
 The interval of time during which the pointer is moved forward 
 is determined by the timing mechanism. This consists of a disk 
 and an actuating mechanism similar to an induction watt-hour 
 meter. The disk is driven at a constant speed, and through a 
 suitable train of gears it operates a trip lever by means of which, 
 
DEMAND INDICATORS 259 
 
 after a definite number of revolutions of the disk, the gear on the 
 ratchet wheel arbor is disconnected from the train permitting the 
 spring on the pointer staff to return the pointer actuating gears 
 to zero. The pointer is held in its extreme position by friction, 
 and hence will not advance unless the energy consumption during 
 some succeeding interval of time exceeds that of the first. The 
 position of the pointer thus indicates the maximum demand. 
 
 223. Graphic Demand Meter, Type G. — Type G demand 
 meter of the General Electrical Co. does not merely indicate the 
 maximum demand during a definite time interval, but it also 
 
 Fig. 215. 
 
 shows the time and duration of the demand. The external ap- 
 pearance of a portable indicator is shown in Fig. 215. Its 
 operating mechanism consists essentially of two parts, a register- 
 ing element and a timing element. In addition to the device 
 proper, the register of the watt-hour meter, with which it is to be 
 used, is equipped with a cam and contact brushes for opening and 
 closing the electromagnet circuit of the demand meter. 
 
 The operation of this demand meter is well exemplified by the 
 diagram, Fig. 216. The recording element consists of the stylus, 
 electromagnet, ratchet and pawl mechanism, and gearing to trans- 
 mit motion from the armature of the electromagnet to the stylus. 
 The timing element is driven by an 8-day clock. 
 
260 
 
 ELECTRICAL METERS 
 
 In service, the demand meter is electrically connected to the 
 watt-hour meter with which it operates, and the contact device 
 placed on the watt-hour meter register alternately makes and 
 breaks the electromagnet circuit of the demand meter. 
 
 When the contact device in the watt-hour meter closes the cir- 
 cuit through the operating coil of the electromagnet of the de- 
 mand meter the armature of the electromagnet is attracted, the 
 armature lever is moved forward, and the pawl at the end of the 
 
 
 fJiHlfJURt 
 
 souRce 
 Fig. 216. 
 
 armature lever turns the ratchet wheel, which through a system of 
 gears moves the stylus upward over the chart. When the con- 
 tact device opens the circuit through the operating coil of the de- 
 mand meter, a spring returns the armature lever and pawl to their 
 original positions. 
 
 The stylus continues to move upward over the chart as the cir- 
 cuit through the operating coil of the demand meter is alternately 
 closed and opened by the contact device until the end of a time 
 interval is reached. At the end of each time interval, a cam, which 
 is driven by the clock mechanism, has rotated to such a position 
 that the first of two trip levers falls, thus disengaging a sliding 
 pinion from the gear with which it meshes. This opening of the 
 
DEMAND INDICATORS 261 
 
 gear train allows a spring to return the stylus mechanism to the 
 zero position. Further rotation of the cam then allows the sec- 
 ond trip lever to operate, thus returning the sliding pinion to its 
 former position, and reestablishing the gear train between the 
 armature and the stylus. 
 
 The mechanism is now in position to again drive the stylus up- 
 ward over the chart as the watt-hour meter registers the energy 
 consumption during the next time interval. Since the clock 
 mechanism rotates the chart continuously, each succeeding 
 curve drawn by the stylus falls in a more advanced position on the 
 chart. 
 
 224. General.- — Several other forms of demand indicators are 
 now on the market. The maximum-demand instrument is used 
 chiefly in connection with the sale of energy in large quantities, 
 especially when this energy is supplied by polyphase systems at 
 high voltage. The use of the maximum-demand meter is made 
 necessary by the attempt to base the rates for electrical energy 
 upon the cost to each customer. One of the elements of the cost 
 of service is the current or power capacity of the generating equip- 
 ment and of the distribution system. This capacity is, however, 
 a function of the time and amount of the maximum demand of 
 the customer, hence the use of demand indicators is at present 
 slightly on the increase, especially among the public utilities 
 that are subject to public regulation. 
 
 With the exception of the thermal types the indications of de- 
 mand indicators are proportional to watts or kilowatts. As the 
 capacity of generating equipment is limited primarily by current 
 rather than by power on a constant-potential system, it would 
 seem more logical to measure maximum demand in amperes or 
 kilovolt-amperes rather than in kilowatts. 
 
 26 
 
CHAPTER XVI 
 INSTRUMENT TESTING 
 
 226. Introduction. — Every person who has the care and use of 
 electrical instruments of any kind should observe certain ore- 
 cautions in handling them. This is especially true with reference 
 to portable instruments which are easily damaged by careless or 
 ignorant use. 
 
 226. General Precautions. — Too much care cannot be exercised 
 in connecting apparatus for experimental or test purposes. The 
 student should in every case do his thinking in advance and not 
 depend upon correcting mistakes after some trouble has devel- 
 oped. Avoid trouble by arranging everything properly before 
 beginning the test. The supply mains should always be con- 
 nected through a double pole in a two-wire system or a three-pole 
 switch and each circuit should be protected by fuses. The main 
 switch should be left open until all other connections have been 
 made. When everything is properly arranged, a diagram should 
 be made of the connections and examined in order to be sure that 
 they are not endangered by overloads or short-circuits. When 
 everything has been examined, the main switch may be quickly 
 closed and opened to see if there is any indication of short-cir- 
 cuits; if everything is in correct working order the main switch 
 may be closed, and the work proceed; a sharp lookout for trouble 
 during the early stages of the work must, however, be main- 
 tained. The best general direction to a student is — do not 
 guess — ^be sure you are right and then go ahead. While making 
 adjustments, gently tap the dials of all indicating instruments so 
 as to free them from frictional errors. 
 
 ' 227. Kinds of Tests. — The kind of test to be used in any case 
 depends upon the degree of accuracy desired and facilities for 
 conducting the test. In practice, there are two kinds of tests; 
 these may be called standardization and checking tests. The 
 standardization test consists in comparing the readings of the 
 instrument tested with the fundamental units; the checking or 
 comparison test consists in comparing the readings of the tested 
 instrument with the readings of a similar instrument that has 
 been previously standardized. The second test is the one usually 
 used in central stations, especially the smaller ones. 
 27 263 
 
264 
 
 ELECTRICAL METERS 
 
 228. Apparatus for Instrument Testing. — Primary standard 
 instruments, that is, instruments for comparing meters with 
 fundamental units, are not suitable for general use, but should 
 be maintained in a few well-equipped laboratories. Large 
 central stations may also be justified in keeping an equipment of 
 these instruments. The instruments used to check working 
 instruments may properly be called secondary standards. From 
 time to time the secondary standards should be checked by some 
 reliable standardizing laboratory, the Bureau of Standards at 
 Washington, D. C, being one of the best. The number and 
 kind of secondary standards to be provided will depend consider- 
 ably upon the number and kind 
 S t "^ J of working instruments. The 
 
 ^ r~ most essential secondary in- 
 
 struments are portable indicating 
 ammeters, electrodynamometers, 
 voltmeters, wattmeters, variable 
 resistances or rheostats, and one 
 or more of the portable stand- 
 ard integrating watt-hour meters. 
 If some of the simpler stand- 
 ardizing tests are to be made, 
 it will be well to include 
 standard cells, galvanometer, 
 potentiometer, and standard 
 shunt resistances. 
 
 229. The Standard Cell.— 
 The International Electrical 
 Congress of 1908 officially adopted the Weston cell as the standard 
 of electromotive force. This cell is constructed of mercury sur- 
 rounded by mercurous and cadmium sulphate paste for the posi- 
 tive pole; cadmium amalgam for the negative pole; and a solu- 
 tion of cadmium sulphate for the electrolyte. The cells must be 
 bunt up according to definite specifications, and when so con- 
 structed pressures of different cells agree to a few thousandths of 1 
 per cent, when tested under like conditions. A cross-section of 
 a saturated cell is shown in Fig. 217. The unsaturated cell is 
 preferable for use with the potentiometer. 
 
 On Jan. 1, 1911, the Bureau of Standards adopted a new value 
 for the electromotive force of the Weston normal cell, namely: 
 E = 1.01830 international volts at 20°C. 
 
 
 ''i!'.^'^':''.'X['''^ 
 
 —Wax seal 
 
 —Cd. amalgam 
 --Ftelectrvde 
 
 — Cd.SO^ 
 
 (Fbiste of 
 anefCdSQ, 
 
 -Pf. eJec frode 
 
 Pig. 217. 
 
INSTRUMENT TESTING 
 
 265 
 
 The effect of temperature on the Weston cell is slight, so that for . 
 commercial measurements no corrections need be made. For 
 more accurate measurements the electromotive force may be 
 calculated from the following formula: 
 Et = 1.01830 - 0.0000406(i° - 20°) - 0.00000095(i° - 20°)^ 
 where the temperature t° is in Centigrade degrees. This new 
 unit of electromotive force is larger than the old, the change being 
 equal to about 0.08 of 1 per cent, in the value of the international 
 volt. This change affects to a slight extent all measurements of 
 the electric current, electromotive force and power, and in some 
 cases necessitates slight changes in measuring instruments. 
 
 Fig. 218. 
 
 230. Galvanometer. — It is beyond the scope of this text to 
 give an extended discussion of all of the characteristics of a 
 galvanometer, since it is usually classed as a laboratory instru- 
 ment. The principle of operation of the galvanometer is the 
 same as that of the permanent magnet, movable-coil ammeter. 
 In fact, the ammeter was developed from the galvanometer. 
 The movable coil of the galvanometer contains many turns and 
 is suspended between the poles of a strong permanent magnet. 
 The controlling force is due to the twisting of the suspension 
 fiber, and the deflection is read by means of a telescope and scale. 
 One make of galvanometer suitable for use with a potentiometer 
 is shown in Fig. 218. The essential difference between a galvan- 
 
266 
 
 ELECTRICAL METERS 
 
 ometer and a milliammeter is the high sensibility of the former. 
 This higher sensibility permits measurements of a much higher 
 degree of accuracy. 
 
 231. Potentiometers. — The potentiometer is a combination of 
 accurately adjusted resistances used for the comparison of un- 
 known electromotive forces with the electromotive force of a 
 standard cell. For simphcity potentiometers may be considered 
 under two heads; namely, the slide-wire type and deflection type. 
 
 232. Slide-wire Type. — The fundamental principle upon which 
 the operation of either form is based is Ohm's law, or in other 
 words, the fact that the voltage drop along a conductor is directly 
 proportional to the resistance so long as the current remains 
 
 <IH 
 
 •D 
 
 ^ r-^W\AAAAAAAAAAAAAAA^ 
 
 \m 
 
 storage Betfterc/ 
 
 Pig. 219. 
 
 constant. The application of this principle to the comparison or 
 measurement of electromotive forces will be best understood by 
 reference to Fig. 219. This figure shows a storage battery con- 
 nected in series with a high resistance AB. A part of this resist- 
 ance is shunted by a circuit CD, the contact D being movable. 
 In the shunt circuit is connected a sensitive galvanometer G and 
 the unknown source of electromotive force E. The connections 
 of E are reversed with reference to those of the storage battery. 
 
 233. Operation. — When a measurement is to be made, the con- 
 tact, D, is moved either to the right or left, as the case demands, 
 until the galvanometer shows no deflection. When this condi- 
 tion is reached there is no current flowing through the shunt 
 circuit, and if I is the current in the battery circuit, whose resist- 
 ance from C to Z) is R, the voltage drop between CD equals IR. 
 Since no current flows through the shunt circuit, this voltage 
 must equal the unknown voltage E, or 
 
 E = IR. 
 
INSTRUMENT TESTING 267 
 
 If now E be replaced by a standard cell and the position of D 
 be again adjusted until the galvanometer shows no deflection, the 
 voltage drop is equal to the electromotive force of the standard 
 cell. Let this new resistance between C and D be Ri, 
 then 
 
 E. = IRi 
 and E _IR _R 
 
 E, IRi Ri 
 
 Thus, if the instrument is adjusted so that R and Ri can be read 
 off from a dial, E can be calculated, for 
 
 ^^^'Rl- 
 
 234. Leeds and Northrup Potentiometer. — One make of the 
 slide-wire type of potentiometer is shown in Fig. 220. A diagram 
 of the internal connections of this instrument is shown in Fig. 221. 
 The similarity between this and the diagram of Fig. 219 is plainly 
 evident. As shown in the diagram, the essential part consists of 
 three resistances, D to A, A to C, and C to B, connected in 
 series. The contact points of resistance, D to A, are marked to 
 correspond to the electromotive force of the standard cell when 
 corrected for temperature according to formula of Article 229. 
 
 The resistance, A to C, consists of fifteen 5-ohm coils adjusted 
 to a high degree of accuracy. CB is a 5. 5-ohm slide-wire wound 
 around a marble cylinder. 
 
 235. Operation. — When an unknown electromotive force is to 
 be measured, the connections are made as indicated in the dia- 
 gram. Fig. 221. The contact T is set at a point corresponding to 
 the electromotive force of the standard cell when corrected for 
 temperature; the switches U and V are moved to the left, and key 
 V is closed. If the galvanometer shows a deflection, rheostat R is 
 adjusted until the galvanometer shows no deflection when V is 
 moved to the right and closed, and balance is again obtained by 
 adjusting R. When this adjustment has been made, the current 
 through AC is exactly 0.02 amp. The voltage drop across any 
 one of the 5-ohm coils is consequently 0.1 volt, and that across CB 
 is 0.11 volt. It will be observed that the unknown electromotive 
 force is connected between M and M' in series with the galvan- 
 ometer. Since both M and M' are movable, the maximum voltage 
 drop from A to 5 is 1.61 volts. To measure the unknown elec- 
 tromotive force M' is placed at zero, U is moved to the right and 
 
268 
 
 ELECTRICAL METERS 
 
 Pig. 220. 
 
 ■<?3a 
 
 Pig. 221. 
 
INSTRUMENT TESTING 
 
 269 
 
 M is moved from lower to higher values until a change of one 
 contact reverses the direction of the deflection of the galvan- 
 ometer. M is then moved back one point so the deflection is in 
 the same direction as before, and M' is adjusted until the galvan- 
 ometer shows that no current is flowing when V is on Ro. The 
 value of the unknown electromotive force may then be read 
 
 PiQ. 222. 
 
 from the positions of M and M'. The value of the electromotive 
 force is marked on the dial in place of the resistance. 
 
 To measure pressures higher than 1.5 volts the unknown pres- 
 sure must be connected across a high resistance commonly called 
 a volt box, while the potentiometer terminals are shunted across 
 a definite fraction of the high resistance. This method of connec- 
 tion is shown in Fig. 222. The potentiometer is connected to 
 
 <7 
 
 Pig. 223. 
 
 6- 
 
 a and h, and by moving switch M the potentiometer reading may 
 be 0.1, 0.01, or 0.001 of the unknown electromotive force. Cur- 
 rent measurements can also be made on the potentiometer by 
 measuring the drop in volts across a standard shunt. The cur- 
 rent is calculated by Ohm's law. The connections for current 
 measurements are shown in Fig. 223, in which S represents the 
 standard shunt whose resistance is known. The potentiometer 
 
270 
 
 ELECTRICAL METERS 
 
 terminals are represented by a and 6. For precision measure- 
 ments of direct current and electromotive force, the potenti- 
 ometer metliod is far superior to any other, and is today the stand- 
 ard method for such measurements. For commercial work, 
 however, which does not require such a high degree of accuracy 
 the method possesses several disadvantages. The two chief 
 disadvantages are the time required to make the measurements, 
 and the cost of the apparatus. 
 
 236. Defiection-type Potentiometer. — For checking portable 
 instruments Mr. H. B. Brooks of the Bureau of Standards has 
 designed a potentiometer which combines to some extent the 
 
 Pig. 224. 
 
 accuracy of the slide-wire potentiometer and the speed of opera- 
 tion of deflection instruments. 
 
 It was pointed out that the final adjustments of the Leeds and 
 Northrup potentiometer are made by moving contact M'. This 
 adjustment is time-consuming and for most commercial measure- 
 ments unnecessary, were it possible to read or estimate the un- 
 balanced electromotive force. Brooks' deflection potentiometer 
 differs from the slide-wire form mainly in that it permits the 
 reading of the unbalanced electromotive force and the modifica- 
 tions necessary to bring this about. 
 
 Fig. 224 shows the complete deflection-type potentiometer as 
 designed by Mr. Brooks and built by Leeds and Northrup Co. It 
 is seen that the galvanometer is built into the apparatus, so that 
 the instrument is self-contained with the exception of the stand- 
 ard cell and auxihary storage cell. If the instrument is to be 
 portable, the storage cell could be replaced by two dry cells, 
 
INSTRUMENT TESTING 
 
 271 
 
 which, with the standard cell, could be enclosed in the case, 
 making the entire apparatus self-contained. 
 
 237. Theory and Operation. — The essential principles of the 
 instrument will be understood from Fig. 225, which is a diagram 
 of the connections of a simple potentiometer for measurements 
 of voltage and current. 
 
 When voltages higher than the voltage of the standard cell are 
 to be measured, it is necessary to use a volt box or some high 
 resistance as already pointed out. Such a connection is shown at 
 
 vwwv^ 
 
 
 ^ 
 
 ^ 
 
 WWXAAA 
 
 VWXAAAA 
 
 ^^j 
 
 y^T 
 
 /'■^>j 
 
 Fig. 225. 
 
 (a), Fig. 225. R is such a resistance. A suitable fraction of 
 this resistance R/p is connected to the circuit rir^. "When ri has 
 been adjusted so that the galvanometer shows no deflection, 
 we have: 
 
 '-E= ^ . 
 
 ei 
 
 or 
 
 E = n 
 
 ei 
 
 P 
 
 where p is the ratio of the whole resistance R to the portion R/p; 
 or p is the multiplying factor of the volt box. The current 
 through the galvanometer is then 
 
 E 
 
 ei 
 
 n 
 
 ■n±n p 
 
 ^^'^ ^eV_z^ 
 
 ri+ra 
 
272 ELECTRICAL METERS 
 
 The first term in the numerator of this expression is the voltage 
 drop in the portion ri of the potentiometer wire when the galvan- 
 ometer circuit is open; it is therefore numerically equal to the 
 setting of the potentiometer. The second term in the numerator 
 is the voltage drop which would exist around the portion R/p 
 if the galvanometer circuit were open. The denominator is the 
 total resistance in the galvanometer circuit. The expression 
 shows that the current through the galvanometer is equal to the 
 unbalanced portion of the electromotive force divided by the 
 total resistance of the galvanometer circuit. 
 
 Similarly, by the aid of (6) , Fig. 225, it can be shown that when 
 the potentiometer is used for current measurements the cur- 
 rent through the galvanometer is given by 
 
 ei — j E 
 
 ri + r-2 
 
 ig = 
 
 , riTi 
 
 ri+Ti 
 
 This and the preceding expression show the possibility of reading 
 any desired part of the pressure on a properly calibrated galvan- 
 ometer scale provided the total resistance of the galvanometer 
 circuit is kept constant. 
 
 When used for current measurements, the current through R 
 is in general not equal to the line current whose value is desired, 
 being greater or less than the line current by the amount of the 
 galvanometer current. It has been found that a simple expedient 
 will correct for this difference and make the reading of the poten- 
 tiometer (when divided by R) give accurately the value of the 
 line current. 
 
 The manner in which these principles are worked out in detail 
 is shown in Fig. 226. Anyone wishing a more complete explana- 
 tion of the principles of the deflection potentiometer is referred 
 to Bulletin of The Bureau of Standards, vol. 8, No. 2, from which 
 the foregoing explanation is abstracted. A view of the potenti- 
 ometer with its accessories is shown in Fig. 227, which also shows 
 a wattmeter connected for test. The voltage supply line is at 
 the left, a slide resistance being used to set at the desired value. 
 The current is supplied by a storage battery, not shown in the 
 figure. The current is controlled by the carbon rheostat at the 
 right. The volt box, auxiliary storage cell, and standard cell 
 are back of the potentiometer. 
 
INSTRUMENT TESTING 
 
 273 
 
 goaa£t tamojA. 
 
 Fig. 226. 
 
 Pig. 227. 
 
274 
 
 ELECTRICAL METERS 
 
 238. Standard Resistances or Shunts. — For accurate measure- 
 ment of current a set of manganin standard resistances is re- 
 quired. These are usually made for oil immersion and give from 
 0.01 to 1.5 volts drop at maximum current, those intended for 
 high currents giving the lower full-load drop. To keep down the 
 
 Fig. 228. 
 
 Fig. 229. 
 
 size of the shunt, the accuracy for very heavy currents is usually 
 less than for more moderate ones. The resistances are made 
 accurate to a small fraction of 1 per cent, so the results obtained 
 by their use leave little to be desired for commercial purposes. 
 The usual values of these shunts are 1.000, 0.1, 0.01, 0.001, and 
 0.0001 ohm. 
 
 The resistances are made in two forms. Fig. 228 shows a 1- 
 ohm standard of the Reichsanstalt form. Fig. 229 is a 0.00002- 
 ohm shunt of different form. 
 
INSTRUMENT TESTING 
 
 275 
 
 With the slide-wire form of potentiometer it has been common 
 practice to use current shunts whose values are decimal multiples 
 or submultiples of an ohm. These, however, are not the most 
 convenient for all cases, as sometimes calculations will have to 
 be made during the test to determine the setting of the potenti- 
 ometer to correspond to the ammeter reading in order to expedite 
 the work. To facilitate and expedite the readings when a de- 
 flection potentiometer is used, it is necessary to choose shunts 
 whose value will not make these calculations necessary. 
 
 Assuming that the fundamental range of the potentiometer is, 
 say, 150 "dial units," for rapid and convenient work, one scale 
 division on an instrument under test should correspond to one 
 dial unit. Under such conditions the resistance of shunt R is 
 given by 
 
 e.m.f. corresponding to one dial unit 
 
 R =- 
 
 amperes per division of ammeter 
 
 If one dial unit equals 0.01 volt, current shunts required for 
 ammeters of 1, 2, 5, 10, and 20 amp. per scale are 0.01, 0.005, 
 0.002, 0.001, and 0.0005 ohm, respectively. A single shunt will 
 
 Fig. 230. 
 
 usually do for several ranges; thus the 0.01-ohm shunt is suit- 
 able for 100-amp. 100-division, 120 amp. 120-division, and 150- 
 amp. 150-division instruments. The same shunts are equally 
 convenient in testing wattmeters of corresponding current range. 
 239. Variable-resistance Rheostat. — In many tests it is neces- 
 sary to connect to the circuit a resistance which can be varied 
 gradually so as to maintain the current constant. One of the 
 most convenient forms of rheostat is shown in Fig. 230. The con- 
 struction and operation of the rheostat is easily understood from 
 the figure. The resistance consists of many carbon plates rest- 
 ing on slides made of insulating material. The resistance is 
 
276 
 
 ELECTRICAL METERS 
 
 varied by compressing, by means of a hand screw, the plates 
 more or less firmly. 
 
 The chief advantages of such a rheostat are the nicety with 
 which the current can be controlled, the large current-carrying 
 capacity and non-inductive property. This last property makes 
 it suitable for alternating as well as direct currents. 
 
 240. Lamp Bank. — A convenient resistance for many tests 
 be made from carbon filament incandescent lamps. A 
 
 can 
 
 suggestive diagram of a lamp bank is shown in Fig. 231. The 
 resistance of the lamp bank can be varied through wide hmits by 
 closing different switches. For instance, if switches a and b 
 
 y \i> \c V \ V 
 
 Mo/ns 
 
 Fig. 231. 
 
 alone are closed, the lamps in circuit 1 will be lighted ; by closing 
 a, 6, and c, circuits 1 and 2 will be in parallel, etc. 
 
 Connecting circuits in parallel, decreases the resistance and 
 increases the current. To increase the resistance, either unscrew 
 enough lamps in one circuit until the current is the required value, 
 or close switches a and d, or a and /, which will connect the cir- 
 cuits 1, 2, and 3, or 1, 2, 3, 4, and 5 in series. The maximum 
 resistance that can be obtained by the device shown is the resist- 
 ance of five lamps in series; the smallest resistance is the resist- 
 ance of all lamps in parallel. An ingenious student can readily 
 modify the arrangement suggested to meet his particular needs. 
 Such a lamp bank can be used for many purposes in a central 
 station. 
 
INSTRUMENT TESTING 277 
 
 241. Water Rheostat. — In case of an emergency or when very 
 heavy currents are to be measured, the water rheostat is about 
 the only controUing device that can be used. The water rheostat 
 consists of two or more metal plates, usually iron, in a vessel of 
 salt water. The vessel is usually a wooden water-tight box or 
 barrel. The resistance of such a rheostat is varied by immersing 
 more or less of the iron plates, by moving them nearer together 
 or farther apart, or by changing the amount of salt in the solution. 
 
 Other forms of apparatus will be discussed in connection with 
 the tests where used. 
 
CHAPTER XVII 
 TESTING AMMETERS 
 
 242. Introduction. — As pointed out in the previous discussion, 
 all ammeters have a very low resistance and are to be connected 
 in series with the circuit in which the current is to be measured. 
 On account of the extremely low resistance great care must be 
 exercised in connecting them to be sure that excessive current 
 will not flow through the instrument when the circuit is closed. 
 In no case should an ammeter be connected to a circuit without 
 a resistance or rheostat in series with it — the resistance being 
 sufficiently large to reduce the current to a proper value. If the 
 conditions do not enable the student to know beforehand the 
 approximate value of the current, the resistance may be cau- 
 tiously cut out after final connections have been made. 
 
 <S' 
 
 AAAAAA/VNA 
 
 PLJPtU 
 
 Pig. 232. 
 
 243. Comparison, of Ammeters. — The readings of two or more 
 ammeters may be compared by connecting them in series to a 
 suitable source of electromotive force. In series with the 
 ammeters should be connected the lamp bank or other suitable 
 resistance. The resistance is varied stepwise beginning with a 
 small current, and both instruments should be read at the same 
 time. If one of the ammeters has previously been standardized, 
 a comparison of its corrected readings with the readings of the 
 other ammeter will enable the student to determine the correction 
 for the second ammeter. The connections for this test are shown 
 in Fig. 232. In this figure, D is the source of electromotive force 
 which is preferably a storage battery; Ai and Ai are the ammeters 
 
 278 
 
TESTING AMMETERS 
 
 279 
 
 to be compared, and R the variable resistance. The lamp bank 
 will serve very nicely for this purpose, although the carbon 
 rheostat is preferable when a low-voltage storage battery is avail- 
 able. S' is a double-pole switch which should be left open until 
 all other connections have been made, and S" is a short-circuiting 
 switch for the ammeters. This switch should be kept closed 
 except when the readings are being taken. When direct-current 
 ammeters are compared or tested, care must be taken to see that 
 they are connected so as to deflect in the proper direction. 
 
 244. Calibration Curve. — A curve showing the relation be- 
 tween the correct values of the quantity measured and the indica- 
 
 eo 
 
 50 
 AO 
 ■30 
 
 eo 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 / 
 
 i 
 
 
 
 !5 
 
 
 
 
 
 
 / 
 
 / 
 
 
 
 
 R 
 
 
 
 
 
 / 
 
 ^ 
 
 
 
 
 
 ^ 
 ^ 
 
 
 
 
 / 
 
 / 
 
 
 
 
 
 
 
 
 
 r/ 
 
 / 
 
 
 
 
 
 
 
 ^ 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 /' 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 We3> 
 
 5/7 Ai 
 
 \l9liL 
 
 DC 
 
 Ami 
 
 r7efei 
 
 ■ 
 
 
 / 
 
 
 
 A 
 
 mme 
 
 terf 
 
 Uae/i 
 
 '^3 
 
 
 
 
 it> eo ■so ■*(? so 60 70- eo so 
 Pig. 233. 
 
 tions of the instrument should be drawn from the data obtained 
 when an instrument is tested. Thus in the case just considered 
 if the readings of one ammeter are known to be correct, these 
 values may be plotted vertically or as ordinates, while the read- 
 ings of the inaccurate ammeter may be plotted horizontally or as 
 abscissas. A curve or line drawn through the points thus deter- 
 mined will show at a glance the variations in the readings; or if 
 a reading on the inaccurate ammeter is known, the correct value 
 of the current can be at once found from the curve. This is 
 brought out more clearly in Fig. 233, which is drawn from data 
 obtained by comparing a Weston direct-current milUammeter 
 with a Kelvin balance. The data are as follows : 
 
 28 
 
280 
 
 ELECTRICAL METERS 
 
 EXAMPLE 
 
 Test No. 1. — Comparison of milliammeter with Kelvin balance. 
 Apparatus. — Weston milliammeter. ^ 
 
 Kelvin centiampere balance. 
 
 Rheostat. 
 Temperature 22°C. 
 
 Table III 
 
 Ammeter readings 
 
 Balance readings 
 
 Correction 
 
 110 
 
 122.48 
 
 + 12.48 
 
 202 
 
 222.25 
 
 +20.25 
 
 230 
 
 250.00 
 
 +20.00 
 
 330 
 
 362.80 
 
 +32.80 
 
 365 
 
 402.00 
 
 +37.00 
 
 425 
 
 463.90 
 
 +38.90 
 
 668 
 
 722.20 
 
 +54.20 
 
 752 
 
 821.80 
 
 +69.80 
 
 800 
 
 870.00 
 
 +70.00 
 
 900 
 
 983.00 
 
 +83.00 
 
 In Fig. 233, the ammeter readings have been plotted horizon- 
 tally and the correct, or balance readings, vertically. Through 
 
 /oo aoo ,300 
 
 4x)0 SCO 600 7O0 eoo 
 Fig. 234. 
 
 900 tOOO 
 
 the points thus determined the straight line has been drawn. 
 This curve shows that the per cent error of the ammeter is practi- 
 cally constant. Furthermore, if the milliammeter has been used 
 in practice and a reading of 600 milliamp. obtained, it is easy 
 to determine the correct value of the current from the curve. 
 Thus, the ammeter reading of 600 corresponds to the vertical 
 ' This milliameter had previously received very severe use. 
 
TESTING AMMETERS 
 
 281 
 
 line marked 60 at the bottom; running vertically on this line 
 we find it intersects the curve at the point A which corresponds 
 to 650 on the vertical scale; hence, the correct reading is 650 
 milliamp. Any other reading can be interpreted in the same way. 
 It is often just as advantageous to draw a curve showing the 
 relation between the correction to be applied and reading. Such 
 
 f^.c, 
 
 
 S. 
 
 
 
 ' 
 
 *_ 
 
 t 
 
 
 
 e 
 
 
 
 11 
 
 TO 
 
 n 
 
 '■n 
 
 A 
 
 *0 
 
 / 
 
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 _n 
 
 
 
 £ 
 
 w 
 
 
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 r 
 
 
 
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 r 
 
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 Amperes 
 
 Fig. 235. 
 
 a curve is shown in Fig. 234, which is also drawn from the data of 
 Table III. The irregularities of curve. Fig. 234, are perhaps in 
 this case due to friction and lack of sensibility as the milliammeter 
 tested had received some rough usage. 
 
 In Fig. 235 are shown the correction curves of eight American- 
 
282 ELECTRICAL METERS 
 
 make switchboard ammeters whose movements are shown in 
 Fig. 26. Since all of these instruments were new when tested, 
 the irregularities seem to indicate that the scales do not fit, and 
 also that the sensibilities were not closely adjusted. Where the 
 deviation is pronounced, the discrepancj^ may be due to non- 
 uniformity of the magnetic field. A straight-line cahbration 
 curve which shows a constant percentage error is due to a change 
 in the strength of the controlhng spring or in the strength of 
 the magnetic field. 
 
 245, Calibration of Direct-current Ammeters by Means of 
 Standard Resistance and Voltmeter. — Since currents can be 
 accurately determined by measuring the voltage drop across a 
 standard resistance, the same principle can be used for calibrating 
 
 Fig. 236. 
 
 ammeters. The only apparatus necessary is a standardized milli- 
 voltmeter and shunt and rheostat or other adjustable receiving 
 circuit. A good instrument for this purpose is shown in Fig. 236. 
 This is a voltmeter with three ranges, 0-1.5, 0-3, and 0-150 
 volts. The lower range is the most convenient for current 
 measurements. The scale is divided in such a way that it can be 
 read accurately to 0.2 of a scale division, and the accuracy of the 
 instrument is such that measurements of potential may be made 
 within 0.1 of 1 per cent. When direct-current ammeters are to be 
 calibrated they are connected in scries with a source of potential, 
 the resistance R, and shunt as shown in Fig. 237. The voltmeter 
 is connected across the terminals of the shunt as shown. The 
 readings of the ammeters and voltmeter are taken simultaneously, 
 the current is changed and new readings taken, etc. By such 
 
TESTING AMMETERS 
 
 283 
 
 a stepwise process the ammeters can be calibrated over the whole 
 scale. The correct values of current are calculated in accordance 
 with Ohm's law. If R, is the resistance of the shunt and E is 
 the millivoltmeter reading, the current for any one reading is 
 
 E 
 
 I = 
 
 R, 
 
 When the current is changed E will change, but in each case the 
 current is obtained in the same way. Thus, if the millivoltmeter 
 reading is 0.456 volts and the shunt resistance is 0.01 ohm the 
 current is 
 
 Sfane^crrcf Mvm ^^^ 
 
 Ammeters tote calibrate(t 
 
 oAaAaa/ L!ML1|— Lj— i: — R 
 
 5huni 
 
 Fig. 237. 
 
 I = 
 
 0.456 
 
 0.01 " ^^'^ ^"^P" 
 The calculated values should be plotted vertically and the am- 
 meter readings horizontally, as shown in Fig. 233. 
 
 When many ammeters of different ranges are to be calibrated, 
 more than one standard shunt will be necessary. Suppose that a 
 full-scale deflection of the millivoltmeter is obtained with a cur- 
 rent of 500 amp. ; with 50 amp. the deflection will be only 10 per 
 cent of the full scale; below this, the percentage error of the 
 readings will impair the result. Thus, if ammeters below 50 
 amp. are to be calibrated, another shunt of ten times the former 
 resistance should be used; it will give a full-scale deflection for 
 60 amp. and may be used down to 5 amp. For smaller currents 
 still other shunts should be used. 
 
 Millivoltmeters are made for any range from 15 millivolts to 
 1,500 millivolts for full-scale deflection, and, therefore, it is 
 necessary to know the relative values of the shunt and millivolt- 
 meter resistances if appreciable errors are to be avoided. For 
 instance, if the resistance of the millivoltmeter is E„ and of the 
 shunt Rs, the current through the instrument is 
 
 R. r 
 
 L = 
 
 R, -\- Rv 
 
284 
 
 ELECTRICAL METERS 
 
 where / is the current through the ammeter, 
 in the caUbration will then be 
 
 100 jg, 
 
 Rg -\- R-a 
 
 When R, = qq72„ the error is 1 per cent. 
 
 The per cent error 
 
 If appreciable errors 
 
 are not to result ^ must be small. 
 
 246. Deflection Potentiometer Method. — When the deflection 
 potentiometer is used, it replaces the millivoltmeter, and if the 
 proper shunts are available the test can be performed without any 
 calculations. The observer at the ammeter sets successively 
 
 on 10, 20, 30, etc divisions of the scale, and the observer 
 
 at the potentiometer sets the main dial to the same numbers, and 
 depresses the key. The small deflection of the galvanometer 
 gives the correction to be applied to the reading of the instrument 
 
 / OM 
 
 suk 
 
 AM 
 
 ^iOM 
 
 under test, one division of the galvanometer corresponding to 
 0.1 division of the ammeter. The correction curve can be plotted 
 at the time the readings are being taken by putting the pencil on 
 the proper vertical line. Fig. 238. If the galvanometer reads two 
 divisions to the right, the ammeter is in error by 0.2 amp., and the 
 pencil mark is made two divisions below the zero line on the chart; 
 if the galvanometer reading is one division to the left, the mark is 
 made one division above the zero line of the chart. The scale 
 points may be checked several times if desired, and a smooth 
 curve drawn through the pencil marks. Thus a correction curve 
 may be quickly drawn without recording a single figure, and with- 
 out any computation. 
 
 For rapid work, where ammeters of different ranges are to be 
 tested the shunts may be arranged as shown in Fig. 239. This 
 method may be used with a millivoltmeter as well as potentiome- 
 ter. As indicated in the figure the shunts are soldered together, 
 
TESTING AMMETERS 
 
 285 
 
 and their free ends are connected to a millivoltmeter. The Une 
 current enters at A, and may leave at B, C, or D. The section 
 AB is of low resistance and large current-carrying capacity; BC 
 is of lower current capacity and higher resistance, etc. 
 
 It will be evident that the method outlined above may be used 
 for calibrating not only ammeters, but shunts and millivoltme- 
 ters as well. Thus, if the ammeter and millivoltmeter have been 
 standardized, the value of the resistance of the shunt can readily 
 
 E 
 be obtained. According to Ohm's law R = j, and, when 
 
 E and I are known, R can be determined. Similarly E = RI, 
 and a standardized ammeter and shunt may be used for calibrat- 
 ing the millivoltmeter. In case the ammeter cannot be depended 
 upon, an ammeter shunt can be calibrated by connecting it in 
 
 ■A/vvwyw^-^-vwvwwi/V"^^ 
 
 jS, 
 
 yytmt 
 
 Pig. 239. 
 
 series with a standard shunt, and connecting the millivoltmeter 
 first across the standard shunt, and then across the shunt to be 
 calibrated. The ratio of the millivoltmeter readings is the ratio 
 of the resistance of standard to the resistance of shunt being cali- 
 brated. This can be shown as follows: 
 
 The current through both resistances is the same and equal to 7. 
 
 Let R = resistance of standard, 
 and R' = resistance of shunt being checked. 
 Then E = IR 
 and E' = IR'. 
 
 E IR _ R 
 IR' ~ R' 
 
 E'R 
 
 Whence "S/ = Td7 
 
 E' 
 and R' = 
 
 E 
 
 where E is the millivoltmeter reading across the standard and E' 
 the reading across the shunt. 
 
286 ELECTRICAL METERS 
 
 247. Difference between Direct-current and Alternating- 
 current Ammeters and Voltmeters. — The essential differences 
 between direct-current and alternating- current instruments have 
 been pointed out in detail. A brief summary of the main points, 
 with reference to calibration, is necessary. In direct-current 
 ammeters and voltmeters, the force actuating the pointer may be 
 any function of the current, although in most cases it is propor- 
 tional to the first or second power of the current; the straight-line 
 relation being the most convenient on account of the consequent 
 uniformity of scale. 
 
 In alternating-current ammeters and voltmeters the instan- 
 taneous value of the actuating force is proportional to the square 
 of the current or electromotive force at that instant. The aver- 
 age force upon which the steady deflection depends is propor- 
 tional to the average square of the current or electromotive 
 force. The indications of alternating-current ammeters and 
 voltmeters are really a measure of the average value of the 
 square of the alternating quantity. 
 
 Alternating-current indicating instruments, whose indications 
 are independent of frequency and wave form, when calibrated 
 by using direct current, indicate correctly effective values when 
 used in measuring alternating current or electromotive force. 
 This relation may be shown as follows: 
 
 Let / = direct current causing a given deflection 
 
 and let I a. = alternating current causing the same deflection. 
 Then the deflection with direct current is equal to KP, and with 
 alternating current it must be K times the average of i^. 
 
 or KI^ = K average i^ 
 
 whence P = average i^ 
 
 and I = V^average i^ = Ia- 
 
 Si nce the instr ument scale is graduated in values of I, it indicates 
 V average i^, or effective values when used on alternating-current 
 circuits. Thus, alternating-current ammeters whose indications 
 are independent of wave form and frequency when calibrated on 
 direct current, indicate correct effective values of alternating 
 current. The instruments which may be calibrated on direct 
 current are the hot-wire, electrodynamometer, and electrostatic 
 types. 
 
 It is evident from previous discussion of the hot-wire indicating 
 
TESTING AMMETERS 287 
 
 instruments that the indications are proportional to 7^ when di- 
 rect current is flowing, and to the average value of P when alter- 
 nating current is being measured. The indications of the 
 instrument are correct effective values when the instrument is 
 used on alternating-current circuits. 
 
 The electrodynamometer when standardized on direct current, 
 indicates effective values when used for measuring alternating 
 currents. When the two coils are connected in series, the torque 
 exerted upon the moving system, for a given relative position of 
 the coils, is proportional to the square of the current as already 
 pointed out, and the torque is independent of the direction of 
 the current. Most makes of this type of instrument give read- 
 ings of equal accuracy on either direct or alternating currents of 
 ordinary commercial frequencies and wave form. Owing to eddy 
 currents in surrounding metal, and non-uniformity of current 
 distribution in conductors, some makes are subject to slight errors 
 on even commercial frequencies, and on circuits of high frequen- 
 cies the same causes will produce errors in the readings of all 
 electrodynamometer type instruments. 
 
 In addition to the foregoing, the electrodynamometer ammeter 
 has certain limitations. If the current is carried into and out of 
 the moving coil by the usual spiral springs only small currents 
 may be used without injury to the springs. In one of the earliest 
 forms the current is taken into and out of the moving coil by 
 mercury cups; in the Kelvin balance the axis about which the 
 moving system turns is horizontal, and ligaments of fine wire are 
 used as supports and conductors. Both of these instruments are 
 slow and inconvenient to use and require that the current to be 
 measured be quite steady. The readings of the Kelvin balance 
 change appreciably with heating, when kept in circuit for any 
 length of time. The balances also have frequency errors which 
 increase with the ampere capacity of the balance. Several 
 European makers arrange the fixed and movable coils in parallel 
 so that the latter carry only a small part of the current to be 
 measured. In order to avoid errors in the division of the current, 
 due to inductance, the ratios of the inductance to the resistance of 
 each coil are made small and as nearly equal as possible by adding 
 non-inductive resistances to each coil. These instruments are 
 suitable for checking alternating-current ammeters which cannot 
 be accurately caUbrated with direct current. 
 
 Both the fixed and movable coils of the electrodynamometer 
 
288 ELECTRICAL METERS 
 
 voltmeter are made of fine wire and connected in series with a 
 non-inductive high resistance. The high-resistance multipUer 
 reduces to a low value the time constant (ratio of inductance to 
 resistance) of the electrodynamometer coils, and, hence, well- 
 made voltmeters of this type, calibrated on direct current, show 
 practically negligible errors on commercial alternating-current 
 circuits. These instruments, if properly made, are suitable for 
 checking other working instruments. 
 
 Since alternating-current voltmeters require considerably 
 larger currents than the moving-coil direct-current types, some 
 provision should be made for ventilation. Unless this provision 
 is made, the relatively large current develops considerable heat, 
 which accumulates, raising the temperature of the springs and 
 other parts of the instruments and affecting the readings. For 
 very accurate work the series resistance should be mounted sepa- 
 rately from the instrument and ventilated. 
 
 248. Calibration of Altemating-ciurent Ammeters. — From the 
 foregoing discussion, it is evident that some types of alternating- 
 current ammeters can be calibrated in exactly the same manner as 
 direct-current ammeters. The soft-iron and induction-type 
 ammeters should, however, be calibrated on alternating current 
 of the same frequency as that on which they are to be used. The 
 most satisfactory method of calibrating these instruments is by 
 the use of an intermediate direct-current alternating-current 
 standard, such as a hot-wire ammeter or an electrodynamometer. 
 A convenient method of connections for such tests is shown in Fig. 
 240. The diagram shows a standard direct-current ammeter 
 connected to a source of direct-current electromotive force. By 
 means of a double-throw switch the instrument C, which may be 
 an electrodynamometer or hot-wire ammeter, can be connected 
 in series first with the direct-current ammeter, and then with the 
 alternating-current ammeter to be calibrated. The instrument 
 C thus acts as an intermediate standard, and if it is a hot-wire 
 ammeter, its zero reading should be maintained. If the pointer 
 does not return to zero, it may be set to zero by means of the ad- 
 justing screw. 
 
 For measuring high-frequency alternating currents of low value, 
 the Duddell thermo-ammeter described in a previous chapter 
 is very convenient. Its chief advantage lies in the fact that it 
 can be calibrated on direct current and when so calibrated will 
 indicate correct effective values of alternating current of any 
 
TESTING AMMETERS 
 
 289 
 
 frequency or wave form. Furthermore, it has very little self- 
 induction or capacity and may be used as an ammeter or volt- 
 
 aC3tonetini 
 Ammeter 
 
 A.C Am meter 
 x> be calibrvit- 
 
 o 
 
 r\ 
 
 AC. Supp/y 
 o 
 
 A.C.-D.C.Ammefer 
 
 Pig. 240. 
 
 meter, according to whether it is constructed with a high- or 
 low-resistance heater. 
 
CHAPTER XVIII 
 
 TESTING VOLTMETERS, WATTMETERS, POWER- 
 FACTOR, AND FREQUENCY METERS 
 
 249. Introduction.- — Some of the most common and convenient 
 methods of checking ammeters are, with shght modifications, 
 appHcable to voltmeter caUbration as well, the main difference 
 being in the manner of connecting the instrument to circuit, and 
 the necessity of some means of adjusting the pressure instead of 
 current. 
 
 260. Comparison of Direct-current Voltmeters. — Fig. 241 shows 
 the connections for comparing a voltmeter Vi with the standard 
 voltmeter ¥2- The standard voltmeter discussed in Article 245 
 
 wvwy\A 
 
 Fig. 241. 
 
 is well suited for direct-current low-range voltmeter tests. As 
 is clear from the diagram, the two instruments are connected 
 in parallel with each other, and in series with a high resistance. 
 Different readings are obtained by varying the series resistance. 
 As pointed out in the discussion on indicating voltmeters, the 
 deflection or indication of the voltmeter is proportional to the 
 current through the instrument. This current, under constant 
 pressure, is determined by the resistance in the circuit. If R„ is 
 the resistance of voltmeter, R the series resistance, and E the 
 electromotive force, the deflection may be expressed by 
 
 d = K 
 
 E 
 
 R + Rv 
 
 From this it is evident that the deflection will depend upon R, 
 
 290 
 
TESTING METERS 
 
 291 
 
 and that increasing R decreases the indication of the instrument. 
 The value of R must be high in order to get a low reading if E 
 is large. Thus, to reduce the reading one-half, the value of R 
 must be equal to Rv. 
 
 If it is not convenient to provide a large enough series resistance 
 for a sufficient number of readings, the connections may be modi- 
 fied as shown in Fig. 242. To get the maximum desired deflection 
 the two voltmeters are connected across a sufiicient number of 
 lamps in series. For lower readings, the voltmeter connections 
 are changed so as to include one lamp less. The deflection in 
 each case will be determined by the voltage drop across the num- 
 ber of lamps included between the voltmeter terminals, so long as 
 the current through the lamps remains constant. Thus, if r is the 
 resistance of one lamp, I the current, the voltage drop across one 
 lamp is Ir, across two lamps 2Ir, etc. 
 
 / £ J ^ ^ 6 
 
 oooooo 
 
 Ata/ns 
 
 f^ 
 
 Fig. 242. 
 
 Where it is possible to vary the electromotive force of the 
 source, the voltmeters may be connected as shown in Fig. 241, 
 with R omitted. Different readings are then obtained by chang- 
 ing the excitation of the generator, if that is used, or by changing 
 the number of cells in series, if a storage battery is used. 
 
 Both instruments must be left in the circuit when readings are 
 taken if the connections of Fig. 241 are used. Both instruments 
 should also be read at the same time. When multipliers and 
 leads are used, they should be checked with the instrument for 
 which they are intended. 
 
 261. Potentiometer Method. — The most accurate method of 
 checking voltmeters is by means of the potentiometer. The de- 
 flection potentiometer is especially well adapted to this class of 
 work. If the procedure outlined in Article 246 is followed, the 
 checking may be done accurately and rapidly. The correction 
 curve. Fig. 238, may be plotted as the work of checking proceeds. 
 
292 
 
 ELECTRICAL METERS 
 
 The connections for such a test are the same as shown for the 
 voltage coil of wattmeter, Fig. 227, the current line being dis- 
 connected. 
 
 252. Testing Alternating-current Voltmeters. — Alternating- 
 current voltmeters, whose indications are not affected by fre- 
 quency and wave form, may be compared in the manner just 
 explained. For calibrating induction voltmeters, an intermediate 
 standard is most convenient. 
 
 The connections for an intermediate standard are shown in 
 Fig. 243, where V is either a hot-wire voltmeter or some other 
 instrument unaffected by frequency and wave form; Vi is a direct- 
 current standard and V2 the alternating-current voltmeter to be 
 tested. The connections of the diagram are practically the same 
 
 Fig. 243. 
 
 as those of Fig. 241. That is, the voltmeters are connected in 
 series with a high resistance R, and the source of electromotive 
 force. Different readings are obtained by changing R. The dia- 
 gram of Fig. 244 shows a system of connections similar to those 
 of Fig. 242. In addition to the two-pole double-throw switch, a 
 single-pole double-throw switch is most convenient to use. In 
 place of this, however, two single-pole single-throw switches will 
 answer. In case this system of connections is used, R may be 
 most conveniently made up of lamps in series, and different read- 
 ings obtained by changing the connection a. 
 
 When the double-pole switch S is closed to the right, the inter- 
 mediate standard and direct-current voltmeter are connected in 
 parallel to the direct-current circuit; and when the switch is closed 
 
TESTING METERS 
 
 293 
 
 to the left, the intermediate standard and alternating-current 
 voltmeter are connected in parallel to the alternating-current 
 circuit. The single-pole switch must be changed every time the 
 main switch S is changed. 
 
 253. Calibration Curves. — CaUbration curves should be drawn 
 for voltmeters in the same way as for ammeters. The following 
 table will show how to arrange the data obtained from a volt- 
 meter test. 
 
 Fig. 244. 
 
 EXAMPLE 
 
 Test No. 2.— Test of voltmeter. 
 
 Apparatus. — Weston direct-current voltmeter No. 19,229.' 
 
 Weston laboratory standard voltmeter No. 316. 
 
 Lamp bank. 
 Temperature 22°C. 
 
 Table IV 
 
 Standard 
 
 Instrument tested 
 
 Correction 
 
 Remarks 
 
 75 
 
 80.0 
 
 83.0 
 
 88.0 
 
 «7.0 
 
 111.0 
 
 116.5 
 
 132.0 
 
 138.5 
 
 147.0 
 
 -5.0 
 -2.0 
 0.0 
 + 1.0 
 +1.0 
 + 1.5 
 +2.0 
 +2.5 
 +3.0 
 
 See curve, Fig. 245 
 
 81 
 
 
 88 
 
 
 98 
 
 
 112 
 
 
 118 
 134 
 
 
 141 
 
 
 150 
 
 
 
 
 Calibration curves for eight switchboard, moving-coil perma- 
 nent-magnet type of voltmeters are given in Fig. 246. Curve A 
 shows that the controlling spring was too strong, or else the 
 
 ' Students had used this voltmeter very carelessly. 
 
294 
 
 ELECTRICAL METERS 
 
 magnetic field too weak for the scale used. The errors as a 
 whole are small. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . — 
 
 -^ 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 O-**^ 
 
 *" 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ? 
 
 
 y 
 
 /^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 Vb/t 7ief\r /^a 
 
 ngs 
 
 
 
 
 
 
 
 mo i/o 120 /jo /40 /so 
 
 Pig. 245. 
 
 
 
 ea 
 
 40 
 
 eo 
 
 eo 
 
 /eo 
 
 /eo 
 
 /■♦a 
 
 /IB 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 H- ^ 
 
 
 
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 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 ^\/^. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 w 
 
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 'tf 
 
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 W 
 
 /< 
 
 o 
 
 Pig. 246. 
 
 264. Test of Electrodynamometer-type Wattmeter. — The 
 
 indications of wattmeters are proportional to the product of 
 amperes and volts supplied. On direct currents, the product of 
 
TESTING METERS 
 
 295 
 
 amperes and volts gives the correct power, but on alternating 
 currents this product must be multiplied by the power-factor of 
 the circuit. This, however, is not a serious objection, for when a 
 wattmeter is calibrated with direct current it indicates correct 
 power when used with alternating current, provided the induct- 
 ance of the pressure coil is negligible. This fact was demonstrated 
 in Chapter X. 
 
 A wattmeter should indicate correct power supplied to a circuit 
 when either the current, or pressure, or both, vary in value within 
 their respective limits stated on the instrument. In connecting a 
 wattmeter to the testing circuit, provision must be made for 
 varying both the current and electromotive force, and for measur- 
 ing these accurately. This is best 
 done by connecting the instruments 
 as indicated in Fig. 247. In this 
 diagram, B represents a storage 
 battery or other source of electromo- 
 tive force ; the battery is shunted by 
 a high resistance, R, to one terminal 
 of which is connected one terminal 
 of the potential coil of the wattmeter 
 Wm, while the other terminal of the 
 wattmeter is connected to a movable 
 contact K, The current coil of the 
 wattmeter is connected in series with 
 the load L and ammeter Am. L may 
 be the adjustable lamp bank already 
 described. A standardized voltmeter 
 Vm is connected in parallel with the 
 potential coil of the wattmeter. When compensated wattmeters 
 are tested, the independent connection is used for potential con- 
 nection; this cuts out the compensating coil as is evident from 
 Fig. 82. When the connections are made as shown, three 
 separate tests can be made as follows: 
 
 1. With constant voltage and variable current. 
 
 2. With variable voltage and constant current. 
 
 3. With variable voltage and variable current. 
 
 To make the test with constant voltage, carefully read the 
 instruments, all circuits being opened. Insert the smallest load 
 desired and close the switch S. By inserting a smaller or greater 
 number of lamps, the desired value of current can be obtained. 
 
 29 
 
 Pig. 247. 
 
296 
 
 ELECTRICAL METERS. 
 
 Close K and move it along until the voltmeter indicates the 
 proper voltage. 
 
 To obtain reading for different currents, vary the number of 
 lamps. For variable-voltage test, adjust the current through 
 the ammeter for the maximum desired value. Move K so as to 
 get the lowest voltage desired. For other readings move K 
 until a sufficient number up to maximum is obtained, the cur- 
 rent in the meantime is kept constant. For variable current 
 and voltage, adjust the number of lamps and move K until 
 suitable readings on the voltmeter and ammeter are obtained. 
 For different readings change these adjustments. In each case, 
 the three instruments should be read simultaneously. The re- 
 sults may be tabulated as follows: 
 
 EXAMPLE 
 
 Test 3. — Calibration of wattmeter. 
 Apparatus. — Weston wattmeter No. 4,263.' 
 
 Standard voltmeter No. 316. 
 
 Standardized ammeter No. 21,131. 
 
 Lamp bank and rheostat. 
 Temperature 22.5°C. 
 
 Table V 
 
 Voltmeter 
 reading 
 
 Cor- 
 rected 
 volts 
 
 Ammeter 
 reading 
 
 Cor- 
 rected 
 amperes 
 
 True 
 
 watts 
 
 Watt- 
 meter 
 reading 
 
 Correc- 
 tion 
 
 Remarks 
 
 110 
 
 111.5 
 111.5 
 111.5 
 111.5 
 111.5 
 111.5 
 111.5 
 111.5 
 
 2.50 
 
 4.50 
 
 6.50 
 
 8.70 
 
 13.00 
 
 17.50 
 
 22.00 
 
 27.00 
 
 2.75 
 
 4.95 
 
 7.20 
 
 9.57 
 
 14.35 
 
 19.25 
 
 24.00 
 
 29.70 
 
 306.62 
 551.92 
 802.80 
 1,067.50 
 1,600.00 
 2,137.00 
 2,675.00 
 3,212.50 
 
 283.90 
 
 511.00 
 747.00 
 1,000.00 
 1,500.00 
 2,000.00 
 2,500.00 
 3,000.00 
 
 +22.7 
 
 40.9 
 
 65.8 
 
 67.5 
 
 100.0 
 
 137.0 
 
 175.0 
 
 212.5 
 
 
 110 
 
 
 110 
 
 
 110 
 
 
 110 
 
 
 110 
 
 
 110 
 
 
 no 
 
 
 
 Curve, Fig. 248 
 
 Fig. 24.8 shows the correction to be applied at any wattmeter 
 reading with constant voltage and changing current. Similar 
 curves may be plotted for the other two cases, viz., when current 
 is kept constant and voltage is changed, and when both current 
 and voltage are varied. 
 
 The foregoing method of calibration applies only to watt- 
 meters whose indications are independent of frequency and wave 
 
 ' This wattmeter had received rough and severe use by students. 
 
TESTING METERS 
 
 297 
 
 form. Induction wattmeters cannot be calibrated on direct 
 current. Wattmeters of this type are most conveniently cali- 
 
 £30 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 ■ 
 
 
 § 
 
 
 
 
 
 
 
 
 
 
 
 ^^ 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 ^^ 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -^ 
 
 -^ 
 
 
 
 
 l4?///7 ?/■«>/■ 
 
 Hec c/ing 3 
 
 
 
 
 
 
 t£00 I6O0 i^OOO 
 
 Fig. 248. 
 
 brated by placing them in circuit with an electrodynamometer 
 wattmeter which has previously been standardized. A good 
 
 Fia. 249. 
 
 instrument for this purpose is the Watt dynamometer shown 
 in Fig. 249. Each phase of a polyphase wattmeter must be 
 calibrated separately. A diagram of connections for testing 
 
298 
 
 ELECTRICAL METERS 
 
 induction wattmeters is shown in Fig. 250, where Ws represents 
 the standardized wattmeter and Wi the induction instrument to 
 be tested. The current through the potential coil is partly 
 determined by the frequency of the alternating current under 
 constant voltage, and hence the frequency at which the instru- 
 ment was calibrated should always be recorded. 
 
 _w_ 
 
 Loacf Line 
 
 l^s 
 
 Fig. 250. 
 
 255. Testing Single-phase Power-factor Meters. — The power- 
 factor of a circuit has been defined as the ratio of the true power 
 to the apparent power being delivered by an alternating current. 
 
 nm 
 
 Wm 
 
 Vm 
 
 
 
 olOlo 
 
 W.C. 
 
 Pig."' 251. 
 
 If 1 and E are the effective values of current and pressure re- 
 spectively, the power is given by the expression W = KIE = IE 
 cos e, where K, or cos d is called the power-factor. Thus K = 
 
 IXE ^ ^^^ ^® measured by means of a standard wattmeter 
 
TESTING METERS 299 
 
 and I and E by means of a suitable ammeter and voltmeter. The 
 correct power-factor can thus be calculated from the readings 
 of three standardized instruments, wattmeter, ammeter, and 
 voltmeter, connected as in the diagram of Fig. 251. The cor- 
 rection to be applied is then obtained by subtracting the indicated 
 power-factor from the calculated power-factor. In order to 
 use this method for calibrating a single-phase power-factor meter, 
 the load L must be inductive and variable. The methods of ob- 
 taining loads of variable power-factor are described in Chapter 
 XX. At this point it may be noted that a small induction or 
 synchronous motor can be used for the inductive load. The 
 power-factor of the induction motor may be varied by loading 
 it more or less, and the power-factor of the synchronous motor 
 may be varied by varying its field excitation. This is not the 
 most satisfactory method, as the range through which power- 
 factor can be varied is limited. 
 
 256. Testing Polyphase Power-factor Meters. — When the 
 separate circuits of a polyphase system have the same power- 
 factor, the power-factor of the whole system is equal to the power- 
 factor of one of the phases. When the load is unbalanced so that 
 the separate phases have different power-factors, there is no 
 one power-factor that has a definite value or physical significance. 
 The power-factors of the separate phases of a three-phase system 
 are cos Q\, cos di, and cos ^3, while by definition the power-factor 
 of the system is 
 
 pf^j + ^2 + Wi 
 Power-factor = -^tt — , -r, r — 1 n t • The polyphase meter, 
 iiiii -|- £12X2 + -C's-'a 
 
 however, gives the mean of cos 6i + cos 62 + cos 63- The power- 
 factor as given by definition is evidently not the same as that 
 indicated by meter. When the load is balanced, the power- 
 factor is 
 
 Power-i actor = 
 
 VsEJi ^ZEI 
 
 where W represents the power expended in balanced load, E 
 the voltage between mains, and I the current in one main. To 
 test such an instrument on balanced load, it is sufficient to deter- 
 mine the power-factor of one phase and compare that with the 
 instrument indication. For tests of polyphase power-factor 
 meters, the testing apparatus necessary are a standardized am- 
 meter, voltmeter, and wattmeter. These must be connected to 
 
300 
 
 ELECTRICAL METERS 
 
 "^^^ 
 
 'EX^M 
 
 Z" 
 
 
 r To am neter 
 
 -o- 
 
 each phase successively in the manner shown in Fig. 251. Pro- 
 visions should be made for transferring the instrument connec- 
 tions from one phase to another without disturbing the flow of 
 energy. This is readily accomplished by the aid of a polyphase 
 meterboard shown in Fig. 252. While the test is under way, some 
 characteristics of the meter may also be observed. Disconnect 
 the potential circuit, and observe the rotation of the vane under 
 the influence of the revolving field produced by the series windings 
 alone. Reverse two of the series connections and observe the 
 effect. The revolving field of an induction motor will behave in a 
 similar manner. Reverse the potential connections and observe 
 the effect. Can you explain this? 
 
 Polyphase power-factor indicators will give correct indications 
 only on balanced circuits, although slight unbalancing will not 
 greatly affect the reading. Determine what effect an unbalanced 
 load has on the indication. The Westinghouse Electric and Manu- 
 facturing Co. suggests the following 
 method for checking their instru- 
 ments: The moving parts should be 
 perfectly balanced; that is, when 
 no current is passing through the 
 coils, the pointer should remain in 
 any position in which it is placed. 
 The instrument should now be cor- 
 rectly connected to the circuit in the usual manner with the 
 exception that the wire to the lower left-hand binding post 
 should remain disconnected. If the meter is correct in calibra- 
 tion, the pointer, with full-load current on the meter, will come 
 to rest at a position coinciding with a red line in the upper left- 
 hand part of the scale. Should the pointer not come to rest at 
 this point, it should be shifted on the shaft until it rests on the 
 red line. Care should be taken not to disturb the balance by 
 moving the pointer. This procedure simply insures the main- 
 tenance of the original calibration. 
 
 257. Testing Frequency Meters. — The frequency of an alter- 
 nating current depends upon the speed and number of poles of 
 the generator. Thus, if the generator has p field poles and makes 
 n revolutions per minute the frequency is 
 
 Fig. 252. 
 
 7? ?l 
 
 / = 2 -^ fiO ''y^^®® P^"^ second. 
 
TESTING METERS 301 
 
 To test the accuracy of a frequency meter it is only necessary to 
 measure the speed of the generator, count the field poles and 
 calculate the correct frequency by the above formula. The speed 
 can easily be determined by means of an accurate tachometer 
 or speed counter. 
 
 Any inaccuracy in the resonance type of frequency meter can 
 be corrected by filing off, or adding to the solder weight at the 
 top of the reed. It is not advisable for an inexperienced person 
 to attempt this. 
 
 In place of a calibration curve it is preferable to arrange a 
 table showing the instrument indication and correct frequency. 
 The induction type of frequency meter may be calibrated in 
 exactly the same way, but adjustment is made by varying the 
 series resistance until the instrument reads correctly. 
 
 258. Testing Recording Meters.— Since recording instruments 
 are mainly modified forms of indicating meters, they may be 
 tested in exactly the same way as indicating meters of the same 
 type. 
 
CHAPTER XIX 
 TESTING WATT-HOUR METERS 
 
 259. Introduction. — In order that higher efficiency in the 
 operation of watt-hour meters may be maintained, not only the 
 most reliable meters must be used, but constant vigilance is neces- 
 sary in keeping these meters accurate. For this purpose, the 
 meter departments of some companies are equipped with the 
 highest grade of primary standards and all necessary appliances 
 for checking the accuracy of the secondary standards which are 
 employed in meter testing. To the secondary standards already 
 mentioned should be added the rotating standard watt-hour 
 meter. 
 
 260. Rotating Standard Watt-hour Meter. — The instrument 
 to which has been given the name "rotating standard" is at best 
 only a secondary standard. The principles of operation of the 
 rotating standard meter are the same as those of the service 
 watt-hour meters, the construction, however, is modified to meet 
 certain conditions. The conditions that necessitated changes in 
 construction are portability, wide range of current capacity, and 
 ease of determining the number of revolutions. The first con- 
 dition is fulfilled by omitting the iron case and enclosing the 
 operating parts of the meter in a carrying case as shown in 
 Fig. 253. 
 
 While it is not difficult to make the series winding so that 
 different loads might be safely carried, for accuracy and rapidity 
 of testing, it is necessary to construct the series coils in such a 
 manner that the torque will be the same at different loads. 
 This is accomplished by making the current coils in sections, and 
 mounting the sections so that they can be connected in series or 
 parallel. The number of ampere-turns of the series coils are made 
 equal at different full-loads by either a sliding contact, or by 
 changing the external connections. The field windings are 
 usually for full-loads of 1, 5, 10, 20, and 40 amp., or for 1, 5, 
 10, 50, and 100 amp. 
 
 The last condition is fulfilled by affixing a pointer to the end 
 30 303 
 
304 
 
 ELECTRICAL METERS 
 
 of the shaft. This pointer moves over a dial graduated into 100 
 parts making it possible to read to 3ioo of a revolution, and 
 even closer. The whole number of revolutions is indicated by 
 
 two smaller pointers, plainly shown in Fig. 253. Fig. 254 shows a 
 side view of the Duncan rotating standard watt-hour meter with 
 case removed. In Fig. 255 is shown a General Electric induction 
 test meter. The figures plainly show the similarity between the 
 
TESTING WATT -HOUR METERS 
 
 305 
 
 regular service meter and the test meter as the rotating standard 
 should be called. The use of the portable standard watt-hour 
 meter has several advantages, among which may be mentioned: 
 
 1. The use of only one instrument greatly facilitates the 
 testing of meters in service. 
 
 2. Both test and tested meters are subjected to the same 
 conditions; and hence, any variation in load during the test is 
 automatically corrected bj^ the test meter. 
 
 3. Only one man is necessary for testing, as the time of starting 
 and stopping the test meter may be controlled by a push button. 
 
 Fig. 254. 
 
 4. The portable test watt-hour meters are more rugged than 
 indicating instruments, and consequently, they will stand harder 
 usage. 
 
 Against these advantages must be placed the fact that the 
 results obtained are liable to be less accurate than those obtained 
 by the use of well-calibrated indicating instruments. 
 
 261. Meter Timing Device. — A very ingenious method of 
 determining the correct interval of time that energy is flowing 
 through a meter under test has been devised by Mr. F. A. Kartak, 
 Director of the Standards Laboratory, University of Wisconsin, 
 
306 
 
 ELECTRICAL METERS 
 
 A simplified diagram of the essential features of the device are 
 shown in Fig. 256. 
 
 The apparatus automatically closes and opens the voltage 
 circuit of the meter under test. The controlling element is a 
 standard seconds-beating clock whose pendulum P operates a 
 three-point magnetic switch. This switch consists of two per- 
 manent magnets, M and M', one of which is mounted at the 
 lower end of the pendulum and swings with the pendulum above 
 the other magnet M' which is pivoted so that as the pendulum 
 
 Pig. 255. 
 
 swings the lower magnet makes contact first with point C and 
 then with point C in each of which positions it remains until 
 it is moved on the return swing of the pendulum. When the 
 pendulum swings to the right, the circuit of battery B is closed 
 at C and relay R is magnetized and its contacts are closed 
 against the action of the spring S. When this secondary cir- 
 cuit is closed, the electromagnet ilfj is energized with a conse- 
 quent forward movement of its armature. This movement 
 of the armature rotates the ratchet wheel Ra one step. 
 
TESTING WATT-HOUR METERS 
 
 307 
 
 Upon the shaft of the ratchet wheel is mounted an insulated 
 selective switch. This switch consists of a circular disk of 
 insulating material carrying on its edge two contact points Ki 
 and K2. These contact points are connected to two slip rings 
 and then to the circuit by means of brushes. The rotation of 
 the ratchet wheel thus moves forward the contact points on the 
 insulating disk. 
 
 When Ki comes into contact with brush /i, and the magnetic 
 switch M' closes the circuit at C, leg Li of the differential relay 
 DR is energized, attracting the armature A, depressing the 
 
 Meter 
 
 ^Potential Qrcoit 
 of Meter Under Test 
 
 Fig. 256. 
 
 needle N into the mercury cup Hg, and closing the voltage circuit 
 of the watt-hour meter. This voltage circuit remains closed 
 until contact K2 is moved forward and closes the circuit with 
 brush /2, and M' again comes into contact with C, when the leg 
 Li of the differential relay is energized with a consequent opening 
 of the voltage circuit of the watt-hour meter. The duration of 
 the energy flow through the meter is thus determined by the in- 
 terval of time between the closing of the circuits by Errand Ks 
 at /i and fi respectively. This interval of time can be varied by 
 changing the space between Ki and K2. The use of the stop 
 
308 ELECTRICAL METERS 
 
 watch with the accompanying inaccuracies is thus eliminated and 
 a much more accurate measurement can be made. 
 
 262. Kinds of Tests. — The meter committee of the National 
 Electric Light Association recommends that in view of the diver- 
 sity of conditions, and the lack of recognized standard testing 
 methods, meter tests be classified as follows: 
 
 1. Shop tests. 5. Inquiry tests. 
 
 2. Installation tests. 6. Retests. 
 
 3. Periodic tests. 7. Repair tests. 
 
 4. Complaint tests. 8. Special tests. 
 
 263. Shop Tests. — Upon the receipt of the meters from manu- 
 facturers, also when removed from service and before being 
 placed in the stock room, all meters should be carefully examined 
 and tested. Any defects that may be discovered should be cor- 
 rected at that time. These tests, preliminary to installation or 
 storing, are called shop tests. 
 
 264. Installation Tests. — Even if a meter is found to be correct 
 in the shop, it is not safe to assume that it will be correct after 
 being placed in service, and therefore, a test after installation is 
 necessary. In the case of commutator meters, a test is impera- 
 tive. One good plan is to inspect the meter immediately after 
 being connected to service, and then after about 4 weeks test 
 the meter to determine its percentage of accuracy. 
 
 The commutator of a new meter is not always in good working 
 condition when installed and it is advisable to place the meter in 
 service for a time before making a final test. Then again, acci- 
 dents affecting the accuracy of the meter are liable to occur 
 during the installation of the meter and it is necessary to deter- 
 mine whether the accuracy of the meter has been affected. 
 Induction meters should be tested as soon after their installation 
 as possible. 
 
 The best method of making installation tests is by means of a 
 standardized portable watt-hour meter. 
 
 265. Periodic Tests. — No matter how good the construction 
 of a meter, nor how accurate its registration, its accuracy will 
 diminish with time. Tests at regular intervals are, therefore, 
 necessary to determine whether the permissible error is not 
 exceeded. 
 
 Those periodic tests should be made at intervals to suit the 
 circumstances. Commutator meters, being more liable to be- 
 
TESTING WATT-HOUR METERS 309 
 
 come inaccurate, should be tested more frequently than induction 
 meters whose rugged construction and absence of commutator 
 makes them immune to certain troubles. No definite rule can be 
 formulated for determining the interval of time between periodic 
 tests of different capacities of meters and for different classes of 
 business, yet every company should appreciate the necessity for 
 testing every class of meters before its maximum error exceeds 
 the permissible limits. The interval between tests must be deter- 
 mined by experience, cost of metering, amount of bill, etc. 
 
 266. Complaint Tests. — When a consumer complains of his bill, 
 it is frequently customary to test the meter unless a test has 
 been made very recently. Complaint tests are conducted in the 
 usual manner, except that it is customary to test the meter, 
 not merely on light and full loads, but also on the other loads, 
 especially on the normal load or load most generally used. 
 
 267. Inquiry Tests. — Inquiry tests are tests ordered by the 
 company itself before the bill is rendered, to determine whether 
 or not the meter has been operating properly. 
 
 268. Retests. — Retests are tests made before current is 
 reintroduced to meter which has been out of service for a long 
 time; or if the meter has been opened by any one not authorized; 
 or if the meter has been moved or reconnected. 
 
 269. Repair Tests. — Meters that have been repaired in service 
 should be tested immediately after the completion of the repairs. 
 Such tests are properly termed repair tests. 
 
 270. Special Tests. — Any tests not properly coming under any 
 of the foregoing headings may be classed as special tests. 
 
 271. Meter Constants. — Since the number of revolutions of the 
 meter disk is merely proportional to the energy that has passed, 
 some constant must be used to convert the number of revolutions 
 into watt-hours or kilowatt-hours. Two kinds of constants are 
 used in practice, namely — dial constant, and test constant. 
 
 272. Dial Constant. — On large-capacity meters the difference 
 between any two readings seldom gives the watt-hours directly. 
 To get the energy that has been registered, the difference between 
 the dial statements must be multiplied by a constant which is 
 usually marked on the dial. This is known as the dial constant. 
 It has different values for meters of different capacities. 
 
 273. Test Constant. — Manufacturers of meters usually stamp 
 or print upon some part of the meter a constant which is used in 
 
310 ELECTRICAL METERS 
 
 testing, but as there is no uniformity in the meaning of this 
 constant, its significance must be explained. 
 
 274. Watt-hour Constant. — Since the meter registers in watt- 
 hours, for every revolution of the disk, a definite quantity of 
 energy must have been delivered to the load circuit. This 
 energy, in watt-hours corresponding to one revolution of the 
 disk, is called the watt-hour constant. 
 
 275. Watt-minute or Watt-second Constant. — A watt-hour is 
 the energy delivered by 1 watt in 1 hr. ; similarly, a watt-minute, 
 or watt-second, is the energy or work done by 1 watt in 1 min. or 
 1 sec, respectively. A watt-minute is thus equal to }4o watt- 
 hr., and a watt-second equal to M,600 watt-hr., and hence, 
 the watt-minute constant is equal to 60 X watt-hour constant, 
 and a watt-second constant is equal to 3,600 X watt-hour constant. 
 
 Let Kh = watt-hour constant, 
 
 Km = watt-minute constant, 
 and Ks = watt-second constant, 
 then Ks = 3,600^^ = 60 X^. 
 
 The test constant as used by manufacturers is either one of these 
 or a multiple of one of these constants. 
 
 276. Use of Constant in Testing. — The accuracy of a meter is 
 
 expressed by the ratio of its indication to the actual watt-hours 
 
 in per centw In algebraic. symbols this may be expressed by 
 
 , „„ , , meter watt-hours ^ , 
 
 100 X actual watt-hours = Percentage of accuracy. 
 
 The numerator is, of course, the indication of the watt-hour 
 meter during a given time, while the denominator is the actual 
 number of watt-hours, as measured by standard instruments. 
 If the actual watt-hours are determined by means of an indicating 
 wattmeter, the indication will have to be multiplied by the time 
 during which the observations were made. Thus, the actual 
 watts as given by the indicating instruments multiplied by 
 r/3,600, will give the actual watt-hours. T is the duration of 
 test in seconds, and 3,600 is the number of seconds in 1 hr. 
 
 It is usually impossible to determine accurately the meter 
 watt-hours for a short time from the dial indications of the meter, 
 and, hence, in practice the number of revolutions of the disk 
 during a definite time is determined by means of a stop watch or 
 other timing device. The meter watt-hours are then computed 
 as above. 
 
 
,i^c 
 
 
 TESTING WATT-HOUR METERS 311 
 
 Since the watt-hour constant has been defined as the number 
 of watt-hours, corresponding to one revolution of the disk, the 
 total number of watt-hours will be equal to the watt-hour con- 
 stant times the number of revolutions, or 
 
 watt-hours = Kh X R 
 
 where R is the number of revolutions counted in time T. We 
 
 can, therefore, write 
 
 T 
 Meter watts X o-qqq = Kh X R 
 
 Tv/r . ^. KhXRX 3,600 
 or Meter watts = —^ 
 
 This is the standard formula as used, in one form or another, 
 by all meter manufacturers. If all meter manufacturers used 
 this formula, the watt-hour constant would be the test constant, 
 but as different manufacturers use different modifications, this 
 simple relation does not hold in every case. The constants as 
 used by the various companies are: 
 
 General Electric Co. : 
 
 Test constant = watt-hour constant 
 or Kh = Kg. 
 Duncan Electric Manufacturing Co.: 
 
 Test constant = watt-minute constant 
 
 Westinghouse Electric and Manufacturing Co. : 
 Test constant = watt-second constant 
 
 Fort Wayne Electric Works: 
 
 Test constant = 36 times the watt-hour constant 
 
 1^ Kf 
 or K, = 3g- 
 
 Where Kh represents the watt-hour constant and Kg, Ka, K„, 
 Kf, represent the test constants of the General Electric, Duncan, 
 Westinghouse, and Fort Wayne companies, respectively. 
 
312 ELECTRICAL METERS 
 
 If a rotating standard watt-hour meter has been used for 
 determining the actual energy passed through the meter under 
 test, the percentage of accuracy is given by 
 
 ,^„ RXK (of meter under test) , . 
 
 100 R'XK' (of standard) = Percentage of accuracy. 
 
 R and K are the number of revolutions and constant of the meter 
 under test, while R' and K' are the corresponding quantities of 
 the rotating standard. It is thus evident that before the above 
 formula can be used, K and K' will have to be reduced to the 
 same basis. That is, a Westinghouse rotating standard cannot 
 be used to test a Fort Wayne meter until the constants have been 
 reduced either to watt-hours or watt-seconds (see Table VI). 
 
 277. Methods of Loading. — In practice there are several differ- 
 ent methods of loading meters under test. The most common 
 
 methods are: 
 
 1. The consumer's load. 
 
 2. Portable lamp bank. 
 
 3. A specially designed and con- 
 structed load box. 
 
 4 Portable storage batteries. 
 5. Step-down transformers. 
 278. The Consumer's Load.— While 
 Fig. 257. this method is convenient, in that little 
 
 accessory apparatus is necessary, the 
 annoyance to the consumer and the liability to misunderstand- 
 ing make it advisable to avoid this method as much as possible. 
 
 279. Portable Lamp-bank Method. — One form of lamp bank 
 which may be used for this purpose has been suggested. These 
 lamps are operated at the lamp voltage and the load is changed 
 by changing the number of lamps in the circuit. 
 
 280. Special Load-box Method. — ^Load boxes may be merely 
 self-contained non-inductive resistances to which may be attached 
 indicating instruments. One form of such a load box is shown 
 in Fig. 257 which is known as the Knopp load box. This is a 
 variable resistance box upon which is mounted an indicating 
 ammeter. The resistance box has several coils which may be 
 connected in different ways for different loads. The exact power 
 consumption under a given voltage may be predetermined and 
 marked on the box. In series with the loading resistance is 
 connected a second resistance whose value may be varied by 
 sliding contacts. By the use of this second resistance the voltage 
 
TESTING WATT-HOUR METERS 
 
 313 
 
 drop across the load coils may be made equal to the voltage at 
 which the power consumption of the coils was determined. The 
 pressure coil of the watt-hour meter is connected so that the 
 voltage impressed upon the meter is the same as that impressed 
 upon the load coils. The reading of the ammeter is thus suffi- 
 cient for determining the load. Fig. 258 shows the internal 
 connections of the Knopp load box. When the box is to be used 
 on 110- volt circuits, the plugs 0, a, b, and c, are used. On 220- 
 volt circuits additional resistance is connected in series by using 
 plugs 0', a', V, and c'. The Knopp load box may be used on 
 either direct-current or alternating-current circuits. 
 
 Source 
 
 
 
 V/atthour Meter 
 Ammefer 
 
 
 AAAA/WW 
 
 . .rAAAAAlAA/^ ■— ^*-' ' 
 
 ^l^(\AAAAA/~- ■— ^-1 
 
 ^TOffi 
 
 LaaAaaa/i 
 
 L-A/VKAAA/ 
 
 Fig. 258. 
 
 Volt-, mpera 
 Meter 
 
 Bofrert/ 
 
 ffiSBSSSHBh 
 
 Plug Resistance 
 
 \Anr7 able Potential Heahfot 
 
 □ 
 
 Wat thou r t^ter 
 
 Pig. 259. 
 
 281. Portable Storage-battery Method. — For testing direct- 
 current meters on the consumer's premises the portable storage 
 battery has many advantages. The load current is supplied at a 
 low voltage and hence the energy required for making the test is 
 much less than when the load current is taken from the line. Any 
 desired current can be obtained in a simple manner, and when once 
 the adjustments are made, the current will remain practically 
 constant. For ease of manipulation and rapidity of operation, 
 some regulating device must be used with the battery. One 
 
314 
 
 ELECTRICAL METERS 
 
 good arrangement of resistances is shown in diagram, Fig. 259. 
 Other devices can easily be designed. 
 
 Fig. 260. 
 
 282. Low-voltage Transformer Method. — There are on the 
 market several different makes of low-voltage transformers com- 
 bined with resistances for alternating-current meter testing. 
 
 //O Vc/t^ 
 
 I 7b Line (V 
 
 
 O n 
 
 Fig. 261. 
 
 The general principles of all are the same, hence only one will be 
 described. The appearance of the RolUnson load box is shown 
 in Fig. 260, the internal connections of which are shown in Fig. 
 261. The diagram clearly shows that the load box is primarily 
 
TESTING WATT-HOUR METERS 
 
 315 
 
 a step-down auto-transformer, the secondary of which supplies 
 current to the series coils of the tested and testing meters. The 
 resistances for controlling the voltage impressed on the primary- 
 are El, Ra, and the circular-dial rheostat. The load current is 
 thus varied by connecting these resistances in series or parallel 
 by adjusting the rheostat, and by connecting in the load a greater 
 or smaller number of secondary turns. 
 
 The manner of connecting the tested and testing meters to the 
 load box is shown in Fig. 262. 
 
 -3 ^ >. , JJ 
 
 » u u — c 
 
 Meftr Officer Tiat Starx^Brv/ Meftr 
 
 Fig. 262. 
 
 Where step-down transformers are used, it is advisable first 
 to make a thorough test of the influence of the transformer upon 
 the power-factor. The power-factor of the testing circuit will in 
 most cases be less than unity and under extreme conditions 
 unduly low power-factors may be obtained. It is thus necessary 
 to test all such load boxes for power-factor under working 
 conditions. 
 
 283. Determination of Watt-hour Constant, Experimentally. — 
 To determine Kk, for a direct-current watt-hour meter experi- 
 mentally, connect the instruments as shown in Fig. 263, where 
 
316 
 
 ELECTRICAL METERS 
 
 M represents a direct-current integrating meter, VM a voltmeter, 
 and MVM a standard millivoltmeter with its shunt S. The 
 source of power is preferably a storage battery. Both the pressure 
 and current are kept constant and the exact time of a definite 
 number of revolutions is determined by means of the stop watch. 
 The current is obtained from the millivoltmeter indications, 
 divided by the resistance of the shunt. K is then calculated 
 
 from 
 
 watts X T 
 
 K = 
 
 R 
 
 ^\ Loot/ 
 
 Pig. 263. 
 
 284. Method of Procedtirie, — ^Before taking any readings, 
 enough time must elapse for the pressure coil to reach normal 
 temperature. This is true of both direct-current and alternating- 
 current meters. This time can be shortened considerably if 
 some provision is made for subjecting the pressure coil to double 
 voltage for a short period. This can easily be done on three- 
 wire circuits, where pressure coils are connected between neutral 
 and one main. Before taking any readings, make a white mark 
 on the disk, adjust the voltage to the proper value, and insert all 
 of the load resistance where a variable reistance is used. If the 
 lamp bank is used, insert three or four lamps in series, and gradu- 
 ally increase the current until the armature commences to rotate. 
 Repeat this three or four times and take the average of the 
 currents. All values of the current below this value are not 
 recorded by the meter, since they do not cause rotation of the 
 armature at the normal voltage. 
 
 Adjust the resistance of lamps so that the full-load current 
 passes through the meter, count the revolutions in 1 min. or 
 some other suitable interval of time. 
 
TESTING WATT-HOUR METERS 
 
 317 
 
 Repeat the test with decreasing values of load current. Care 
 must be taken that the speed is not affected by external causes, 
 such as air draughts, touching with the hand, etc. If the test 
 constant, as given by the manufacturers, is not given in watt- 
 hours, it can readily be obtained by means of relations already 
 given. 
 
 This constant should be 
 determined at different loads 
 and different temperatures. 
 When this is done, it will be 
 observed that the value of the ^ 
 constant depends to some ex- 
 tent upon the temperature 
 and load. A diagram show- 
 ing this relation for a com- 
 mutator-type watt-hour 
 meter is shown in Fig. 264. 
 It will be observed that the 
 constant at any given temperature first decreases to a minimum 
 and then increases with increase in load. This increase is even 
 more prominent at overloads. A change in temperature has a 
 similar effect, namely, as the temperature increases the constant, 
 K, decreases. 
 
 a4 ae 
 
 LOAD 
 
 Fia. 264. 
 
 ^A 
 
 r 
 
 c 
 
 s 
 
 OOOQ 
 
 
 III-—- H|lF 
 
 A/wyw-* 
 
 Fig. 265. 
 
 In Fig. 263 a storage battery is represented as the source of 
 current for the series coils. For testing the commutator type, or 
 direct-current watt-hour meters, it is a good plan to provide a 
 few cells of a storage battery, preferably of the portable form, 
 for supplying the load current, and many small cells for the 
 excitation of the voltage circuit. When two sources of pressure 
 
318 
 
 ELECTRICAL METERS 
 
 Table VI. — Table Testing Constants op Standard Types op Watt- 
 hour Meters 
 
 Capacity of 
 meters in 
 amperes 
 
 Sangamo types "F" and "D" 
 
 Testing constant 
 
 100-125 volts 
 
 Watt- Watt- 
 houis seconds 
 
 200-250 volts 
 
 Watt- Watt- 
 liours seconds 
 
 G. E. types "C6," "J2," and "D2" 
 
 Testing constant 
 
 100-120 volts 
 
 Watt- Watt- 
 bours seconds 
 
 200-220 volts 
 
 Watt- Watt- 
 hours seconds 
 
 2K 
 
 3 
 
 6 
 
 5 
 
 10 
 
 15 
 
 20 
 
 25 
 
 30 
 
 40 
 
 50 
 
 60 
 
 75 
 
 80 
 
 100 
 
 150 
 
 200 
 
 300 
 
 H 
 
 2 
 2H 
 
 6K 
 10 
 
 13M 
 20 
 
 1,800 "F" 
 
 2,400 "D" 
 
 2,400 
 
 4,800 
 
 7,200 
 9,600 
 
 14,400 
 
 19,200 
 24,000 
 36,000 
 48,000 
 72,000 
 
 450 
 
 1 
 
 m 
 
 IH 
 
 2H 
 
 4 
 5>^ 
 
 8 
 
 105^ 
 
 13K 
 
 20 
 
 26?^ 
 
 40 
 
 3,600 "F" 
 4,800 "D" 
 4,800 
 
 9,000 
 
 14,400 
 19,200 
 
 28,800 
 
 38,400 
 48,000 
 72,000 
 96,000 
 144,000 
 
 2 
 
 3 
 
 4 
 6 
 
 12>i! 
 
 720 
 1,440 
 2,160 
 
 3,600 
 
 7,200 
 
 10,800 
 
 14,400 
 21,600 
 
 45,000 
 
 H 
 
 4 
 6 
 
 12K 
 25 
 
 900 
 
 1,440 
 2,700 
 4,600 
 
 7,200 
 
 14,400 
 21,600 
 
 27,000 
 45,000 
 
 90,000 
 
 Table VI — Continued 
 
 
 G. E. 
 
 types "J," ' 
 "DN," 
 
 JI," "JN 
 and "DI 
 
 ,, ..pj,j .. 
 
 G. E. type-"I" 
 
 Capacity of 
 meters in 
 amperes 
 
 
 Testing 
 
 constant 
 
 
 
 Testing 
 
 constant 
 
 100-101 volts 
 
 200-220 volts 
 
 100-130 volts 
 
 200-260 volts 
 
 
 Watt- 
 
 Watt- 
 
 Watt- 
 
 
 Watt- 
 
 Watt- 
 
 Watt- 
 
 Watt- 
 
 Watt- 
 
 
 hours 
 
 seconds 
 
 hours 
 
 
 seconds 
 
 hours 
 
 seconds 
 
 hours 
 
 seconds 
 
 2M 
 
 
 
 
 
 
 
 
 
 
 3 
 
 H 
 
 720 
 
 H 
 
 
 1,440 
 
 H 
 
 720 
 
 H 
 
 1,440 
 
 5 
 
 M 
 
 1,800 
 
 1 
 
 
 3,600 
 
 51o 
 
 1,080 
 
 H 
 
 2,160 
 
 10 
 
 >i 
 
 1,800 
 
 1 
 
 
 3,600 
 
 'A 
 
 2,160 
 
 ni 
 
 4,500 
 
 15 
 
 1 
 
 3,000 
 
 2 
 
 
 7,200 
 
 1 
 
 3,600 
 
 2 
 
 7,200 
 
 20 
 
 
 
 
 
 
 
 
 
 
 25 
 
 1 
 
 3,600 
 
 2 
 
 
 7,200 
 
 IH 
 
 5,400 
 
 3 
 
 10,800 
 
 30 
 
 
 
 
 
 
 
 
 
 
 40 
 
 
 
 
 
 
 
 
 
 
 50 
 
 2 
 
 7,200 
 
 4 
 
 
 14,400 
 
 3 
 
 10,800 
 
 6 
 
 21,600 
 
 60 
 
 
 
 
 
 
 
 
 
 
 75 
 
 
 
 
 
 
 5 
 
 18,000 
 
 10 
 
 36,000 
 
 80 
 
 
 
 
 
 
 
 
 
 
 100 
 
 
 
 
 
 
 6 
 
 21,600 
 
 12H 
 
 45,000 
 
 150 
 
 
 
 
 
 
 10 
 
 36,000 
 
 20 
 
 72,000 
 
 200 
 
 
 
 
 
 
 12M 
 
 45,000 
 
 25 
 
 90,000 
 
 300 
 
 
 
 
 
 
 20 
 
 72,000 
 
 40 
 
 144,000 
 
TESTING WATT-HOUR METERS 
 Table VI — Continued 
 
 319 
 
 
 Westinghouse types "B" and "C" 
 
 Fort Wayne type "K" (345,000 
 and above) 
 
 Capacity of 
 
 Testing constant 
 
 Testing constant 
 
 meters in 
 amperes 
 
 100-110 volts 
 
 200-220 volts 
 
 110 voIts-2w 
 
 220 volt8-2w 
 
 
 Watt- 
 hours 
 
 Watt- 
 seconds 
 
 Watt- 
 hours 
 
 Watt- 
 seconds 
 
 Watt- 
 hours 
 
 Watt- 
 seconds 
 
 Watt- 
 hours 
 
 Watt- 
 seconds 
 
 2H 
 
 
 1,200 
 2,400 
 4,800 
 
 9,600 
 9,600 
 
 H 
 'l>^ 
 
 
 .... 
 
 "h 
 
 1 
 IM 
 
 2 
 '2H 
 
 3?i 
 
 5 
 
 7M 
 10 
 
 900 
 
 1,800 
 2,700 
 3,600 
 4,500 
 
 7,200 
 
 9,000 
 13,500 
 
 18,000 
 27,000 
 36,000 
 
 1 
 
 IH 
 2 
 2H 
 
 4 
 
 5 
 
 10 
 15 
 
 ISH 
 
 
 3 
 
 5 
 
 S 
 
 10 
 
 15 
 
 2 
 4 
 
 ,400 
 800 
 
 1,800 
 
 3,600 
 5,400 
 
 20 
 25 
 
 9 
 
 600 
 
 7,200 
 9,000 
 
 14,400 
 
 30 
 40 
 SO 
 
 19 
 
 200 
 
 60 
 
 
 
 18,000 
 
 75 
 
 
 
 27,000 
 
 36,000 
 54,000 
 57,000 
 
 80 
 100 
 150 
 
 19 
 
 200 
 
 200 
 
 
 
 300 
 
 
 
 
 
 
 
 
 
 
 Fable 
 
 VI — Continued 
 
 
 
 
 
 Fort Wayne type "K" (344,999 
 and less) 
 
 Gutniann meters 
 
 Capacity of 
 
 Testing constant 
 
 Testing constant 
 
 meters in 
 amperes 
 
 110 voIts-2w 
 
 220 volts-2w 
 
 50 volts 
 
 100 volts 
 
 
 Watt- 
 hours 
 
 Watt- 
 seconds 
 
 Watt- 
 hours 
 
 Watt- 
 seconds 
 
 Watt- 
 hours 
 
 Watt- 
 seconds 
 
 Watt- 
 hours 
 
 Watt- 
 seconds 
 
 2M 
 
 « 
 
 1 
 1 
 1 
 2 
 2 
 2 
 3 
 3 
 
 4 
 6 
 8 
 
 900 
 
 900 
 
 1,800 
 
 3,600 
 
 3,600 
 
 3,600 
 
 7,200 
 
 7,200 
 
 7,200 
 
 10,800 
 
 10,800 
 
 14,400 
 21,600 
 28,800 
 
 1 
 
 m 
 
 2 
 
 2 
 
 3 
 
 4 
 5 
 
 6 
 
 8 
 12 
 16 
 
 1,800 
 
 1,800 
 
 3,600 
 
 5,400 
 
 7,200 
 
 7,200 
 
 9,000 
 
 10,800 
 
 14,400 
 
 18,000 
 
 21,600 
 
 28,800 
 43,200 
 67,600 
 
 1 
 
 2 
 
 2 
 3 
 6 
 
 
 
 
 3 
 5 
 10 
 15 
 20 
 25 
 30 
 
 1,200 
 1,200 
 
 1,800 
 
 1 
 
 900 
 1,200 
 1,200 
 
 3,600 
 
 40 
 
 
 
 
 60 
 60 
 
 3,600 
 
 2 
 
 7,200 
 
 75 
 
 80 
 
 100 
 
 150 
 
 200 
 
 7,200 
 
 7,200 
 10,800 
 21,600 
 
 2 
 
 3 
 6 
 
 7,200 
 
 10,800 
 21,600 
 
 31 
 
320 
 
 ELECTRICAL METERS 
 
 Table VI — Continued 
 
 
 Duncan meters 
 
 Columbia meters 
 
 Capacity of 
 
 Testing constant 
 
 Testing constant 
 
 meters in 
 amperes 
 
 100- 
 
 125 volts 
 
 200-250 volts 
 
 110 volts 
 
 220 volts 
 
 
 Watt- 
 hours 
 
 Watt- 
 seconds 
 
 Watt- 
 hours 
 
 Watt- 
 seconds 
 
 Watt- 
 hours 
 
 Watt- 
 seconds 
 
 Watt- 
 hours 
 
 Watt- 
 seoonds 
 
 2H 
 
 3 
 
 5 
 10 
 15 
 20 
 
 H 
 
 450 
 
 Vl 
 
 1,800 
 
 «6 
 
 500 
 
 Ms 
 
 1,000 
 
 1 
 
 900 
 1,800 
 3,600 
 
 1 
 2 
 
 1,800 
 3,600 
 7,200 
 
 Ms 
 
 1,000 
 2,000 
 3,000 
 
 1% 
 
 2,000 
 4,000 
 6,000 
 
 25 
 30 
 
 1 
 
 3,600 
 
 2 
 
 7,200 
 
 IMs 
 
 5,000 
 
 2^ 
 
 10,000 
 
 40 
 
 
 
 • > > ■ 
 
 
 • > . • 
 
 
 
 
 50 
 60 
 
 2 
 
 7,200 
 
 4 
 
 14,400 
 
 2J« 
 
 10,000 
 
 6 Mo 
 
 20,000 
 
 75 
 80 
 
 3 
 
 10,800 
 
 6 
 
 21,600 
 
 4H 
 
 15,000 
 
 8M 
 
 30,000 
 
 100 
 150 
 200 
 300 
 
 4 
 6 
 8 
 
 14,400 
 21,600 
 28,800 
 
 8 
 12 
 16 
 
 28,800 
 43,200 
 57,600 
 
 5 54 
 
 8M 
 
 11 H 
 
 16K 
 
 20,000 
 30,000 
 40,000 
 60,000 
 
 11 H 
 16 54 
 22 54 
 33K 
 
 40,000 
 
 60,000 
 
 80,000 
 
 120,000 
 
 are used, the connections of the voltmeter and voltage circuit 
 of watt-hour meter are to be made according to Fig. 265. 
 
 In making the foregoing test, it is best to taks at least three 
 readings at each load, and to vary the load so that the constant 
 may be determined at 10, 25, 50, 100, and 125 per cent, of the load. 
 
 From data obtained, a curve similar to that shown in Fig. 
 264 should be drawn. If any reading is wrong, it will easily 
 be detected by the corresponding point not coming on the curve. 
 
 285. Test for Percentage of Accuracy. — In commercial practice, 
 it is not often necessary to determine K% or the watt-hour 
 constant, as the test constant is given by the maker, as well as 
 the formula by which the number of revolutions are to be 
 translated into watt-hours. The quantity that is of most interest 
 commercially is the percentage of accuracy which is defined as 
 the ratio of the registered watt-hours, expressed as a percentage, 
 in a given time to the true watt-hours, or kilowatt-hours. That 
 is, the important question is how much too fast or too slow is 
 the meter, rather than the characteristics of the meter. 
 
TESTING WATT-HOUR METERS 
 
 321 
 
 When an ammeter and voltmeter are to be used in testing a 
 direct-current watt-hour meter, the connections shown in Figs. 
 263 and 265 may be used. The watts registered are calculated 
 from the constant of the meter, number of revolutions of disk, 
 and duration of test, thus : 
 
 KhXRX 3,600 
 
 Meter watts 
 
 T 
 
 The true watts are obtained from the readings of the indicating 
 instruments and are equal to I X E. The percentage of accuracy 
 is then equal to 
 
 lOOi*:* X J? X 3,600 
 
 Percentage of accuracy 
 
 TXIXE 
 
 It must be remembered that Kh is the watt-hour constant, and 
 as some manufacturers of meters use other constants, the value 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 5 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 1 
 
 
 ^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 / 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 / 
 
 
 
 
 
 
 '^ri. 
 
 ent L 
 
 oad 
 
 
 
 
 
 oo *o so eo 
 
 70 ao 9o too //o i^o lao 
 
 Pia. 266. 
 
 of the manufacturer's constant in terms of Kh will first have to 
 be determined before substituting in the above formula. The 
 percentage of accuracy should be determined for 10, 25, 50, 100, 
 and 125 per cent of load, and a curve plotted for the load and 
 percentage of accuracy. . The form of such a curve is shown in 
 Fig. 266. 
 
 EXAMPLE 
 
 Test No. 4. — 
 
 Test of Scheefer direct-current watt-hour meter. 
 Capacity 30 amp. 
 
 ApTparaius. — 
 
 Portable wattmeter, Weston. 
 
 Stop watcli. 
 
 Lamp bank. 
 Temperature 20°C. 
 
322 
 
 ELECTRICAL METERS 
 
 
 
 
 Table 
 
 VII 
 
 
 
 Per cent 
 
 No. revo- 
 
 Time, 
 
 Meter 
 
 Correct 
 
 Per cent 
 
 
 load 
 
 lutions 
 
 seconds 
 
 watts 
 
 watts 
 
 accuracy 
 
 
 10 
 
 10 
 
 185.3 
 
 259.0 
 
 300 
 
 82.5 
 
 
 25 
 
 10 
 
 68.8 
 
 67.5 
 
 750 
 
 90.2 
 
 Poorly com- 
 
 50 
 
 20 
 
 67.3 
 
 1,426.0 
 
 1,500 
 
 95.1 
 
 pensated 
 
 100 
 
 30 
 
 50.0 
 
 2,880.0 
 
 3,000 
 
 96.0 
 
 for friction. 
 
 125 
 
 40 
 
 53.6 
 
 3,581.0 
 
 3,750 
 
 95.5 
 
 Curve, Fig. 266 
 
 It is evident from the form of the curve that the friction of the 
 bearings and commutator is not properly compensated at light 
 
 loads. The speed of the rotat- 
 ing element in a well-designed 
 meter should be proportional 
 to the load. Whether this 
 relation is fulfilled is well shown 
 by the curve of Fig. 267, where 
 the load current is plotted hori- 
 zontally and speed vertically. 
 286. Test of a Direct-current 
 Three-wire Meter. — The three- 
 wire-direct current meter dif- 
 fers from the two-wire meter 
 in having its series or current 
 coil divided into two coils that 
 are, or should be, exactly alike. 
 These two coils are connected, 
 one in each outside wire of a 
 three-wire circuit, while the common voltage coil may be con- 
 nected between the neutral and an outside wire, or across the 
 outside wires, according to the design of the meter. The limita- 
 tions of the different connections have already been discussed. 
 The second method of connection is shown in Fig. 268 in which 
 CC are the current coils and S the shunt or pressure coil. 
 
 The connections for testing such a meter are shown in Fig. 269. 
 The current coils are connected in series and also in series with 
 one wire of a two-wire circuit. If potential cells are available, 
 the best plan is to connect the voltage coil to a separate source 
 of electromotive force, as shown, otherwise it may be connected 
 in parallel with the current coils. The operation of the test is 
 
TESTING WATT-HOUR METERS 
 
 323 
 
 the same as other tests that have been described in which a 
 millivoltmeter is used to measure the current and a standard 
 voltmeter to measure the voltage. A wattmeter may be used 
 in place of voltmeter and millivoltmeter. 
 
 Pig. 268. 
 
 287. Test for Balance. — In addition to the foregoing test for 
 balanced load, it is also necessary to determine the effect of each 
 current coil in causing rotation. In a well-designed meter, the 
 coils should supply equal torques. To determine whether the 
 torques are equal, two simple tests may be made. The simplest 
 method consists in connecting the two-current coils in series, but 
 
 Fig. 269. 
 
 in such a way that the resulting torques are in opposition. If 
 the two coils exert equal torques, no motion will result. When 
 this is not the case, the armature will rotate either forward or 
 backward, depending upon which coil exerts the greater torque. 
 The resulting speed will undoubtedly be very slow, and for that 
 reason it will be advisable to overload the coils for a short time. 
 
 32 
 
324 ELECTRICAL METERS 
 
 The second method consists in connecting to the circuit only 
 one of the series coils at a time. If the two coils are exactly 
 balanced, the resulting speeds should be exactly equal, so long as 
 voltage and current remain unchanged. The speed with only 
 one current coil should also be equal to one-half the speed when 
 both coils are operating, current and voltage remaining constant. 
 
 288. Test of Ampere-hour Meters. — The simplest and most 
 convenient method of testing an ampere-hour meter is by means 
 of a standardized ammeter of proper range and a stop watch. 
 The ammeter is connected in series with the ampere-hour meter 
 through a rheostat or lamp bank. The current is adjusted to the 
 value desired and maintained constant throughout the test. 
 The ammeter reading multiplied by the duration of test in hours 
 gives the actual ampere-hours passed through the meter. The 
 calculated ampere-hours compared with the registration of the 
 meter will indicate the error. The number of ampere-hours 
 registered by the ampere-hour meter may be calculated from 
 the number of rotations of the disk and ampere-hour constant. 
 The chemical ampere-hour meters that are graduated in watt- 
 hours can be tested either with a wattmeter or standard test 
 watt-hour meter in the same way as watt-hour meters. 
 
CHAPTER XX 
 
 METHODS OF OBTAINING DIFFERENT POWER- 
 FACTORS 
 
 289. Introduction. — Since alternating-current meters must be 
 tested on loads of different power-factors, it will be advisable 
 first to discuss some methods of obtaining these. Several 
 methods may be used for this purpose; the particular one to be 
 used in any case will depend upon conditions present and appara- 
 tus available. 
 
 290. Reactance-coil Method. — As has already been pointed 
 
 out, the current flowing through an inductive circuit is expressed 
 
 by 
 
 E 
 
 I = 
 
 {R^ + Z,2co2) !^ 
 
 and the difference in phase between the pressure E and current 
 I is obtained from tan 9 = ~p' Evidently, if Loj is varied, tan 6, 
 
 ADJUSTING 
 RESISTANCE 
 
 o! 
 
 LI 
 
 2i ^' 
 o 
 
 Fig. 270. 
 
 and hence 9, can also be varied. This relation will perhaps be 
 better understood by referring to Fig. 270. An alternating 
 current of frequency/, supplies current to a resistance and induct- 
 ance coil. If I is the current flowing through the inductance 
 coil R2L2 and E the electromotive force between its terminals, 
 the relation between these quantities is then shown by the vector 
 diagram. The voltage drop due to the resistance of the inductance 
 coil is R2I, while that due to self-inductance is 2-wjLiI. Rzl is 
 33 325 
 
326 
 
 ELECTRICAL METERS 
 
 in phase with the current, and 2TrjLiI is at right angles or 90° 
 ahead of I. Drawing OC = R2I, and CA = 2TfLiI, we get the 
 right-angled triangle OCA, of which OA, the vector sum of OC 
 and CA, is the electromotive force E. The value of 9 thus 
 depends upon OC and CA and can be changed by changing either. 
 In practice, the change in power-factor is commonly obtained by 
 changing the inductance. This is accomplished by providing 
 a movable iron core for the inductance coil as shown in Fig. 
 271. By introducing or withdrawing the laminated iron core, 
 different values of power-factor can readily be obtained. The 
 exact value of the power-factor is calculated from the readings 
 of the wattmeter, voltmeter, and ammeter. It has already 
 
 Aj^ Zrrcull 
 
 "^ Counter 
 Ba/anca 
 
 Fig. 271. 
 
 been pointed out that at low power-factors corrections must 
 be made to the wattmeter readings. 
 
 291, Two-transformer Method. — Another method of securing 
 an inductive load for single-phase watt-hour meters is by means 
 of two transformers connected one to each phase of a two-phase 
 circuit. The secondaries of the transformers are provided with 
 several taps and are connected in series. The manner of con- 
 necting transformers and instruments to the circuits are shown 
 in Fig. 272. As is evident from the diagram, the current coil 
 of the meter to be tested is connected to one phase of the two- 
 phase circuit, while the pressure coil is connected in series with 
 the secondaries of the transformers. The ammeter, wattmeter, 
 and voltmeter are connected as usual. The value and position 
 
OBTAINING DIFFERENT POWER-FACTORS 327 
 
 of the pressure applied to the meter will evidently be equal to the 
 vector sum of the secondary voltages of the transformers. By 
 varying the relative values of these, different values of power-fac- 
 
 e Phaae 
 A.C Sarvlea 
 
 Leoe/ or trans- 
 /at/ng dei^/ce 
 
 Fig. 272. 
 
 tor can be obtained. The vector diagram of Fig. 273 shows how 
 this is accomplished. Let OA = Ei represent the secondary 
 voltage of transformer Ti. This voltage will be in phase with 
 I, the current through the meter. 
 
 If the secondary voltages of the trans- 
 formers are equal in magnitude, OB will 
 represent the secondary pressure of the 
 transformer T^. The resultant voltage, 
 or that impressed upon the pressure coil 
 of the meter, is then equal to OC, which 
 leads the current by the angle 6. By 
 changing the relative values of the sec- 
 ondary voltages, the value of 6 can be 
 changed from to 90°. The vector 
 diagram shows the relative values of these pressures for a phase 
 difference 6'. It is clear that not only the power-factor, but the im- 
 pressed pressure may be varied between wide limits by changing 
 connections A and A' in Fig. 272. If two transformers are spe- 
 
328 
 
 ELECTRICAL METERS 
 
 cially constructed for this test, the connection of Si and Sz may- 
 be made to a circular switch. The power-factor and voltage for a 
 given position of the switch may be calculated once for all and 
 marked on the switch. If that is done, the position of the switch 
 will indicate the voltage and power-factor, and the voltmeter and 
 ammeter may be omitted, unless needed for other measurements. 
 
 AC. Seri//ee 
 
 
 4-e 
 
 e 
 
 -> e' 
 
 l^»l 
 
 ^ 
 
 □ 
 
 .Wm.. 
 
 A/77 
 
 3j 
 
 55 
 
 Loan/ or 
 Oefice 
 
 Fig. 274. 
 
 292. Two-resistance Method. — Perhaps a simpler method con- 
 sists in replacing the two transformers by two slide contact re- 
 sistances as shown in Fig. 274. A vector diagram similar to that 
 in Fig. 273 will show the relation of the quantities involved. The 
 
 value and position of E is determined 
 by the position of the sliding contacts 
 El and ^2. That is, E is the vector 
 sum of e and e'. Fig. 275, which rep- 
 resent the potentials between the 
 sliding contacts and middle wire. 
 The resistances R\ and Ri must be 
 non-inductive and capable of with- 
 standing the line voltage, and have 
 a current capacity of 1 to 2 amp. A non-inductive load is con- 
 nected to the meter as in the transformer method. 
 
 By adjusting J?i and Ri, any desired value and phase position 
 of E may be obtained. In most cases it may be possible to use 
 lamps in place of resistances. The adjustment, however, will be 
 much more troublesome. The power-factors may be calculated 
 for certain positions of the contacts and the points so determined 
 
 PiQ. 275. 
 
OBTAINING DIFFERENT POWER-FACTORS 329 
 
 may be marked with the corresponding power-factor. When this 
 is done, the ammeter and voltmeter may be omitted and the re- 
 quired power-factor reproduced by simply setting the contacts at 
 the same points. 
 
 293. Two-generator Method. — A very convenient, and at the 
 same time accurate, method of varying the power-factor for test- 
 ing purposes may be obtained by providing a special motor- 
 generator set consisting of one driving motor and two similar 
 alternating-current generators, all connected to the same shaft. 
 The alternators need not be alike in every respect, but should 
 have the same frequency. One generator may preferably be 
 of low voltage and comparatively large current output for supply- 
 
 m 
 
 Current 
 CircLi//- 
 
 '5 » \//ov 
 
 '^ 
 
 f^tentia/ 
 C/rcu/f 
 
 PT 
 
 Vm 
 
 u 
 
 1=3 
 
 > M < 
 
 □ 
 
 Loact or 
 translating 
 
 Q 
 
 Fig. 276. 
 
 ing current to meters under test. The other generator may be 
 of low current capacity but relatively high voltage to serve as 
 a source of pressure. Fig. 276 shows the connections for such 
 a system. If the generators are low-voltage, the current and 
 potential transformers may be omitted. 
 
 One of the generators must be connected to the shaft in such a 
 way that the position of its armature may be shifted with reference 
 to the other. The frequencies of the two generators will always 
 be the same on account of the rigid connection, and by shifting 
 the armature of one with reference to the other, any power-factor 
 can be obtained. Furthermore, the power-factor can be calcu- 
 lated from the relative position of the armatures if the position of 
 
330 ELECTRICAL METERS 
 
 zero, or unity power-factor is accurately known. Thus, if each 
 generator has four poles for every revolution of the armature, the 
 current or voltage will pass through two cycles. That is, for 
 every 360° of armature motion, the electromotive force passes 
 through 720 electrical degrees, or 1 angular degree equals 2 elec- 
 trical degrees. If then the armatures are in a position of unity 
 power-factor, and one is rotated 5° on the shaft, there will re- 
 sult a displacement of 10° between the electromotive forces. The 
 power-factor has then been changed from cos 0° to cos 10°. In 
 general, then, if ^ is the angle through which the armature of one 
 machine has been shifted with reference to the other, p is the num- 
 ber of poles on each generator, and cos 6 is the power-factor, we 
 can express cos 9 in terms of 4> and p thus, 
 
 V 
 cos 6 = cos 2 ^ *^- 
 
 Measuring 4>, the power-factor can be calculated. Any error in 
 
 V 
 <j) is, however, multiplied ^ times, and, hence, for very accurate 
 
 work should be determined by the aid of a vernier. In some 
 cases it may be more convenient to have the machines constructed 
 in such a way that the armatures remain rigidly connected to the 
 shaft, while the field of one is movable. Of course, the same 
 effect is obtained as in the previous case. 
 
 294. Phase-shifting Transformer. — The troubles accompany- 
 ing the use of inductance coils for varying the power-factor for 
 testing meters are readily obviated by the use of a so-called "phase- 
 shifting transformer." The construction of such a transformer 
 is very similar to that of an induction motor. The stator is 
 wound with two sets of coils at right angles to each other as indi- 
 cated in Fig. 44, when the supply is two-phase or single-phase, 
 or with three sets of coils spaced 120° apart when the trans- 
 former is to be used on three-phase circuits. The secondary is 
 wound on a cylindrical iron core and consists of a single diametral 
 coil. 
 
 The relative position of the stator and rotor windings for a 
 two-phase shifting-transformer is shown in Fig. 277, where 
 A A' and BB' are the primary coils and MN is the secondary coil. 
 The connections of such a transformer to a power circuit and to 
 meters are shown in Fig. 278. 
 
 The principles nf operation will readily be understood from a 
 
OBTAINING DIFFERENT POWER-FACTORS 331 
 
 consideration of the interactions of the primary and secondary- 
 coils when the secondary is turned on its axis. If the plane of 
 the secondary coil is parallel to that of the primary coil AA', it 
 will have induced in it an electromotive force in phase with the 
 
 N 
 
 Fia.277, 
 
 pressure applied to AA'. Strictly speaking, the induced voltage 
 will be nearly 180° out of phase with the primary voltage applied 
 to AA'. 
 
 1 I I I J 
 
 Meters Standard 
 Meter 
 
 a.70' 
 
 Fig. 278. 
 
 When coil MN is in this position, the flux due to current in, 
 coil BB' will have no effect upon MN. When MN is turned 
 through 90°, the electromotive force induced will be in phase 
 with the pressure applied to BB' , hence, it will have been shifted 
 
332 
 
 ELECTRICAL METERS 
 
 through 90° from its previous phase. If MN is turned through 
 an angle d, other than 90°, the electromotive force induced in 
 it will be due to the resultant flux due to both coils AA' and BB'. 
 
 0° 
 
 120° Pbose^ 
 
 sMtinq 
 
 Transforms 
 
 Z40' 
 
 Meter 
 
 Fig. 279. 
 
 This flux rotates, as has been shown in Article 72, and is equal to the 
 maximum flux due to one coil. The phase of the electromotive 
 force induced in coil M'N is thus, likewise, shifted by an angle Q. 
 
 Fig. 2S0. 
 
 Any power-factor from 1 to can thus easily be obtained by 
 merely shifting the secondary with reference to the primary. 
 The connections of a three-phase, variable-phase transformer 
 
OBTAINING DIFFERENT POWER-FACTORS 333 
 
 are shown in Fig. 279, and the complete transformer as manu- 
 factured by the General Electric Co. is shown in Fig. 280. 
 
 295. Ammeter Method of Measuring Power-factors. — For 
 the want of a better name, the author, having devised the two 
 
 PiQ. 281. 
 
 following methods, has decided to call them "Ammeter Methods." 
 The reason for this is that at most only two ammeters, and with 
 the use of a polyphase switchboard, only one ammeter is necessary 
 for an approximate determination of the power-factor. 
 
 In plants using quarter-phase — com- 
 monly called two-phase — or three-phase 
 generators, the methods will undoubt- 
 edly prove useful and accurate enough 
 for commercial purposes. 
 
 296. Ammeter Method on Two-phase 
 Circuits. — The connections for testing 
 the watt-hour meter on a two-phase 
 three- wire circuit are shown in Fig. 281. 
 The series coil of the watt-hour meter 
 carries the vector sum of the two-phase 
 currents. When the voltage coil of the 
 watt-hour meter is connected as in- 
 dicated in the diagram, the power- 
 factor is the cosine of the angle between 
 the series current and pressure across 
 
 mains 1 and 2. Thus in Fig. 282 let OEi represent the voltage be- 
 tween mains 1 and 2, and OE2. the voltage between mains 2 and 3. 
 Since the load is supposed to be non-inductive, 0/iand Oh may be 
 considered as representing the currents in the separate phases. 
 
 Pig. 282. 
 
334 
 
 ELECTRICAL METERS 
 
 The current in main 2 is the vector sum of OIi and 01^ and is, 
 therefore, represented by 01.^ The power-factor of the load 
 registered by the watt-hour meter, when connected as indicated 
 in Fig. 281, is cos B, where B is the angle between OEi and 01. 
 The value of B is determined from the relative values of the cur- 
 rents in lamp banks Li and La. That is, if 7i is the current in 
 load Lj, and Iz the current in load La, the power-factor is equal to 
 
 and hence, can be determined from the readings of two ammeters, 
 one placed in main 1 and the other in main 3. Since, (/i^ + /a")^^ 
 = 7, the current in the series coil of watt-hour meter, an ammeter 
 placed in main 2 will indicate (Zi^ -f- /a^)''^ of /. The power-factor 
 then reduces to 
 
 cos 9 = -^ • 
 
 When 1 2 = 0, the total load is on Li; I\ = 7, and cos 6 = 1. 
 When 7i = 0, the total load is on La, and cos B = y — Q- 
 
 o 
 o 
 
 ^ 
 
 
 
 s 
 
 
 |bocs| 
 
 P 2 
 
 
 •E' 
 
 
 o 
 
 
 
 a 
 
 Pia. 283. 
 
 Hence, by adjusting the load between Li and La, any power- 
 factor between and 1 can be approximately determined. 
 According to the foregoing discussion, two ammeters are needed; 
 later it will be shown how the connections may be made so that 
 one ammeter will suffice. 
 
 In case the generator is not wound for three-wire connection, 
 which the foregoing method presupposes, a three-wire circuit 
 can be obtained by connecting two transformers, as shown in 
 Fig. 283. The primary circuits of the transformers are connected 
 
 ' To be exact the current in main 2 should be represented by dotted line 
 Oh. The value of the power-factor will be the same in either case. 
 
OBTAINING DIFFERENT POWER-FACTORS 335 
 
 to the separate phases of the generators and the secondaries are 
 interconnected as shown. 
 
 297. Ammeter Method on Three-phase Circuits. — When three- 
 phase alternators are available, the same general plan may be 
 
 FiQ. 284. 
 
 followed. When the series coil of the meter to be tested is 
 connected to the middle wire, as indicated in Fig. 284, and the 
 pressure coil across Ei, the power-factor is 
 
 . , y Is~ I2 li ~ I2 
 
 cos P = 72 
 
 
 21 
 
 Fig. 285. 
 
 where /, h, and h are currents in middle and outside wires, 
 respectively. 
 
 When the potential circuit is connected acrass E3, the power- 
 factor is 
 
 2/3 -I- h 2h +h 
 
 cos e = J^ 
 
 ih' + hh + h')^ 
 
 21 
 
336 ELECTRICAL METERS 
 
 These formulas can be derived as follows: 
 
 Assuming the time-phase displacements of the electromotive 
 forces of the three-phase generator to be 120°, Fig. 285 is a vector 
 diagram of the quantities involved. From this diagram it is 
 plainly evident that both the magnitude and time phase of I 
 with reference to Et depend upon the relative magnitudes of 
 li and Is. 
 
 Let 6 be the angle between I and Ei, then the angle between /a 
 and El is 60° when the load is non-inductive. Hence, 
 
 cos 6 = cos (7 -f- 60) 
 
 = }'2 cos 7 — }4V3 sin 7. 
 
 From the triangle whose sides are /, I2, and I3, we get 
 Is-.h:: sin (60 — t) : sin 7, 
 
 whence sin 7 = V^h ^^-.-^^^-^-j^ 
 
 J 1/ 2/3 + 1 2 
 
 and C0S7 = V2 jf^T^rjJ^^rf^- 
 
 Substituting these values in the expression for cos d and reducing, 
 we get, 
 
 But ih' + hh + h')^ = I 
 
 , ^ , , (73 - I2) 
 hence, cos 9 = }^ j - 
 
 When h = h, or when both phases are equally loaded, cos 6 = 0. 
 When 1 2 = 0, Is = /, and cos = 0.5; and when 1 3 = 0, h = 
 — 1, and cos 6 = —0.5. Hence, by such a connection the 
 power-factor can be varied between —0.5 and -1-0.5. 
 
 By a similar process of reasoning it can be shown that when 
 the pressure coil is connected across Ez, the power-factor is 
 
 rn^ fl _ 1/ 2Z3 + h _ 2/3 -I- h 
 
 When I2 = 0, I3 = I, and cos 8 = 1. 
 
 When h = 0, cos 8 = 0.5. That is, when all the load is on L3 
 the power-factor is 1, and when all the load is on L2 the power- 
 factor is 0.5. 
 
 The advantage of this method lies in the ease with which both 
 the connections and calculations can be made. The ordinary 
 ammeter — voltmeter — wattmeter method necessitates three in- 
 
OBTAINING DIFFERENT POWER-FACTORS 337 
 
 Btruments, and it is a well-known fact that at low power-factors 
 the inductance of the pressure coil of the wattmeter introduces 
 errors which are proportional to sin d. This error, due to the 
 inductance of the pressure coil, may be as great as that due to 
 the unbalancing of the pressures in the method under consid- 
 eration. The fact that one ammeter is sufficient, makes this 
 method especially advantageous for small power plants whose 
 supply of instruments is limited. 
 
 In order to use only one ammeter, the polyphase switchboard, 
 shown in Fig. 252 may be used. The three mains are connected 
 to binding posts 1, 2, 3, and the three load terminals to posts 1', 2', 
 and 3', while the ammeter is connected to leads indicated. This 
 connection is shown in Fig. 286. An examination of the diar 
 
 I 
 
 /W5U^ 
 
 fJ^^lE 
 
 '^t^ 
 
 :r 
 
 m^B^ 
 
 Am 
 
 tx 
 
 ■6' 
 
 Fig. 286. 
 
 gram will show that when the three-pole, and three single-pole 
 switches are closed, the ammeter will register no current. When, 
 however, both double-pole, double-throw switches are closed to 
 the left and single-pole switch C is opened, the ammeter will 
 give the current in one lamp bank. An examination of the 
 diagram will show the operations necessary to obtain in succes- 
 sion the currents in the other lamp bank and in the middle wire. 
 It has been shown by experiment that for the purpose of watt- 
 hour meter testing the method is accurate enough for commercial 
 purposes, and in fact the results obtained by the ammeter method 
 are just as accurate as the three-instrument method unless 
 accurately calibrated instruments of proper range are available. 
 The adjustable load must be non-inductive. 
 
CHAPTER XXI 
 
 SPECIAL TESTS OF ALTERNATING-CURRENT WATT- 
 HOUR METERS 
 
 298. Test for Quarter-phasing. — ^As pointed out in Article 184, 
 the displacement between the magnetic field due to the current 
 coil and that due to the voltage coil must be 90° for accurate 
 registration on inductive load. One of the first tests to be made 
 on a single-phase meter is to determine whether this relation 
 exists. 
 
 Since no torque should be exerted upon the rotating disk when 
 the current lags or leads by an angle of 90°, in order to determine 
 
 ZPhaaa 
 
 ^ 
 
 
 
 
 
 A.C. Serv/ca 
 
 '^ 
 
 
 
 \ ) 
 
 
 ► 
 
 E' 
 
 H 
 
 
 
 
 Locu/ or 
 Tranalat/ng 
 
 
 ^ 
 9 
 
 ^ 
 
 
 Oei^ico 
 
 
 1 
 
 
 
 
 
 
 Wm 
 
 
 Am 
 'm 
 
 — 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 Fig. 287. 
 
 whether the meter is properly quarter-phased, the absence of 
 torque under proper conditions is the criterion of the test. In 
 making the test, connect the current coil to one phase of a quarter- 
 phase circuit and the voltage coil to the other phase. A suitable 
 method of making these connections is shown in Fig. 287. The 
 exact phase difference is calculated from the readings of the 
 ammeter, voltmeter, and wattmeter, thus, 
 
 watts 
 
 cos 
 
 I XE 
 
 338 
 
TESTS OF WATT-HOUR METERS 
 
 339 
 
 If the quarter-phase relation exists, the wattmeter reading will 
 be zero if corrections are made for resistance, hysteresis, and eddy- 
 current losses. Any inaccuracy in the wattmeter will, however, 
 vitiate the result. Accurate measurements of alternating-cur- 
 rent power in circuits of low power-factors require special methods 
 and apparatiis. 
 
 299. Test of Single-phase Meter on Non-inductive Load. — For 
 non-inductive load test, connect the meter as shown in Fig. 288. 
 It must be remembered that the connections shown are diagram- 
 
 S 
 
 iik^y 1 
 
 AC. Supply 
 
 Wt 
 
 
 ss 
 
 Pig. 288. 
 
 matic only. For any particular make of meter, the connections 
 will have to conform to the diagrams and directions sent out by 
 the makers. 
 
 The voltage during the test should be constant, and the time 
 of a definite number of revolutions of the disk determined by the 
 aid of an accurate stop watch. It is more accurate to count a 
 definite number of revolutions than to count the revolutions 
 during a definite time, as the fraction of a second is more easily 
 determined than the fraction of a revolution. The per cent 
 accuracy is then determined by 
 
 100 X K R 
 Per cent accuracy = ^,^^^-^ 
 
 where K, R, and T have the significance already explained. The 
 non-inductive load test is to be made at various percentages of 
 load, but with the constant voltage. Then repeat the test with 
 both an increase and decrease in voltage of 15 to 20 per cent, 
 but the same loads as before. That is, first increase the voltage by 
 20 per cent above the rated voltage and ascertain the accuracy on 
 10, 50, 100, and 125 per cent of load. Second, decrease the 
 voltage by 20 per cent and ascertain the accuracy at the previ- 
 ously mentioned fractions of load. When the accuracy for the 
 various voltages and loads has been determined, curves should 
 be plotted from the data, the per cent of load being plotted 
 horizontally and the percentage of accuracy vertically. 
 
340 
 
 ELECTRICAL METERS 
 
 EXAMPLE 
 
 Test No. 5. — Test of single-phase watt-hour meter. 
 
 Apparatus. — Fort Wayne 110-volt, 60-cycle, 5-amp. watt-hour meter. 
 
 Weston wattmeter No. 4,123. 
 
 Lamp bank. 
 
 Stop watch No. A. 
 
 Temperature 21 °C. 
 
 
 
 
 Table 
 
 VIII 
 
 
 
 Per cent 
 load 
 
 No. revo- 
 lutions 
 
 Time, 
 seconds 
 
 Meter 
 watts 
 
 Correct 
 watts 
 
 Percentage 
 accuracy 
 
 Remarks 
 
 10 
 25 
 
 50 
 
 75 
 
 100 
 
 125 
 
 2 
 
 8 
 
 12 
 
 16 
 
 20 
 
 25 
 
 32.7 
 52.4 
 39.6 
 35.1 
 33.4 
 33.5 
 
 55.0 
 137.5 
 273.4 
 408.4 
 540.5 
 673.7 
 
 55.0 
 
 137.5 
 275.0 
 412.5 
 550.0 
 687.5 
 
 100.0 
 100.0 
 99.5 
 99.0 
 98.3 
 98.0 
 
 Voltage con- 
 stant at 110 
 volts. 
 Curve, Fig. 289a. 
 
 Fig. 289. 
 
TESTS OF WATT-HOUR METERS 
 
 341 
 
 300. Test of Single-phase Watt-hour Meter on Inductive Load. 
 
 — For an inductive load test, any of the methods for varying the 
 power-factor previously discussed may be used. If the station 
 is provided with a three-phase generator, the three-phase am- 
 meter method is perhaps the most convenient. A diagram of 
 connections for a test board as described by Mr. H. B. Taylor in 
 the Electric Journal for November, 1906, is shown in Fig. 290. 
 
 C«TFtA UiNt ran 
 Shunt Circuit 
 
 Scfiies Connection for 
 
 CuMtlMT IN ONt PHASt ONLV 
 
 Fia. 290. 
 
 This diagram is for a three-phase circuit and both non-inductive 
 and inductive load tests can readily be made by the aid of a board 
 or table wired as here shown. The three-phase terminals are 
 indicated by A, B, and C. At the left is indicated a potential 
 regulator by means of which gradual changes in secondary 
 voltage from maximum in one direction to maximum in the 
 other direction can be obtained. It may also serve as a phase 
 shifter, depending on whether the primary is connected to the 
 same phase as the meter or to another phase. In the lower left- 
 hand corner is shown a small transformer with taps, connected 
 to the potential circuit. The series auto-transformer shown at 
 the bottom of the diagram is put in simply to economize in energy 
 in testing heavy current meters. This transformer is cut in or 
 out by means of the plug switches and is used only when the cur- 
 
 34 
 
342 
 
 ELECTRICAL METERS 
 
 rent is above 10 amp. The lamp board is connected between the 
 switches as indicated. When the load is all on one lamp board 
 and the potential circuit is connected to the wires supplying the 
 lamps, the conditions are the same as on any single-phase circuit. 
 Thus, when the lamps are connected to A and B, and the poten- 
 tial plug is inserted at A' and B', the test may be made on prac- 
 tically unity power-factor. Transferring the plug to B'C gives 
 about zero power-factor. The power-factor will not necessarily 
 be exactly zero, but near enough for commercial practice. For 
 inductive load test, the load is divided between the two lamp 
 boards, and the shunt is connected to outside mains. When the 
 load is evenly divided between the two lamp boards, the power- 
 factor is 0. Changing the load on either lamp board changes the 
 power-factor, as previously explained. 
 
 EXAMPLE 
 
 Test No. 6. — Test of watt-hour meter on inductive load. 
 Apparatus. — Same as in Test No. 5. 
 
 Weston ammeter. 
 
 Weston voltmeter. 
 Temperature. 
 
 Table IX 
 Part I 
 
 VoUa 
 
 Amperes 
 
 Watts 
 
 Power- 
 factor, 
 per cent 
 
 No. 
 revolu- 
 tions 
 
 Time, 
 sec- 
 onds 
 
 Meter 
 watts 
 
 Per cent 
 accuracy 
 
 Remarks 
 
 110 
 110 
 
 10.20 
 8.18 
 
 225 
 225 
 
 20 
 25 
 
 12 
 12 
 
 46.7 
 47.5 
 
 230.6 
 227.5 
 
 102.5 
 101.0 
 
 Load oon- 
 stanti vary- 
 ing power- 
 factor. 
 
 110 
 
 no 
 
 4.10 
 2.72 
 
 225 
 225 
 
 50 
 75 
 
 12 
 12 
 
 48.2 
 48.5 
 
 244.0 
 223.0 
 
 99.5 
 99.1 
 
 110 
 
 2.05 
 
 225 
 
 100 
 
 12 
 
 48.7 
 
 222.7 
 
 99.0 
 
 
 
 
 
 
 
 
 
 Curve, Fig. 2896. 
 
 Part II 
 
 Volts 
 
 Amperes 
 
 Watts 
 
 Power- 
 factor, 
 per cent 
 
 No. 
 revolu- 
 tions 
 
 Time, 
 sec- 
 onds 
 
 Meter 
 watts 
 
 Per cent 
 accuracy 
 
 Remarks 
 
 110 
 110 
 110 
 110 
 110 
 
 7.5 
 7.5 
 7.5 
 7.5 
 7.5 
 
 165.0 
 206.2 
 412.5 
 618.6 
 825.0 
 
 20 
 25 
 50 
 75 
 100 
 
 6 
 12 
 22 
 30 
 
 44 
 
 32.4 
 52.4 
 49.0 
 44.6 
 48.7 
 
 167.5 
 206.0 
 403.7 
 604.9 
 813.0 
 
 101.5 
 
 100.0 
 
 98.0 
 
 97.8 
 
 98.5 
 
 Current con- 
 stant. 
 
 Curve, Fig. 289c. 
 
TESTS OF WATT-HOUR METERS 
 
 343 
 
 The power-factor had comparatively little effect on the accu- 
 racy of this particular meter, but this is not always the case. The 
 curve of Fig. 291 shows what variations in the percentage of ac- 
 curacy are possible when the meter is not properly adjusted. 
 
 301. Testing with Standard Test Meter. — The connections for 
 testing a two-wire meter by means of a standard test meter are 
 shown in Fig. 292. This method of testing is fast superseding 
 the indicating instrument method. The operation of testing 
 with a standard test meter is very simple and consists merely in 
 the determination of the number of rotations of the moving ele- 
 ment of the test meter corresponding to a definite number of 
 rotations of the tested meter. 
 
 To facilitate the work, some companies equip the test meter 
 with an electrical contact which closes a circuit through a tele- 
 phone receiver, every rotation giving a click. When this method 
 is used, observations are made by what is called an " eye and ear 
 method." The operator observes the rotations and fractions of 
 a rotation of tested meter corresponding to a whole number of 
 rotations of the disk of the test meter, noting the latter by the aid 
 of the telephone receiver. 
 
 In some cases, arrangements are made for starting and stopping 
 the test meter at the instant the spot on the disk of the tested 
 meter passes the observation window in the case. This starting 
 
344 
 
 ELECTRICAL METERS 
 
 or stopping may be accomplished by opening the voltage coil of 
 the test meter, or by short-circuiting its current coil. Instead of 
 stopping the disk, the moving element may be caused to pick up 
 and drop the hand through the agency of a little magnetic clutch. 
 The chief advantages of the test meter have been pointed out. 
 It evidently eliminates the use of stop watches, which are always 
 troublesome in meter testing; it minimizes the effect of voltage 
 fluctuations; and reduces the work of calculation to a minimum. 
 
 Source 
 
 Ampere Switch 
 
 ^[~~|)CXDOOOOOCXy^ ~Q 
 >=OTENTiAL Switch 
 
 J^-y^CURRENT — y-*? 
 
 
 ELEASE Test 
 Load 
 
 Portable 
 
 Pressure Tei^iminals 
 Fig. 292. 
 
 Resistance 
 
 When a test meter is used whose constant is not the same as 
 that of the service meter tested, the two meters will not make the 
 same number of rotations. To facilitate the conversion of the 
 number of rotations of the test meter to the equivalent of those of 
 the service meter. Table X has been prepared. The table con- 
 tains the constants of the meters most commonly used. 
 
 The table is used as follows : 
 
 Suppose a Westinghouse 5-amp. test meter is used to check a 
 Fort Wayne service meter of the same capacity. If both meters 
 are for 110-volt circuits, the constants are }4 watt-hour and J<^ 
 watt-hour respectively. Opposite the test-meter constant }i and 
 under the service meter 0.25 we find 7.5, which means that for 
 every ten rotations of the service meter the test meter should 
 make 7.5 rotations. 
 
TESTS OF WATT-HOUR METERS 345 
 
 If a meter is used whose constant is not found in the table, the 
 conversion can be made as follows: 
 
 Let Ki = test-meter constant, 
 
 Ki = service-meter constant. 
 
 Then R = ^ X 10 
 
 where R = number of rotations of the standard corresponding to 
 ten rotations of the service meter. The percentage of accuracy 
 is then calculated as follows: 
 
 Count a definite number of revolutions of the service meter, 
 and from Table X find the number of rotations the standard 
 should have made in'the same time. The ratio of the number 
 of rotations the test meter should have made to the actual 
 number it did make will give the percentage of accuracy. 
 
 EXAMPLE 
 
 A 50-amp., 110-volt, type C, General Electric meter was tested with a 5- 
 to 100-amp. Duncan test meter. The service meter made 20 rotations 
 while the test meter made 15; what is the percentage of accuracy of the 
 service meter? The constant of the Duncan test meter is 2.5 and that of the 
 service meter 2; hence, opposite 2.5 and under 2 is found the figure 8. The 
 test meter should have made 16 rotations, but as it made only 15 the per- 
 centage of accuracy is 1^5 = 106.6. 
 
 302, Testing of Polyphase Meters. — Since polyphase meters 
 are simply a combination of two single-phase meters, they may 
 be tested as single-phase meters, each phase being tested sepa- 
 rately. Both potential coils must, however, be connected to the 
 cirSttit during the test. A diagram of connections is shown in Fig. 
 293. It will be noticed that the current is passed through only 
 one series coil at a time. This is accomplished by changing the 
 connections of the three-point switch. When one circuit of the 
 watt-hour meter is fully loaded, the rotating element makes one- 
 half the normal number of revolutions. Pass through the circuit 
 a given number of watts which must be kept constant while read- 
 ings are being taken. Time the number of revolutions of the 
 disk with a stop watch, and compute the percentage of accu- 
 racy in the same manner as in testing single-phase meters. The 
 proper constants to be used will depend upon the make of meter 
 as previously pointed out. When the percentage of accuracy of 
 one circuit has been determined, load the other circuit and repeat 
 the test. 
 
346 
 
 ELECTRICAL METERS 
 
 Another method of testing polyphase meters consists in con- 
 necting the current coils in series, and the potential coils in paral- 
 lel. An objection to this method is the inability to determine 
 any unbalancing of one of the circuits. Should the meter be 
 found to be inaccurate, and be adjusted when unbalanced, the 
 meter will give inaccurate results when connected to polyphase 
 circuits. 
 
 While conducting tests in accordance with either method, care 
 should be exercised not to reverse either of the potential circuits 
 when connected in parallel. If the series connection of current 
 coils is used, the connections of one of the circuits should be Te- 
 
 Load 
 
 25 
 
 Wattmeter^ 
 
 Line 
 
 Three Ftoint Switch 
 
 /'-Jl , fi)/yphase ^ 
 
 I \ 7 I I I ias2sai y^—j\— 
 
 ^ 0|0|<> —I 1 c=3 >— ' 
 
 
 □ 
 
 Pig. 293. 
 
 versed in order that the action of both coils may be in the same 
 direction. 
 
 On account of the inconvenience mentioned and the liability 
 of inaccurate results, it is preferable to test each circuit sepa- 
 rately, the potential circuits remaining connected in parallel, or, if 
 the test is made on polyphase circuit, the potentials may be left 
 connected to the same phase as in service. 
 
 303. Test for Interference of the Two Metering Elements. — 
 By means of a long series of tests the Electrical Laboratories 
 found that various makes of meters differed considerably with 
 respect to the electromagnetic interaction of the two elements of 
 polyphase, watt-hour meters. In some makes the interference 
 was so small that careful tests failed to detect it. In other makes 
 the interference was so large that serious errors might, under 
 certain conditions, be introduced by it. As a result of these 
 investigations the following specifications for the test of indepen- 
 dence of elements has been incorporated in the Meter Code of the 
 National Electric Light Association. 
 
 Element A of the meter under test is connected to phase I of a 
 two-phase circuit and a certain current is sent through its current 
 
WATT-HOUR CONSTANT OF TEST METER 
 
 
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TESTS OF WATT-HOUR METERS 
 
 347 
 
 coil. The voltage coil of element B is also connected to phase I 
 and accuracy readings are taken with the current in the volatge 
 coil of B direct and reversed. Next the voltage coil of B is con- 
 nected to phase II and similar readings are taken. Finally, with 
 the voltage coil of element B disconnected, a current equal in 
 value to the current passing through current coil of element A, is 
 sent through the current coil of element B. The current through 
 element B is first taken from phase I and then from phase II, and 
 in each case both direct- and reverse-current readings are taken 
 and compared. Tests are to be made with both light and full- 
 load currents. Under any given set of conditions the difference 
 between the direct and reversed readings must not exceed 1 per 
 
 A/ 
 
 □= 
 
 >fice 
 
 G "^ 
 
 £ S 
 
 Clamp 
 
 Merer- 
 Shaft- 
 
 O. 
 
 Pig. 294. 
 
 cent. In case a meter shows a greater correction than this it 
 must be tested on a polyphase circuit with the direction of rota- 
 tion on each phase given, so that in installing the meter the same 
 direction may be preserved. If the variation in direct and re- 
 versed readings is not over 1 per cent, the meter may be tested 
 on a single-phase circuit, the current coils being connected in 
 series and the potential coils in parallel. 
 
 304. Test to Determine Torque. — ^As previously pointed out, 
 other things being equal, the watt-hour meter whose torque- 
 weight ratio of moving element is the largest, is the best meter; 
 hence, a knowledge of the torque is essential. Fig. 294 shows a 
 so-called torque balance, an instrument for determining this 
 quantity. As shown in the diagram, the instrument consists of 
 
348 ELECTRICAL METERS 
 
 two arms at right angles to each other, balanced on a knife edge 
 C. With the instrument is provided a clamp to which is attached 
 a light extension rod EN. In operation, the arm EN is securely- 
 clamped to the shaft of the meter, and connected by the link to 
 the vertical arm of the balance. Normally, the weight G overbal- 
 ances the arm H, and the pointer swings to the right. When the 
 meter is loaded, the torque exerted by the disk pulls the pointer 
 back to 0. The load necessary to secure balance is measured on 
 an indicating wattmeter, and the torque in gram-centimeters is 
 calculated from the weight G and the levers GC, CV, and EN thus: 
 
 Let w = weight of G in grams, 
 / = the pull along link L, 
 and let T = torque of meter. 
 
 Then T = f X EN 
 and f X YC = w X CG. 
 
 Eliminating /, we get 
 
 T EN 
 
 
 w X CG YC 
 ENXwXCG 
 
 YC 
 
 When w is in grams and the other quantities are in centimeters, 
 the above expression gives the torque in gram-centimeters direct. 
 The rods Y and EN are provided with several loops, and two 
 weights are also supplied to permit the use of the balance for 
 measuring a wide range of torques. By accurately weighing the 
 moving elements, the torque-weight ratio is obtained by dividing 
 the torque by the weight. Also the torque per watt of load may 
 readily be obtained from the calculated torque and the reading of 
 the indicating wattmeter. 
 
 Another device for measuring the torque of electrical instru- 
 ments has been devised by Dr. Agnew of the Bureau of Standards 
 and is illustrated in Fig. 295. As the figure clearly shows, it 
 operates on the pendulum principle, the characteristic feature 
 being scale iS on a concave spherical surface of 1-meter radius 
 turned from a brass casting. The bob D is supported from an 
 adjustable arm so arranged that the point of support P is at the 
 center of the sphere of which the scale S is the surface. The silk 
 fiber supporting the bob is wound on a friction pin A and passes 
 through a V-shaped notch in the end of the adjustable brass strip 
 
TESTS OF WATT-HOUR METERS 
 
 349 
 
 B. The whole instrument is mounted on an ordinary clamp 
 stand, the tripod of which is fitted with leveling screws. 
 
 The graduations of the scale S consist of 153 concentric circles, 
 the distance between successive circles being so spaced as to give 
 the tangents of the angles of deflection directly. In milli- 
 meters the distance be- 
 tween circles is 1,000 X 
 tangent of angle of de- 
 flection. The bob consists 
 of a small hollow brass 
 cylinder with a fine sewing 
 needle passed through it 
 perpendicular to the axis, 
 as shown in Fig. 296. 
 
 The silk fiber, by which 
 the horizontal force to be 
 measured is transmitted to 
 the bob, is attached to the 
 needle and passes out along 
 the axis of the hollow cyl- 
 inder. The point of at- 
 tachment is made at the 
 center of mass of the bob 
 
 acz^cj 
 
 Fig. 295. 
 
 Pig. 29G. 
 
 which is adjusted to 0.5 gram. For changing the range of the 
 instrument, concentric cylinders, each cut in halves, are made 
 to fit snugly over the inner cylinder as indicated in Fig. 296. 
 
 In measuring the torque of a deflection instrument a horizontal 
 thread, one end of which is connected at D, Fig. 295, is fastened 
 to the pointer of the meter at a convenient distance from the pivot, 
 the torque balance adjusted to the proper height, and the deflec- 
 
 35 
 
350 ELECTRICAL METERS 
 
 tion instrument moved horizontally until the desired deflection 
 is obtained. The torque is then given by 
 
 Torque T = I X mg X 0.001 X d 
 
 where I = distance from pivot to point of attachment of silk fiber 
 on pointer, mg is weight of bob, and d is the number of divisions 
 on scale S. 
 
 In measuring the torque of a watt-hour meter it is necessary only 
 to attach the thread to the edge of the disk, apply the current and 
 voltage to the meter, and allow the meter to deflect as far as it 
 will. The calculations for torque may then be made as above. 
 The horizontal thread must be kept tangent to the disk, if this is 
 done the distance I equals the radius of the disk. 
 
 Tests made show that the torque of alternating-current watt- 
 hour meters ranges from 3.06 to 7.74 gram-cm. 
 
 305. Test of Influence of Friction. — In connection with the 
 foregoing test, the influence of friction upon the torque may be 
 advantageously determined. First adjust the friction compensa- 
 tion so that the meter is just balanced at no load. To secure this, 
 the compensation should be just sufficient to cause the meter to 
 creep at no load when slightly jarred. When the compensation 
 has been properly adjusted, full load is applied and speed deter- 
 mined. Then the compensating coil is disconnected and the 
 speed is again determined at the same load. The so-called "fric- 
 tion-torque ratio" is the ratio of the decrease in speed with com- 
 pensating coil disconnected to the speed with coil in circuit. Thus 
 a decrease of 5 per cent in speed would mean a ratio of 1 : 20. 
 The smaller this ratio, the less the influence of friction, and from 
 this view point, the better the meter. 
 
 306. Test to Determine Influence of Stray Field. — For this 
 test, mount the meter in such a way that current-carrying con- 
 ductors may be conveniently brought near. 
 
 First, test the meter under conditions making impossible the 
 existence of an external magnetic field. Having determined the 
 accuracy under these conditions, place a conductor carrying a 
 current in various positions. Direct-current meters should be 
 tested under the influence of a direct-current field, and alternat- 
 ing-current meters under the influence of alternating-current 
 fields of the same frequency and in phase with the current in the 
 meter. Run the conductor in a horizontal position back of the 
 meter at a distance of 15 in. from the axis of the moving element 
 
TESTS OF WATT-HOUR METERS 361 
 
 Pass a current equal to twice the capacity of the meter through 
 the conductor, and determine the accuracy of the meter at 100 
 per cent load. Change the position of the conductor, and repeat 
 the test. 
 
 For determining the influence of a stray field on the accuracy of 
 alternating-current meters, the meter committee of the National 
 Electric Light Association recommends the following: 
 
 "The meter to be tested shall be subjected to an alternating 
 stray field of the same frequency as that of the testing current, 
 and produced by a straight conductor six (6) feet long, with re- 
 turn leads arranged to form a rectangle six (6) feet square, lying 
 in a plane parallel to the switchboard. A current of fifty (50) 
 amperes in phase with the voltage applied to the meter shall be 
 passed through this conductor." 
 
 Separate tests are to be made when the stray field conductor is 
 placed successively in the following positions: 
 
 1. "Behind the meter in a horizontal position at the level of 
 the moving element and at a distance of fifteen (15) inches from 
 the axis of the moving element. 
 
 2. "Directly behind the center line of the meter, in a vertical 
 position and at a distance of fifteen (15) inches from the axis of 
 the moving element. 
 
 3. "Vertically, at the same distance in front of the switch- 
 board as the axis of the element and at a distance of fifteen (15) 
 inches to the right or left of the meter center line, the return leads 
 being so arranged that the loop which they form does not sur- 
 round or include the meter." 
 
 In connection with the foregoing, tests may be made to deter- 
 mine the minimum distance which should be maintained between 
 meters when in service. To do this, first determine the accuracy 
 of two meters on 5 and 10 per cent loads. Test each meter sep- 
 arately when there is no load on the other meter. Maintain 
 a constant load of 100 per cent on one meter and determine the 
 accuracy of the other meter at various distances apart. In 
 varying the distances, always move the meter having the con- 
 stant load. From the data thus obtained, the distance at which 
 the accuracy of the meter is within permissible limits, can readily 
 be determined. 
 
 307. Test to Determine Loss in Potential Coil. — To determine 
 this loss, two methods are available; it can be measured directly 
 or computed from the resistance and voltage. The method of 
 
352 ELECTRICAL METERS 
 
 measurement will perhaps be the most convenient for alternating- 
 current meters, while for direct-current meters, the method of 
 calculation will give more accurate results. 
 
 To measure these losses, connect the potential coils of several 
 meters of the same rated voltage in parallel and, if the meters are 
 for direct-current circuits, measure the total current and voltage 
 applied. The energy lost will be equal to the product of current 
 and applied voltage, which divided by the number of meters will 
 give the average loss per meter. 
 
 On account of the low power-factor of the voltage circuit of 
 alternating-current meters it is preferable to measure the resist- 
 ance of the coil and calculate the loss by 
 
 Watt loss = PR 
 
 where I is the voltage-coil current and R the coil resistance. If 
 a low-reading wattmeter is available, this may be used, providing 
 proper corrections are made for its inaccuracy on low power-fac- 
 tors. If the resistance of the voltage coil is not known, it can be 
 measured in a variety of ways. When direct current is available, 
 it can be measured by the drop of potential method which will 
 necessitate a milliammeter and a high-resistance voltmeter. 
 
 The loss in current coil can be calculated more accurately than 
 measured. First, the resistance of the coil must be accurately 
 measured, and then the loss at any current will be given by 
 
 Watts loss = PR as above. 
 
 Since the resistance of the current coil is small, special precautions 
 must be taken in its measurement. The drop of potential method 
 may also be used, but in this case the voltage drop will be small, 
 and hence, a comparatively high-resistance millivoltmeter will be 
 necessary. The current can be measured by an accurate amme- 
 ter of proper range. 
 
 308. Test for Proper Connections. — To connect a single-phase 
 meter properly to a circuit is a comparatively simple process. 
 When, however, it is desired to connect a polyphase meter, the 
 likelihood or probability of securing a proper connection is much 
 less. The difficulty encountered will depend somewhat upon the 
 coil connections within the meter. As is evident from Figs. 190 
 and 191, the polyphase meter consists of two metering elements 
 each containing one current and one voltage coil. The ends of 
 each coil may be connected to a separate terminal or the coils may 
 
TESTS OF WATT-HOUR METERS 353 
 
 be interconnected. If the former system of connections is em- 
 ployed, there will be eight terminals to be connected to the three- 
 wire circuit. Under these conditions there are theoretically 
 possible 192 different connections some of which are very improb- 
 able and only four of which are correct. The usual method of 
 checking the connections is to open the current or voltage circuit 
 of first one element, and then the other and to note the direction 
 of rotation in each case. If the power-factor of the load is above 
 0.5, the torque on each element is in the same direction when the 
 meter is properly connected, hence under these conditions, the 
 direction of rotation of the meter is a criterion of the correctness 
 of the connections. It is not an absolute criterion, however, for 
 certain incorrect connections will also cause rotation of the mov- 
 able element in the right direction when this procedure is followed 
 and the power-factor is above 0.5 and below 1 . The opening of the 
 voltage or current circuits of each element alternately can be re- 
 lied upon as a correct check upon the correctness of the connec- 
 tions only when the power-factor of the load is unity. 
 
 A more reliable method of determing whether a meter is prop- 
 erly connected is to interchange the voltage-coil connections of 
 the two elements. For this check the load must be balanced or 
 nearly so. The reasons for and character of this check will be 
 readily understood from Fig. 191 which shows diagrammatically 
 a polyphase meter properly connected to a three-wire circuit. 
 When connected as shown, the torque on the movable element ia 
 directly proportional to the power as shown in Article 199. If, 
 however, the connections of the voltage coils to mains 1 and 2 
 be interchanged, we will have the following result for the torque: 
 
 T = i'lBi — i'iCi 
 
 and the average torque must be av. T = av. (^'162 — i'zei). On 
 balanced load the average of i'lea must equal the average of {'261; 
 hence, the average torque is zero, and the meter stands still. If 
 the meter is improperly connected, an interchange of the connec- 
 tions of the voltage coils will not reduce the torque to zero, and 
 hence this method of checking the connections of a polyphase 
 meter gives reliable results. The only objectionable feature is 
 the necessity of a balanced load.^ 
 
 • See KouwENHOVEN, "A Method of Determining the Correctness of 
 Polyphase Wattmeter Connections," Proceedings A.I.E.E., February, 1916. 
 
 36 
 
CHAPTER XXII 
 
 INSTRUMENT ERRORS 
 
 309. Sources of Error. — So far, very little has been said in a 
 systematic way about errors to which measuring instruments 
 are liable, although some of the most important sources of error 
 have been pointed out. The following discussion is adapted 
 from a bulletin on "Testing of Electrical Measuring Instru- 
 ments," issued by the Bureau of Standards, and from other 
 sources, and is the result of many investigations and tests. 
 
 An important matter in connection with the use of electrical 
 instruments, is the question of sources of error and the best 
 means of securing a required degree of accuracy from a given set 
 of instruments. It may be said in the beginning that in very 
 many cases the user underestimates the errors and overestimates 
 the accuracy of the result. This is partly due, in many cases, 
 to the lack of means for checking the results obtained; as there 
 is no check, inaccurate results are passed without suspicion of 
 their inaccuracy, and the maker's representations as to accuracy, 
 which are sometimes much exaggerated, are accepted as correct 
 for an unlimited time after the maker's test and for all conditions 
 of use. Portable instruments are often used in places subject 
 to strong magnetic stray fields or extreme temperatures; sub- 
 sequent comparison with other instruments in the testing room 
 may show that the working instruments have small errors, while 
 their performance under unfavorable conditions may have been 
 5 per cent or more in error. 
 
 In all physical measurements, to attain a relatively high degree 
 of accuracy, care must be exercised to distinguish between at 
 least three possible sources of error. These are : 
 
 1. Inherent errors of the instrument. 
 
 2. Errors due to the method of measurement. 
 
 3. Errors of observation. 
 
 310. Inherent Errors. — Inherent errors are those due to im- 
 perfections of materials, limitations of accuracy in construction, 
 physical conditions determined by quantities measured, etc. 
 In short, the properties of materials used and the inevitable 
 
 37 355 
 
356 ELECTRICAL METERS 
 
 inaccuracies of construction make it impossible to construct a 
 perfect measuring instrument. Inherent errors cannot be 
 entirely eliminated although by improved and refined methods 
 of construction, and by a knowledge of their presence, their 
 influence may be reduced. 
 
 311. Inherent Temperature Errors. — Among inherent errors 
 may first be mentioned those due to the effect of change in the 
 temperature of the various parts of the instrument. Taking, 
 for example, a voltmeter of the permanent-magnet moving-coil 
 type; if it reads correctly at a given point at a certain tempera- 
 ture, it will, in general, show a small error at any other tempera- 
 ture. An increase in temperature of the working parts of an 
 instrument has three effects: a decrease in the strength of the 
 magnet, which tends to reduce the reading at any given voltage; 
 an increase in the resistance of the moving coil which also tends 
 to reduce the reading; and a third effect is the weakening of 
 the controlling spring, which, to some extent, compensates the 
 other two. The temperature coefficient of the spring is about 
 0.04 per cent per degree Centigrade; that of the magnet is not 
 so definite. The resultant temperature coefficient of the instru- 
 ment is quite small, as a rule. The question of making such an 
 instrument practically free from temperature error is then re- 
 latively simple as it is only necessary to have a low value of the 
 resistance temperature coefficient of the circuit. This is accom- 
 plished by making the moving coil of low resistance, usually of 
 copper, and mounting in series with it an external resistance of 
 manganin whose resistance temperature coefficient is negligible 
 within the working temperature range of the instrument. Thus, 
 if the value of the external series resistance is ten times the 
 resistance of the coil, the resistance temperature coefficient of both 
 will be reduced to one-tenth. The higher the series manganin 
 resistance, the lower the resulting temperature coefficient. It 
 is thus seen that where a voltmeter has low and high ranges, a 
 greater inaccuracy due to temperature changes is to be expected 
 on the lower ranges. If a low-range voltmeter is to have a low 
 temperature coefficient, the moving coil must be constructed with 
 few turns and have a very low resistance. 
 
 So far, it has been assumed that the temperature within the 
 instrument is uniform. This would be the case if no source of 
 heat existed within the instrument. Most instruments, however, 
 contain sources of heat. Unequal heating is, therefore, possible, 
 
INSTRUMENT ERRORS 357 
 
 and some error will result from this cause. When, as in alter- 
 nating-current voltmeters and wattmeters, a large portion of the 
 resistance is so-called dead resistance in series with the working 
 element, this heat-producing resistance should be partitioned 
 off from the working system and properly ventilated. Unless 
 this is done, the instrument cannot be left in circuit for any 
 length of time without error. 
 
 An important instance of large errors through unequal heating 
 within the instrument is found in connection with the permanent- 
 magnet moving-coil ammeter with internal copper shunt. In 
 this instrument the moving coil of copper is connected to the 
 terminals of a copper shunt within the instrument case. The 
 temperature coefficient of the moving coil used alone as an 
 ammeter is quite small, and, as changes of room temperature 
 will not alter the relative values of current in moving coil and 
 shunt, such an instrument would seem at first sight to be almost 
 an ideal one. The performance of the low-range instruments is 
 quite good. The performance of the higher-range instruments is 
 not very satisfactory and they are suitable only for rough work. 
 In general, it may be said that up to about 25 amp., well-made 
 instruments of this type will give fairly good service; for cur- 
 rents above that they should not be used for accurate work. 
 The use of manganin for precision shunts is now recognized as 
 the best practice. For large currents, the shunt should be 
 separate from the instrument. In practice, it is desirable to 
 keep down the weight of ammeter shunts as well as the waste 
 of power in them. To fulfill these conditions, milivoltmeters 
 are made to give full-scale reading for very low voltages across 
 the terminals. A very common value of this voltage is 50 
 millivolts, where the instruments are intended for switchboard 
 use. As the shunts are usually made of a material of a low 
 temperature coefficient, while the millivoltmeter circuit consists 
 largely of copper, the error due to varying room temperature 
 may be considerable. When the instrument is intended for 
 commercial switchboard use, this effect of room temperature is 
 of no great moment; for precision work in the laboratory, or in 
 the testing of direct-current watt-hour meters, the tempera- 
 ture errors above referred to become quite objectionable. To 
 remedy this, most makers manufacture a line of millivoltmeters 
 which have added to copper coil a manganin resistance which 
 has from four to nine times the resistance of the copper coil. 
 
358 ELECTRICAL METERS 
 
 This cuts down the temperature coefficient of the instrument, 
 but requires a higher drop across the shunt, namely, from 150 
 to 200 milHvolts at full load. 
 
 Aside from the errors due to heating, changes of several per 
 cent in the resistance are caused by the method of bolting the 
 copper bar to the shunt. To overcome this difficulty, the 
 terminal blocks should be made longer, so as to make the lines 
 of current flow more nearly parallel at the junction of terminal 
 and resistance metal, near which junction the potential terminals 
 should be located. The same result may be attained by con- 
 stricting the section of the terminal block considerably between 
 the current and potential terminals. 
 
 For precision ammeter shunts, the most satisfactory material 
 is manganin, and the best makers are adopting it in spite of 
 some additional trouble involved in the manufacture of the 
 shunts. 
 
 The influence of temperature upon the electromagnetic (soft- 
 iron) ammeter, with spring control, is to lower the permeability 
 of the iron, and also to reduce the elasticity of the spring. Since 
 the effect on the spring just about neutralizes the effect on the 
 soft-iron core, the ammeter is very nearly independent of ordinary 
 temperature changes. 
 
 In the electrodynamometer type of instrument, a tempera- 
 ture change affects mainly the spring. Such instruments will 
 read too low at temperatures below that at which they are 
 calibrated, the temperature correction being about 0.04 per cent 
 per degree Centigrade. This assumes that the potential or 
 shunt circuits contain so small a percentage of copper that their 
 change in resistance with temperature does not sensibly affect 
 the result. For ordinary ranges of voltage, this is the case. 
 
 In the soft-iron voltmeter the temperature coefficient depends 
 mainly upon the ratio of the resistance of the copper coil to the 
 total resistance of the instrument. This ratio is a question of 
 design, depending upon the range of the instrument and the 
 amount of power required for its operation. The temperature 
 coefficient of well-made voltmeters of this type, for the usual 
 commercial voltages, is quite small, and for practical work need 
 not be taken into account, except in extreme cases. 
 
 Much data on the physical characteristics and performance 
 of the voltmeters and ammeters whose correction curves are 
 shown on pages 281 and 294 were determined by Fitch and Huber 
 
INSTRUMENT ERRORS 
 
 359 
 
 at the Bureau of Standards and are given in the following 
 tables : 
 
 Table XI. — Performance of Voltmeters 
 
 Voltmeter 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 F 
 
 G 
 
 H 
 
 ReBiatance (ohms) 
 
 12,450 
 1.81 
 
 -0.2 
 
 0.8 
 
 0.8 
 
 0.0 
 >75 
 -0.01 
 
 16,180 
 1.39 
 
 -0.2 
 
 2.2 
 
 4.8 
 
 0.4 
 
 15 
 
 -0.03 
 
 18,400 
 1.22 
 
 -0.1 
 
 1.5 
 
 2.1 
 
 0.2 
 
 37 
 
 -0.03 
 
 7,540 
 2.99 
 
 -0.1 
 
 1.1 
 
 1.2 
 
 0.1 
 >75 
 -0.02 
 
 12,350 
 1.82 
 
 -0.3 
 
 2.5 
 
 4.6 
 
 0.3 
 
 75 
 -0.02 
 
 14,380 
 1.56 
 
 0.0 
 
 2.3 
 
 2.4 
 
 0.1 
 
 >75 
 -0.01 
 
 16,760 
 1.34 
 
 +0.1 
 
 1.2 
 
 2.8 
 
 0.1 
 
 25 
 
 +0.02 
 
 14 190 
 
 Watts at 150 volts 
 
 1 58 
 
 Per cent change from stand- 
 ing 1 hr. at 150 volts' 
 
 Per cent change from revers- 
 ing a stray field of 4 gausses. 
 
 Damping. Time in seconds 
 to come to rest after closing 
 on 120 volts 
 
 -0.2 
 1.7 
 
 3 7 
 
 Mechanical balance. Maxi- 
 mum deviation of index, per 
 
 0.1 
 
 Insulation resistance between 
 coil and case, in megohms. . . . 
 
 Temperature coeflSoient. Per 
 cent change per degree C.». . . 
 
 >75 
 -0.01 
 
 ' The minus sign indicates that less voltage was required at the end of the period. 
 
 2 In this test the instrument is turned at different angles. 
 
 I The minus sign indicates that less voltage was required at the higher temperature. 
 
 It will be observed that the effect of temperature upon the 
 indications of the ammeters is much greater than upon the 
 indications of the voltmeters. 
 
 The temperature error of watt-hour meters is the resultant 
 of the effects of temperature changes on the several parts of the 
 meter, namely: 
 
 1. Effect on voltage circuit. 
 
 2. Effect on series circuit. 
 
 3. Effect on retarding disk. 
 
 4. Effect on retarding magnets. 
 
 5. Effect on frame of the meter. 
 
 6. Effect on lubricant. 
 
 The accuracy of the electrodynamometer-type watt-hour meter 
 is affected primarily by the resultant of the first four effects. 
 Any change in the temperature of the voltage and compensating 
 coils and retarding disk produces a like change in the resistance 
 of the coils and disk. Thus, when the temperature increases, 
 the resistance increases. This result decreases the voltage-coil 
 current and eddy currents in the disk and, hence, the driving and 
 retarding torques are both decreased. As these two effects are 
 
360 ELECTRICAL METERS 
 
 Table XII. — Performance op Ammeters 
 
 Ammeter 
 
 Resistance of millivoltmeter 
 (ohms) 
 
 Shunts; 
 
 MilUvolts at full load 
 
 Watts loss at full load 
 
 Temperature rise in plates 
 
 at full load °C 
 
 Temperature rise in lugs 
 
 at full load "C 
 
 Thermal e.m.f. after 1 hr. at 
 
 full load, millivolts 
 
 Total change of resistance 
 from 25° to 50°C. (per 
 cent)i 
 
 Per cent, change from stand- 
 ing deflected at full load 
 for 1 hr.2 
 
 Per cent change from revers- 
 ing a stray field of 4 gausses.. 
 
 Damping. Time in seconds 
 to come to rest after closing 
 circuit on 160 amp 
 
 Mechanical balance. Maxi- 
 mum deviation of index, 
 per cent of full scale." 
 
 Insulation resistance between 
 case and coil, in megohms. , . . 
 
 Temperature coefficient. Per 
 cent change per degree C*. .. 
 
 50 
 10.0 
 
 53 
 
 40 
 
 0.0 
 
 +0.5 
 
 -0.5 
 0.7 
 
 1.1 
 
 0.9 
 
 75 
 
 +0.11 
 
 3.7 
 
 74 
 14.8 
 
 73 
 
 59 
 
 0.7 
 
 +0.1 
 
 -1.2 
 1.5 
 
 2.6 
 
 0.7 
 
 75 
 
 + 0.08 
 
 2.1 
 
 60 
 12.0 
 
 69 
 
 58 
 
 0.0 
 
 + 0.2 
 
 -0.9 
 1.4 
 
 1.6 
 
 0.7 
 
 37 
 
 + 0.09 
 
 0.9 
 
 49 
 9.8 
 
 20 
 0.0 
 
 +0.1 
 
 -0.1 
 1.1 
 
 1.4 
 
 0.4 
 
 75 
 
 + 0.15 
 
 2.0 
 
 70 
 14.0 
 
 70 
 
 45 
 
 0.4 
 
 +0.4 
 
 -1.0 
 3.5 
 
 5.8 
 
 0.6 
 >75 
 +0.15 
 
 f 
 
 1.3 
 
 50 
 10.0 
 
 66 
 
 58 
 
 0.3 
 
 0.0 
 
 -0.4 
 1.6 
 
 2.1 
 
 0.6 
 >75 
 +0.32 
 
 4.8 
 
 61 
 12.2 
 
 62 
 
 50 
 
 0.1 
 
 +0.1 
 
 -0.3 
 0.8 
 
 2.4 
 
 0.8 
 9 
 
 + 0.28 
 
 3.2 
 
 97 
 19.4 
 
 82 
 
 43 
 
 0.1 
 
 +0.1 
 
 -0.6 
 1.9 
 
 2.4 
 
 0.7 
 
 75 
 
 + 0.20 
 
 1 The plus sign indicates an increase in resistance with rise of temperature. 
 ^ The minus sign indicates that less current was required at the end of the period. 
 ■ In this test the instrument is turned at different angles. 
 
 ' The plus sign indicates that more current was required at the higher temperature 
 for the same indication. 
 
 in a measure compensating, theoretically, the two circuits may 
 be designed so as to neutralize the temperature effects of each 
 other; actually this is not realized in practice. 
 
 The heating of the series coil is not negligible as was determined 
 by Fitch and Huber.^ The influence of heating the current coil 
 on the accuracy of fine electrodynamoineter-type watt-hour 
 meters is shown in Fig. 297. 
 
 A change in temperature of the retarding magnets changes 
 their magnetic properties, and also changes the length of the air 
 gap. The combined effect is to reduce the flux with increase in 
 temperature. 
 
 ' Fitch and Hubek, "Study of American Direct-current Watt-hour 
 Meters," Bulletin of the Bureau of Standards, vol. 10. 
 
INSTRUMENT ERRORS 
 
 361 
 
 If we define the temperature coefficient of the meter as the 
 per cent change in accuracy per degree change in temperature, 
 the temperature coefficient of the meter is the resultant of the 
 temperature coefficients of the several parts. As the retarding 
 torque is proportional to the square of the flux between the poles 
 
 1.010 
 
 
 
 
 
 
 
 
 
 
 
 — — 
 
 
 
 A 
 
 
 
 
 LOOO 
 0.990 
 
 
 
 
 
 
 
 
 
 r:::^ 
 
 
 
 
 
 
 
 
 
 LOlO 
 
 
 
 
 
 
 
 
 
 ^^ 
 
 
 
 =5= 
 
 _ 
 
 B 
 
 
 
 
 1.000 
 0.990 
 
 
 
 
 
 
 
 =^=r 
 
 ;^— o 
 
 
 
 
 
 
 
 
 
 1010 
 
 
 
 
 
 
 
 
 
 LOOO 
 0.990 
 
 ^^ 
 
 
 ■— — — — 
 
 — — - 
 
 C 
 
 
 
 
 
 
 
 
 
 "~""~-- 
 
 ■~,^ 
 
 ° 
 
 
 
 
 
 
 
 
 "- 
 
 LOlO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 D 
 
 — '— — 
 
 
 
 1 ■ 
 
 1.000 
 0.990 
 
 
 
 
 
 
 
 
 e 
 
 
 
 
 
 
 
 
 
 1.010 
 1.000 
 0.990 
 
 
 
 
 
 
 
 
 
 
 — o 
 
 'ZZH 
 
 — ~ — 
 
 t: 
 
 
 
 
 
 
 
 
 
 ^- 
 
 --~.^ 
 
 " 
 
 
 
 
 
 
 
 
 ^^ 
 
 1.010 
 1.000 
 0.990 
 
 
 
 
 
 
 
 
 
 ^„£=- 
 
 -r!~; — 
 
 =5:=^ 
 
 
 F 
 
 
 
 
 
 
 
 
 
 
 
 -7-^ 
 
 20 
 
 40 
 
 60 SO 100 
 
 Per Cent Full Load 
 
 Fig. 297. 
 
 120 
 
 140 160 
 
 of the drag magnets, the resulting per cent change in the torque 
 is twice the per cent change in the flux causing it. Hence, the 
 temperature coefficient of the magnets must be doubled in calcu- 
 lating the meter coefficient. Table XIII gives the temperature 
 coefficients of six direct-current watt-hour meters.^ 
 
 » Tables XIII, XIV, XV, XVI, and XVII are taken from Fitch and 
 Hcber's paper referred to above. 
 
362 ELECTRICAL METERS 
 
 Table XIII. — TEMPEnATTjRE Coefficients (Per Cent per Degree C.) 
 
 Watt-hour meter 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 F 
 
 Potential circuit 
 
 Disk 
 
 +0.17 
 +0.39 
 -0.03 
 +0.28 
 +0.26 
 
 +0.35 
 +0.38 
 -0.01 
 +0.05 
 +0.10 
 
 +0.41 
 +0.39 
 -0.01 
 0.00 
 +0.10 
 
 +0.30 
 +0.40 
 -0.01 
 +0.12 
 +0.12 
 
 +0.41 
 +0.37 
 -0.02 
 0.00 
 +0.07 
 
 +0.38 
 +0.38 
 
 
 -0.03 
 
 Algebraic sum'.^ 
 
 Meter 
 
 +0.06 
 +0.11 
 
 
 
 1 In taking the sums, the coefficients of magnets were doubled and the eign reversed for 
 both potential circuit and magnet coefficients. 
 
 20 40 60 80 100 
 
 Temperature in Degrees Fahrenheit 
 
 Pig. 298. 
 
 The effect of a cyclic change of temperature on the accuracy 
 of five different makes of direct-current watt-hour meters was 
 recently made by Royce and Andrew at the Electrical Labora- 
 
INSTRUMENT ERRORS 
 
 363 
 
 tories of the University of Wisconsin. Typical curves showing 
 the changes in accuracy with changes in temperature, are given 
 in Fig. 298. 
 
 The characteristics of the other meters tested are similar 
 although they differ in magnitude. 
 
 The effect of temperature changes on induction meters is less 
 than upon the electrodynamometer type. This is mainly due 
 to the fact that both the driving and retarding forces operate 
 
 -20 
 
 120 
 
 160 
 
 20 40 60 80 100 
 
 Temperature in Degrees Fahrenheit 
 
 Pig. 299. 
 
 upon the same disk. The error in induction meters is about 1 
 per cent per 10°C. This will vary somewhat with the design 
 of the meter and the absolute temperature. Typical curves for 
 the effect of cyclic changes of temperature are shown in Fig. 
 299.1 
 
 312. Inherent Errors Due to Time and Use. — Other errors, 
 to which most instruments are liable, are due to changes 
 in the properties of the materials of which the instruments are 
 made, with time and use. In spite of the labor which has been 
 
 1 B. E. Miller, Electrical World, Sept. 18, 1915. 
 
364 ELECTRICAL METERS 
 
 expended on making permanent magnets and the investigations 
 concerning their properties, individual magnets of the best 
 makes will occasionally show changes with time. When the 
 instrument is new, it may, for a time increase in strength; later, 
 it is more likely to decrease. Controlling springs also show slight 
 changes with time. If the effect of the weakening of the magnet 
 is offset by the weakening of the springs in a direct-current 
 instrument, the accuracy is unchanged. 
 
 When direct-current instruments are used in the neighborhood 
 of dynamos or motors, or in other locations subject to strong 
 stray fields, as, for example, near conductors carrying heavy 
 currents, their indications will be considerably affected at the 
 time of use, and in addition permanent changes may occur in 
 the permanent magnets. Stray fields are liable to be found in 
 the neighborhood of switchboard instruments and hence these 
 should be shielded from them. The iron case very generally used 
 for such instruments affords considerable protection, but, in 
 addition, it is advisable to keep heavy currents well away from 
 the instruments, and, as a further precaution, important instru- 
 ments that are permanently attached to the switchboard, should 
 be checked in position, under working conditions. Care must 
 be taken that the portable instruments used in this checking 
 are in a location not exposed to stray fields; if this is impossible, 
 the mean of two readings should be taken; for the second reading, 
 the instrument is turned 180° from its first position. The magni- 
 tudes of these errors are given in Tables XI and XII for ammeters 
 and voltmeters and in Table XIV for direct-current watt-hour 
 meters. 
 
 313. Inherent Mechanical Errors. — Among the most common 
 sources of error may be mentioned friction, defective preformance 
 of springs, scale marking, and lack of balance of moving coil. 
 The friction of pivots on a good indicating instrument should 
 not be noticeable, unless it is old or has been roughly used. The 
 friction of the pen on recording instruments is the main cause of 
 inaccuracy of these instruments. It is evident that friction can- 
 not be entirely ehminated, and hence, the problem is to have a 
 spring strong enough to cause the coil to take up its proper 
 position irrespective of friction. If the spring is strong, the 
 torque for a full-scale deflection will also have to be high. Ac- 
 cording to one writer, this torque expressed in gram-centimeters 
 should not be less than one-sixth the weight of the coil in grams; 
 
INSTRUMENT ERRORS 365 
 
 Table XIV. — ^Pekfobmance op Watt-hour Meters 
 
 Watt-hour meter 
 
 Hated lull-load r.p.m 
 
 Per cent difference in balance of current 
 elements: 
 
 No. 1 
 
 No. 2 
 
 No. 3 
 
 Per cent change from reversing stray 
 
 field of 1 gauss at full load 
 
 Per cent change from removing covers; 
 
 Heatingi 
 
 Magnetic 
 
 Per cent change from reversing polarity: 
 
 50 per cent load 
 
 100 per cent load 
 
 Polarity marked 
 
 Range of light-load adjustment, per cent. 
 Range of full-load adjustment, per cent. . 
 Per cent change of full-load rate by maxi- 
 mum change of light-load adjustment. . 
 Per cent change of light-load rate by 
 maximum change of full-load adjust- 
 ment 
 
 Per cent change from short-circuit on 120 
 
 volts 
 
 Maximum amperes on 120-volt short- 
 circuit 
 
 Per cent change by short-circuit on 240 
 
 volts 
 
 Maximum amperes on 240-volt short- 
 circuit 
 
 Full-load back e.m.f. in volts 
 
 Starting current, in amperes: 
 
 No. 1 
 
 No. 2 
 
 No. 3 
 
 Creeping voltage, in volts: 
 
 No. 1 
 
 No. 2 
 
 No. 3 
 
 33.0 
 
 1.1 
 3.2 
 4.2 
 
 2.2 
 
 -1-0.3 
 +0.2 
 
 0.8 
 0.5 
 
 Yes 
 4.6 
 
 86 
 
 0.5 
 
 85 
 
 2.5 
 
 240 
 
 34.0 
 
 400 
 0.13 
 
 0.06 
 0.07 
 0.07 
 
 130 
 130 
 130 
 
 36.7 
 
 5.1 
 1.5 
 3.6 
 
 2.2 
 
 +0.1 
 0.0 
 
 O.G 
 0.3 
 Yea 
 5.6 
 155 
 
 0.3 
 
 154 
 
 2.9 
 
 260 
 
 11.6 
 
 400 
 0.13 
 
 0.02 
 0.06 
 
 120 
 130 
 100 
 
 45.8 
 
 0.4 
 1.6 
 0.8 
 
 2.3 
 
 +0.6 
 -0.4 
 
 0.5 
 0.2 
 No 
 
 13.8 
 
 68 
 
 0.7 
 
 66 
 
 1.1 
 
 260 
 
 5.6 
 
 430 
 0.19 
 
 0.04 
 0.05 
 0.03 
 
 27.5 
 
 130 
 130 
 130 
 
 0.0 
 
 0.0 
 0.0 
 
 2.9 
 1.9 
 No 
 4.6 
 35 
 
 -1.5 
 
 38 
 
 2.3 
 
 >500 
 
 0.0 
 
 730 
 0.0001 
 
 0.02 
 
 160 
 260 
 
 180 
 
 45.8 
 
 0.6 
 0.0 
 0.8 
 
 2.6 
 
 +0.7 
 -0.3 
 
 0.9 
 
 0.4 
 
 Yes 
 
 22.0 
 
 92 
 
 1.5 
 
 104 
 
 1.9 
 270 
 
 4.7 
 
 440 
 0.17 
 
 0.09 
 0.07 
 0.08 
 
 130 
 130 
 130 
 
 55. 
 
 2.6 
 3.2 
 0.3 
 
 2.7 
 
 0.0 
 0.0 
 
 0.5 
 
 0.2 
 
 Yes 
 
 12.2 
 
 65 
 
 1.1 
 
 65 
 
 -2.2 
 
 340 
 
 -3.4 
 
 560 
 0.07 
 
 0.08 
 0.04 
 0.11 
 
 130 
 130 
 130 
 
 ' The plus sign indicates an increase in speed. 
 
 • Where no figure is given of the starting current it indicates creeping on voltage only. 
 
 this weight includes that of springs, index, etc. Another author 
 gives a minimum value considerably lower, namely, one-twen- 
 tieth. Both authorities assume a deflection of about 90°, this 
 being nearly the full-scale deflection for direct-current indicat- 
 ing instruments. It is desirable to keep the ratio of torque to 
 weight as high as possible in all electrical measuring instruments. 
 It should be noted, however, that an instrument with a very 
 high torque may really be a poor instrument, if the high torque 
 is obtained by using an excessively heavy moving system. 
 
366 
 
 ELECTRICAL METERS 
 
 The most important factor affecting the accuracy of inte- 
 grating meters is friction of brushes, bearings, and registering 
 mechanism. If this friction were constant, any errors intro- 
 duced by it could be compensated, but since it is an extremely 
 variable factor, under favorable conditions the error due to it 
 may be appreciable. Tightening the brushes on a commutator 
 meter may cause a 10 per cent error on a 10 per cent load. To 
 reduce the effect of friction to a minimum, the meter should 
 operate at a comparatively low speed and the ratio of driving 
 torque to weight of moving element should be high. High-speed 
 and heavy-moving elements increase friction. 
 
 Table XV. — Constants op the Coils 
 
 Watt-hour meter 
 
 A 
 
 B 
 
 C 
 
 DI 
 
 E 
 
 F 
 
 Hesiatance of potential 
 circuit in ohms: 
 
 3,080 
 
 230 
 
 2,300 
 
 1,340 
 
 12 
 
 1,290 
 
 1,790 
 930 
 
 
 1,710 
 980 
 
 
 
 
 Armature 
 
 1,360 
 
 
 
 Total 
 
 5,610 
 
 2,640 
 
 2,720 
 
 5,290 
 
 2,690 
 
 4,580 
 
 
 
 Potential-circuit watts. . . 
 Current element: Resist- 
 
 2.2 
 
 0.200 
 6.5 
 
 70 
 
 4.6 
 
 0.230 
 5.7 
 
 85 
 
 4.4 
 
 0.230 
 5.7 
 
 75 
 
 9.2 
 
 0.002 
 0.2 
 
 4.5 
 
 0.210 
 5.2 
 
 70 
 
 2.6 
 0.100 
 
 Watts loss, full load 
 
 Flux density full load, 
 
 2.5 
 85 
 
 
 
 'Bated voltage of meter D was 220; of the others, 110. 
 
 Table XVI.' — Constants op Moving Elements 
 
 Watt-hour meter 
 
 Torque in centimeter-grams 
 
 Weight in grams 
 
 Ratio of torque to weight 
 
 Diameter of commutator, centimeter 
 
 Number of commutator segments 
 
 Thickness of disk, centimeter 
 
 Diameter of disk, centimeter 
 
 %^oltage drop across armature with 110 volts 
 
 on potential circuit 
 
 Brush pressure, grams, 
 
 7.47 
 98.4 
 
 0.076 
 
 0.265 
 
 3 
 
 ■0.115 
 11.40 
 
 45.1 
 0.24 
 
 14.31 
 156.2 
 
 0.092 
 
 0.465 
 
 S 
 
 0.150 
 13.35 
 
 53.8 
 0.57 
 
 16.69 
 101.8 
 
 0.164 
 
 0.240 
 
 8 
 
 0.065 
 12.66 
 
 37.6 
 1.50 
 
 3.92 
 7.2 
 
 0.545 
 
 0.090 
 10.18 
 
 14.92 
 96.1 
 
 0.155 
 
 0.240 
 
 8 
 
 0.065 
 12.70 
 
 40.1 
 1.80 
 
 2.85 
 97.4 
 0.029 
 0.195 
 3 
 
 0.115 
 8.54 
 
 32.7 
 0.34 
 
INSTRUMENT ERRORS 367 
 
 I'ABLB XVII. — Constants op Magnets 
 [The dimensions are given in centimeters and the flux densities in gausses.] 
 
 Watt-hour meter 
 
 A 
 
 B 
 
 C 
 
 D 
 
 E 
 
 F 
 
 Number of magnets 
 
 2 
 
 19.4 
 2.2 
 
 0.28 
 5.3 
 167 
 9,700 
 
 2 
 
 26.2 
 2.0 
 
 0.36 
 6.8 
 247 
 14,400 
 
 4 
 
 23.2 
 1.4 
 
 0.24 
 4.4 
 304 
 7,300 
 
 2 
 
 18.1 
 2.2 
 
 0.29 
 3.1 
 
 88 
 8,100 
 
 4 
 
 24.0. 
 1.4 
 
 0.25 
 4.4 
 302 
 7,300 
 
 1 
 
 Steel: 
 Length 
 
 13 3 
 
 Cross-section 
 
 2 5 
 
 Air gap : 
 Leneth 
 
 Adjustable 
 2 5 
 
 Cross-section 
 
 K' 
 
 
 Total flux 
 
 1,300' 
 
 
 1 Taken with 2.5-mm. air gap. 
 
 2 K is the ratio of the length of the manegt to its cross-section divided by the ratio of the 
 air gap to its cross-section, 
 
 314. Defective Performance of Springs. — An indicating instru- 
 ment whose pointer stands exactly at zero with no current flowing, 
 will not always indicate zero after use on full load. If the full 
 load is on for only a moment, the pointer will usually return to 
 zero within the limit of reading. If full-scale deflection be main- 
 tained for an hour or so, it will probably be found that the pointer 
 does not return exactly to zero when the circuit is broken ; if the 
 full-scale deflection lasts several hours, the discrepancy will be 
 still greater. This zero shift is only temporary, and gradually 
 disappears. The amount of this zero shift varies in different 
 classes of instruments, and in different instruments of the same 
 class. In first-class voltmeters it should be just noticeable; 
 in millivoltmeters, as a rule, it is considerably greater, although 
 occasionally a millivoltmeter will show very good performance in 
 this respect. The inaccuracy due to zero shift is most marked 
 if the instrument is used for a small deflection soon after it has 
 sustained a large deflection for a considerable length of time. 
 The reason for the poorer performance of millivoltmeters lies in 
 the necessity of using springs whose electrical properties approach 
 those of copper. For voltmeters no such limitations exist, and 
 the springs may be made of bronze whose mechanical properties 
 are best suited for the purpose irrespective of electrical resistance. 
 The design of a spring determines its performance, as well as the 
 material of which it is made; the shape, length, and thickness 
 determine its elastic limit when made of a given material. 
 
368 
 
 ELECTRICAL METERS 
 
 In discussing controlling springs, it was stated that the torque 
 is proportional to the angle or distance through which it has been 
 distorted. This proportionality is not exact, and any measure- 
 ments based upon the exactness of the assumption may lead to 
 errors of 1 per cent or more. This fact is brought out more 
 clearly in Fig. 300, which shows some calibration curves of several 
 Siemen's dynamometers and a precision instrument. These 
 curves are due to Bradshaw. The error in deflection is plotted 
 vertically and the actual deflection horizontally. Thus, when 
 
 c 
 o 
 
 > 
 
 1/ 
 
 50 
 
 100 ISO 
 
 Divisions 
 Fig. 300. 
 
 200 
 
 250 
 
 the deflection on the precision instrument is 150, the instrument 
 whose curve is marked 1 reads two divisions too high. At 50 
 the reading is 1.5 divisions too low, which shows that the torque 
 of the spring does not follow exactly the assumed law. In the 
 ordinary direct-reading instruments this variation does not 
 appear if the scale has been properly graduated. However, if 
 by accident the spring should be distorted or bent out of its 
 original shape, the scale will no longer be correct, even though 
 by shifting the spring holder the pointer be brought back to 
 zero. 
 
 From the foregoing, it is evident that a first-class instrument 
 should have a scale graduated for that particular instrument. 
 It is not necessary to determine every division by exact test, 
 
INSTRUMENT ERRORS 369 
 
 especially on instruments for commercial use. It is usually con- 
 sidered sufficient to determine, say ten or fifteen points, and fill 
 in the intermediate points, preferably by some mechanical 
 method. 
 
 Any change in the relative position of the working parts of an 
 instrument will affect its calibration. Thus, the simple removal 
 and replacement of the pole pieces of a direct-current instrument 
 — in fact, even the tightening of the screws that hold the pole 
 pieces — will affect the distribution of the magnetic flux so that a 
 scale, which fitted before the operation, will now show appreci- 
 able errors. Any accident, and mechanical change or adjust- 
 ment of an instrument should be followed by a test. Some 
 makers claim for their portable direct-current instruments a 
 possible accuracy of 0.1 scale division. No such accuracy need 
 be expected in the average instrument. 
 
 ' 315. Errors Due to Balancing. — When a portable instrument 
 is held in different positions when not connected to a circuit, it 
 will be observed that the pointer will not remain at the zero 
 position. This deviation is due to imperfect balancing of the 
 moving parts of the instrument. A portable direct-current 
 voltmeter examined in this way will show a deviation of not more 
 than a few tenths of a scale division if in good balance; milli- 
 voltmeters, wattmeters, and alternating-current instruments, all 
 of which usually have a smaller ratio of torque to weight of mov- 
 ing parts than the direct-current voltmeter, may show devia- 
 tions as great as one division. Most portable instruments are 
 intended to be used on a level support in a horizontal position, 
 and to avoid errors on account of imperfect balancing they should 
 be used and tested in that position. All other instruments should 
 be tested in the position in which they are to be used. 
 
 ' 316. Errors of Use. — In addition to the foregoing inherent 
 errors of construction, there are what may be called inherent 
 errors of use. The instrument may be used under circumstances 
 such that errors in the result are inevitable. One of the most 
 common sources of error of this kind is due to stray magnetic 
 fields either from other instruments, or conductors carrying 
 heavy currents. Even the proximity of unmagnetized masses of 
 iron may influence the readings. The effect of stray field depends 
 upon the nature of the field, and the design of the instrument. 
 The influence of a direct-current field is constant so long as the 
 current is constant, and varies with the current. Its effect upou 
 
370 ELECTRICAL METERS 
 
 a direct-current moving-coil instrument may be obtained by 
 reading the instrument in a given position, quickly turning it 
 through an angle of 180° and reading it again. One-half the 
 sum of the readings will be the true reading. So long as the 
 stray field remains constant, the error may be determined as 
 above and may be allowed for by a percentage correction for 
 readings on any part of the scale, the instrument remaining in a 
 fixed position. 
 
 The effect of the stray field is to change the strength of the 
 field of the magnets of the instrument; the distribution of the 
 field is not perceptibly changed. The resulting deflection of the 
 instrument may then be considered as proportional to the 
 product of the current in the moving coil and composite field. 
 
 Thus let H = original magnet field 
 
 let H' — component of stray field parallel to magnet 
 
 field 
 and I — current in moving coil of instrument. 
 
 Then the reading of the instrument in one position may be 
 written 
 
 R = K{IH + IE'). 
 
 With the instrument turned through an angle of 180° the effect 
 of the stray field will be opposite to that in the former case, hence, 
 
 R' = K {IH - IH'). 
 
 Adding the two deflections or readings we get 
 
 {R + R') = 2KIH 
 
 whence ^ = KIH, the true reading. 
 
 Subtracting the two readings the difference is 
 R-R' = 2KIH' 
 
 or ?~^ = KIH' 
 
 the effect or change in reading due to stray field. The percentage 
 
 error is then 
 
 R-R' 
 
 2 KIH ' 
 
 R + R' KIH 
 
 2 
 
 R-R' H' 
 
 or = — 
 
 R + R' H 
 
INSTRUMENT ERRORS 371 
 
 This shows that so long as H' remains constant, the error is a 
 constant percentage of the true reading. 
 
 Since, in most cases it is necessary to calculate the true reading 
 from the indication of the instrument, it is better to give the 
 error as a per cent of the instrument indication. This can 
 readily be done as follows: 
 
 ^ ~^' = KIH' 
 
 or change in true reading due to influence of stray field. If R 
 is the indication of the instrument in the original position, the 
 percentage error of JR is 
 
 R - R' 
 
 2 _ KIH' ^ H' 
 R KI{H + H') H + H' 
 
 and is also constant. When this percentage error has once been 
 determined, it may be applied for obtaining the true reading at 
 other indications of the instrument. The true reading will be 
 equal to 
 
 R 
 
 i^^'^) 
 
 the plus sign being used when the actual indication of the instru- 
 ment is less than the true reading, and the minus sign when the 
 conditions are the reverse. With instruments of the electro- 
 dynamometer type the case is different. Since the deflection in 
 this type of instrument is due to the reaction of the fields in two 
 coils, a position of the instrument can be found such that the 
 stray field produces no effect for a given reading of the instru- 
 ment; that is, at a given position of the moving coil the stray 
 field exerts no torque upon the moving coil. At any other posi- 
 tion of the moving coil the stray field will have some effect, and 
 this effect will vary with the deflection. Even weak fields, such 
 as that of the earth, have appreciable effects, and the usual 
 method of avoiding error in the test of such instruments, consists 
 in measuring with standard instruments the current, voltage, or 
 power required to bring the pointer of the instrument under test 
 to a given point on the scale; the direction of current is then 
 reversed, and a second measurement made with the same reading 
 of the instrument under test. The arithmetical mean of the two 
 readings of the standard instruments will give the correct value 
 
 38 
 
372 ELECTRICAL METERS 
 
 of the quantity measured, and what should be indicated by the 
 instrument under test were no external field present. 
 
 When such instruments are used on alternating currents, the 
 constant stray fields will have no effect. Here the trouble is 
 more likely to come from heavy alternating currents of the same, 
 or nearly the same, frequency as those of the quantity being 
 measured. Errors due to this cause may best be avoided by 
 twisting the leads together in such a way that the inductive 
 effect of the current is eliminated or at least very much weakened. 
 If other sources of stray field are supposed to exist, the instru- 
 ment may be turned through an angle of 180° and the effect 
 determined, as explained above. 
 
 A strong magnetic field, due to an alternating current, is liable 
 to partially demagnetize the permanent magnet and cause the 
 instrument to read low permanently unless repaired. Unless the 
 field is strong enough to cause this partial demagnetization it will 
 have no effect whatever upon the reading. Instruments of the 
 electrodynamometer type are sometimes made astatic to avoid 
 the errors due to stray field. This is accomplished by construct- 
 ing the instrument with two moving coils which are so connected 
 that a stray field produces equal and opposing torques on the two 
 coils. If the stray field is the same at the two coils, no error is 
 produced. It is not safe, however, to assume that such instru- 
 ments may be used without error in close proximity to heavy 
 currents, as both theory and experiment show that appreciable 
 errors may result. The same precautions should be taken with 
 astatic instruments as with those of ordinary form. 
 
 The hot-wire and electrostatic instruments are not affected to 
 any appreciable extent by stray fields, as their action is not based 
 on magnetic reaction. Induction instruments are also free from 
 serious error from the influence of stray fields, since their air gap 
 is small and their fields quite strong. 
 
 317. Electrostatic Effect. — The electrostatic attraction or re- 
 pulsion between the moving parts of an instrument and some sta- 
 tionary part may cause appreciable errors. Rubbing the cover- 
 glass with a handkerchief, cloth, or even the hand will often 
 cause the pointer to have an initial deflection. The remedy 
 for this consists in breathing upon the glass, the moisture of the 
 breath causing the charge to disappear. 
 
 In calibrating indicating wattmeters by means of two separate 
 sources of electromotive force, a similar effect is likely to be 
 
INSTRUMENT ERRORS 373 
 
 experienced. When the potential applied to the fixed coil is 
 much different from that applied to the moving coil, an electro- 
 static force is exerted between the two, and an appreciable error 
 in the reading may result. 
 
 318. Contact Errors. — Still another source of error is the lack 
 of good contact. This may be the fault of the individual con- 
 necting the instrument to the circuit, or it may be due to faulty 
 construction. Millivoltmeter readings are especially liable to be 
 erroneous due to this cause. A millivoltmeter is usually con- 
 nected to the shunt by two leads, and in most instruments now 
 in use this involves four contacts in the instrument circuit, two 
 at the shunt and two at the binding posts. As the resistance of 
 the instrument is only a few ohms, a corroded or dirty terminal 
 or binding-post surface may introduce errors which may amount 
 to several per cent. Binding posts and lead terminals of all 
 precision instruments should be nickel-plated to avoid corrosion. 
 The use of any substance which is liable to corrode the contacts 
 should not be permitted in either the construction or use of the 
 instrument. Soft-rubber tubing contains sulphur which will 
 corrode copper, and for that reason should be avoided in instru- 
 ment construction. 
 
 / 319, Errors Due to Thermo-electromotive Forces. — In ordinary 
 "station shunts" some errors are due to thermo-electric effects. 
 That is, the heating of the junction of the resistance metal to 
 the terminal block sets up thermo-electric currents which may be 
 quite appreciable. 
 
 Errors due to thermo-electric effect may be observed by allow- 
 ing the current to flow until the shunt has assumed working 
 temperature. On breaking the circuit, the millivoltmeter will 
 show a small current flowing under the action of thermal-electro- 
 motive forces. This may be distinguished from zero shift by 
 opening the millivoltmeter circuit. 
 
 A bad contact at one end of an ammeter shunt, or even the use 
 of too small a current cable at one end of the shunt, will cause that 
 end to be heated more than the other. With many shunts now 
 in use, this will cause considerable error from thermal-electro- 
 motive forces. For accurate work the shunts should be placed 
 in oil and the temperature equalized by constant stirring. 
 Some provision for cooling and constant stirring of the oil must 
 be made when large currents are used unless it is arranged to 
 short-circuit the shunt terminals for most of the time. 
 
374 
 
 ELECTRICAL METERS 
 
 320. Errors Due to Combination of Instruments. — The amount 
 of energy consumed by the ordinary electrical measuring instru- 
 ments is small, and may be neglected when the instruments are 
 used in commercial practice. When, however, the instruments 
 themselves are being tested, and for accurate measurements, it 
 is necessary to know what errors may be introduced by neglect- 
 
 CI 
 
 m7? 
 
 /Im 
 
 Vn 
 
 u 
 
 Load 
 
 'MW 
 
 Pig. 301. 
 
 ing these losses. Some arrangements of instruments introduce 
 larger errors than others, and also the percentage error with the 
 same arrangement may be higher in one case than in another, 
 depending upon the characteristics and ranges of instruments 
 used. When a wattmeter, ammeter, and a voltmeter are used, 
 
 ^ 
 
 Am 
 
 r-\ 
 
 Wm 
 
 Vm 
 
 Fig. 302. 
 
 
 the instruments may be connected in several ways, two of which 
 are indicated in Figs. 301 and 302. In Fig. 301 the ammeter and 
 voltmeter are both connected between the wattmeter and load. 
 When such a connection is used, the current indicated by the 
 ammeter is less than the current passing through the current coil 
 of the wattmeter. If the wattmeter is being tested, the product 
 
INSTRUMENT ERRORS 375 
 
 of current and pressure, I X E,\s too low; and if power consump- 
 tion of load is being determined, the wattmeter indication is too 
 high. The excess in current is plainly that flowing through the 
 voltmeter and pressure coil of the wattmeter. If the wattmeter 
 is properly compensated, no correction need be made for its pres- 
 
 E^ 
 sure coil current. The voltmeter correction will be -5-) where 
 
 R 
 
 E is the load pressure and R the resistance of voltmeter coil. 
 
 When the connections of Fig. 302 are used, the wattmeter 
 indication should equal IE, but this is greater than the power 
 consumption of load. 
 
 In the combined use of the three instruments the best method 
 of connection will depend somewhat upon the conditions of test. 
 The instruments should be so connected that if corrections are 
 necessary they can easily be made. 
 
 321. Errors Due to Voltage and Current Transformers. — 
 In order that excessive errors may not be introduced in the 
 measurement of electrical quantities when instrument trans- 
 formers are used, it is necessary to know the ratio of transfor- 
 mation and phase relation between primary and secondary 
 currents. In current transformers, the ratio of transformation 
 must be known in connection with the ammeter and leads with 
 which it is to be used. Slight phase shifting due to the fact that 
 primary and secondary quantities are not exactly in opposition, 
 introduces no errors in current and voltage measurements. In 
 connection with the measurement of power, it is necessary to 
 consider the phase displacement, and make the necessary 
 corrections. A more complete discussion of instrument trans- 
 formers is given in Chapter XXIII. 
 
 322. Errors Due to Frequency and Wave Form. — The errors 
 due to changes in frequency, and those due to deviations of the 
 current and electromotive-force waves from a true sine wave 
 will differ with the type of instrument. The reading of all in- 
 struments that contain iron in their operating elements, unless ac- 
 curately compensated, will be influenced by changes in frequency. 
 Many modern instruments can now be obtained in which the 
 compensation makes them practically free from this error. It 
 is a good plan, nevertheless, to test a meter at the frequency on 
 which it is to be used. The inductance of the meter coils is 
 primarily responsible for frequency errors. The mathematical 
 expression for this error in meters whose coils are connected as 
 
376 ELECTRICAL METERS 
 
 diagrammatically indicated in Fig. 566, may be determined as 
 follows : 
 
 Let Ro = resistance of shunt, 
 
 Lo = self-inductance of shunt, 
 Ri = resistance of movable-coil circuit, 
 Li = self-inductance of movable-coil circuit, 
 M = mutual inductance of movable and fixed coils. 
 This varies with the position of the coils. 
 Let I = effective current in fixed coil, 
 
 7i = effective current in movable coil, 
 E = pressure across the shunt, 
 
 CO = 27r/. 
 
 Then, by using the notation of the complex quantity, which in 
 this instance is perhaps the more simple, we have: 
 
 E = hRi + jwLJi + joiMI 
 
 where j represents \^ — 1, coLi/i and ooMI are components of 
 pressure 90° out of phase with I. 
 This gives 
 
 E - jcoMI 
 
 h 
 
 But 
 and 
 
 Ri -h jwLi 
 
 E 
 Jo = ^f; — ; — r—^ = current through shunt 
 Ko + Ji^L^ 
 
 Ri + joiLi Ra + jcoLo 
 
 Solving this for E we have: 
 
 ^ ^ I[{Ri + icoLi)(fio + jcoLo) -I- joiM{Ro + ja>Lo)] 
 Ro + jcoLo + Ri + juiLi 
 
 Substituting this value of E in the expression for 7i and reducing, 
 we get: 
 
 /i = 
 
 (Ei+7Jo)^ + ^Hii + io)^ 
 This expression consists of a rational term and an imaginary 
 term. The rational part 
 
 /[fioCfio + Ji!i) + co'(Li + Lo)(£o - M)] 
 (Ri + RoV + w^Li + LoY 
 
INSTRUMENT ERRORS 
 
 377 
 
 is the component of /i in phase with I, and hence it is that part 
 of /i which produces a torque. The torque due to / and this 
 component of 7i is : 
 
 ^ KP[Ro{Ra + Ri) + to^(Li + Lo)(Lo - M)] 
 ^ {Ro + RiY + co2(Lo + LiY 
 
 AU+U) (Lo-M) 
 
 = KP.- 
 
 Ro 
 
 1 + u- 
 
 {Ro + Ri) Ro 
 
 1 + w 
 
 , (Lo + LiY 
 
 Ro + J?i 
 
 In order to reduce this to simpler form, let: 
 
 Lo + Li 
 
 Ro + Ri 
 Lo-M 
 
 Ro 
 
 = T 
 
 = To. 
 
 Then 
 
 T = KP 
 = K72 
 
 J2o 
 
 iio "I" R 
 
 Ro 
 Ro + Ri 
 
 K' = K 
 
 r l + gjT X To l 
 
 \l 1 + co^r^ J 
 
 + 
 
 K'Poi^TiTo- T) 
 
 Ro 
 
 1 + w'T^ 
 
 jRi + Ra 
 
 But iiC/2 
 
 Xto 
 
 is the torque when the coils are non-inductive, 
 
 Ro -^r Rl 
 or it is the torque that a direct current of I amp. would produce. 
 
 Call this torque to. Then: 
 
 T = To + 
 
 K'Pu'TjTo - T) 
 
 1 + w^r^ 
 
 The effective alternating current is proportional to the square 
 root of t; we then have: 
 
 Vt = -Uto + 
 
 Vt — Vt^ = to + 
 Hence per cent error 
 
 ,Vt — VtO _ .r.^L° 
 
 = 100 
 
 30 
 
 2(1 + 0)^2) 
 
 100- 
 
 K'Poi^TjTo - T) 
 1 + oj^T^ 
 
 1 + co^f^ — J "^"''• 
 
 K'Poj^TjTo - T) ^ 
 1 + w^r^ J 
 
 Vto Vto 
 
 120^!?(l4^). approximately. 
 
 100 
 
378 ELECTRICAL METERS 
 
 Example. — A shunted dynamometer ammeter haa the following con- 
 stants:' 
 
 iJi = 4 ohms, 
 L = 0.03 X 10-3 henrys, 
 To = - 5.36 X 10-', 
 T = 0.75 X 10-«, 
 w = 27r X 100. 
 Here per cent error = 
 
 ?^ X 100 X (27r X 100)' X 0.75 X IQ-' X 6.11 X 10-' 
 1 + (27r X 100)=i(0.75 X 10-6)2 
 _ _ 27r' X 0.75 X 6.11 X 10-* 
 1 + 4,r2 X 0.6625 X 10-6 
 = 0.09 of 1 per cent, low, approximately. 
 
 The effect of wave form upon the reading of any instrument 
 will depend to a considerable extent upon the relation between 
 the actuating force and current causing it. This relation in most 
 alternating-current instruments is expressed by : 
 
 r = KI^ 
 and the influence of wave form upon the readings of such meters 
 may be investigated as follows : 
 
 As shown in Article 55 an alternating-current wave may be ex- 
 pressed by a series of sine and cosine functions. As the current 
 supplied by commercial alternators contains no even harmonics, 
 the practical current wave may be expressed by: 
 
 i = Ai sin a; + .A3 sin 3a; -f . . . A„ sin n x 
 + Bi cos X + Bi COS.ZX + ... Bn cos n x 
 
 Where n is an odd number, and e may be expressed by a similar 
 series. 
 
 In an instrument whose impelling force is proportional to the 
 square of the current we have: 
 
 T = Ki"^ = K[Ai sin a; + A3 sin 3a; + . . . + A„ sin n a; 
 
 + 5i cos x + Bi cos Zx -\- ... + 5„ cos n xY, 
 and average torque 
 
 K C" 
 = — I [Ai sin a; + A3 sin 3a; + . . . + A„ sin n a; 
 
 + Bi cos a; + 53 cos 3a; + ... + 5„ cos n xfdx. 
 Squaring the quantity within the brackets this becomes: 
 
 - 1 I Ai^ sin2 xdx + j A3- sin^ Zxdx + . . . + 1 A„2 sin^ n xdx 
 
 + \ Bi^ cos^ xdx + I S3' COS32 xdx+ ... -\-\B\ cos' n dx 1 
 ' See RisDALE, loc. cit. 
 
INSTRUMENT ERRORS 379 
 
 plus the integral of a series of terms of the following form: 
 AnAm sin nx sin mxdx, A^Bm sin nx cos mxdx and B^B^ cos nx 
 sin mxdx. The integrals of these terms between the limits of 
 zero and x reduce to zero and we have left as the average torque : 
 
 av. T = — I Ai^ sin^ xdx + ( Ai^ sin^ Zxdx -^ . . . + I yln^sin^ 
 T LJo Jo Jo 
 
 nxdx -\- I Bi2 cos^ xdx + I i?3^ cos ^"ixdx + ... 
 Jo Jo 
 
 r 1 
 
 + I B„^ cos^ n xdx 
 Jo 
 
 But 
 
 2 ° T' 
 
 2 2 
 
 A„2 + B„2 IJ 
 
 2 = T' 
 
 where /i, Is, etc., /«, are the maximum values of the fundamental, 
 and harmonics, respectively. The average torque is thus pro- 
 portional to: 
 
 J 1 I ■'3 I I £n_ 
 
 2 -t- 2 "I" ■ ■ ^" 2 
 
 and 
 
 = V¥+¥ 
 
 2 T 2 
 
 -r ■• ^ 2 
 
 where / is the reading of the instrument if an ammeter. If the 
 instrument is a voltmeter, it can be shown by a similar process 
 of analysis that : 
 
 ^ = V'2' + ^ + + ^ 
 
 This shows that in ammeters and voltmeters of the electrodyna- 
 mometer type the torque is the sum of the independent torques 
 of the component harmonics, and that these torques do not 
 interact with each other to produce a torque. This is an im- 
 portant result and simplifies considerably the analysis of the 
 
380 ELECTRICAL METERS 
 
 problem of the influence of wave form upon the errors of electro- 
 dynamometer instruments. 
 
 In a preceding discussion it was shown that the percentage 
 error in a two-circuit electrodynamometer ammeter is given with 
 close approximation by: 
 
 Per cent error = 2(1 + co^T^) ' 
 
 when measuring a current whose wave form is a sine curve. If 
 the current measured contains harmonics, each harmonic will 
 produce its own torque and its own error. The resultant error 
 will then consist of a series of terms of which the above is a type. 
 The torque due to the first harmonic or fundamental is: 
 
 .,rl + <^^T X T o-] 
 
 1 + 0)272 
 
 Similarly, the torque due to the third harmonic is: 
 
 _ r ,K'{ ^ + <^'T X To l 
 
 T3 
 
 h'K 
 
 ,rl+ (3o,yT X Tol 
 
 H 
 
 and in general 
 
 + (3a))2r2 
 
 _ ^.,^,r i + nvrx To -] 
 
 T„ - J„ /I L 1 +n'o^'T^ y 
 
 The total torque is equal to the sum of these, hence: 
 
 A [- 1 + nVr X To ] 
 
 ^ " L l+n2^2y2 J 
 
 n 
 
 where ^ means the sum of all terms obtained by substituting 
 
 1 
 1, 3, 5, 7, etc., for n, depending upon the number of harmonics 
 present, or 
 
 n 
 
 But ^ K'lJ would be the torque were the coils non-inductive, 
 
 1 
 or it is the torque due to direct current of the same value. 
 Hence: 
 
 -\/r — \/t, 
 
 , V iT'T- J n'w-'TjTo - TU 
 
 To 
 
 Vr 
 
 1 + 
 
 'T(To - r)A n2/„2 
 
 Sr 
 
 
 H 
 
 - 1 
 
INSTRUMENT ERRORS 381 
 
 and per cent error = 
 
 1 
 
 If the form of the current wave is known, the per cent error, 
 due to wave form, can be readily calculated. 
 
 Wave-form Errors in Dynamometer Voltmeters. — The coils of 
 an electrodynamometer voltmeter are invariably connected 
 in series, hence it is a comparatively simple matter to derive an 
 expression for frequency and wave-form errors. If L is the self- 
 inductance of the coils, and M the mutual inductance, which 
 varies with the position of the coils, then the effective value of 
 the current through the instrument, due to a sine wave of electro- 
 motive force, is: 
 
 E 
 
 where R is the total resistance of the instrument. The torque 
 due to the first harmonic or fundamental is, then: 
 
 n = KP = K ^2 _,_ ^2(^ + My 
 Similarly, for the nth harmonic the torque is: 
 
 ''" = ^ W^fnh^HL~+Mr 
 and 
 
 EJ 
 
 = tK 
 
 j?2 _|_ „2„2(L + My 
 
 _j^^EJ__K^ EAn'o>KL -t- MY] 
 - -"-2/ 112 ji2 2^ Hi ^ n^w'{L + My 
 
 K -A 
 But -^ 2j En^ is the torque due to a constant electromotive 
 R ^ 
 
 force. Hence: 
 
 ui^L + MyK A n^g„' 
 
 r - TO ^i— Zi R2j^ n-'^^L + My 
 
 ■\/ti 
 
 TO 
 
 ~V~ R^To ^lR^ + n^o>KL + My]i " 
 
382 ELECTRICAL METERS 
 
 Per cent error 
 
 _ 100 0)2 (L + M)2^ r n^Er, 
 
 " r 
 
 1 
 
 When n is 1, this reduces to: 
 
 _, ^ 100 co2(L + M)" 
 
 Fer cent error = —^ 
 
 , approximately. 
 
 2 R^ + co\L + MY 
 EXAMPLE 
 
 Ah electrodynamometer voltmeter has the following constants ! 
 R = 2,000 ohms, 
 L = 102 millihenrys, 
 M = 3 millihenrys maximum. 
 
 Calculate the per cent error in the reading of the instrument when used 
 on a circuit whose frequency is 133K cycles. 
 
 Solution. — 
 
 100 «2(z, + My 
 
 Per cent error = 
 
 2 R' + w%L + My 
 100 ^ ,^, ^ w ^ 0^05, 
 
 = 2,000^ + 4^^-XW X 0.105= 
 = 0.1 of 1 per cent, approximately. 
 
 Wave-form Errors in Electrodynamometer Wattmeters. — The 
 error due to the self-inductance of the potential coil when both 
 electromotive force and current waves are simple sine curves has 
 been discussed in Article 112. It remains to investigate briefly 
 the influence of upper harmonics. 
 
 If power is measured in a circuit in which the electromotive- 
 force wave is a simple sine wave, and the current wave is com- 
 posite, we may express the wave forms as follows: 
 
 e = Em sin ut 
 
 i = Iim sin (oit + d) + Jam sin {Swt + P) + Lm sin {5ut + y), etc. 
 and ei = Emhm sin oot sin {ut + 6) + E„Ii„, sin ost 
 
 sin (3iot 4- /3) + Emhm sin ut sin (5co« -|- 7), etc. 
 
 1 T" 1 /*" 
 
 and average ei = - I E^hm sin ut sin (o^t + 6) + - | E^hm 
 1" Jo ■n-Jo 
 
 sin o}t sin {3oit + 6) + - I i/m/e™ sin cot sin (5U + 7), etc. 
 IT Jo 
 
INSTRUMENT ERRORS 383 
 
 depending upon the number of harmonics in the current wave 
 
 E I 
 The integral of the first term is plainly —^ ■ —^ cos 6. The 
 
 integrals of the second and subsequent terms all reduce to zero 
 as can easily be shown. Hence, the average torque of the watt- 
 meter is proportional to the product of the effective value of the 
 electromotive force by the effective value of the fundamental 
 of the current curve. The indication of an electrodynamometer 
 wattmeter is thus independent of the upper harmonics when 
 either the electromotive force or current is simple harmonic. 
 
 If both the electromotive force and current waves contain 
 upper harmonics, then the resultant torque is proportional to the 
 sum of the products obtained by multiplying the effective value 
 of each electromotive force harmonic by the effective value of 
 the current harmonic of the same frequency and by the cosine 
 of the phase difference, or, in mathematical symbols: 
 
 T = Kei = K „ cos 9 + A — ^ — cos 63 +, . . . 
 K — s — cos Bi. 
 
 This relation can be demonstrated mathematically, but a long 
 analysis is not necessary, for if the first harmonic of the electro- 
 motive-force wave does not produce a torque with the upper 
 harmonics of the current wave, it follows that any upper harmonic 
 of the electromotive-force wave will not produce a torque with 
 any harmonic of the current curve except the one of the same 
 frequency. Hence, the conclusion is obvious. The error due 
 to upper harmonics when self-inductance alone is considered 
 may be derived as follows: 
 
 1 + tan d„ tan a„ 
 
 cos On by Article 112. 
 
 = kV£'„7„[cos2 q,^ cos dn + sin a„ cos «„ sin e„] 
 1 
 
 n » 
 
 = K^EJn COS e„ + K'^E Jnlsin ol„ sin (e„ - a„)] 
 
384 ELECTRICAL METERS 
 
 n 
 lOO^Bn/n 
 
 Per cent error = X 100 = — ■ 
 
 lOOcoT 
 
 2^EJn COS e„ 
 
 1 
 
 [sin a„sin(e„ — «„)] 
 
 ^EJ„ cos (9„ ' 
 1 
 
 Where T is the time constant of the instrument circuit, 0„ 
 is the phase difference between the nth electromotive force and 
 current harmonics. When the shape of the current and voltage 
 curves and the constants of the instrument are known, the per 
 cent error may be calculated. 
 
 Induction watt-hour meters are considerably affected by fre- 
 quency and wave form; a 5 per cent variation in frequency 
 may cause from 1 to 2 per cent error on one-half load. A certain 
 meter registered correctly on a current from one generator but 
 showed a 15 per cent error on current of same frequency but 
 different wave form supplied by another generator. 
 ' 323. Errors of Observation. — The errors due to reading are 
 very variable and depend iipon two factors, one upon the con- 
 struction of the instrument, and the other upon the skill and 
 care of the observer. For accurate readings, the pointer should 
 be constructed with a flattened end, the plane of the pointer being 
 perpendicular to the scale, under which should be mounted a 
 mirror. The reading is then made by closing one eye and with 
 the other noting that the pointer is exactly over its reflection 
 from the mirror. In this way errors due to parallax are easily 
 avoided. 
 
 In any series of measurements of the same physical quantity, 
 we find that the results differ slightly one from another owing to 
 imperfections in the instruments, or errors in making observa- 
 tions. Errors of observaition are likely to be positive as often 
 as negative, and, if a sufficient number of readings are taken, may 
 in the long run, be considered as having little influence upon the 
 result. The greater the number of individual observations, the 
 less likely will the mean of the individual observations deviate 
 very far from the correct value. The conditions, and degree 
 of accuracy desired, will in each case determine the number of 
 readings to be taken. 
 
CHAPTER XXIII 
 INSTRUMENT TRANSFORMERS 
 
 324. Definitions. — Instrument transformers are transformers 
 specially designed to be used in connection with alternating-cur- 
 rent meters. They are of two kinds: current, and voltage or 
 potential transformers, sometimes designated as series and shunt 
 transformers, respectively. The first designation is based on 
 the quantity transformed, and the second upon the manner of 
 the transformer's connection to the circuit. The names current 
 and voltage transformers are preferable and will be used in the 
 following discussion. 
 
 325. Reasons for Use. — There are two main reasons for using 
 transformers in connection with alternating-current instru- 
 ments. The first has already been pointed out, namely, that it 
 is impractical to construct meters of sufficient capacity to 
 measure directly very large currents or pressures. Another 
 important reason is that their use makes it possible to measure 
 high voltages by means of instruments which can be properly 
 insulated without difficulty and great expense. 
 
 326. General Theory. — An extended and complete theory of 
 instrument transformers is beyond the scope of this text. Only 
 so much is given as will give the reader some understanding of 
 the influence of the constants of the transformer upon the read- 
 ings of the instruments connected to it, and the errors resulting 
 from the interactions of the transformer and instrument constants. 
 In its simplest form the instrument transformer consists of an 
 iron core upon which are wound two distinct or separate coils, as 
 shown in Fig. 303. In this respect it is exactly like the ordinary 
 power transformer, but as it is used with precision instruments, 
 it is designed and constructed with more care and refinement. 
 
 327. Current Transformer. — From a purely mechanical view- 
 point, there is little difference between the current transformer 
 and the common power transformer; nevertheless, electrically 
 they have somewhat different characteristics. In the ordinary 
 power transformer the .primary current changes with, and de- 
 pends upon the secondary current. In the current transformer, 
 however, the effect of the secondary current upon the primary 
 
 385 
 
386 
 
 ELECTRICAL METERS 
 
 current is negligible. The primary or main current is determined 
 by the constants of the load circuit, and within practical limits 
 is entirely independent of the current in the secondary circuit. 
 
 The function of the current transformer is to supply current 
 to a secondary circuit of constant relative value and having con- 
 stant phase relation with respect to the current in the primary. 
 There are thus two quantities upon the constancy of which 
 depends the accuracy of meters connected to the secondary 
 circuit: namely, the ratio of the primary to the secondary cur- 
 rent, and the phase difference between them. 
 
 ^ 
 
 ^^ 
 
 r X 
 
 A/wwxxrJ 
 
 HJ 
 
 \Load 
 
 Fig. 303. 
 
 The readings of ammeters and voltmeters are affected only by 
 variations in the ratio of transformation ; the indications of power- 
 factor meters and synchroscopes fire affected only by variations 
 in the phase relation; but power and energy meters are affected 
 by changes in both the ratio of transformation and in the phase 
 angle. 
 
 The ratio of transformation, and phase angle depend upon cer- 
 tain constants of the transformer, constants of the primary or 
 load circuit, and constants of the secondary or meter circuit. 
 These constants are designated in Fig. 303 as follows: 
 
 R, X = resistance and reactance of load circuit respectively. 
 Ti, 'Xi = resistance and reactance of primary winding of 
 
 transformer. 
 Ti, X2 = resistance and reactance of secondary winding of 
 transformer. 
 r, X = resistance and reactance of meter circuit. 
 The influence of these quantities upon the ratio of trans- 
 formation and phase angle will be more readily understood from 
 
INSTRUMENT TRANSFORMERS 
 
 387 
 
 a consideration of Fig. 304 in which 7i and h are drawn in length 
 proportional to the ampere-turns in the primary and secondary 
 circuit. No attempt is made to show actual values, hence the 
 vector diagram is merely illustrative. 
 
 Let E, the pressure across the load circuit, be taken as the 
 reference vector. Then 7i, the primary current, will lag behind 
 
 Ii reversed 
 
 *-e: 
 
 Fig. 304. 
 
 E by an angle 6, where cos 9 is the power-factor of the load. This 
 primary current sets up a magnetomotive force and magnetic 
 flux in phase with it. This flux is nearly neutralized by the 
 secondary current I2. Some flux must nevertheless be developed 
 in order to induce an electromotive force in the secondary cir- 
 cuit of sufficient magnitude to force the secondary current through 
 it. This flux as well as the current to which it is due is the re- 
 sultant of 7i and I2. Let this flux be represented by $ and the 
 exciting current by le. The fluctuating flux $ will induce an 
 electromotive force in both the primary and secondary circuits. 
 These two electromotive forces will be in phase and will lag 90" 
 behind *. The induced secondary voltage is represented by 
 E2. The applied electromotive force, which neutralizes the in- 
 duced electromotive force in the primary is represented by Ei, 
 opposite in phase with reference to E2. The terminal secondary 
 pressure of the transformer is the vector difference between E2 
 and the impedance drop in the secondary circuit. This terminal 
 pressure is represented by E2'. In a well-designed current trans- 
 39 
 
388 
 
 ELECTRICAL METERS 
 
 former ^2' is practically in phase with E^; that is, the reactance 
 of the secondary of the transformer is inappreciable. The 
 secondary current I2 will lag behind Ei by an angle a which is 
 
 determined by tan a = -' 
 
 r 
 
 If the transformer has an appreciable core loss, the exciting 
 current le may be considered as the resultant of two components, 
 Jm the magnetizing component, and /„ the energy component. 
 
 103 
 
 40 eo 
 
 %full. load 
 
 Fig. 305. 
 
 lOO 
 
 The ratio of /i to h and the angle p are the quantities which 
 affect the accuracy of a meter operated by the transformer. An 
 examination of the diagram shows that these quantities vary 
 
 200 
 
 D leo 
 
 o 
 
 u 
 m 120 
 
 y 
 
 § eof 
 
 AO 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 .^ 
 
 
 
 
 
 
 
 :::^ 
 
 
 
 ^^ 
 
 --Hi; 
 
 ;::;: 
 
 
 - — 
 
 
 
 
 
 "■•— 
 
 =^ 
 
 ^^= 
 
 - — 
 
 
 
 
 20 AO 60 80 100 
 
 % full load sco amps. 
 Fig. 306. 
 
 with the core loss of the transformer, the impedance of the 
 secondary circuit including that of the meter circuit, and the 
 ampere-turns for which the transformer is designed. 
 
 Fig. 305 shows some typical ratio-current curves for current 
 transformers, the ordinates being the ratios of the primary to the 
 secondary current expressed in per cent of nominal ratio, while 
 the abscissas are the secondary current expressed as a per cent 
 of full load. 
 
 In Fig. 306 are typical curves showing the variations in phase 
 
INSTRUMENT TRANSFORMERS 389 
 
 angle with secondary load. It will be observed that both the 
 ratio of transformation and phase angle approach a constant 
 value near full load. 
 
 328. Potential or Voltage Transformer. — The general principles 
 of the potential transformer are the same as those of the current 
 transformer. The principal difference between the two types of 
 transformers is in the manner of their connection to the circuit. 
 The primary current in the current transformer is determined 
 by the condition of the main or load circuit, the primary electro- 
 motive force being merely the impedance drop across the trans- 
 former. In the voltage transformer, the primary electromotive 
 force is determined by the conditions of the main circuit, while 
 the primary current resulting is determined by the electromotive 
 force applied and the impedance of the transformer. • Thus the 
 vector diagram of Fig. 304 may, with certain modifications, be 
 applied to the potential transformer. If E'l is the applied elec- 
 
 E'l . . 
 tromotive force the ratio of transformation will be -gv" which is 
 
 Ni 
 nearly -rf- where A''i and N2 are the numbers of turns on the pri- 
 
 mary and secondary winding; and the phase angle is the angle, 
 7, between the vector E'l reversed and E'i- These two quan- 
 tities are also of importance in power and energy measurements. 
 
 329. Influence of Transformer Constants in Power Measure- 
 ments. — The influence of the transformer constants upon power 
 measurements is the same as upon energy measurements and ac- 
 cordingly only the former will be discussed. To understand the 
 effect of the ratio of transformation and phase angle upon the 
 reading of a wattmeter let us briefly consider Figs. 307 and 308, 
 the first of which shows a wattmeter connected to a power 
 circuit through transformers and the second is a vector diagram 
 illustrating the phase relations between the quantities involved. 
 Both the secondary current and voltage are shown as leading the 
 corresponding quantities in the primary circuit. From this dia- 
 gram it is evident that the correct reading of the wattmeter, 
 assuming it to be direct reading, is 
 
 Power = 7i Ei cos 9 
 
 = RERihE2 cos d. 
 But the actual reading of the wattmeter is 
 
 Reading = R'ER'ihEi cos {6 - fi-\-i). 
 If ;8 and 7 are lagging their signs must be reversed. 
 
390 
 
 ELECTRICAL METERS 
 
 In the above expressions R'e and R'l are the actual ratios of 
 transformations which to give the true power should be Re and R,. 
 Due to the phase angles /3 and y and to inaccurate ratios of trans- 
 formation, the per cent error is 
 
 RsRihEi cos d - R'sR'ihEi cos (d-^+y) 
 
 Per cent error = 1 00 
 
 = 100 
 
 [>- 
 
 RERiEili cos d 
 R'eR'i cos {e- ^ + 7)' 
 ReRi cos d 
 
 Transform r 
 
 sssmssxL 
 
 Fig. 307. 
 
 :o 
 
 Wattmeter 
 
 Rei vrsvd I. ( 
 
 Fig. 308. 
 
 If the ratios of transformation are correct, that is if R'e = Re 
 and R'l = Ri, the resulting error is due to phase angle alone. 
 
 330. Variation of Error with Power-factor. — The per cent error 
 due to the phase angle of the transformer increases rapidly as 
 the power-factor of the main load decreases. 
 This may be shown as follows: 
 Let X = per cent error. 
 
 cos (e - ;3 -H ^) 
 cos Q 
 
 Then a; = 100 - lOO/c^/c^ 
 
INSTRUMENT TRANSFORMERS 391 
 
 and the rate of change of x with respect to d is 
 
 - = - 100 k^ki \ ~ ^'" ^^ ~ ^'^'^^ ^°^ ^ "^ ^°^ ^^ - |3+ 7)sing ] 
 56 L cos^ d J 
 
 cos^ 
 
 = ioow.^y^-^. 
 
 cos^ 6 
 
 8x 
 With a fixed p and 7 the value of — evidently increases rapidly 
 
 with a decrease in cos 0, or with an increase in 6. To a reader 
 unacquainted with the calculus, a numerical example may be 
 more intelligible. 
 
 EXAMPLE 
 
 Given /3 — 7 = 3°. Calculate the per cent error in the wattmeter read- 
 ing at power-factors of 0.1, 0.5 and 0.9. 
 
 Solution. — 
 
 Assume keki = 1. 
 When cos 8 = O.IO, 6 = 84° 15'. 
 When cos 9 = 0.50, fl = 60°. 
 When cos 8 = 0.90, 8 = 25° 50'. 
 
 TV. <. inn 100 cos (.8 -0 + y) 
 Then per cent, error = 100 ^ - 
 
 cos 8 
 
 100 cos (84° 15' - 3°) 
 ~ ■^"" 0.1 
 
 = 52.12 per cent when cos 8 = 0.1. 
 
 Likewise when the power-factor is 0.5 the per cent error is found to be 8.9 per 
 cent and when the power-factor is 0.9, the error is only 2.4 per cent; that is, 
 in so far as the error depends upon phase angle it increases with a decrease 
 in the power-factor. 
 
 331. Variation of Error with Phase Angle. — Assuming the 
 power-factor of the load to remain constant, it is of interest to 
 determine the variation in the per cent error with variations in 
 phase angle of the transformers. Let /S — 7 = tj), and represent 
 the per cent error by y, then 
 
 J, = 100 - 100 ^^^-^^ 
 " cos 6 
 
 and 
 
 5^ ^ 100 sin {e-<l>) 
 8<j) cos 8 
 
 which shows that the rate of change in the per cent error due to 
 
392 ELECTRICAL METERS 
 
 changes in 4> is not constant, but depends both upon B and 0. 
 When S = 0, or nearly zero, we may write without appreciable 
 error, 
 
 -~ = 100 sin 4>. 
 
 As (j} is small in well-designed transformers, — varies as sin (/>. 
 
 For changes of from to 4°, sin changes from to 0.07, 
 or within these limits the graph between y and is practically a 
 
 straight line. When 6 is near „ the expression for — becomes 
 
 8y 100 cos (^ . ^ , 
 
 and again for changes in <j> from to 4° the change in — is only 
 
 about 0.004, hence at low power-factors the graph between y 
 and <j) deviates less from a straight line than at high power-factors. 
 If then a chart is prepared on which are drawn lines showing 
 the relation between per cent error and phase angle, this chart 
 may be used to determine the per cent error of any other power- 
 factor and phase angle. Such a chart is shown in Fig. 309. In 
 the foregoing discussion <^ = (3 — 7. If only a current trans- 
 former is used, the same principles still apply as will be evident 
 by letting 7 = 0. 
 
 332. Testing Instrument Transformers. — Many different meth- 
 ods have been devised for measuring the phase angle and ratio 
 of transformation of instrument transformers. Some of the 
 methods are very elaborate and hardly suitable for commercial 
 practice. Only two of the more simple methods will be described 
 in this text. 
 
 333. Watt -hour Meter and Standard Transformer Method." — 
 The fundamental principle of this method consists in comparing 
 the effect of the phase angle and ratio of the transformer on the 
 registration of a watt-hour meter with the like effect of the 
 known constants of another transformer. The necessary appara- 
 tus consists of two identical induction watt-hour meters, a trans- 
 former, whose constants are known, of the same range as the 
 transformer to be tested, an auxiliary load circuit, and two 
 double-pole double-throw switches. A diagram of connections for 
 
 ' Dr. p. G. Aqnew, Bulletin Bureau of Standards, vol. 11, p. 347. 
 
INSTRUMENT TRRNSFORMERS 
 
 393 
 
 testing a potential transformer is shown in Fig. 310. The two 
 current coils of the watt-hour meters are connected in series and 
 the voltage coils are connected through the two switches to the 
 secondaries of the transformers whose primaries are connected 
 across a voltage supply circuit. 
 
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 tsSL 
 
 
 
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 ^1 
 
 
 ?/ 
 
 
 ¥ 
 
 / 
 
 
 
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 14 
 
 
 
 
 
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 4/ 
 
 
 
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 C 
 
 s 
 
 
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 ^r 
 
 fy 
 
 
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 / 
 
 
 12 
 
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 £ 
 
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 ^ 
 
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 ^ 
 
 
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 Bfom 
 
 - a 
 
 er 
 
 3' U 
 
 ' 4 
 
 The connections for testing current transformers are very 
 similar as is shown in Fig. 311. 
 
 334. Test for Ratio of Transformation, Watt-hour Meter 
 Method. — The test for the ratio of transformation consists in first 
 connecting the voltage coil of meter A to ^i, and of meter B to B^ 
 
394 
 
 ELECTRICAL METERS 
 
 and carefully noting the number of rotations of the meter disks in 
 a definite time interval. The connections are then shifted from 
 Ai to Ai and from Sa to 5i and again the number of rotations 
 in a given time is observed. From the known constants of the 
 standard transformer, the load circuit, and the number of rota- 
 
 TI 
 
 gQQQP 
 
 LofiflaoflJ 
 
 OOOOOO' 
 
 TRAHSl 
 
 o 
 
 /4I 
 
 
 
 
 BX 
 
 Lflttsflj 
 
 O— 
 
 TRANS, a. 
 
 t& 
 
 M- 
 
 AUX. CURRENT SUPPiy 
 
 METER A. 
 
 JJL 
 
 MereRB 
 
 000 
 
 Fia. 310. 
 
 tions of the watt-hour meters the constants of the transformer 
 under test are determined. Let transformer 1 be the standard 
 transformer, and transformer 2 be the one whose constants are 
 to be determined. Also: 
 
 WO'OWff 
 
 TRANS I 
 
 h d 
 
 
 TRANS. S 
 
 cum mnD 
 
 MX 
 VOLTASe 
 SUPPLY 
 
 Fig. 311. 
 
 let Ri and R^ = ratio of transformers 1 and 2 respectively, 
 ai and a^ = phase angles of transformers, 
 tia and n'^ = number of rotations of meter A when con- 
 nected to Ai and Ai respectively, 
 
INSTRUMENT TRANSFORMERS 395 
 
 Wfl and n'fi = the number of rotations of meter B when 
 
 connected to Si and B^ respectively, 
 Pa and pa = percentage of accuracy of meters A and B, 
 k = energy constant of the watt-hour meters. 
 Then in tia rotations, meter A will register kn^ watt-hr. The 
 actual energy that has passed is lEi cos {d + ai) when 6 is the 
 power-factor of the load. 
 
 Hence kn^ = PaIEi cos (6 + ai) 
 
 and 
 
 IE, = '^~^- 
 
 Pa cos (e + ai) 
 
 But RiIEi cos is the power in terms of the primary pressure, 
 and current in auxiliary circuit; multiplying both sides of the 
 above equation by Ri cos B we get, 
 
 RJEi cos e = rr-j r- 
 
 Pa cos {6 + QTi) 
 
 In exactly the same way we have 
 
 u'a R2k cos e . ^, , 
 
 — „„„ /„ I r tor the actual power in terms of the constants 
 
 Pa cos (tf -t ai) 
 
 of meter A and transformer 2. 
 
 The corresponding expressions for meter B are 
 
 Rinak cos 6 , R^n'sk cos B 
 
 and 
 
 Pb cos {fi -j- ai) Pb cos (0+02) 
 
 As each of these expressions is the actual power, they must be 
 equal; hence equating simultaneous readings, we have, 
 riARik cos B _ n'BRjk cos B 
 Pa cos (B + ai) ~ Pb COS {d + as) 
 and 
 
 n'ARjk cos Q nsRik cos B 
 
 Pa cos {8 + (Xi) ~ Pb cos (B + ai) 
 
 Dividing the equations term by term we get, 
 
 Ua Ri cos (6 + aa) _ UbRj cos (6 -^ ai) 
 ti'a R2 cos (6 + oil) ~ UbRi cos {6 + ai) 
 Whence 
 
 R^ _ UaUb cos' (6 + ai) 
 Ri'^^ n'An's cos' (6 + ai) 
 and 
 
 Ri = Ri-J / f approximately, 
 
396 ELECTRICAL METERS 
 
 ^°^ TflTL' — \ ^^ practically unity at unity power-factor, that 
 
 is when 6 = 0. tia, Ub, n' a and u'b are the numbers of rotations 
 of the watt-hour meters at unity power-factor. 
 
 Since jia, Vb, and k do not appear in the result, the ratio is 
 independent of these quantities, and the accuracy of the method 
 can be increased by increasing the speed of the watt-hour meters. 
 This can be done by shunting the retarding magnets. 
 
 335. Test for Phase Angle, Watt-hour Meter Method. — It has 
 already been shown that the effect of phase angle upon the ac- 
 curacy of meter readings is much greater at low power-factors 
 than at high power-factors. At high power-factors the influence 
 of the ratio with reference to accuracy predominates. Upon 
 this fact is based the method of determining the phase angle. 
 If the readings of the watt-hour meters are taken as before, but 
 at low power-factors we have 
 
 Ri^ r '"'A^B 1 C0S2 {d -\- az) 
 
 /££ _ r riAUB 1 
 
 C0S2 (e -\- ai) 
 
 whence 
 
 .. , ^ Ri^ n'An'B '}'^ ,. , s 
 COS (e -f a2) = p- — — — cos (0 + ai). 
 
 r = \/ / f where Ua, Ub, n' a and n's are the readings 
 
 The subscript Q means that ua, tib, n' a and u'b are readings at 
 power-factor cos Q and Q is large. 
 
 Ri 
 
 Rx 
 
 at unity power-factor. Since all the quantities in the right-hand 
 member of the above expression are known, aj can be calculated. 
 In commenting upon this method, Dr. Agnew, its author, 
 says: 
 
 "It is important that the ratio and the phase angle of the standard 
 transformer, whether of the current or voltage type, be determined 
 under actual working conditions of load, including the meter. Multiple 
 range transformers are very convenient as standards and good trans- 
 formers have very accurately the same constants for the different 
 series-parallel arrangement of coils. If the no-load ratio of a voltage 
 transformer is required, it may be obtained very closely by adding a 
 second or duplicate meter as load, and then extrapolating to the no- 
 load condition. 
 
 While the present method has neither the high precision nor ele- 
 gance of the null laboratory methods, it has ample accuracy for com- 
 
INSTRUMENT TRANSFORMERS 397 
 
 mercial requirements, it is indepeiident of ordinary line fluctuations, 
 and no specialized apparatus is required." 
 
 The equation 
 
 Rj^ ^ nAUa cos'' (g + g;) 
 
 Ri^ nAUa' cos^ (e + ai) 
 
 can be transformed so that instead of calculating aa by trigo- 
 nometry, it may be obtained from the chart, Fig. 309. To do 
 this we must find the per cent error due to phase angle. Trans- 
 forming the above equation we have 
 
 cos (e + aa) _ R2 VnA'riB 
 
 cos (e + a,) ~ R, v"^;^ 
 
 and 
 
 (cos 6 + uj) _ ^ RtVnTnl 
 
 (cos e+aO ~ R^ V^a^ 
 
 and per cent error = 
 
 1 
 
 rcos {e + a,) _ -1 _ r^xATw 1 
 '""Lcos {d + aO ij - 100 [i2, ^r^^^ - ij 
 
 Let + ai = <^ 
 Then 100 p« ['^ + ("^ " ">)] _ 1 ^ [^hV^S J 
 
 If a three-phase circuit is used, and the auxiliary circuit be 
 taken from one phase and the pressure from another phase, 
 cos 4> becomes the power factor under which the watt-hour 
 meters operate when connected to the standard transformer. 
 a-2 — Oil is the difference in power-factor under which the 
 meters operate when connected to transformer 2. The left 
 hand member of the above expression is the per cent error due 
 to this difference in phase at a power-factor cos </>. The right 
 hand member contains known quantities only and can thus 
 be evaluated. R^ and jffii are the ratios of transformation at 
 the particular load, n^, Ub, Ua , Ub are the rotations of the 
 meters at power-factor cos d. Substituting and reducing we 
 get the per cent error by the aid of which 012 — ai can be read 
 off the chart. For example, if cos <^ is .5 and the per cent error 
 is 8, we find that where the horizontal line corresponding to 8 
 per cent error crosses the 50 per cent power-factor corresponds 
 
398 ELECTRICAL METERS 
 
 to a phase angle of 2° 40'. This is a^ — ai. As ai is known then 
 as is at once obtained. 
 
 336. Ratio by Wattmeter and Standard Transformer Method. 
 — A practical method of determining the ratio of potential trans- 
 formers consists in connecting the secondary of the transformer, 
 whose ratio is known, in opposition to the secondary of the trans- 
 former whose ratio is desired, while the primary circuits are con- 
 nected in parallel, and measuring the difference in the secondary 
 voltages as indicated in Fig. 312. If the standard and trans- 
 former under test have the same nominal ratio, the difference 
 between the secondary voltages will be small, hence to measure 
 this difference its effect must be enhanced. This is accomplished 
 by sending a current from an auxiliary source through the current 
 coil of a low-range wattmeter while the voltage coil is energized 
 by the difference in the secondary voltages of the transformers. 
 The desired ratio of transformation may then be calculated 
 from the reading of the wattmeter, the auxiliary current, primary 
 voltage and the ratio of the standard transformer, thus: 
 
 let E = primary voltage, 
 I = auxiliary current, 
 Ri = ratio of standard, 
 R2 — ratio of transformer under test, 
 ai = phase angle of standard transformer, 
 0:2 = phase angle of transformer under test, 
 B = phase difference between current and pres- 
 sure in wattmeter circuit. 
 
 Since ai and a-i are very small, and Ri is nearly equal to R2, 
 will be approximately zero when the auxiliary circuit is non- 
 inductive and the connections are as indicated in Fig. 312. The 
 wattmeter reading is then, with close approximation, 
 
 XRi RJ 
 whence 
 
 lER, 
 
 il2 
 
 RiW + IE 
 If the secondary voltages of the two transformers are equal, 
 
 W = 
 and 
 
 R2 — Ri- 
 
INSTRUMENT TRANSFORMERS 
 
 399 
 
 To determine whether RJV is positive or negative, that is whether 
 Ri is less or greater than Ri, it is merely necessary to connect a 
 non-inductive load, L, to the secondary of the transformer under 
 test. The effect of such a load is to increase the ratio of trans- 
 formation or decrease the secondary voltage. If the deflection 
 
 3 
 
 LaofloJ 
 
 o 
 
 8 
 
 O 
 
 I 
 
 Ufiofij 
 
 Rr™ 
 
 L^ 
 
 
 Fig. 312. 
 
 of the wattmeter is up scale when there is no load on the secondary, 
 and if the addition of such a load increases the deflection, then at 
 no load Ri is greater, than Ri and vice versa. 
 
 337. Phase Angle by Wattmeter Method. — To determine the 
 phase angle of a potential transformer by means of a wattmeter 
 
 — £ 
 
 Fig. 313. 
 
 and standard transformer the two transformers are connected as 
 in Fig. 312, but the auxiUary current is taken from the other 
 phase of a two-phase circuit. Before proceeding with the test 
 the ratio of the transformers should be made equal by loading. 
 
400 ELECTRICAL METERS 
 
 with a non-inductive load, the transformer with the lower ratio. 
 The current taken by this load should be measured. If the load 
 must be applied to the standard transformer, the phase angle of 
 this transformer corresponding to the secondary current may 
 then be obtained from curves plotted showing the relation be- 
 tween phase angle and secondary current. 
 
 Diagram Fig. 313 shows the phase relations, exaggerated, of 
 the several quantities involved. From this diagram it is evident 
 that the wattmeter reading is 
 
 W = Eol cos e. 
 But 
 
 ^0 = 2Ei sin "'~°' 
 
 and 
 
 02 + ai 
 ^= ~^ 
 Hence 
 
 W = 2EJ cos — 2 — sm ( — ^ — ) 
 
 = Ell [sin az — sin ai] 
 
 and 
 
 , W 
 sm a2 = sm ai ± -^FTT' 
 
 Jill 
 
 As all the quantities on the right-hand side are known, a^ can be 
 calculated. 
 
 EXAMPLE 
 
 Given 
 
 CCl 
 
 = 
 
 20 minutes, Ei =110 volts, 
 
 
 1 
 
 = 
 
 5 amp., and W= 1.5 watts. 
 
 Calculate 
 
 ai 
 
 
 Solution. — 
 
 
 
 sm aj = sin ai H 
 
 Ell 
 
 a, = 20', sin ai = 0.00582, 
 
 W = 1.5 watts. 
 
 / = 5 amp. 
 
 .El = 110 volts. 
 
 Hence 
 
 
 
 W 1.5 
 
 
 EJ -5X 110 - °°°^^^- 
 
 Theinfore 
 
 sin ai = 0.00582 + 0.00272 
 = 0.0031 or 0.00854 
 and aj = 11 minutes, or 29 minutes. 
 
INSTRUMENT TRANSFORMERS 401 
 
 It remains to determine which value of aa is correct. To deter- 
 mine this a non-inductive load is connected to the secondary of 
 the transformer under test. If the deflection of the wattmeter is 
 increased it shows that aa is greater than a, and the second value 
 must be taken. If the introduction of the non-inductive load 
 reduces the wattmeter reading, aa is less than a,. 
 
 If a two-phase circuit is not available, a three-phase to two- 
 phase arrangement of power transformers may be used, or the 
 current for the series coil of the wattmeter may be taken from 
 another phase of a three-phase circuit. The reading of the 
 wattmeter under this condition will be 
 
 W = 2EJ sin ^^' cos (sO" - "^) ■ 
 
 or 
 
 W = 2EJ sin ^^ cos (l50° - "^^^) ■ 
 
 according to which of the two other phases the auxiliary circuit 
 is connected. 
 
 When reduced, both these expressions give the same numerical 
 value, namely, 
 
 W = ^i7[0.866 (sin as - sin a,) - 0.5 (cos as - cos ai)]. 
 
 But as the difference between cos aa and cos ai is negligible we 
 
 have 
 
 W = 0.866£']Z (sin aa - sin ai) 
 
 and 
 
 I.IQW , . 
 sm Q!2 = E, T — r sm ai 
 
 Mi\i 
 
 as before.^ 
 
 338. Potential Transformer Comparator Voltmeter. — To facili- 
 tate rapid and accurate tests of potential transformers, the Weston 
 Electrical Instrument Co., has recently placed on the market a 
 voltmeter which takes the place of the wattmeter in the test de- 
 scribed in the foregoing section. The instrument is a voltmeter 
 of the electrodynamometer type, the field coils of which are 
 separately excited from a source of constant voltage. The scale 
 is therefore practically uniform which permits more accurate 
 reading. As the operation of the instrument in testing is exactly 
 
 ' Other methods of testing instrument transformers can be found in 
 "Electrical Meterman's Handbook," Transactions of the American Insti- 
 tute of Electrical Engineers, and other technical publications. 
 
402 
 
 ELECTRICAL METERS 
 
 the same as that of the wattmeter already described, no further 
 discussion is necessary. 
 
 Fig. 314. 
 
 SOUftCE. 
 
 Standard ^ ff^^- 
 
 TtiMiSFORMSfL, 
 
 Fig. 315. 
 
 The instrument has three ranges: 2.50-0-250, 25-025, and 
 2.5-02.5 volts, with the zero in the middle. The field coil cir- 
 cuit is provided with a plug switch so arranged that it may be 
 
INSTRUMENT TRANSFORMERS 403 
 
 supplied from any voltage from 95 to 125 volts in steps of 5 
 volts. The lowest range scale is divided into 0.05-volt divisions. 
 In testing a transformer having a 110-volt secondary, each 
 division, therefore, represents less than 0.05 of 1 per cent, differ- 
 ence in the ratio. The complete instrument is shown in Fig. 314. 
 Phase angle may also be determined by the aid of this voltmeter 
 in exactly the same way as with the wattmeter described above. 
 The instrument itself will not introduce any phase error as the 
 two circuits are compensated for phase angle so that if both 
 circuits are connected to the same source of electromotive force 
 the currents in the two circuits will be exactly in phase. A 
 diagram of connections is shown in Fig. 315. 
 
 lU 
 
INDEX 
 
 Numbers refer to pages. 
 
 Alternating currents, 47 
 
 average value, 51 
 
 definition, 47 
 
 effective value, 54 
 
 generation of, 47 
 
 instantaneous value, 53 
 
 law of fluctuation of current and 
 pressure, 49 
 
 maximum value, 54 
 
 root — mean square value, 54 
 
 sine wave of, 50 
 A.c. and d.c. ammeters and volt- 
 meters, 286 
 
 a.c. indicate effective values, 
 286 
 
 calibration of a.c. ammeters, 288 
 
 ventilation of, 288 
 Alternation, 53 
 Ammeter method of measuring 
 
 power-factor, 333 
 
 advantages of, 337 
 
 on three-phase circuits, 335 
 
 on two-phase circuits, 333 
 
 theory of, 334 
 
 use of polyphase-switch board, 
 337 
 Ammeters, 32 
 
 ampere balance, 91 
 
 Bristol recording, 149 
 
 electrodynamometer type, 83, 
 84 
 
 General Electric inclined coil, 37 
 
 General Electric recording, 154 
 
 hot-wire, 105 
 
 induction type, 75 
 
 method of connecting to circuit, 
 32 
 
 movable coil, permanent mag- 
 net type, 40 
 
 Ammeters, movable core type, 36 
 
 ranges of, 33 
 
 recording, 149, 154 
 
 shunts for, 33 
 
 thermo-ammeter, 106 
 
 uses of, 32 
 
 Westinghouse induction type, 
 76,77 
 
 Westinghouse plunger type, 36 
 
 Westinghouse recording, 159, 
 162 
 
 Weston soft iron type, 38 
 Ammeters, testing of, 278 
 
 calibration curve, 279 
 
 calibration of a.c, 288 
 
 comparison of, 278 
 
 correction curves, 279, 280 
 
 potentiometer method, 284, 
 285 
 
 standard resistance and volt- 
 meter method, 282 
 Ampere-hour meters, 241 
 
 Bastian meter, 241 
 
 electromagnetic type, 241 
 
 Sangamo, 242 
 
 test of, 324 
 
 theory of, 241, 242 
 Apparatus for instrument testing, 
 264 
 
 galvanometer, 265 
 
 lamp bank, 276 
 
 low voltage transformer, 314 
 
 phase-shifting transformer, 330 
 
 portable sortage battery, 313 
 
 potentiometers, 265, 270 
 
 special load box, 312, 315 
 
 standard cell, 264 
 resistances, 274 
 
 variable resistance, 275 
 
 water rheostat, 277 
 Arago's discovery, 65 
 
 405 
 
406 
 
 INDEX 
 
 Armature, watt-hour meter, 183 
 cylindrical, 183 
 spherical, 183 
 three coil, 183 
 Attraction of induced and inducing 
 currents, 28 
 of permanent magnets, 28 
 Average value of an alternating 
 current, 54 
 
 B 
 
 Balance, Kelvin's ampere, 91 
 Balance of meter elements, 190, 205 
 
 test for, 323 
 Bases of energy rates, 238 
 Bastian ampere-hour meter, 245 
 Bearings, watt-hour meter, 184 
 
 ball, 185 
 
 pivot, 185 
 Bristol meters, 149 
 
 ammeter, 149 
 
 voltmeter, 150, 152, 153 
 
 wattmeter, 151 
 Brooks deflection potentiometer, 270 
 Brushes, watt-hour meter, 181 
 
 Calibration curve for ammeters, 279 
 Calibration of ammeters, 282 
 
 of a.c. ammeters, 288 
 
 of millivoltmeters, 284 
 
 of shunts, 285 
 Capacity, electrical, 21 
 
 definition, 22 
 
 effect of, 56 
 
 farrad, 22 
 Carbon plate rheostat, 275 
 Cell, standard, 264 
 Checking tests, 263 
 Circuits, 61 
 
 polyphase, 61 
 quarter-phase, 62 
 three-phase, 62 
 
 single-phase, 61 
 Classes of meters, 26 
 
 basis of classification, 26 
 
 Coefficient, temperature coefficient 
 of resistance, 16 
 of inductance, 21 
 negative temperature coeffi- 
 cient, 16 
 positive temperature coefficient, 
 16 
 Columbia induction watt-hour meter, 
 205 
 light load compensation, 216 
 Combination of instruments, errors, 
 
 374 
 Comparison of d.c. voltmeters, 290 
 Compensation, for frequency, 76 
 
 for temperature effect, 81 
 Compensating coil for wattmeter, 116 
 Complaint tests, 309 
 Commutator, watt-hour meter, 182 
 Connection of polyphase meter, 352 
 Constants, meter, 309 
 
 determination of experiment- 
 ally, 315 
 effect of temperature on, 316 
 Controlling forces, 28 
 
 attraction of gravity, 28 
 attraction of induced and in- 
 ducing currents, 28 
 attraction of permanent mag- 
 nets, 28 
 mechanical friction of rotating 
 
 fan, 28 
 resisting force of spring, 28 
 torsion of filament, 28 
 Contact errors, 373 
 Correction, curve for ammeters, 279 
 factor for wattmeters, 117 
 for power loss in wattmeters, 
 114 
 Coulomb, 19 
 
 Creeping of watt-hour meters, 180 
 Current, 17 
 
 electrical, 17 
 
 practical electromagnet unit of 
 
 current, 17 
 unit current, 17 
 water, 17 
 
 current and voltage in three- 
 phase circuits, 63 
 Cycle, 53 
 
INDEX 
 
 407 
 
 D 
 
 Damping, 42 
 
 electromagnetic, 43 
 
 mechanical, 42 
 
 of electrostatic voltmeter, 101 
 
 of hot-wire instruments, 105 
 
 of induction ammeters, 82 
 
 of recording meters, 161 
 Defective performance of springs, 367 
 Deflection type potentiometer, 270 
 
 theory of, 269 
 Delta connected circuits, 63, 228, 229 
 Demand indicators, 247 
 
 graphic, 259 
 
 induction type, 248 
 
 mechanical type, 254 
 
 thermal type, 247 
 
 time lag, 250 
 
 use of, 252 
 Difference between d.c. and a.c. am- 
 meters and voltmeters, 286 
 Direct acting recording meters, 148 
 
 Bristol, 149 
 
 Esterline, 157 
 
 General Electric, 154 
 
 Pen, 156 
 Duncan induction watt-hour meter, 
 206 
 
 E 
 
 Earth's magnetic field, influence of, 
 
 95, 369 
 Eddy currents in rotating disk, 65 
 Eifect of inductance, 55 
 Effective value of alternating cur- 
 rent, 54 
 Electric current, 17 
 
 analogy for, 17 
 
 definition, 17 
 
 unit of, 17 
 Electrical quantities that are meas- 
 urable, 26 
 Electrical units, practical, 14 
 
 ampere, 14, 24 
 
 coulomb, 14, 24 
 
 farad, 14, 25 
 
 henry, 14, 25 
 
 joule, 14, 24 
 
 Electrical units, kilowatt, 24 
 
 kilowatt-hour, 25 
 
 ohm, 15, 24 
 
 volt, 15, 24 
 
 watt, 15, 24 
 Electrodynamic instruments, 26, 83 
 Electrodynamometer ammeter, 83 
 
 relation between current and 
 deflection, 84 
 
 shunted, 85 
 Electrodynamometer ammeter and 
 voltmeter on a.c. circuits, 
 287 
 
 frequency errors, 287 
 
 limitations of, 287 
 
 use for calibrating a.c. meters, 
 288 
 Electrodynamometer power-factor 
 meter, 128 
 
 coils of, 132 
 Electrodynamometer type synchro- 
 scope, 143 
 
 Weston, 143 
 Electrodynamometer type watt- 
 hour meter, 170 
 
 armature, 183 
 
 bearings, 184 
 
 brushes, 181 
 
 Columbia, 174 
 
 commutator, 182 
 
 compensation for friction, 178 
 
 creeping, 180 
 
 Duncan, 174, 176 
 
 General Electric, 173, 175 
 
 jewels, 185 
 
 on a.c. circuits, 187 
 
 Westinghouse, 172 
 Electrodynamometer voltmeter, 87 
 
 advantages, 96 
 
 ampere balance, 91 
 
 construction, 89 
 
 disadvantages, 96 
 
 effect of inductance upon, 88 
 
 General Electric, 90 
 
 non-uniformity of scale, 91 
 
 reading, 91 
 
 Roller-Smith, 90 
 
 Westinghouse, 90, 94 
 
 Weston, 90 
 
408 
 
 INDEX 
 
 Electrodynamometer wattmeter, 109 
 
 compensation for power con- 
 sumed in meter, 114 
 
 General Electric, 113 
 
 relation between torque and 
 power, 110 
 
 RoUer-Smith, 90 
 
 theory of, 110 
 
 Westinghouse, 112 
 
 Weston, 110, 113 
 
 Weston polyphase, 114 
 
 test of, 294 
 Electrolytic ampere-hour meter, 242 
 Electrolytic ampere-hour meter, 
 242 
 
 Bastian, 245 
 
 Edison, 245 
 Electrolytic conduction, 12 
 
 electrochemical equivalents, 13 
 
 electrolytes, 13 
 
 Faraday's laws, 13 
 Electromagnet, 8 
 
 flux density in, 10 
 
 iron cores of, 10 
 
 magnetic field in, 9 
 Electromagnetic ampere-hour meter, 
 241 
 
 Sangamo, 242 
 Electromagnetic instruments, 26 
 
 definition, 26 
 
 induction type, 26 
 
 movable coil permanent magnet 
 type, 26, 40 
 
 movable core type, 26, 36 
 Electromotive force, 18 
 
 analogy for, 18 
 
 definition, 18 
 
 how generated, 18 
 
 of self induction, 22 
 
 value of, 18 
 
 volt, 18 
 Electrostatic errors, 372 
 Electrostatic meters, 27 
 
 advantages, 102 
 Electrostatic voltmeter, 97 
 
 advantages, 102 
 
 damping, 101 
 
 Hartmann & Braun, 102 
 
 insulation, 101 
 
 Electrostatic voltmeter, multicellu- 
 lar, 99 
 theory of, 97 
 Westinghouse, 99 
 Energy, 1 
 
 comparison between electrical 
 
 and mechanical, 2 
 conservation, 2 
 conversion of potential into 
 
 kinetic, 1 
 definition, 1 
 electrical, 2, 19 
 kinetic, 1 
 loss of, 23 
 potential, 1 
 
 similar expressions for electrical 
 and mechanical, 3 
 Errors, meter, 355 
 Equation for ampere balance, 91 
 
 Factor, correction for wattmeters, 
 
 119 
 Faraday's laws, 13 
 Flux density in electromagnet, 10 
 Force between parallel electric wires, 
 
 11 
 Force exerted upon an electric wire 
 in a magnetic field, 10 
 
 direction of force, 11 
 Fort Wayne Electric Works, 204 
 
 double lagging of meters, 219 
 
 induction watt-hour meter, 204 
 
 light load compensation, 213 
 
 polyphase meter, 224 
 Frequency, 53 
 
 compensation for effect of, 76 
 
 errors due to, 375 
 
 influence of, 81, 217 
 Frequency-meters, 134 
 
 Campbell, 136 
 
 Hartmann & Braun, 136 
 
 induction type, 138 
 
 movable core type, 140 
 
 polarized reeds, 138 
 
 recording, 163 
 
 resonance type, 135 
 
 testing, 300 
 
INDEX 
 
 409 
 
 Friction of supports, 30 
 
 compensation for on electro- 
 dynamometer watt-hour 
 meter, 178 
 induction watt-hour meter, 213 
 mercury watt-hour meters, 193, 
 
 195 
 resilient support, 31 
 test for influence of, 350 
 Full-load adjustment on induction 
 watt-hour meter, 208 
 mercury watt-hour meter, 195 
 
 G 
 
 Galvanometer, 265 
 General Electric meters, 37 
 
 ammeters, 37 
 
 ampere demand indicator, 247 
 
 light load compensation, 213 
 
 pen, 156 
 
 prepayment meter, 236 
 
 recording meters, 154 
 
 single-phase watt-hour meter, 
 197 
 
 voltmeters, 86 
 
 watt-demand indicator, 249 
 
 watt-hour meters, 173, 197 
 
 wattmeters, 113 
 Graphic meters, 148 
 Gravity control, 29, 175 
 Groups of measuring instruments, 26 
 
 electrodynamic, 26 
 
 electromagnetic, 26 
 
 electrostatic, 26 
 
 thermal, 27 
 
 H 
 
 Heat effect of electric current, 14 
 Henry, 21 
 
 Hot-wire instrument, 102 
 ammeter, 105 
 advantages, 106 
 use of shunts with, 105 
 damping, 105 
 voltmeter, 102 
 advantages, 106 
 Hartmann & Braun, 103 
 
 Hot-wire instruments influence, of 
 stray field, 106 
 influence of wave form, 106 
 Roller-Smith, 104 
 theory of, 102 
 
 Induction, 19 
 
 coefficient of, 21 
 
 effect of, 55, 88 
 
 electromotive force of, 21 
 
 henry, 21 
 
 mutual induction, 21 
 
 principle, 65 
 
 self induction, 21 
 
 Induction ammeters and voltmeters, 
 75 
 influence of frequency on, 81 
 influence of temperature on, 81 
 relation between current and 
 torque, 79 
 
 Induction type frequency meter, 138 
 theory, 138 
 Westinghouse, 138 
 
 Induction type wattmeter, 120 
 
 Induction type watt-hour meter, 
 196 
 balance of metering elements, 
 
 205, 231 
 double lagging, 219 
 effect of over lagging, 213 
 effect of under lagging, 213 
 effect of power-factor, 232 
 four-wire polyphase, 229 
 full-load adjustment, 208 
 improper connections of poly- 
 phase meters, 233 
 influence of frequency, 217 
 interference of elements, 231 
 lagging, 207, 212 
 light load compensation, 213 
 parts of General Electric meter, 
 
 197 
 phases, difference between vol- 
 tage coil and series currents, 
 200, 212 
 polyphase meters, 224 
 practical construction, 202 
 
410 
 
 INDEX 
 
 Induction type watt-hour meter, 
 pressure element of Columbia 
 
 meter, 204 
 relation between torque and 
 
 power, 210 
 shifting magnetic field, 201 
 single-phase meters on poly- 
 phase circuits, 220 
 theory of operation, 198 
 three-wire meters, 220 
 Induction type wattmeters, 120 
 influence of inductance on, 117 
 lagging, 123 
 operation of Westinghouse 
 
 meter, 121 
 relation between torque and 
 
 power, 121 
 scale, 125 
 theory, 120 
 Influence, of earth's magnetic field, 
 95, 353 
 of wave form on hot-wire me- 
 ters, 104 
 Inherent errors, 355 
 Inquiry tests, 309 
 Installation tests, 308 
 Instantaneous value of alternating 
 
 current, 53 
 Instrument testing, 263 
 Instrument transformers, 385 
 current transformer, 385 
 general theory, 385 
 influence of transformer con- 
 stants, 389 
 phase angle, 386 
 potential or voltage trans- 
 former, 389 
 ratio of transformer, 386 
 reasons for use, 385 
 variation of error with power- 
 factor, 390 
 variation of error with phase 
 angle, 391 
 Integrating meters, definition, 169 
 ampere-hour, 241 
 watt-hour, 169 
 
 Jewels, 185 
 
 Joule, 19 
 
 K 
 
 Kelvin balance, 91 
 
 as ammeter, 91 
 
 as voltmeter, 93 
 
 disadvantages of, 96 
 
 equation for, 94 
 
 recording meters, 159 
 Kilowatt-hour, 25 
 Kinds of tests, 263, 310 
 
 checking tests, 263 
 
 complaint tests, 309 
 
 inquiry tests, 309 
 
 installation tests, 308 
 
 periodic tests, 308 
 
 repair tests, 309 
 
 re-tests, 309 
 
 shop tests, 308 
 
 special tests, 309 
 
 standardization tests, 263 
 
 Lagging induction wattmeters, 123 
 by secondary winding in mag- 
 
 metic circuit, 124 
 by shunting series coil, 124 
 Lagging watt-hour meters, 187 
 double-lagging, 219 
 effect of overlagging, 213 
 effect of underlagging, 214 
 induction meters, 213 
 shunting series coil, 188 
 Lamp bank resistance, 276 
 Law of magnetic circuit, 10 
 Leeds & Northrup potentiometer, 268 
 Light load compensation on induc- 
 tion watt-hour meters, 214 
 flux shunting method, 216 
 unbalanced shifting-field 
 method, 214 
 Loading watt-hour meters, 312 
 consumer's load, 312 
 low voltage transformer, 314, 
 portable lamp bank, 312 
 portable storage battery, 206 
 special load box, 312 
 
INDEX 
 
 411 
 
 Loss in pressure coil, test for, 351 
 
 M 
 
 Magnetic circuit, law of, 1 
 
 relation between flux, m.m.f., 
 and reluctance, 10 
 Magnetic field, 4 
 air-gap, 6 
 arrangement of magnetic lines 
 
 between poles, 5 
 conventional statement in re- 
 gard to magnetic lines, 4 
 force exerted upon a wire, 10 
 magnetic flux, flux density, 4, 6 
 method of representing field, 6 
 methods of exploring, 3 
 properties of, 4 
 relation between tension and 
 
 flux density in, 6 
 revolving, 68 
 rotating, 68 
 seat of force of attraction and 
 
 repulsion, 5 
 shifting, 201 
 strength of field, 6 
 Magnetic field around a wire carry- 
 ing a current, 6, 7 
 direction of, 7 
 field of circular coil, 7 
 rule for determining direction, 7 
 strength of magnetic field in 
 solenoid, 8 
 Magnetic shielding, 30 
 Magnetism, 3 
 
 definition of magnetic bodies, 3 
 permanent magnet, how to 
 make, 3 
 Magnetizing force, m.m.f. of sole- 
 noid, 10 
 Magnetomotive force, 4 
 Magnets, watt-hour meter, 186 
 Manganin, 16 
 
 temperature coefficient, 16 
 Maximum demand indicators, 247 
 ampere demand indicator, 247 
 graphic, 259 
 mechanical type, 264 
 time lag, 250 
 
 Maximum demand indicators, watt 
 
 demand indicator, 249 
 Maximum value of alternating cur- 
 rent, 54 
 Measurable electrical quantities, 26 
 Mechanical, errors, 364 
 
 friction of rotating fan control, 
 28 
 
 type demand indicator, 254 
 operation, 255 
 Mercury watt-hour meter, 192 
 
 compensation for friction, 195 
 
 for d.c. circuits, 192 
 
 full-load adjustment, 195 
 Meter constants, 309 
 
 table of, 318 
 Meter errors, 355 
 
 contact errors, 373 
 
 defective performance of 
 springs, 367 
 
 due to balancing, 369 
 
 due to combination of instru- 
 ments, 374 
 
 due to frequency and wave 
 form, 375, 378 
 
 due to thermo-electromotive 
 forces, 373 
 
 due to time and use, 369 
 
 due to transformers, 375, 390 
 
 effect of stray field, 369 
 
 electrostatic effect, 372 
 
 errors of use, 369 
 
 inherent, 355 
 
 mechanical errors, 364 
 
 of observation, 384 
 
 sources of, 355 
 
 temperature, 359 
 Meter testing, 263 
 
 ammeters a.c, 288 
 
 ammeters d.c, 278 
 
 ampere-hour meter, 324 
 
 apparatus for testing, 264 
 
 frequency meters, 300 
 
 general, 263 
 
 kinds of tests, 263 
 
 percentage of accuracy, 321 
 
 polyphase power-factor meter, 
 299 
 
 recording meters, 301 
 
412 
 
 INDEX 
 
 Meter testing, single-phase power- 
 factor meter, 298 
 voltmeters d.c, 290 
 watt-hour meters, 303 
 wattmeters, dynamometer type, 
 294 
 Mil system, 15 
 
 circular mil, 15 
 mil, 15 
 
 square mil, 15 
 Movable-coil permanent magnet 
 
 type, 40 
 Movable core type ammeters and 
 
 voltmeters, 36 
 Movable core type frequency meter, 
 140 
 theory, 141 
 Weston, 140 
 Movable core type synchroscope, 145 
 Lincoln type, 146 
 Westinghouse, 145 
 Multipliers for voltmeters, 35 
 
 O 
 
 Ohm, 14, 24 
 Ohm's law, 22 
 
 Percentage of accuracy, 320 
 definition, 320 
 test for, 321 
 Percentage error due to inductance 
 
 of wattmeter, 117, 382 
 Period, definition, 53 
 Periodic tests, 308 
 Phase angle, 60 
 difference, 57 
 analogy for, 57 
 Polyphase circuits, 61 
 Polyphase, power-factor meter, 132 
 switchboard, 337 
 watt-hour meters, 224 
 balance of elements, 231 
 diagrams of connections, 226 
 difference between four-wire 
 and three-wire meters, 229 
 effect of power-factor on, 232 
 four-wire meters, 229 
 improper connections, 233 
 
 Polyphase, watt-hour meters, inter- 
 ference of elements, 231, 346 
 relation of torque to power on 
 
 Y-connected loads, 227 
 relation of torque to power on 
 
 A-conneoted loads, 228 
 testing, 299 
 Potentiometers, 266 
 
 deflection type, 270 
 Leeds & Northrup, 268 
 slide-wire type, 266 
 theory of, 269 
 Power, definition, 19 
 horse power, 19 
 in a.c. circuits, 58 
 in d.c. circuits, 58 
 loss, 24 
 watt, 19 
 Power-factor, definition, 60, 127 
 determination of by ammeter, 
 voltmeter, and wattmeter, 
 127 
 effect of on operation of poly- 
 phase watt-hour meters, 232 
 effect of on wattmeters, 117 
 Power-factor meters, 128 
 
 analytical proof of principles, 129 
 electrodynamometer type, 128 
 movable core type, 133 
 recording, 163 
 polyphase, 132 
 principles, 129 
 testing, polyphase, 299 
 
 single-phase, 298 
 Westinghouse, 133 
 Weston, 131 
 Power-factor, methods for obtaining, 
 325 
 ammeter or unbalanced load 
 
 method, 333 
 phase-shifting transformer meth- 
 od, 326 
 reactance coil method, 325 
 two generator method, 329 
 two resistance method, 328 
 two transformer method, 326 
 Power measuring instruments, 109 
 Prepayment watt-hour meters, 235 
 operation of, 237 
 prepayment attachment, 235 
 
INDEX 
 
 413 
 
 Pressure drop in d.c. circuits, 23 
 Proper connection of polyphase 
 
 meter, 352 
 Pull of solenoid on iron core, 39 
 
 Q 
 
 Quantity of electricity, 18 
 
 Coulomb, 19 
 Quarter-phase or two-phase circuit, 
 61 
 
 R 
 
 Range of instruments, 33 
 
 of ammeters and voltmeters, 33, 
 34 
 
 of wattmeters, 119 
 Rates, bases for, 238 
 Reactance method of changing 
 
 power-factor, 325 
 Reaction between shifting field and 
 
 induced currents, 76 
 Recording or graphic meters, 148 
 
 Bristol ammeter, 149 
 
 damping, 161 
 
 definition, 148 
 
 direct acting, 148 
 
 disadvantages, 149, 166 
 
 Esterline, 156 
 
 General Electric, 164 
 
 relay type, 158 
 
 Sangamo, 164 
 
 testing, 301 
 
 Westinghouse, 159, 162 
 Registering mechanism, 187 
 Relation between current and torque 
 of induction-ammeters, 79 
 Relay type of recording meters, 158 
 
 construction, 158 
 
 damping, 161 
 
 frequency meter, 162 
 
 general principles, 158 
 
 operation, 160 
 
 power-factor meter, 163 
 
 right line pen motion, 166 
 
 sensibility, 162 
 
 Westinghouse voltmeter, 159 
 Reluctance, 10 
 
 Repair tests, 309 
 Resistance, 14 
 
 analogy for resistance, 14 
 the ohm, 15 
 
 change with temperature, 16 
 
 lamp bank, 276 
 
 resistance of mil-foot, 16 
 
 standard, 267 
 
 variable, 275 
 
 water, 277 
 Resistance method of changing 
 
 power-factor, 328 
 Resisting force of springs, 28 
 Re-tests, 309 
 Revolving magnetic field, 68, 72 
 
 how produced, 72 
 
 speed of, 74 
 Rheostat, 275 
 
 carbon, 275 
 
 water, 277 
 Rollinson's load box, 314 
 Rotating magnetic field, 68 
 
 produced by equal component 
 field, 68 
 
 produced by unequal compo- 
 nent fields, 70 
 Rotating standard or test meter, 303 
 
 Duncan, 304 
 
 General Electric, 305 
 Root-mean-square value, 54 
 
 Sangamo ampere-hour meter, 242 
 Sangamo watt-hour meter, 191, 205 
 Sangamo graphic meters, 164 
 for d.c. circuits, 192 
 friction compensation, 195 
 full-load adjustment, 196 
 Scale, lack of uniformity, 29 
 
 on electrodynamometer amme- 
 ters and voltmeters, 91, 92 
 on electrodynamometer watt- 
 meters, 112 
 on gravity ' control meters, 29, 
 
 30, 38 
 on hot-wire meters, 103 
 on induction ammeters, 82 
 on induction wattmeters, 126 
 
414 
 
 INDEX 
 
 Scale, on permanent magnet mov- 
 able coil meters, 46 
 Sensibility of recording meters, 162 
 Series transformer principle, 77 
 Shifting magnetic field, 73, 201 
 Shop tests, 308 
 Shunted watt-hour meter, 176 
 Shunts for ammeters, 33 
 Sine wave of alternating current and 
 
 pressure, 50 
 Single-phase circuits, 61 
 watt-hour meters, 196 
 on polyphase circuits, 220 
 test for quarter phasing, 338 
 test on inductive load, 341 
 test on non-inductive load, 
 
 339 
 test with standard test meter, 
 43 
 three-wire meters, 220 
 Solenoid, 8 
 
 magnetic field in, 8, 9 
 magnetizing force, m.m.f. of, 10 
 Special tests, 309 
 Speed of revolving field, 74 
 Standard cell, 264 
 Standardization tests, 263 
 Standard resistances, 267 
 Stray magnetic field, test for, 351 
 correction for, 370 
 errors, 369 
 Summary of electric and magnetic 
 
 principles, 24 
 Summation of power, 172 
 Switchboard polyphase, 337 
 Synchronizing, 142 
 lamps, 142 
 principles, 142 
 Synchroscopes, 142 
 
 electrodynamometer type, 143 
 movable core type, 145 
 speed of rotation, 147 
 Westinghouse, 145 
 Weston, 143 
 
 Table of watt-hour meter constants, 
 318 
 
 Temperature, coefficient of resist- 
 ance, 16 
 errors due to, 356 
 influence on induction amme- 
 ters, 81 
 on resistance, 16 
 Testing instruments, 263 
 ammeters a.c, 288 
 ammeters d.c, 278 
 calibration curve, 279, 281 
 checking tests, 263 
 frequency meters, 300 
 kinds of tests, 263 
 proper connection, 352 
 polyphase power-factor meter, 
 
 299 
 recording meters, 301 
 single-phase power-factor meter, 
 
 298 
 standardization tests, 263 
 voltmeters a.c, 292 
 
 d.c, 290 
 watt-hour meters, 303 
 wattmeter dynamometer type, 
 294 
 Tests of a.c. watt-hour meters, 338 
 diagram of testing board, 341 
 influence of power-factor, 343 
 single-phase meter on inductive 
 load, 341 
 on non-inductive load, 339 
 test for quarter-phasing, 338 
 testing polyphase meters, 345 
 with standard test meter, 
 343 
 Thermal instruments, 28 
 Thermo-ammeter, 106 
 theory of, 106 
 use in testing, 288 
 Thermo-electromotive forces, 373 
 Three-phase circuits, 62 
 
 current and voltage in Y-con- 
 nected, 63 
 in A-connected, 64 
 Three-wire d-c. watt-hour meters, 
 189 
 on balanced load, 189 
 on unbalanced load, 190 
 teat of, 322, 323 
 
INDEX 
 
 415 
 
 Three-wire single-phase watt-hour 
 meters, 220 
 on balanced load, 221 
 on unbalanced load, 223 
 voltage coil connections, 221, 224 
 Time lag of demand indicators, 250 
 curve for, 252 
 theory of, 250 
 Torque, 347 
 
 balance, 347, 348, 349 
 test for, 347 
 Torque exerted by a magnetic field 
 upon a rectangular coil, 44 
 Torque of induction watt-hour 
 meters, 210 
 of four-wire polyphase meters, 
 
 229 
 of polyphase meters on Y-con- 
 
 nected systems, 227 
 on A-connected systems, 228 
 Torsion of filament, 28 
 Transformer method of varying 
 
 power-factor, 326 
 Transformer testing, 392 
 
 potential transformer-compara- 
 tor voltmeter, 401 
 test for phase angle, 396, 399 
 test for ratio of transformation, 
 
 393, 398 
 watt-hour meter method, 392 
 wattmeter method, 398 
 Two-phase or quarter-phase circuit, 
 
 61 
 Two-rate meters, 239 
 
 U 
 
 Unbalanced load method of varying 
 
 power-factor, 333 
 Use of ammeters, 32 
 
 of constants in testing, 310 
 
 of voltmeters, 32 
 
 V 
 
 Vector diagram for series transfor- 
 mer, 78, 387 
 Ventilation of a.c. voltmeters, 288 
 Voltmeters, 32 
 
 calibration curve, 293 
 
 comparison of d.c, 290 
 
 Voltmeters, correction curves, 295 
 
 electrodynamometer type, 87 
 
 electrostatic, 97 
 
 hot-wire, 102 
 
 induction type, 75 
 
 method of connecting to circuit, 
 32 
 
 movable coil permanent mag- 
 net type, 40 
 core type, 36 
 
 multipliers, 34 
 
 potentiometer method, 291 
 
 range of, 34 
 
 testing of a.c. meters, 292 
 
 uses of, 32 
 
 ventilation of a.c, 288 
 
 Westinghouse induction type, 
 76,79 
 Voltmeters, recording, 151, 162 
 
 Bristol, 151 
 
 Esterline, 156 
 
 General Electric, 156 
 
 Westinghouse, 162 
 
 W 
 
 Water-rheostat, 277 
 Watt, 19 
 
 Watt-hour, 19, 109 
 Watt-hour meters, 169 
 
 armature, 183 
 
 bearings, 184 
 
 brushes, 181 
 
 commutating type, 171 
 
 commutator, 182 
 
 compensation for friction, 178 
 
 counter torque, 171 
 
 creeping, 180 
 
 electrodynamometer type, 170 
 on a.c. currents, 186, 188 
 with iron, 177 
 without iron, 170 
 
 friction compensation, 178 
 
 induction type, 196 
 
 jewels, 185 
 
 lagging, 187, 209 
 
 large current capacity, 174 
 
 magnets, 186 
 
 mercury type, 192 
 
416 
 
 INDEX 
 
 Watt-hour meters, polyphase, 224 
 prepayment, 235 
 registering mechanism, 186 
 shunted, 176 
 single-phase, 220 
 summation of power, 172 
 theory of, 169 
 three-wire d.c, 189 
 two-rate, 239 
 Watt-hour meter constants, 310 
 
 determination of, experiment- 
 ally, 315 
 dial constant, 309 
 Duncan meter constant, 311 
 effect of temperature, 316 
 Fort Wayne meter constant, 311 
 General Electric meter con- 
 stant, 311 
 table of meter constants, 318 
 test constant, 309 
 use of constants in testing, 310 
 watt-hour constant, 310 
 watt-minute constant, 310 
 watt-second constant, 310 
 Westinghouse meter constant, 
 311 
 Watt-hour meter testing, 303 
 constants, 310 
 influence of friction, 350 
 influence of stray field, 350 
 loss in pressure coil, 351 
 methods of loading, 312 
 rotating standard or test meter, 
 
 303 
 test of polyphase, 345 
 test of single-phase, 339 
 Wattmeters, 109 
 
 compensation for power con- 
 sumed in meter, 114 
 correction curve, 297 
 correction factor, 117, 382 
 electrodynamometer type, 109, 
 
 110 
 induction type, 120, 121 
 mercury type, 125 
 Wattmeters, influence of inductance 
 of voltage coil, 117 
 method of connecting to cu'cuit, 
 110 
 
 Wattmeters, range of, 119 
 recording, 148 to 168 
 
 scale, 125 
 
 standard watt-dynamometer, 
 297 
 
 test of, 295 
 Wave form, errors due to, 378 
 Westinghouse 
 
 ammeter, induction type, 76, 77 
 
 ammeter, movable coil type, 41 
 
 ammeter, plunger type, 36 
 
 demand indicator, 252 
 
 frequency meter, 138 
 
 power-factor meter, 133 
 
 recording meters, 145 
 
 synchroscope, 145 
 
 voltmeter electrodynamometer 
 type, 90 
 
 voltmeter induction type, 77 
 
 watt-hour meter, electrodyna- 
 mometer type, 172 
 
 wattmeter electrodynamometer 
 type, 112 
 Westinghouse wattmeter, induction 
 
 type, 121 
 Westinghouse induction watt-hour 
 meter, 203 
 
 light-load compensation, 214 
 Westinghouse recording meters, 162 
 
 ammeters, 162 
 
 frequency meters, 162 
 
 voltmeters, 162 
 Weston 
 
 dynamometer voltmeter, 90 
 
 frequency meter, 141, 142 
 
 multipliers, 35 
 
 power-factor meter, 131 
 
 shunts, 35 
 
 soft iron voltmeter, 38 
 
 standard cell, 264 
 
 synchroscope, 143 
 
 wattmeter, 113 
 Wire gauge, 16 
 Wright demand indicator, 247 
 
 Y-connected system, 63, 64, 227, 
 229