r 
 
 REESE LIBRARY 
 
 UNIVERSITY OF CALIFORNIA 
 
A HANDBOOK 
 
 FOR THE 
 
 ELECTRICAL LABORATORY 
 
 AND 
 
 TESTING ROOM. 
 
 BY 
 
 J. A. FLEMIiMG, M.A., D.So., F.R.S. 
 
 M 
 
 PROFESSOR OF ELECTRICAL ENGINEERING IN UNIVERSITY COLLEGE, LONDON ; 
 MEMBER OF THE INSTITUTION OF ELECTRICAL ENGINEERS ; 
 FELLOW OF THE PHYSICAL SOCIETY OF LONDON, &c., &c. 
 
 VOLUME I. 
 
 UNIVERSITY 
 
 CALI 
 
 
 LONDON : 
 
 THE ELECTRICIAN" PRINTING AND PUBLISHING COMPANY, 
 LIMITED, 
 
 SALISBURY COURT, FLBLT STREET, 
 [All Rights Reserved.] 
 
' 
 
 WORKS BY DR. J. A. FLEMING 
 
 ALL FULLY ILLUSTRATED. 
 
 A Treatise on The Alternate Current Transformer in Theory 
 and Practice. 
 
 Vol. I. THE INDUCTION OF ELECTRIC CURRENTS. 612 pp. 
 3rd Edition. 12s. 6d. 
 
 Vol. II. THE UTILISATION OF INDUCED CURRENTS. 600 pp. 
 12s. 6d. 
 
 Electric Lamps and Electric Lighting. 
 
 A Course of Lectures delivered at the Royal Institution of 
 Great Britain. 93 Original Illustrations. 2nd Edition. 
 Extended and revised. 6s. 
 
 Magnets and Electric Currents. 
 
 An Elementary Treatise for the use of Electrical Artisans and 
 Science Teachers. 136 Illustrations. 408 pp. 7s. 6d. 
 
 Electrical Laboratory Notes and Forms. 
 
 A series of 40 Elementary and Advanced Laboratory Sheets for 
 the use of Demonstrators and Students in Electrical Labora- 
 tories. Each Sheet contains full practical instructions (illus- 
 trated when necessary) for carrying out some one particular 
 measurement in electrical testing, and a ruled-up form for 
 entering observations. The Laboratory Notes are useful to 
 all engaged in any description of Electrical Testing. Price 4d. 
 each, 3s. 6d. per dozen ; complete set, 10s. 6d. ; in portofolio, 
 12s. ; bound in cloth, 12s. 6d. 
 
 A Cheaper Set, half the above prices, is issued for the use of 
 Students in Polytechnics and Science Classes. 
 
 The Centenary of the Electric Current, 1799-1899. 
 
 A Lecture delivered before the British Association at Dover, 
 September, 1899. Price Is. 
 
PREFACE. 
 
 r I ^HE only excuse that can be offered for adding 
 another book to the already full catalogue of 
 Electrical literature, especially under the heading 
 of Electrical Measurements, is that, in spite of the 
 numerous excellent works on this subject, there seemed 
 room for one dealing more particularly with the require- 
 ments of electrical engineers as distinguished from electrical 
 physicists. Several valuable handbooks exist dealing with 
 the subject of Electrical Testing from the point of view of 
 the telegraphist or physicist, but these generally contain 
 either too much or two little for the purposes of those who 
 have to deal with the class of electrical measurements 
 which it is necessary to make in electrical stations or 
 factories. 
 
 For this latter purpose, what is required is not a multi- 
 plication of methods gathered together without regard to 
 their applicability or accuracy, but a selection of approved 
 and well-tried methods. 
 
 In many text-books on Electrical Measurements there 
 is an absence of critical discussion on the intrinsic utility 
 of the various methods of measurement given. A process 
 which looks well on paper does not always work out well 
 in practice, and the practical engineer, therefore, requires 
 to have placed before him a series of selected methods of 
 measurement rather than a collection made as inclusive as 
 possible. The present treatise has therefore been divided 
 into a series of chapters, each of which deals with one 
 particular class of measurements. No attempt, however, 
 has been made to include a description of all the methods 
 under that particular heading, far less of all the implements 
 or instruments, but certain processes which experience has 
 
 95814 
 
IV. PREFACE. 
 
 shown to give good results are described as fully as pos- 
 sible, and a detailed description given of certain typical 
 forms of widely used instruments. 
 
 In the case of electrical instruments there is a process 
 of evolution and a survival of the fittest. Many ingenious 
 or otherwise interesting instruments for some particular 
 reason drop out of existence, whilst other forms survive, 
 and it is to these surviving forms that attention has been 
 most directed. 
 
 In the First Volume, in addition to a chapter on the 
 Equipment of electrical laboratories, the subject of the 
 measurement of Electrical Resistance, Electric Current, 
 Electromotive Force and Electric Power is dealt with in 
 the remaining chapters. 
 
 It is intended that the Second Volume shall contain 
 chapters devoted to the measurement of Capacity and 
 Inductance, Electric Quantity and Energy, including Bat- 
 tery and Meter testing, the Magnetic testing of iron, 
 Photometric and Electric lamp testing, and the testing of 
 Dynamos, Motors and Transformers. 
 
 Each chapter is as far as possible complete in itself, and 
 where tables or numerical data are given they are placed 
 at the end of the chapter to which they belong, and not, as 
 usual, at the end of the book. 
 
 As the object has been to place in the hands of the 
 reader a practical handbook rather than a theoretical 
 treatise, such brief mathematical discussions as are intro- 
 duced have generally been placed in smaller type so that the 
 non-mathematical reader may leave them out of considera- 
 tion ; and as the desire has been to produce a handbook 
 useful in the test rooms of electrical factories and stations, 
 descriptions of instruments more usually found in a physical 
 laboratory than a testing room have been omitted. 
 
 J. A. F- 
 
 University College, London, 
 August, 1901. 
 
TABLE OF CONTENTS. 
 
 CHAPTER I. 
 
 PAGE. 
 
 EQUIPMENT OF AN ELECTRICAL TESTING BOOM ] 
 
 1. The Equipment of an Electrical Testing Room or Laboratory ; The 
 Dynamo Room ; The Electrical Laboratory ; The Accumulator 
 Room. 2. The Fundamental Standards of Length, Mass and 
 Time. 3. The Principal Electrical Units and Standards. 4. 
 The Practical Standard of Electrical Resistance ; Mercury Stan- 
 dards; Resistance Alloys ; Standard Resistance Coils. 5. Current 
 Carrying Standard Resistances. 6. The Recovery of the Standard 
 or Unit Electric Current ; The Board of Trade Specification ; 
 Ampere Balances. 7. The Regulation of Current ; Rheostats, 
 8. The Practical Standard of Electromotive Force ; the Clark 
 Cell ; Standard Cells. 9. The Literature of the Mercury Standard 
 Cell. 10. Mechanical Standards of Electromotive Force. 11. 
 The Instrumental Outfit of an Electrical Laboratory. 12. Current 
 Measuring Instruments. 13. Voltage Measuring Instruments. 
 13a. Resistance Measuring Instruments ; Wheatstone's Bridge. 
 14. Electric Quantity Measuring Instruments. 15. Instru- 
 ments for the Measurement of Electric Power ; Wattmeters. 
 16. General Hints on the Outfit of a Testing Laboratory ; the 
 Board of Trade Electrical Laboratory. 
 
 CHAPTER II. 
 
 THE MEASUREMENT OF ELECTRICAL RESISTANCE ... 191 
 
 1. The Comparison of Electrical Resistance. 2. Networks of Con- 
 ductors ; Calculation of Resistance of Networks of Conductors. 
 3. The Slide Wire Form of Wheatstone's Bridge. 4. The Plug 
 Pattern of Resistance Bridge. 5. Portable Forms of Wheatstone's 
 Bridge ; The Trotter Bridge. 6. Theory of the Wheatstone 
 Bridge. 7. The Matthiessen and Hockin Bridge. 8. Calibration 
 of a Slide Wire. 9. The Determination of the Temperature 
 Coefficient of a Coil. 10. The Mean Temperature Coefficient of a 
 Metallic Alloy ; Variation of Resistance of Metals with Tempera- 
 ture. 11. The Determination of the Specific Resistance of a 
 Metal or Alloy ; Volume Resistivity ; Mass Resistivity. 12. The 
 Determination of the Volume and Mass Resistivity of Metals and 
 
vi. TABLE OF CONTENTS. 
 
 CHAPTER II. (Continued). 
 
 Alloys ; Matthiessen's Standard for the Resistivity of Copper. 
 13. The Determination of Low Resistance by Fall of Potential. 
 14. The Measurement of Low Resistance by the Matthiessen 
 and Hockin Bridge. '15. The Kelvin Double Bridge. 16. 
 Modifications of the Kelvin Double Bridge for Low Resistance 
 Measurement. 17. Modifications of the Ordinary Wheatstone 
 Bridge for Low Resistance Measurement. 18. Measurement of 
 High Resistances by Direct Galvanometer Deflection. 19. 
 Measurement of Insulation Resistance; Price's' Guard Wire. 
 20. Measurement of Dielectric Resistance by Time of Fall to 
 Half Charge. 21. Cardew's Differential Method for Measuring 
 High Resistance. 22. Practical Measurement of Electric Light 
 Wiring Insulation; The Ohmmeter. 23. Regulations for House 
 Wiring Insulation. 24. Measurement of the Resistivity of 
 Liquids. 25. The Absolute Measurement of Electrical Resistance. 
 26. Resistance of Conductors to Alternating Currents. 
 Table I. Atomic Weights and Densities of Metals. Table II. 
 Electrical Mass-Resistivity of Metals. Tables III., IV. and V. 
 Electrical Volume Resistivity of Pure Metals. Table VI. Elec- 
 trical Conductivity of Metals. Table VII. Volume Resistivity of 
 Alloys. Table VIII. Volume Resistivity of Liquids. Table IX. 
 Volume Resistivity of Badly Conducting Liquids. Table X. Volume 
 Resistivity of Solutions of Copper and Zinc Sulphate. Table XI. 
 Volume Resistivity of Dielectrics. Table XII. Resistance of 
 Various Sizes of Platinoid Wire. Table XIII. Resistance of Various 
 Sizes of Manganin Wire. Table XIV. Resistance of Various Sizes 
 of Copper Wire. Table XV. The Value of the Ohm. Table XVI. 
 The Resistance of Copper Conductors to Alternating Currents. 
 Table XVII. The Resistivity of Various Materials. 
 
 CHAPTEE III. 
 THE MEASUEEMENT OF ELECTRIC CURRENT 339 
 
 1. Classification of Electric Currents. 2. The Measurement of 
 Current by the Electrolysis of a Solution of Copper Sulphate ; The 
 Standardisation of an Ammeter. 3. The Measurement of Current 
 by the Electrolysis of Silver Nitrate. 4. Standard Current- 
 Measuring Instruments ; Magnetic Field of a Circular Conductor. 
 5. Absolute Galvanometers ; Helmholtz Standard Tangent Galva- 
 nometer. 6. The Electro-Dynamometer. 7. Current Balances. 
 8. Laboratory Ampere-Meters. 9. Calibration of Laboratory 
 Ammeters. 10. Measurement of Current by the Potentiometer. 
 11. Current Carrying Capacity of Wires. 12. The Calibration of 
 a Galvanometer by the Potentiometer ; The Measurement of Small 
 Currents ; Shunt Boxes. 13. Alternating- Current Measurement. 
 
TABLE OF CONTENTS. vii. 
 
 CHAPTER III. (Continued.}. 
 
 14. Wave-Form Measurement ; Oscillographs. 15. The Use 
 of Transformers in Alternating-Current Measurement. 16. 
 Measurement of the Frequency of an Alternating Current ; 
 Frequency Tellers. 17. Measurement of the Phase Difference 
 of a Periodic Current ; Phase Meters. Table I. Fuse- Wire Currents 
 (Sir W. H. Preece). .Table II. Electro-Chemical Equivalents. 
 
 CHAPTER IV. 
 
 THE MEASUREMENT OF ELECTROMOTIVE FORCE 421 
 
 1. Electromotive-Force Measurement. 2. The Practical Recovery 
 of a Standard Potential Difference. 3. The Potentiometer 
 Measurement of Electromotive Force. - 4. The Measurement of 
 Small Potential Differences ; A Combined Potentiometer and 
 Wheatstone's Bridge ; The Elliott Potentiometer ; The Fleming 
 Potentiometer. 5. Calibration of a Low-Tension Voltmeter ; 
 Error Curve of a Voltmeter. 6. The Calibration of a High- 
 Tension Voltmeter ; An Inductionless Safety Resistance. 7. Self- 
 Recording Voltmeters. 8. Extra High-Pressure Voltmeters. 
 9. Laboratory and Switchboard Voltmeters ; Qualifications for a 
 Good Switchboard Voltmeter. Table I. Electromotive Force of 
 the Clark Cell at Various Temperatures. 
 
 CHAPTER V. 
 THE MEASUREMENT OF ELECTRIC POWER 469 
 
 1. Electric Power, Mean Power and Power Factor. 2. Measurement 
 of Power in the Case of Unvarying, Continuous or Direct Currents. 
 3. Measurement of Continuous-Current Power by the Wattmeter. 
 4. Measurement of Alternating- Current Power. 5. Measure- 
 ment of Power taken up in the Case of High-Tension Alternating- 
 Current Circuits. 6. Power Measurements in theCaseof Circuitsof 
 Small Power Factor. 7: Power Measurement by Direct Measure- 
 ment of Power Factor. 8- The Three- Voltmeter Method of 
 Measuring Alternating-Current Power ; Limitations of the Method. 
 9- The Three Ammeter Method. 10. Dynamometer Methods 
 of Measuring Power. 11. Power Measurement in the Case of 
 Polyphase Circuits. 12. Practical Forms of Wattmeters ; Siemens 
 Wattmeter ; Fleming Wattmeter ; Kelvin Wattmeter ; Kelvin 
 Engine-Room Wattmeter ; Kelvin Three-Phase Wattmeter ; Elec- 
 trostatic Voltmeters. 13. Wattmeter Testing ; Construction of 
 a Coil of Maximum Inductance and Known Power Factor ; The 
 Measurement of Small-Power Factors. 
 
ERRATA. 
 
 Page 40. First line of footnote, for Platinum read Platinoid. 
 144. Line 9, for 13 read 13A. 
 tt 455. Line 3 from bottom of page, for small read simple. 
 
FOR THE 
 
 ELECTRICAL TESTING-ROOM AND LABORATORY 
 
 CHAPTER I. 
 
 THE EQUIPMENT OF AN ELECTRICAL 
 TESTING ROOM. 
 
 1. The Equipment of an Electrical Testing Room or 
 Laboratory. In the following pages the class of electrical 
 measurements we shall chiefly consider are those required in 
 the engineering applications of electricity and magnetism as 
 far as regards that range of work included in the so-called 
 heavy electrical engineering. We shall omit all references to 
 measurements and tests particularly limited to Telegraphic 
 and Telephonic work, as on this part of the subject several 
 excellent text-books already exist. 
 
 In the establishment of an electrical testing laboratory 
 the electrician will not often be called upon to design 
 the structure or enjoy the advantages of a building erected 
 especially to meet his own views. Usually he will have 
 to adapt or utilise for the purpose some existing rooms 
 in a factory, electric supply station, college, or technical 
 institution. If, however, the opportunity presents itself of 
 being able to begin by designing the laboratory buildings to 
 be occupied, a great advantage is gained at the outset. If, 
 
2 ELECTRICAL LABORATORY EQUIPMENT. 
 
 moreover, the space available can be arranged in the most 
 convenient and suitable way, and if initial outlay is not an 
 obstacle to the possession of the most desirable arrangements, 
 the following conditions may be realised. We shall assume 
 that, in the testing room or electrical laboratory being 
 arranged, at least one or more large and convenient rooms 
 are available for the purposes of a general testing labora- 
 tory, and that, in addition, a dynamo room and also an 
 accumulator room are provided. If the laboratory is in 
 a technical teaching institution, an apparatus room, at least 
 one, and preferably several, private rooms, as well as a 
 lecture and preparation room, will also be required. It is a 
 great convenience to have, if possible, all these rooms located 
 on one level. Time and labour are economised in the day's 
 work, and it is easier to take heavy apparatus backwards 
 and forwards. 
 
 At one end of each electrical laboratory a partition should 
 be run up separating off a space at least 5ft. wide and 30ft. 
 long to form a photometric gallery. Then with regard to the 
 special arrangement and equipment of each apartment, these 
 should be as follows: 
 
 Dynamo Room. Even although current is obtainable from 
 public electric supply circuits or from factory lighting 
 dynamos, it will generally be necessary to provide special 
 means for generating the testing currents. Many tests are 
 impossible unless the electric pressure is exceedingly steady, 
 and ordinary public electric supply or that from a gas engine 
 and dynamo is generally quite useless for the purposes of 
 incandescent lamp tests, transformer tests, and numerous 
 other purposes. Hence provision has to be made in the first 
 place for continuous current supply. This should be taken 
 from secondary batteries which are regularly charged by a 
 dynamo set apart for the purpose. It is better, if possible, 
 to charge by a steam engine than a gas engine, as the charging 
 current is then more uniform and the cell plates are less 
 rapidly deteriorated. If continuous current is supplied from 
 
ELECTRICAL LABORATORY EQUIPMENT. 3 
 
 public electric supply circuits at 100 or 110 volts it- may 
 be used to run a motor-generator or "booster" to take 
 power from the mains at 100 or 110 volts and reduce it to 
 35 or 40 volts. This machine consists of an electromotor and a 
 dynamo coupled together and bolted on to the same bedplate. 
 The motor takes current at 100 or 110 volts and drives the 
 dynamo. The dynamo can generate a current equal to the 
 maximum required for charging the cells at a pressure 
 of 35 or 40 volts. This voltage, added in series with 
 the circuit voltage of 100, will give the necessary 135 or 
 140 volts pressure for charging a local battery of 53 or 54 
 cells. Proper controlling resistances must be inserted in 
 series with the motor armature circuit of the booster, and in 
 series with the motor and dynamo fields. In addition to 
 means for providing continuous current at 100 volts, it is 
 necessary to be able to obtain a supply at pressures of 10 or 
 15 volts or less, and at about 200 volts or more. This is best 
 obtained by having two similar dynamo machines bolted on 
 one bedplate, so that the machines can be coupled with their 
 shafts in one line. One of these machines is a motor, and 
 takes current at 100 or 110 volts from the secondary battery, 
 resistances being provided in the armature circuit and fields 
 for regulating the speed; the other coupled machine is a 
 dynamo, and should be provided with three separate armatures, 
 which can be inserted at pleasure, one giving, say, 10 volts at 
 the standard or proper motor speed, one giving, say, 100 
 volts, and the other 200 or 250 volts. The fields of each 
 machine are best separately excited at 100 volts. A com- 
 bined motor-generator, consisting of these two coupled 
 machines, each of one or two kilowatts output and running 
 at 1,800 or 2,000 revolutions per minute, is a very convenient 
 appliance. 
 
 In the next place, provision must be made for generating 
 alternating currents. This is best done by means of an 
 alternator coupled directly to a continuous current motor. A 
 very convenient arrangement, designed by the Author for use 
 
 B2 
 
4 'ELECTRICAL LABORATORY EQUIPMENT. 
 
 in the electrical laboratory at University College, London, 
 consists of a pair of alternators of 5-kilowatt capacity, each 
 coupled to a continuous current motor, so as to be driven by 
 it, and provision made by a coupling to join the shafts of 
 both sets in one line. The four machines are bolted down to 
 one bedplate, and a flanged pulley on the inner end of each 
 shaft has the flange pierced with holes so that the pulleys 
 can be coupled in such positions that the alternating currents 
 from the two alternators are in any desired relative phase. 
 Eesistances are provided in the field and armature circuit of 
 all machines, so that the speeds and electromotive forces are 
 under complete control. 
 
 This compound machine provides alternating current of 
 single or two-phase kind, and of any required electromotive 
 force up to 200 volts. Machines so coupled should be well 
 bedded down. It is worth while to expend the necessary 
 sum on good foundations to secure perfect steadiness of 
 running and freedom from vibration, as the commutators 
 are thus more easily kept in order. One or both ends of the 
 double alternator shaft can be provided with a curve tracer, 
 to be described later on, by means of which the curves of 
 alternating currents can be taken. 
 
 Well insulated cables from the dynamo terminals should 
 be brought along covered chases in the floor, from the 
 dynamo room to the electrical laboratories to double- pole 
 switches and terminals suitably placed. Whilst laying 
 these leads it is a good plan to run a number of pairs of 
 spare cables and wires of different sizes for voltmeter wires, 
 telephone or bell wires, extra circuits, and other purposes, 
 so that the use of temporary cables lying about on the 
 floor may be avoided. Positive and negative cables should 
 be distinguished by being coloured red and black as usual. 
 
 In the selection of dynamo plant for purely experimental 
 purposes much must depend on the resources and purpose of the 
 laboratory. As far, however, as regards the generation of 
 current for most purposes in the electrical laboratory, nothing 
 
ELECTRICAL LABORATORY EQUIPMENT. 5 
 
 is so convenient as the coupled motors and continuous or 
 alternating current generators ; the motors being worked off 
 a secondary battery. This arrangement leaves nothing to be 
 desired in steadiness of pressure and ease of working. The 
 speed is more easily regulated than in the case of a dynamo 
 driven off counter-shafting with coned pulley speed regulator. 
 For the dynamo room at University College a combined 
 motor-alternator plant, as above described, was built in 
 1893, by Messrs. Johnson and Phillips, to the Author's 
 specification and to Mr. Kapp's designs, of which a general 
 description is as follows : 
 
 "The machine consists of four separate machines bolted 
 on to the same bedplate, viz., two Kapp alternators and two 
 continuous-current motors (see Figs. 1 and 2). Each alter- 
 nator is coupled permanently to its own motor, the com- 
 mutators of the continuous-current machines being on the 
 outside end of the shaft. The shafts of each pair of machines 
 are truly lined, and the inside ends each carry a flange 
 pulley. These pulleys can be coupled together through the 
 flanges by bolts, so as to drive the whole as one machine, 
 or they can be separated for use as two machines. By 
 coupling them together with the armatures in the proper 
 relative position, two-phase currents can be got out of the 
 united machine. Each of the continuous-current motors is a 
 5-H.P. motor, designed to work at 100 volts. The armature 
 is ring- wound, and there are 216 turns of wire on it, 
 connected to a 72-part commutator. The magnets of the 
 motors are of cast steel, 6f in. in diameter. Each armature 
 can carry 35 or 40 amperes comfortably. The alternator 
 armatures contain an iron core, and are wound over with 
 eight coils, each having 16 turns of wire. The field magnets 
 have eight poles, and corresponding poles are opposite to one 
 another. The alternators, when driven at a speed of 1,250 
 revolutions, give an electromotive force of 100 volts. 
 
 "The four machines are fixed on a cast-iron bedplate 9ft. 
 long and 2ft. wide, which is carried on slide rails in the 
 usual manner. The ends of all the armature and field 
 magnet circuits are brought to terminals fixed in a box 
 on the front of the machine. In the field-magnet circuit 
 of each machine is an appropriate resistance, and in the 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 armature circuits of the motors there are also resistances for 
 starting the motors. To the shafts of both motors is fixed a 
 hydraulic speed indicator. A small centrifugal pump is 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
8 ELECTRICAL LABORATORY EQUIPMENT. 
 
 driven by the shaft, and this pump forces coloured water 
 from a small reservoir placed over the pump through a pipe 
 into which are connected two vertical glass tube pressure 
 gauges, one of which is placed on the wall of the dynamo 
 room, and the other is placed on the wall of the electrical 
 laboratory 30ft. away. When the motor alternator is running, 
 the centrifugal pump forces the water up these tubes, until 
 the hydrostatic pressure of the column of liquid supported 
 in the tube balances the pressure due to the pump. The 
 height of the column of liquid, therefore, can be made to 
 measure the speed of the machine after these gauges have 
 been carefully calibrated. The special advantage of this 
 hydraulic speed indicator is that it is so exceedingly 
 responsive to changes in speed. A change in speed of less 
 than one per cent, can be certainly detected and measured, 
 whilst the accuracy of the indication is independent of the 
 density of the liquid used. The speed of the motor can be 
 regulated from the laboratory by the use of a carbon rheostat 
 inserted in the field or armature circuit and can thus be 
 kept exceedingly constant." 
 
 The above described motor-alternator plant has many uses. 
 The alternators can be run in parallel either coupled or free. 
 They can be coupled and joined in series, so as to give a 
 current at 200 volts pressure. They can be set to give a two- 
 phase current. Efficiency tests can be made with the direct 
 current motors, driven as coupled machines, or with the 
 alternators. Alternating current curve tracing can be 
 carried out in many different experiments. For experimental 
 work with polyphase currents, a very convenient appliance 
 is a small three-phase alternator coupled direct to and driven 
 by a continuous current motor ; the fields of both being 
 separately excited at 100 volts. 
 
 Electrical Laboratory. In the design of the electrical 
 laboratory the important matter is to provide sufficiently 
 steady tables or supports for galvanometers and instruments. 
 It is not a good plan to build up, as is sometimes done, brick 
 tables in the middle of the laboratory, because these cannot 
 afterwards be moved if space is required for special work. It 
 
ELECTRICAL LABORATORY EQUIPMENT. 9 
 
 is best to provide round the room, at a standard height of say 
 3ft. Gin. from the floor, strong stone or slate slabs, let into the 
 main walls of the building. If the main walls are strongly 
 built, and have good foundations, very steady supports can 
 in this way be obtained. Circumstances, however, must 
 decide what is best to be done. In any case, several firm 
 slabs must be provided, either by building up brick pillars, 
 covered with a slate surface, on independent foundations, 
 thus forming solid tables, or by building up stone supports 
 to the level of, but not touching, the floor, on which can 
 rest the legs of special steady wooden tables for carrying 
 the galvanometers, ampere balances, and other instruments. 
 All that is necessary is to secure steadiness for certain 
 particular pieces of apparatus. In some instances special 
 precautions may have to be taken to eliminate the effects of 
 vibration due to adjacent machinery or traffic. In these 
 cases the galvanometers may be placed on slabs of slate 
 which are suspended at the four corners by stout india- 
 rubber bands from brackets let into the wall, and heavier 
 instruments, such as ampere balances, may be placed on 
 slabs of Yorkshire stone carried on three or four blocks 
 of india-rubber. 
 
 One of the greatest difficulties which generally presents itself in arranging 
 an electro-technical laboratory is the contrivance of suitable means to prevent 
 the mirror instruments being disturbed by vibrations of the building due' to 
 machinery or traffic in the neighbourhood. The usual method of securing 
 steadiness is to build up brick pillars on very solid foundations formed in the 
 ground, as supports for the legs of ordinary stout deal tables, and to keep the 
 laboratory floor from contact with these pillars. This plan, however, is not 
 always entirely a success, and then sometimes a remedy may be found by 
 placing the galvanometer or mirror instruments, as above suggested, on a slab 
 of slate or flagstone of considerable weight, resting the slab on four india- 
 rubber blocks. Or it may be possible to suspend from the ceiling, by india- 
 rubber door springes, a heavy wooden slab or board on which the instrument is 
 placed, and so take up the vibrations. A combination of the independent 
 brick pillar with capstone resting on india-rubber blocks is the best method 
 in difficult cases. One device, said to be very effective, is to support the 
 galvanometer on a wooden base placed on a thick pad of hair felt laid in a 
 tray, the corners of the base board and tray being connected by stretched 
 india-rubber bands. See Electrical Review, 1898, Vol. 42, p. 592. 
 
10 ELECTRICAL LABORATORY EQUIPMENT. 
 
 In the next place, it is convenient to arrange a standard 
 height and size of working table. A convenient size is 5ft. 
 long, 2ft. Gin. wide, and 3ft. Sin. in height. These tables can be 
 arranged together as required. Around the room, however, 
 should be fixed benches or tables with strong top surfaces, 
 having cupboards and drawers underneath, and on which may 
 be arranged certain sets of apparatus never to be moved. It is 
 essential that such standard sets of apparatus as the Bridge for 
 resistances measurements, the Potentiometer for electromotive 
 force measurements, and the Ballistic Galvanometer, should 
 never be moved, but should be kept always connected up 
 and be available at a moment's notice for use. Apparatus 
 stored in glass cases, and therefore not ready when required, 
 is a fruitful source of waste of time and energy, and the 
 plan of so keeping it should be avoided. Dust and light 
 may be kept off the arranged apparatus by simply throwing 
 over the articles a black velveteen cloth, or, better still, 
 keeping every important piece of apparatus in a wooden 
 or cardboard box, which is shut up when the apparatus 
 is not in use. The laboratory should be provided, if possible, 
 with double windows, and these windows be darkened 
 when required by blinds made of black American oilcloth or 
 some material impervious to light. The laboratory can 
 then be kept in the proper state of illumination necessary to 
 see well the spots of light on galvanometer scales. As far as 
 possible an equable temperature should be maintained in 
 the rooms all the year round. A sink with hot and cold 
 water, and a fume cupboard must be provided, and a table, 
 having a top covered with sheet lead, with a narrow fillet or 
 edge round it, and drainage tube, is useful for experiments 
 with primary batteries or secondary cells, and other things 
 likely to be messy. It is a good plan in preparing the room to 
 form covered floor chases around and across the room in which 
 wires and cables can be laid. The permanent leads and cables 
 are placed in casing fixed to the floor of these chases. The 
 cover boards of the chase can be made to take up in sections 
 
ELECTRICAL LABORATORY EQUIPMENT. 11 
 
 so as to lay temporary cables, and thus avoid the danger and 
 nuisance of loose electric cables lying about all over the 
 floor. Eound the room should run several separate insulated 
 circuits, having terminals, fuses, and switches at each place 
 where current is likely to be required. One of these should 
 be a circuit from the battery for supplying current to incan- 
 descent lamps to be used for galvanometer scale lamps, and 
 for a special table lamp if required. 
 
 The incandescent lamps best adapted for galvanometer purposes are the 
 Edison form with single horse-shoe shaped carbon filament. The lamp bulb 
 should be covered with a cylindrical asbestos hood having a slit in it which 
 permits the light from one leg of the filament loop to pass out. The galvano- 
 meter is then arranged so that the mirror, with or without the assistance of a 
 lens, throws an image of this straight incandescent carbon on to a divided 
 ground glass or semi-transparent celluloid scale suitably placed. In this 
 manner an exceedingly sharp, bright line, being the image of a part of the 
 filament is thrown on the divided scale. This image can be seen in daylight 
 or in a slightly darkened room. If the scale is placed at the right focal 
 distance from the mirror, and if the scale is divided into millimetres, a reading 
 to one quarter of a millimetre can be taken, provided the galvanometer 
 mirror is a good one. 
 
 This circuit should be provided with numerous wall plugs 
 (preferably of the concentric pattern) by which a lamp with 
 a socket and flexible cord can be plugged in where required. 
 Another circuit should run from the main secondary battery 
 and provide, where required, at several places larger currents 
 at 100 volts pressure. A third circuit should give continuous 
 current at various pressures from the continuous motor gene- 
 rator in the dynamo room, and a fourth circuit should bring 
 alternating currents from the alternators. In laying out these 
 circuits, blank terminals with double-pole porcelain cut-outs 
 and double-pole switches should be provided in as many 
 places as possible. Comfort and convenience in subsequent 
 work will greatly depend on the care with which all these 
 little details are thought out by the electrician in arranging 
 his laboratory. In order to avoid disturbing magnetic needle 
 galvanometers by strong stray magnetic fields, it is desirable 
 to run all these laboratory supply circuits with concentric 
 cable. 
 
12 ELECTRICAL LABORATORY EQUIPMENT. 
 
 Accumulator Room. This room may be at any con- 
 venient and necessary distance from the laboratory working 
 rooms. It should, if possible, have walls built with glazed 
 brick, and a ceiling of glazed tiles. In any case, all exposed 
 wood and metal work and all cables should be thickly painted 
 with anti-sulphuric paint or enamel. The cells should be 
 placed on low brick table supports covered with slate slabs, 
 or on the usual painted wooden supports. In any case, they 
 should be well insulated. Cables joined' to various points 
 on the battery should be brought out through th walls 
 of the battery room, to a switchboard outside, by leading 
 them through porcelain tubes plugged with slag-wool, so 
 that they are spray-tight. Changes in the electromotive 
 force of the working circuit can then be made as required 
 without entering the battery room. If possible, a separate 
 battery should be provided for incandescent lamp tests 
 or for any special purposes when great uniformity of 
 pressure is required. The choice and size of cell must be 
 left to the user of the laboratory to determine. One or 
 more large accumulator cells are useful. These can be 
 charged from the low voltage side of the motor-generator 
 set, and are very useful in yielding the large currents required 
 for testing ammeters. 
 
 An additional essential is a series of small secondary cells, 
 for giving high electromotive forces. Of these the most 
 convenient are the cells known as Lithanode cells. 
 
 Lithanode is not compressed peroxide of lead, as is sometimes stated, 
 for, however strongly lead peroxide may be compressed, the resulting 
 mass will disintegrate when immersed in a liquid electrolyte. It is 
 produced from litharge, made into a pasty mass with a solution of sulphate of 
 ammonia, which causes the material to "set," so that it will no longer 
 disintegrate when placed in a fluid. The " forming," according to the 
 original idea, was performed in a bath of sulphate of magnesia. In ordinary 
 practice the elements are made up of a number of small slabs of lithanode, 
 whose outer edges are V-shaped. These slabs or pellets are arranged in a 
 casting mould of any suitable dimensions, and are placed at such a distance 
 apart and from the edges of the casting frame as to allow of sufficient space 
 for the requisite quantity of metal to run in and impart adequate mechanical 
 strength to the completed element. After the pellets have been arranged 
 
ELECTRICAL LABORATORY EQUIPMENT. 13 
 
 in this manner, an alloy of lead and antimony is run into the interstices, and 
 1;hus a complete plate is formed. Before being cast up, the positive pellets 
 are converted into peroxide of lead in a forming bath ; those for the negative 
 plate are simply dried and cast up direct, the lithanode in the latter case 
 being reduced to a condition of spongy lead by the ordinary electrolytic 
 method. 
 
 These cells are contained in small glass tubes or cylinders, 
 about lin. in diameter and 4in. high. A series of 50 of these 
 cells, contained in a portable box or case, can be charged 
 through an incandescent lamp off a 200-volt circuit. Two or 
 more sets of 50 cells each of these small testing cells are most 
 useful for insulation tests and voltmeter testing. Finally, 
 some sets of single or double cells, having a capacity of about 
 40 or 50 ampere-hours, are requisite for the potentiometer 
 testing. In a well-organised laboratory there should be 
 regular days when all these cells are recharged by being 
 suitably arranged in series with resistances or lamps, so that 
 the cells are charged with their proper charging current taken 
 from the dynamo circuit. The particular type and size of 
 cells are matters which must be determined by the work to 
 be done. If many tests are likely to be made on complete 
 batteries, it is an advantage to have the accumulator room as 
 near as possible to the electrical laboratory. In any case, it 
 must have well fitting double doors, to prevent the egress of 
 acid vapours. Assuming a certain area available on the 
 ground floor to be arranged as an electrical laboratory, the 
 space might be conveniently divided up as shown in Fig. 3. 
 
 The battery room should be separated completely from the 
 engine and dynamo room and from the private room, but 
 cables should be carried spray- tight through the walls, as 
 above suggested, to the regulator switchboard and to the 
 various laboratories. 
 
 In each electrical laboratory should be a photometric 
 gallery, forming a completely closed and darkened space of 
 about 30ft. long, 5ft. wide, and 10ft. high. The cables 
 bringing current from the dynamo room to each laboratory 
 should be laid along a chase in the floor of the passage, and 
 
14 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 distributed to each room as required. Every room except 
 the dynamo and battery room should have windows, provided 
 with black opaque cloth blinds, which can be drawn down so 
 as to darken the room more or less as required. Dimensions 
 are not added in the sketch plan below, because various 
 circumstances must determine the space required, but an 
 arrangement of rooms as here suggested forms a convenient 
 one for a small testing or teaching electrical laboratory. 
 
 tofel DIRECTOR'S 
 pljj PRIVATE 
 ROOM 
 
 (C 
 
 V A 
 
 ' V >, s 
 
 
 ^/ PASSAGE A m O 
 
 V 
 
 '<?*" 
 
 '<" !\ 
 
 STORES 
 
 LABORATORY 
 
 1 I 
 
 WORKSHOP 1 
 
 1 HEAVY 
 
 PHOTOMETER 
 ROOM 
 
 J 
 
 FIG. 3. 
 
 As an example of the arrangements of an electrical 
 laboratory, which, though not large, is well equipped, 
 a| brief description may here be given of the Fender 
 Electrical Engineering Laboratories in University College, 
 London, the internal arrangements for which were designed 
 by the Author, and embody some thought and experience in 
 this work* : 
 
 " The portion of the buildings allotted for the purpose of an 
 electrical engineering laboratory consists of six rooms, in all 
 
 * The architect of these buildings was Prof. Roger Smith, F.R.I.B.A., 
 Professor of Architecture in University College, London. A full description 
 of these laboratories, given by the architect and the professors who 
 collaborated with him in their internal design and fittings, is given in the 
 Journal of the Royal Institute of British Architects, Vol. L, 3rd series, 
 p. 294, from which, by kind permission of the Council of the Institute, this 
 description of the electrical laboratories, written by the Author, is taken. 
 
ELECTRICAL LABORATORY EQUIPMENT. 15 
 
 of which the interior arrangements have been very carefully 
 designed. The four principal rooms open into one another. 
 These are the dynamo room, the lecture theatre, the 
 apparatus room, and the electrical laboratory. The general 
 arrangement of the building permitted the dynamo room floor 
 to be placed on solid ground, and thus secured the possibility 
 of making both floor and machine foundations of great 
 steadiness. This dynamo room is 31ft. long and 22ft. wide, 
 built in white glazed brick. The plant placed in the 
 dynamo room consists in the first place of a 9-H.P. nominal 
 Otto-Crossley gas engine, capable of working up to 19 
 I.H.P. This engine is fitted with all the most recent 
 improvements. It is bedded on a slab of Yorkshire stone 
 resting on the concrete foundation floor, 24in. in thickness, 
 which is carried over the whole room. In this concrete floor 
 all the pipe trenches are formed, and these last are lined with 
 brick and covered with the usual cast-iron chequer plates. 
 The engine is provided with a self-starting arrangement 
 designed by Messrs. Crossley Bros. This contrivance consists 
 simply of a massive cast-iron chamber, into which a charge 
 of gas and air is pumped by an auxiliary hand-pump. If 
 the engine is stopped, so that the crank is on the middle ot 
 the top stroke, it suffices to fire the compressed charge at a 
 touch-hole to start the engine even under full load. This 
 arrangement is as simple as it is effective, and not the 
 slightest difficulty has ever been experienced in starting 
 the engine with it. The engine is provided with two very 
 massive flywheels, to secure steady running, and the crank 
 shaft carries outside the left-hand wheel a Mather and Platt 
 clutch pulley 60in. in diameter, and on the right-hand side a 
 36in. pulley for driving on to a counter-shaft. From the 
 Mather and Platt clutch pulley is driven by a belt a 
 Crompton continuous current six-unit dynamo, which is 
 employed exclusively for charging the secondary battery. 
 This clutch pulley permits the charging dynamo to be 
 thrown into and out of action whilst the engine is running. 
 The engine is provided with a double service of cylinder 
 cooling water : one service being brought from two wrought- 
 iron tanks placed on an elevated platform in one corner of 
 the engine-room, and the other service comes direct from the 
 water supply mains of the building, and is taken through 
 a water meter. The water circulating through the cylinder 
 jacket from the continuous supply is carried away by 
 
16 ELECTRICAL LABORATORY EQUIPMENT. 
 
 a funnel into the main drain. The temperature of the 
 in-coming and out-going water can be taken with thermometers, 
 and the quantity of water which circulates is registered by 
 the meter. Hence the number of units of heat removed 
 from the cylinder becomes known. The gas for the engine is 
 taken direct from the street mains, through a separate gas 
 meter. The indicating gear fixed to the engine operates 
 a suitable high-speed indicator, designed to give a good 
 indicator diagram on gas engines. It will be seen that 
 arrangements have been provided for making a technical 
 study of the gas engine itself as a prime motor. Against 
 one wall of the dynamo room is fixed a series of cast- 
 iron brackets, which carry a 2in. steel counter-shaft. This 
 counter-shaft is driven by a belt from the right-hand drum of 
 the engine, at a speed of 280 revolutions per minute. This 
 counter-shaft carries a fast and loose driving pulley with belt- 
 shifting gear. The shaft is cut in the centre and provided 
 with a clutch-gear and two driving pulleys, one on each 
 side of the clutch. The counter-shaft is supported upon 
 ball-bearings, which are carried on cast-iron brackets, 
 built into the 14-in. wall set in cement which carries 
 them. 
 
 "Keturning, then, to the construction of the dynamo-room 
 floor, it has already been mentioned that this consists of a 
 concrete floor 24in. in thickness. This concrete is finished 
 2in. from the wall all round the room, and slag wool packed 
 into the interspace. On the concrete are laid, 18in. apart r 
 teak beams Gin. deep by 4in. wide. These beams are held 
 down by 24-inch holding-down bolts, which pass right 
 through the concrete, and are terminated in anchor plates at 
 the bottom. The space between the beams is filled in 
 with granolithic cement^ The cement is cupped out between 
 the beams, and given a slight cant towards a main drain 
 running down the room formed in the cement. By this 
 means oil or water spilt on the floor is easily got rid of and 
 the floor kept dry. The floor has proved itself to be so- 
 satisfactory that no sensible vibration is propagated up the 
 building when the engines and dynamos are at work; and 
 delicate electrical instruments can be used in the room when 
 the engine is in operation. The silencing chamber of the gas 
 engine is placed in a pit in one corner of the room, and is air- 
 jacketed to keep the temperature of the room down. The 
 engine discharges into an exhaust pipe carried up a brick 
 
ELECTRICAL LABORATORY EQUIPMENT. 17 
 
 chase in one corner of the room, and then through the 
 roof. 
 
 "Turning next to the dynamo plant, this consists, in the 
 first place, of a Crompton continuous-current dynamo, giving 
 an output of 45 amperes at 140 volts. This dynamo is 
 driven through an intermediate Kummer transmission dyna- 
 mometer, which measures the mechanical power given to it 
 from the Mather and Platt pulley of the dynamo. It can 
 also be driven by a Bumsted and Chandler steam engine in 
 the adjoining room. This engine can be belted when required 
 to the main countershaft. The duty of this dynamo is to 
 provide the charging current of the secondary battery. The 
 electromotive force of this machine is regulated by a variable 
 resistance placed in the circuit of its field magnets, whilst an 
 automatic cut-out is placed in the main circuit to prevent the 
 charge of the cells from coming back into the dynamo. In 
 addition to this dynamo, the room contains the motor- 
 alternator plant by Messrs. Johnson and Phillips, already 
 described. This machine consists of four independent 
 dynamos, bolted down on to one common cast-iron bedplate 
 10ft. in length. Each half of the machine comprises a direct- 
 current motor, which is directly coupled to a Kapp 
 alternator, each dynamo being of 5 H.P., or capable of an 
 output of 3,500 watts. Each coupled motor-alternator has a 
 pulley with a flange on it, and the machines are so set on the 
 bedplate that the pulley flanges are in close contiguity 
 with each other, but do not quite touch. The flanges can, if 
 need be, be coupled by two bolts, so as to unite the two 
 halves of the shaft into one, and make all four dynamos 
 drive together as one machine. With this compound motor- 
 alternator it is possible to carry out a large range of 
 instructional work. Thus, either motor can be driven by the 
 current from the secondary batteries, and will drive its own 
 coupled alternator. Hence, by properly exciting the fields of 
 the motor and alternator, an alternating current is furnished 
 by the alternator of any required frequency and electro- 
 motive force within certain limits. The two halves of the 
 plant can be driven together or separately, and the 
 alternating currents delivered by the alternators may be put 
 in any relative difference of phase by properly uniting the 
 pulley flanges with the coupling bolts. As an illustration of 
 the work which may be done with this plant in teaching, 
 besides employing it for the generation of either continuous 
 
18 ELECTRICAL LABORATORY EQUIPMENT. 
 
 or alternating currents, we may point out that the following 
 experimental work can be carried out : 
 
 " 1. Either plant may be run separately by a belt from 
 pulleys on the counter-shaft, and will produce from the 
 alternator an alternating current of 100 volts or 150 volts, 
 according as the fields are arranged, the current being 35 
 amperes, and from the continuous - current machines a 
 continuous current of 35 amperes and 100 volts or less. 
 
 " 2. By coupling the shafts rigidly together they may be 
 run as one plant, and either the currents or potentials of the 
 two similar machines added together, thus giving continuous 
 or alternating currents of 35 amperes at 200 volts, or 70 
 amperes at 100 volts. 
 
 " 3. Either of the continuous-current machines can be run 
 as a motor by current from the secondary battery, which is 
 charged by the Crompton dynamo. By regulating resistances 
 the speed may be regulated within wide limits. In this way 
 alternating currents of various frequencies can be drawn 
 off from the alternators either separately or running as one 
 machine. 
 
 " 4. The two separate plants may be coupled together 
 by the bolts through the respective pulley flanges, so that 
 the alternating currents given by the two alternators are 
 in any relative phase. They may be coupled together so as 
 to give the effect of a two-phase generator, with the 
 alternating currents 90deg. different in phase. 
 
 u 5. Efficiency tests can be made on the combination either 
 of continuous and alternating current machines or of two 
 similar machines. 
 
 " 6. The alternators can be run in parallel, each being 
 driven by its own separate motor, and the conditions of 
 parallel working thus explored. 
 
 " In addition to these dynamos there is also a small J-H.P. 
 continuous -current Crompton dynamo and a pair of small 
 coupled two-kilowatt dynamos, which serve for Hopkinson 
 tests or as a motor-generator for experimental purposes. On 
 a spare set of slide rails any dynamo can be bolted down for 
 test, and driven from the counter-shaft or by a continuous- 
 current motor. The walls of the dynamo room are occupied 
 with the switches and resistances for operating these 
 dynamos and motors. There is, in the first place, a 
 resistance frame which acts as a standard power absorber. 
 This consists of 80 wires of a high resistance alloy, each 25ft. 
 
ELECTRICAL LABORATORY EQUIPMENT. 19 
 
 long, stretched up and down one side of the room over 
 porcelain insulators. The wires can be joined in parallel as 
 required by a set of special switches. When so arranged, 
 their resistance is capable of dissipating a power of 8,000 
 watts, or about 11 H.P. This is used for taking up the 
 power of dynamo machines under test. Other resistances are 
 provided for starting the continuous current motors, for 
 varying the fields of the alternators and continuous current 
 machines. A bank of 30 100- c.p. incandescence lamps is 
 .also fixed to the wall, and serves as an adjustable load for any 
 dynamo to work on. The dynamo room is well lit by a 
 skylight roof, and is warmed by hot- water pipes, and provided 
 with gas, water, and electric incandescent lighting. A small 
 vice-bench under the window enables all small repairs to be 
 done on the spot. 
 
 " The dynamo room opens into the lecture theatre, which is 
 32ft. wide and 35ft. long. On a platform is placed a lecture 
 table 20ft. in length. To the back of this platform are 
 brought the electric mains from the dynamo room. These 
 are laid in covered chases on the floor, and all this cable 
 work has been carried out with the highest quality of 
 india-rubber covered cable laid in white wood casing, and no 
 joints are made in any position under the floors. The cables 
 from the dynamo room conducting the current from the 
 various machines all terminate in lock-up cupboards at each 
 end of the lecture table, and thence proceed to a main 
 switchboard at the back of the lecture table. The battery 
 charging current from the Crompton dynamo is brought 
 through an ammeter and voltmeter to a main battery switch- 
 board, and thence it is distributed to the secondary battery in 
 the room beneath. From this switchboard a main runs all 
 round the laboratories, distributing at various points as 
 required continuous current at a pressure of 100 volts. The 
 currents from the two alternators are brought to the lecture 
 table, one to one end and the other to the other. 
 Experiments with two-phase currents can thus be shown. 
 The arrangements for charging and discharging the secondary 
 battery are conveniently to hand, and the instruments show 
 at a glance what current is going into the battery and what 
 is coming out of it. In front of the lecture table is a raised 
 gallery of seats capable of seating 60 students. At the back 
 of this gallery, in a space 8ft. wide under the windows, is a 
 long work-bench fitted with vices, at which instrument 
 
 c2 
 
20 ELECTRICAL LABORATORY EQUIPMENT. 
 
 making and other simple metal and wood-work is carried 
 out. The lecture room is well lighted by pendent incan- 
 descent electric lamps, and the switchboard for controlling 
 the supply of the lighting current, which comes from the St. 
 Pancras Electric Lighting Station, is placed at the back of 
 the lecture table. 
 
 " At the end of the lecture table is a specially designed 
 vertical electric lantern, for projection work. This is fitted with 
 a Brockie arc lamp having inclined carbons. The arrangement 
 has been so worked out that not only lantern slides but any 
 apparatus, whether horizontal or vertical, capable of projection 
 can be immediately shown on a 10-ft. screen by simply 
 switching on the arc lamp. The lecture-room can be darkened 
 in a few seconds by pulling up dark blinds over the three win- 
 dows which light the room. These blinds are pulled up by cords, 
 which are brought over the ceiling to the back of the lecture 
 table. Every arrangement has been made for quickly and 
 readily enabling any experiment to be shown which requires 
 the optical lantern to exhibit it. At the sides of the room 
 and at the back of the lecture table are suitable screens for 
 carrying diagrams and plans. 
 
 " The electrical laboratory opens out of the lecture room. 
 This is a room 50ft. long and 32ft. wide. In order to secure 
 quietness and to keep out the dust, the room has been built 
 with double windows, the outer ones being ordinary sashes. 
 and the inner ones French windows. Black blinds are 
 provided, so as to darken each window when required. All 
 round the room a series of stout stone slabs are let into the 
 wall at a height of 4ft. above the floor, between the windows. 
 These stone slabs are intended as steady tables to carry 
 various measuring instruments. It is found by experience 
 that it is better to arrange the steady tables in this way than 
 to build them up as brick pedestals through the floor of the 
 room, because advantage is then taken of the greater 
 steadiness of the footings of the main walls, and the central 
 portion of the room is kept clear. Across and around the 
 floor of the laboratory chases are left, covered in by floor 
 boards, in which electrical mains are carried, and these 
 terminate in lock-up switch and fuse boxes in various parts 
 of the room. At one end of the laboratory is a long photo- 
 metric gallery, 30ft. long, 10ft. high, and 6ft. wide. In this 
 gallery is placed the photometer and various apparatus 
 required in testing arc and incandescent lamps. One end of 
 
ELECTRICAL LABORATORY EQUIPMENT. 21 
 
 this gallery is formed into a small dark room for photo- 
 graphic purposes. Around the room are placed a series of 
 strong tables having drawers and cupboards, and each of 
 these tables is provided with electric currents from the 
 mains, and with a special circuit for working the incan- 
 descent lamps required by the galvanometers. In the centre 
 of this room numerous other tables are arranged for special 
 work. On the stone steady slabs are placed all the standard 
 electrical instruments, and the general principle has been 
 adopted of having each particular piece of apparatus 
 required for each special electrical measurement set up and 
 arranged so that it is never disturbed, and is always ready at 
 a moment's notice for use and experiments. One side of 
 the room is devoted to the current- weighing instruments and 
 standard voltmeters. The laboratory is provided with a very 
 fine set of Lord Kelvin's standard electrical balances and 
 electrostatic voltmeters. These balances are checked by 
 weighing the copper deposit produced in a voltmeter in 
 circuit with them, and for this purpose an Oertling chemical 
 balance has been specially built, and which is a remarkably 
 fine instrument. On other tables are set up the apparatus 
 for the measurement of resistances, insulation tests, magnetic 
 induction, electrical capacity and potential, and as these 
 permanent pieces of apparatus are never disturbed, a great 
 economy of time is effected in setting up and taking down 
 apparatus. In addition to the above, the experimental 
 apparatus is provided for complete tests of alternating 
 current transformers and other alternating current appliances. 
 Beneath the lecture-room is a large accumulator room built 
 in white glazed brick. On stone shelves round the room 
 are placed fifty-four cells of a D.P. battery. This battery 
 has a storage capacity of 250 ampere-hours, and will discharge 
 at the rate of 50 amperes. The current from the battery 
 is laid on to all the working benches of the laboratory. 
 
 "The general plan of the laboratory, of having all the 
 rooms opening one into another, is an immense convenience, 
 and saves much time. The arrangement of apparatus in 
 permanent groups for special measurement effects also a 
 great economy in time, as apparatus once set up is not 
 unnecessarily disturbed. The care with which the heating 
 and ventilation have been considered, as well as the universal 
 adoption of the electric light, has made these laboratories 
 exceedingly comfortable to work in. The rooms are all 
 
22 ELECTRICAL LABORATORY EQUIPMENT. 
 
 excellently lighted. Although the lahoratory stands in a 
 main street, no difficulty has been found to arise from 
 vibration. The stone steady shelves let into the main walls 
 provide all that is necessary in the way of support for the 
 instruments which must be kept steady. 
 
 "Besides the above rooms, a diagram and model room r 
 apparatus room, and professor's private room are included. 
 The apparatus room opens into the lecture room close to the 
 lecture table. The apparatus room is well provided with 
 dust-tight apparatus cases and cupboards for the laboratory 
 apparatus. Access is obtained to the accumulator room 
 when required by a cellar-flap door opening out of the 
 lecture room, and through this opening any cells can 
 be hoisted up or let down which are required for exam- 
 ination." 
 
 2. The Fundamental Standards of Length, Mass, and 
 Time. The outfit of an electrical laboratory or testing room 
 must include, in the first place, means for making comparisons 
 with the fundamental standards of Mass, Length, and Time. 
 These comparisons involve the possession of standard 
 weights, a good balance, standard lengths, scales and callipers^ 
 and an adjusted chronometer. The degree of refinement 
 necessary in these fundamental measurements will depend 
 upon the nature of the work to be done in the electrical 
 laboratory. In a standardising laboratory the actual working 
 instruments viz., the scales, weights, and watches used for 
 observations should be checked by comparison with certain 
 more carefully preserved and seldom used principal standards. 
 These last should be brought into careful comparison with 
 the legal standards kept at the Standards Office of the 
 Board of Trade in Great Britain or with the principal legal 
 standards in other countries. 
 
 The Unit or Standard of Length to which all other measure- 
 ments of length in scientific work are now referred in Europe 
 is the Metre International, or Standard Metre. It is a bar of 
 platinum-iridium deposited with the International Committee 
 of Weights and Measures, and is carefully preserved at 
 
ELECTRICAL LABORATORY EQUIPMENT. 23 
 
 Sevres, near Paris. The length between two marks on it, 
 taken at 0C., is defined to be the standard of length, and is 
 called the Metre. 
 
 The metre is equal to 39*37011 British standard inches or 
 to 1-09361426 British standard yards. 
 
 Comparisons of actual metre scales or yard measures are, 
 or can be, made at the Standards Office of the Board of 
 Trade with a certified copy of the standard yard or metre. 
 Every electrical laboratory in which accurate work is being 
 carried out should possess certain metre scales for working 
 use, and a standard comparison scale which has been thus 
 compared and certified at the Standards Office of the Board 
 of Trade. 
 
 Similarly the Standard or Unit of Mass in scientific work 
 is the Kilogramme International, preserved at the same place 
 as the standard metre. The kilogramme is equal to 2'20462 
 British standard pounds. 
 
 The Unit of Time in scientific operations is the mean solar 
 second as defined by the mean solar clock at Greenwich 
 Observatory. 
 
 The time of one complete revolution of the earth on its 
 polar axis is called a sidereal day, and is the ultimate unit or 
 standard of reference in measuring duration. It is equal to 
 86164*09 mean solar seconds. The mean solar day is the 
 average time interval between two successive transits of the 
 sun across a meridian, and it is divided into 86,400 mean 
 solar seconds. 
 
 A good chronometer should be provided, and should be 
 adjusted to show Greenwich mean time or mean solar time, 
 and, from time to time, should be rated by comparison with 
 the mean solar clock at Greenwich. 
 
 It seems hardly necessary to say that the standard chronometer, unless 
 a non-magnetic one, should be kept carefully at a distance from all dynamos 
 and strong magnets or currents. 
 
 The electrical laboratory should also be provided with a 
 good standard metre scale, divided into centimetres and 
 
24 ELECTRICAL LABORATORY EQUIPMENT. 
 
 millimetres ; a box of standard gramme weights, multiples, 
 and submultiples ; and the above-mentioned standard 
 chronometer, showing Greenwich mean time. 
 
 Comparisons with the principal standards of length, mass, 
 and time are made by means of working scales, various 
 working balances, and stop-watches or pocket chronometers. 
 The laboratory must, in the first place, be provided with a 
 number of suitable measuring instruments for determining- 
 lengths. A number of metre scales, divided into centimetres 
 and millimetres, engraved on steel, brass, or boxwood, are 
 essential. Outside and inside callipers, measuring by a 
 vernier to one-ten-thousandth of an inch or one-four-hundredth 
 of a millimetre, are required. A spherometer for measuring 
 the thickness of thin metal plates is useful. 
 
 For measuring the diameters of exceedingly fine wires a 
 microscope micrometer may occasionally be required. In its 
 best form this consists of an ordinary achromatic microscope 
 with a calliper eye-piece. It is provided with a slide con- 
 sisting of a glass slip on which has been engraved with a 
 diamond a scale in hundredths and thousandths of an inch. 
 The eye-piece of the microscope has two needle points 
 projecting inwards and moved by external screws, so that 
 these points can be made to approach or recede from each 
 other in one plane. These needles are fixed in the focus 
 of the eye lens of the eye-piece. To measure the diameter 
 of a fine wire or, say, the filament of an incandescent lamp, 
 the wire is placed in the focus of the microscope and the 
 needle points screwed in or out until they appear to touch 
 the two edges of the image of the object to be callipered. 
 The eye-piece must, of course, be turned round until the 
 needles are exactly at right angles to the image of the wire. 
 This being done, the wire is removed from the microscope 
 stage and the divided glass scale placed on it. The image of 
 the scale will then be formed in the plane of the needle 
 points. The observer can read off on the scale the length of 
 the interval between the needle points, which is therefore 
 
ELECTRICAL LABORATORY EQUIPMENT. 25 
 
 the diameter of the wire or filament. The arrangement 
 forms an optical calliper, and is a very convenient one 
 to employ in determining the diameter of a very fine 
 wire. 
 
 For measuring short lengths or large diameters, a calliper 
 of the following kind is found to be useful.* A steel tube 
 has two flat surfaces planed on it at right angles to each 
 other. The tube has a scale of centimetres and millimetres 
 engraved on it. Two brass blocks slide on this tube, and 
 can be clamped. One of them has a slow motion screw, and 
 carries a vernier. These blocks carry straight steel trans- 
 verse bars, which act as calliper jaws and remain parallel 
 when placed any distance apart. The object to be callipered 
 is placed between the jaws, and contact is judged as usual 
 by the "feel." One or two of the ordinary inside and outside 
 steel vernier callipers should also be provided, and the best 
 forms have a loose head screw which prevents undue pressure 
 being put upon the object measured. 
 
 The laboratory must be provided with a standard balance 
 and with other rougher balances for ordinary weighing. The 
 chief standard balance should be one of the type called a 
 short-beam chemical balance, which is adjusted to carry at 
 least 200 grammes and turn to a tenth of a milligramme. 
 Another balance, to carry 500 grammes and turn to a milli- 
 gramme, may be used for less accurate weighings. 
 
 These balances should stand on stone shelves let into the 
 wall of the laboratory, and be enclosed in glass cases. In 
 each case should stand a beaker containing some lumps of 
 well-baked pumice stone saturated with strong sulphuric 
 acid. The use of this is to dry the air in the balance case 
 and keep all steel parts bright. The standard balance case 
 should be kept locked when not in use. Young students or 
 assistants should not be allowed to use a very good balance 
 without proper instruction as to its employment. On the 
 side of the case should be fastened a notice with four rules 
 
 * Made by the Cambridge Scientific Instrument Company. 
 
26 ELECTRICAL LABORATORY EQUIPMENT. 
 
 distinctly printed thereon for the guidance of the inex- 
 perienced : 
 
 1. Never put any object directly on the balance pans, but 
 always weigh it in a tared porcelain crucible, watch glass, or 
 on a disc of glazed writing paper. 
 
 2. Never add weights to or remove from the pans unless 
 the balance is clutched or off its knife edges. 
 
 3. Never leave the balance case open when making the 
 final adjustment of the rider. 
 
 4. Never omit to return the weights to their proper places 
 in the weight box as they are taken off the pan, or to 
 remove the balance from its knife edges when the weighing 
 is finished. 
 
 From time to time a careful adjustment of the balance 
 should be made by an experienced person. 
 
 The balance should be provided with a special short suspen- 
 sion scale pan called a specific gravity pan, and a glass stoppered 
 bottle should be kept by the case containing well-boiled 
 distilled water for use in taking specific gravities. 
 
 The object of which the specific gravity is required should 
 be suspended from the hook at the bottom of the short pan 
 and so hung by a fine hair taken from a horse's tail that it 
 hangs freely in the distilled water. The temperature of the 
 balance case should be taken at the same time. In 
 using the balance to determine the mean diameter of a wire 
 which is one of the operations the electrician may 
 occasionally have to perform the known length of wire 
 may be folded up into a suitable compact coil so that 
 it can be suspended in the water in a small beaker. Air 
 is then entangled in the meshes. This should be removed 
 by boiling the wire in the water and letting the wire cool 
 in the water and not removing it until the weight of the 
 mass hanging freely in the water has been taken. 
 
 In many operations in the electrical laboratory, such as in 
 meter testing, time has to be determined very accurately. 
 For this purpose a good stop-watch or working chronometer 
 
ELECTRICAL LABORATORY EQUIPMENT. 27 
 
 (preferably non-magnetic) is required. It is often possible 
 to purchase a second-hand ship's chronometer by a first-class 
 maker at a reduced price. If the chronometer is in good 
 order it may be sent to Kew Observatory or to Greenwich 
 to be rated and its true time and temperature rate errors 
 determined. The laboratory will then be provided with 
 a good timekeeper by which other watches may be 
 checked. 
 
 It is useless to make very careful observations of meter 
 errors or electrolytical experiments with a common watch 
 having a possible large rate error. Under the head of time 
 standards, reference may be made to the speed indicators and 
 speed counters which are in frequent use in the dynamo 
 room. A most useful form of speed counter is one supplied 
 by Messrs. O. Berend & Co., consisting of a revolution counter 
 of the usual kind combined with a stop-watch counting 
 seconds. The stop-watch is thrown into action by the act 
 of pressing the contact point against the end of the shaft, 
 the speed of which is required. The time and number of 
 revolutions in that time are thus recorded in the same 
 period. There are many forms of mechanical speed indica- 
 tors or tachometers which record directly on a dial the 
 revolutions per minute. None of these, however, are accurate 
 instruments or can be depended upon to give the actual 
 speed within 5 per cent. In careful dynamo and motor trials- 
 the actual revolutions per minute must always be taken by 
 one observer. 
 
 A very accurate speed indicator which can be practically 
 applied to dynamo machines is one depending on the centri- 
 fugal pressure of a revolving mass of liquid. A small, flat 
 cylindrical box has in it a small four-vane paddle-wheel r 
 the shaft coming out through a stuffing box or gland. The 
 paddle shaft is attached to the axis or shaft, the speed of 
 which is to be measured. The box is carried on an indepen- 
 dent support. Two pipes lead to this box, one entering near 
 the centre and one leaving near the circumference. The 
 
28 ELECTRICAL LABORATORY EQUIPMENT. 
 
 pipe to the centre communicates with a small reservoir of 
 coloured water. The pipe from the circumference leads to a 
 vertical glass stand-pipe which may be fixed at any distance 
 from the dynamo. When the paddle revolves it acts as a 
 centrifugal pump, and pumps water from the reservoir up the 
 stand-pipe. Equilibrium is established when the hydrostatic 
 pressure of the column of liquid in the stand-pipe just 
 balances the centrifugal pressure at the circumference of the 
 revolving mass of liquid in the paddle-box. The apparatus 
 can be calibrated once for all, and the true speeds, corre- 
 sponding to various heights of liquid in the stand-pipe, 
 marked on a wooden scale-board behind the pipe. An 
 arrangement of this kind attached to an alternator is very 
 useful in enabling the operator to set the machine to give a 
 certain frequency and to keep it at this frequency during 
 the test. 
 
 In cases where the above hydrostatic tachometer cannot 
 be fixed on account of the power required to drive it, 
 recourse must be had to a simple worm-wheel gearing by 
 which the speed of the shaft is made to turn a wheel at 
 one-tenth, one-hundredth, or less of its own speed. This 
 slow-revolving wheel can be made to close the circuit of a 
 single-stroke electric bell once every revolution, and thus 
 strike a blow at every ten or hundred revolutions of the 
 shaft. 
 
 By counting the bell strokes per minute or the time in 
 seconds extending over ten bell strokes the speed of the 
 shaft is ascertained. 
 
 3. The Principal Electrical Units and Standards. 
 
 Next in importance in the equipment of an electrical testing 
 room to the standards and instruments for making the 
 fundamental measurements of length, mass, and time come 
 the principal standards of electrical resistance, electromotive 
 force, and the means for recovering the standard or unit 
 electric current. 
 
ELECTRICAL LABORATORY EQUIPMENT. 20 
 
 These principal electrical units have been given legal 
 definition in Great Britain, and identical units have been 
 adopted in other countries. They are accordingly now 
 called the International units of resistance, electromotive 
 force and current, and are defined as follows : 
 
 The, electrical resistance offered to an unvarying electric 
 current by a column of pure mercury at the melting point 
 of ice, 106'3 centimetres long and weighing 14' 4 521 
 grammes, and of constant cross-section, is defined as the 
 unit of resistance, and is called one ohm. 
 
 The ohm so defined is intended to represent 10 9 absolute 
 electromagnetic units (C.G.S.) of resistance. 
 
 The unit electric current is defined by an operation of 
 electrolysis performed with a solution of a silver salt, as 
 follows : 
 
 The electric current of unvarying strength ivhich, when 
 passed through a neutral solution of nitrate of silver 
 containing 15 parts ~by weight of the salt to 85 of u -cater -, 
 using a silver anode and a platinum cathode, deposits silver 
 at the rate of G'001118 of a gramme per second, is defined 
 as the unit of electric current and is called one ampere* 
 
 The ampere so defined is intended to represent or repro- 
 duce 10- 1 of an absolute electromagnetic (C.G.S.) unit of 
 current. 
 
 From the unit of resistance and current is defined the unit 
 of electromotive force : 
 
 The unvarying electromotive force which creates in a 
 circuit having a resistance equal to one ohm an unvarying 
 current of one ampere is defined as the -unit of electro- 
 motive force, and is called one volt. 
 
 * See remarks on page 58 with reference to more recent determinations of 
 the Electro-chemical Equivalent of Silver. 
 
30 ELECTRICAL LABORATORY EQUIPMENT. 
 
 The electromotive force so defined is intended to represent 
 or reproduce 10 8 absolute electromagnetic units (C.G.S.) of 
 electromotive force. 
 
 The above units are defined and recovered in the laboratory 
 by the use of certain practical standards of resistance, electro- 
 motive force and appliances or processes, for electric current 
 measurement. - 
 
 A principal necessity in an electrical laboratory is, then, 
 the possession of satisfactory means for recovering or repro- 
 ducing the International ohm, the volt, and ampere. 
 
 Carefully constructed apparatus made for this purpose is 
 in use at the British Board of Trade Electrical Laboratory, 
 in accordance with the following regulations : 
 
 /. Standard of Electrical Resistance. 
 
 The standard of electrical resistance denominated one ohm 
 shall be and is the resistance between the copper terminals of 
 the instrument marked " Board of Trade Ohm Standard, 
 verified 1894," to the passage of an unvarying electrical 
 current when the coil of insulated wire forming part of the 
 aforesaid instrument and connected to the aforesaid terminals 
 is in all parts at a temperature of 15'4C. 
 
 The ohm so reproduced is generally called the Board of Trade Standard 
 ohm, to distinguish it from the theoretical or true ohm, which is defined as 10 9 
 centimetres per second in C.G.S. measure. The density of pure mercury at 
 0C. is 13'5956. Hence a volume of mercury having the form of a right 
 circular cylinder 106'3cms. in length and a mass of 14*4521 grammes, has a 
 <;ross- sectional area of one square millimetre or 0*01 sq. cm. The actual 
 principal standard ohm of the Board of Trade has been constructed to repre- 
 sent as nearly as possible the International ohm. This last may be otherwise 
 defined as the true electrical resistance at 0C. of a column of mercury 
 106'3cms. long and one square millimetre in section. Present knowledge 
 seems to show that the actual Board of Trade ohm standard is 0'02 per cent, 
 larger than the true ohm. 
 
 II. Standard of Electrical Current. 
 
 The standard of electrical current denominated one ampere 
 shall be and is the current which is passing in and through 
 the coils of wire forming part of the instrument marked 
 " Board of Trade Ampere Standard, verified 1894," when on 
 reversing the current in the fixed coils the change in the 
 
ELECTRICAL LABORATORY EQUIPMENT. 31 
 
 forces acting upon the suspended coil in its sighted position 
 is exactly balanced by the force exerted by gravity in West- 
 minster upon the iridio -platinum weight marked A and 
 forming part of the said instrument. 
 
 ///. Standard of Electrical Pressure. 
 
 The standard of electrical pressure denominated one volt 
 shall be and is one-hundredth part of the pressure which when 
 applied between the terminals forming part of the instrument 
 marked "Board of Trade Volt Standard, verified 1894," 
 causes that rotation of the suspended portion of the instru- 
 ment which is exactly measured by the coincidence of the 
 sighting wire with the image of the fiducial mark A before 
 and after application of the pressure and with that of the 
 fiducial mark B during the application of the pressure, these 
 images being produced by the suspended mirror and observed 
 by means of the eyepiece. 
 
 In the use of the above standards the limits of accuracy 
 attainable are as follows : 
 
 For the ohm, within one-hundredth part of 1 per cent. 
 For the ampere, within one-tenth part of 1 per cent. 
 For the volt, within one-tenth part of 1 per cent. 
 
 4. The Practical Standard of Electrical Resistance. 
 
 The practical standard or unit of electrical resistance is 
 officially denned as above-stated in terms of a certain length 
 and mass of pure mercury. Great labour has been expended, 
 both in England and in other countries, on the determination 
 of the absolute specific resistance or the resistivity of pure 
 mercury.* The following are some of the values which have 
 
 * See " The Specific Resistance of Mercury," Lord Rayleigh and Mrs. 
 Sidgwick, Phil. Trans. Roy. Soc., 1883, Part I., p. 173. Also R. T. Glaze- 
 brook, Phil. Mag., October, 1885. Also R. T. Glazebrook and T. C. Fitz- 
 patrick, " On the Specific Resistance of Mercury," Phil. Trans. Roy. Soc., 
 June, 1883; or Pros. R>y. S>c., Vol XLIV., No. 270; or The Electrician, 
 Vol. XXL, p. 533, 1888 ; Kohlrausch, Abhandt der K. Biyer Akad der Wiss, 
 Vol. XVI., Abth III., 1887 ; Mtscart, Nerville and Benoit, Jour nil de Phy- 
 sique, 188^ ; Sorecker, Wiedemann Ann%len, Vol. XXV., 1835 ; L. Loreaz, 
 Wie lemann Annalen, Vol. XXV., 1885; Rowland, Proc. British Association, 
 1887. Also Hutchinson and Wilkes, " John H opkin's University Circular," 
 May, 1889. Also " Recent Determinations of the Absolute Resistance of 
 Mercury," R. T. Glazebrook, The Electrician, Vol. XXV., pp. 543, 588, 1890. 
 Also see Prof. J. V. Jones, " On the Determination of the Specific Resistance 
 of Mercury in Absolute Measure," Phil. Trjtns. Roy. Soc., 1891, A, p. 2. 
 
32 ELECTRICAL LABORATORY EQUIPMENT. 
 
 been obtained for the resistivity of pure mercury at 0C. in 
 C.G.S. units per centimetre cube : 
 
 Observer. Date. Resistivity. 
 
 Lord Rayleigh and Mrs. Sidgwick 1883 ...... 94,133 
 
 Mascart, Nerville and Benoit 1884 94,096 
 
 Strecker 1885 94,057 
 
 L. Lorenz '..., 1885 94,108 
 
 Eowland 1887 94,072 
 
 Kohlrausch 1887 94,054 
 
 Glazebrook and Fitzpatrick 1888 94,074 
 
 Hutchinson and Wilkes '... 1890 94,064 
 
 J.V.Jones _, .. 1890 94,067 
 
 The present accepted value of the specific electrical resistance or resistivity 
 of pure mercury at 0C. is 94,070 C.G.S. units. Hence, a column of mercury 
 one metre in length and everywhere of 1 sq. millimetre in cross section has at 
 the temperature of melting ice a resistance of 0'94070 ohms, as far as the 
 mean of the best determinations will allow us to pronounce. 
 
 The following are the values obtained by the above observers 
 for the length in centimetres of a column of mercury 
 one square millimetre in section and having a resistance 
 of one ohm at 0C. : 
 
 Observer Length of column 
 
 in centimetres. 
 
 Lord Rayleigh and Mrs. Sidgwick 106'23 
 
 Mascart, Nerville and Benoit 106-33 
 
 Strecker 106'32 
 
 L.Lorenz 106'26 
 
 Rowland , ... 106'32 
 
 Kohlrausch 106'32 
 
 Glazebrook and Fitzpatrick 106'29 
 
 Hutchinson and Wilkes 106'34 
 
 J. V. Jones 106-31 
 
 The value now accepted for the length of the column of mercury one square 
 millimetre in section, which has at 0C a resistance of one International ohm, is 
 106-3 cms. 
 
 Continental physicists have devoted considerable time and 
 knowledge to the construction of primary and secondary 
 mercury resistances, consisting of mercury specially purified 
 and preserved in glass tubes of known dimensions, and 
 intended to practically realise the Board of Trade or Inter- 
 national definition of the practical unit of resistance. 
 
 For the most part, English investigators have given their 
 attention to the re-determination in absolute measure of 
 
ELECTRICAL LABORATORY EQUIPMENT, 33 
 
 the electrical resistance of certain wire standards, notably that 
 called the mean British Association unit, and hence from the 
 known resistivity of mercury proceeded to construct the 
 most closely approximate realisation of the ohm in wire 
 resistances.* 
 
 In the majority of instances the standards of resistance 
 used in an electrical laboratory are preserved in the form of 
 a uniform metallic wire drawn from an alloy of permanent 
 composition, and having a small change of resistance with 
 temperature. 
 
 a End of mercury tube, s Platinum wire electrode, g Platinum wire, 
 galvanometer wires. 
 
 FIG. 4. Glass Spherical Terminal Vessel of the Berlin Reichsanstalt Standard 
 
 Mercury Ohm. 
 
 Owing to its fragility and non-portability, a standard of 
 resistance consisting of mercury in a glass tube is not 
 likely to be constructed or used in any but a national standard- 
 ising laboratory. The construction of an original mercury- 
 in-glass resistance by which to reproduce the standard or 
 international ohm from its definition is a matter requiring 
 the highest skill and knowledge. Broadly speaking, it 
 consists in preparing and filling a glass tube of known 
 dimensions with pure mercury, the weight of which at 0C. is 
 
 * For additional information on the determination of resistance in absolute 
 measure see Chap. II., RESISTANCE MEASUREMENT ; also Tables at the end of 
 the same chapter. 
 
34 ELECTRICAL LABORATORY EQUIPMENT. 
 
 accurately determined.* This tube has its ends included in 
 large spherical vessels of mercury to which electrical connection 
 is made by means of platinum wires (see Fig. 4). In calculat- 
 ing the resistance of the column of mercury from the 
 dimensions of the tube and the resistivity of the mercury, a 
 correction has to be made in accordance with known 
 principles by which the effective length of the tube is taken 
 as greater than the actual length by 0'82 of the diameter of 
 the tube. For the full details of the construction of an 
 original mercury-in-glass standard of electrical resistance the 
 reader must be referred to the detailed accounts which have 
 been given of the production of the mercury standard set up 
 in the Physikalisch-Technische Keichsanstalt, in Berlin, and 
 the similar work carried out in Parisf by Benoit (see Fig. 5). 
 Mercury-in-glass standards are, however, used only as 
 original reference standards. The labour involved in their 
 construction and the necessity for great precautions in their 
 employment to reduce the whole mass of glass and mercury to 
 a known temperature before making a measurement with 
 them renders them unfit for ordinary laboratory use. For 
 all ordinary standards, multiples and submultiples of the ohm, 
 a wire resistance standard is much more convenient and is 
 usually employed. The two principal alloys which have been 
 found sufficiently permanent and of sufficiently small tem- 
 perature coefficient to use in the construction of such a wire 
 standard are a platinum-silver alloy and a ternary alloy of 
 copper-manganese and nickel called Manganin. There are 
 therefore, preserved in the various national electrical labora- 
 tories numerous copies of the ohm in the form of wire 
 standards, which are intended to have, as nearly as possible, 
 a resistance equal to the true ohm. 
 
 * For instructions for the purification of the mercury, see the Keichsanstalt 
 directions, as set forth by Dr. Jaeger, The Electrician, Vol. XXX.. p. 395. 
 
 f See The Electrician, Vol. XXXVII., p. 569, " On the Standard Mercury 
 Ohm of the Physikalisch-Technische Eeichsanstalt," by Dr. Jaeger, translated 
 from the Zeitschrift fur Instrumentenkunde, Vol. XVI., pp. 134-146, May, 
 1896. Also see Benoit, Comptes Rendus, Vol. XCIX, p.. 864, 1884. 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 35 
 
 D2 
 
36 ELECTRICAL LABORATORY EQUIPMENT. 
 
 The original British Association wire resistance standards 
 are in the custody of the Secretary of the British Associa- 
 tion Committee on Electrical Standards ; the Board of Trade 
 standards are kept at the Government Electrical Laboratory, 
 Whitehall, London ; and carefully constructed standards 
 of electrical resistance of the same character are preserved 
 at the Physikalisch-Technische Eeichsanstalt, in Berlin, 
 and at the Bureau International des Poids et Mesures, near 
 Paris. 
 
 FIG. 6. Secondary Standard Mercury Ohm. 
 
 Secondary standards or copies of the ohm, consisting of 
 mercury contained in tubes of Jena glass with platinum 
 electrodes sealed through the glass, have also been con- 
 structed at the Physikalisch-Technische Eeichsanstalt, in 
 Berlin (see Fig. 6) and by Benoit, in Paris. These secondary 
 mercury standards consist of u or W shaped tubes of glass 
 
ELECTRICAL LABORATORY EQUIPMENT. 37 
 
 most carefully filled in vacuo with mercury and then fixed in 
 a suitable case. 
 
 A comparison in 1892 and 1894 of all the mercury and 
 manganin copies of the ohm, made at the Eeichsanstalt in 
 Berlin, showed that these standards had remained constant in 
 resistance for two years to within one or two parts in one 
 hundred thousand. 
 
 A series of very elaborate experiments were made in the 
 year 1892 on the variation of resistance with temperature 
 of mercury-in-glass tubes between and 28C., and it was 
 found by Drs. Kreichgauer and Jaeger* that the resistance 
 at tPC. (K,) of mercury in Jena glass tubes can be expressed 
 between 0C. and 28C. as follows : 
 
 K, = K (1 + 0-000875 * + 0-00000125 1 2 ), 
 
 where E is the apparent resistance at 0C. 
 
 The true resistance of mercury (r t ) at tC. is related to its 
 resistance (r ) at 0C. by the relation 
 
 r t = r (1 + 0*0008827 Z + 0'00000126 * 2 ) 
 
 for a range of temperature between 0C. and 28C. These 
 values are not very different from those found by Benoit* 
 Guilleaume, and others in 1890.t 
 
 In spite, therefore, of the advantages gained by the use of 
 a, pure, unchangeable and fluid metal, such as mercury, as 
 against the supposed possible non-permanency of structure 
 of a solid metallic alloy, we have to take into account the 
 difficulties raised by the larger temperature coefficient of the 
 pure metal. 
 
 Experience is as yet wanting to show how far the various 
 alloys, now used for the resistance wires of standard 
 
 * See Wied. Ann., No. 1, 1893 ; also The Electrician, Vol. XXX. p. 567. 
 f Researches carried out in 1889-1890 by M. C. E. Guillaume, at the 
 Bureau International dea Poids et Mesures (see The Electrician, Vol. XXIX., 
 p. 553), gave by two determinations the true temperature variation of mercury 
 between 0C. and 61C. as follows : 
 
 (a) n = TO (1 + 0-00088745 1 + O'OOOOOIOISI 2 ) 
 (6) r t = ro ( 1 + 0-00088879 1 + 0*0000010022 1 2 ) 
 
38 ELECTRICAL LABORATORY EQUIPMENT. 
 
 coils, will remain absolutely unaltered over long periods 
 of time. It is certainly to a considerable degree dependent 
 on the manner in which the standards are made, and how 
 far they are allowed to undergo changes of temperature 
 in use. 
 
 In the employment of a wire of a metallic alloy as a 
 standard of electrical resistance there is always an element 
 of uncertainty as to the extent to which time may affect the 
 electrical qualities of the alloy. Experiments made by the 
 author in 1878 and 1879 on the original British Association 
 standard coils (fourteen in number) made of various alloys 
 showed that this fear was not altogether groundless, some 
 coils in the course of 14 or 15 years having certainly 
 changed in electrical resistance. Attention has, therefore, 
 been devoted to this question especially in connection with 
 the use of manganin and platinum-silver. In 1894 a 
 number of resistance coils of manganin (42 coils) and of 
 constantan (three coils) were tested at Berlin which had 
 been in use about three years. Of these 
 
 25 coils showed a variation of from O'OO to 0*01 per cent. 
 
 13 0-01 to 0-02 
 
 5 0-02 to 0-05 
 
 2 0-05 to 0-25 
 when re-compared with primary standards. 
 
 Confidence in the absolute permanency of electrical resist- 
 ance in the case of wire standards can hardly be said to have 
 been established beyond doubt. The balance of evidence 
 seems to show that for coils carefully made of well aged 
 manganin or platinum-silver it will not be serious. 
 
 One argument which has been used to support the conten- 
 tion that an ultimate standard should take the form of 
 mercury in glass is the assumed unalterable character of the 
 materials thus used. There is a possibility, however, that 
 the platinum electrodes may in time slightly dissolve and 
 thus contaminate the mercury. 
 
 The alloys which have been found practically satisfactory 
 
ELECTRICAL LABORATORY EQUIPMENT. 39 
 
 as materials to employ in the construction of wire-resistance 
 standards are 
 
 1. Platinum Silver. An alloy consisting of two parts of 
 silver and one of platinum. This alloy was originally recom- 
 mended by the Electrical Standards Committee of the 
 British Association. It has a resistivity of 25 to 30 microhms 
 per centimetre-cube and a temperature coefficient of nearly 
 0-0003, or nearly 0*03 per cent, per degree centigrade. 
 
 2. Manganin. This alloy is composed of 84 parts of 
 copper, 12 of manganese and 4 of nickel. Its electrical 
 properties and suitability for employment as an electrical 
 resistance material were made known by experiments con- 
 ducted in the Physikalisch-Technische Keichsanstalt in Berlin. 
 Its specific resistance is about 42 microhms per centimetre- 
 cube. Between 0C. and 10C. its temperature coefficient is 
 0*000025. At some temperature generally lying between 
 15C. and 30C. it has a nearly zero temperature coefficient, 
 and beyond about 30C. a negative temperature coefficient. 
 It has not nearly so great a thermo-electric power with 
 copper as German silver or platinoid. It must, however, 
 be aged for use as a resistance material by first heating it 
 to a temperature of 140C. for five or ten hours in an air 
 bath to prevent subsequent changes in resistance. It is 
 somewhat easily oxidised, and when used exposed to air must 
 be either gilt or varnished. It must not be soldered with 
 solder containing zinc.* 
 
 In the manufacture of commercial resistance coils not 
 intended as standards the following alloys are useful : 
 
 3. German Silver. This is an alloy of copper (50 to 66 
 parts), nickel (13 to 18 parts) and zinc (19 to 31 parts), and 
 is of somewhat variable composition in different specimens. 
 It is not suitable for the construction of other than commercial 
 
 * See Dr. St. Lindeck, The Electrician, Vol. XXX., p. 119, " On Alloys for 
 Resistance Coils." " On the Permanency of Manganin Resistances," see Prof. 
 W. E. Ayrton, The Electrician, Vol. XL., p. 39, also p. 227 ; also W. Watson, 
 Proc. Phys. Soe., Lend., Vol. XVI., p. 25 ; also Drs. Jaeger and St. Lindeck, 
 Science Abstracts, Vol. I., p. 336. 
 
40 ELECTRICAL LABORATORY EQUIPMENT. 
 
 resistances, on account of its rather large temperature coeffi- 
 cient (0-0004). It has a resistivity varying from 20 to 30 
 microhms per centimetre-cube. 
 
 4. Platinoid. An alloy resembling German silver in com- 
 position, but containing in addition about 2 per cent, of 
 tungsten. It has a smaller temperature coefficient (0*0003) 
 than German silver, and preserves a better surface in air. 
 In some specimens, however, time and temperature produce 
 a certain brittleness, and it seems to be attacked when 
 exposed in moist air containing carbonic acid."* It has in 
 some specimens as high a resistivity as manganin, viz., 40 to 
 45 microhms per centimetre-cube, but in other samples the 
 resistivity is as low as 30 microhms per centimetre-cube. 
 
 In addition to the above well-known alloys of definite 
 composition, a number of patented and commercial alloys, 
 the composition of which is not made public, are in use for 
 the construction of resistances in which a small temperature 
 coefficient is not of the greatest importance. These alloys 
 are employed in the manufacture of regulating resistances, 
 but are not used for resistance standards. Such alloys are 
 
 5. Rheostene. A nickel-steel alloy, having a resistivity of 
 about 77 microhms per centimetre-cube and a temperature 
 coefficient of 0-00119.f 
 
 6. Kruppin. An alloy having a resistivity of 83 microhms 
 per centimetre-cube and a temperature coefficient of 0'0013.J 
 
 7. Hadfield's Resista. An alloy having a resistivity of 76 
 microhms per centimetre-cube and a temperature coefficient 
 of 0-0011. 
 
 8. Eureka. An alloy having much the same electrical 
 qualities as platinoid, but not so liable to brittleness. Its 
 
 * See Mr. Hollo Appleyard, " On the Failure of German Silver and Platinum 
 Wires," The Electrician, Vol. XL., p. 227, 1897 ; also ibid. Electrical Review, 
 Vol. XLIL, p. 536 ; Science Abstracts, Vol. I., p. 412 ; Proc. Phys. Soc., Lond., 
 Vol. XVI., p. 17. 
 
 t See Van Aubel, The Electrician, Vol. XL., p. 315 ; or Science Abstracts, 
 Vol. I., p. 19. 
 
 t See The Electrician, Vol. XXXII., p. 351 ; also Electrotechnische Zeitschrift, 
 December 15, 1893 ; also see Van Aubel, The Electrician, Vol. XXXI1L, p. 122. 
 
ELECTRICAL LABORATORY EQUIPMENT. 41 
 
 chief mechanical fault is its considerable extensibility and 
 non-elastic yielding under tension. 
 
 9. Bruntoris Beacon Alloy. An alloy having a resistivity 
 of 60 to 80 microhms per centimetre-cube and a temperature 
 coefficient of 0'0007. 
 
 A large number of alloys have been found which have high 
 resistivity and small temperature coefficient, but in many 
 cases they have also poor mechanical qualities and are brittle, 
 or ill suited for being drawn into fine wire.* 
 
 As made at present, a standard of electrical resistance 
 consists of a carefully-drawn and well-annealed wire of 
 manganin or platinum-silver. If made of manganin it has to 
 be aged, as above described. This wire is then spun over 
 with two or three layers of white silk, and is wound on a 
 bobbin and preserved in a case in such manner that its 
 temperature can be controlled. 
 
 The actual resistance wire has to be attached at both ends 
 to terminal blocks or rods of copper, and has to be enclosed 
 for security in a metal case of some form or immersed in an 
 insulating oil. 
 
 Many English electricians are still somewhat sceptical 
 as to the permanency of manganin. t It has been stated that 
 all alloys containing zinc are liable to erratic changes of 
 resistance. Zinc solder or soft solder should never be em- 
 ployed in the construction of standard coils. Silver solder, 
 containing 75 per cent, of silver, should be used in soldering 
 manganin, and shellac varnish, and not paraffin wax, should 
 be used as an insulator. 
 
 * For further information see " Alloys for Resistance Standards," E. G. 
 Willyoung, Journal of Franklin Institute, or The Electrician, Vol. XXIX., 
 p. 277 ; " Experiments on Nickel Steel Alloys," C. E. Guillaume, The 
 Electrician, Vol. XL., p. 348; "The Composition of Various Alloys for 
 Resistance Coils," Drs. Feussner and St. Lindeck, The Electrician, VoLXXVL, 
 p. 493. Also The Electrician, Vol. XXX., p. 119. 
 
 t In all these more or less complicated alloys there may be variations of 
 electrical and mechanical qualities caused by irregularities in manufacture. 
 It is not unusual to find samples of German silver and platinoid, and perhaps 
 manganin, which seem quite inferior to the general run of specimens of these 
 particular materials. 
 
42 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 The authorities of the Berlin Eeichsanstalt have devoted 
 great attention to the consideration of the best form to give 
 to a wire standard of electrical resistance, and the following 
 is a description of the form adopted at present (1900). A 
 section of the standard is shown in Fig. 7. 
 
 FIG. 7. Berlin Keichsanstalt Wire Standard of Electrical Resistance or Standard Ohm.* 
 
 The resistance wire is a carefully insulated wire wound on 
 a brass cylinder, the wire being doubled on itself to annul 
 inductance as much as possible. The wire is laid on in a 
 single layer. The ends of the wire are silver soldered to 
 square nuts, which are in turn soft soldered to heavy copper 
 terminal rods. The final adjustment of resistance is made by 
 shortening a much finer parallel wire. Thus the 0*1 ohm 
 standard consists of two wires in parallel : one the principal 
 
ELECTRICAL LABORATORY EQUIPMENT. 43- 
 
 wire, and another wire one-tenth of the section and ten times 
 as long as the first. Hence a change in length of one metre 
 of the fine wire is equivalent to only one millimetre change 
 in length of the principal wire. The coil so wound and 
 adjusted is hung in a bath of paraffin oil and contact is made 
 with the copper leads of the coil by means of the mercury 
 cups. When in use the oil is kept well stirred by a stirrer 
 driven by a small electromotor. In preparing the coil the 
 silk-covered resistance wires are wound on the brass core 
 and made to adhere to it by melted shellac. The coil 
 is then heated for ten hours to 140C. This baking not 
 only gives the coil the necessary insulation from layer to 
 layer (which is of the order of a million megohms), but 
 ages the manganin and prevents subsequent secular change 
 in resistance. 
 
 In the use of a coil of the above kind as a standard ot 
 resistance it is desirable, if extreme accuracy of comparison 
 is required, that the power wasted in the resistance coil shaE 
 not exceed one watt. The oil in which the coil is immersed 
 must be kept in thorough circulation, preferably by means of 
 a stirrer driven by a small electromotor, when a measurement 
 of resistance is being made. For further and fuller information 
 on the details of the construction and mode of use of the Keich- 
 sanstalt standard wire coils, the reader is referred to a paper 
 by Drs. K. Feussner and St. Lindeck in the Zeitschrift fur 
 Instrumentenkunde, November and December, 1895.* 
 
 In addition to the principal standards of resistance in a 
 laboratory, which must always be carefully used, it is neces- 
 sary to possess certain working standards for general use. A 
 convenient form for these secondary reference standards ha& 
 been designed by the author.! 
 
 This laboratory standard resistance coil is made as follows: 
 The brass case or shell which contains the coil is in the form 
 
 * See The Electrician, Vol. XXXVI., p. 509, 1896 ; also Drs. Jaeger and 
 K. Kahle, Wied. Ann., No. 3, 1898 ; The Electrician, Vol. XL., p. 847 ; Science 
 Abstracts, Vol. I., p. 412. 
 
 f See Phil. Mag., January, 1889. 
 
44 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 of a ring (see Fig. 8). This ring consists of a pair of square- 
 sectioned circular troughs provided with flanges which can 
 be screwed together so as to form a square-sectioned, hollow, 
 circular ring. 
 
ELECTRICAL LABORATORY EQUIPMENT. 45 
 
 From this ring proceed upwards two brass tubes about five 
 or six inches in length. Down these brass tubes pass the 
 copper electrodes or rods, and these rods are insulated from 
 the tubes at the top and bottom by ebonite insulators. The 
 insulator at the bottom of the tube, where it enters the ring, 
 is a simple collar, that at the top has the form of a funnel 
 corrugated on its outer surface. The use of this funnel will 
 be referred to presently. The actual resistance-coil is a 
 length of platinum-silver wire three-fold silk-covered. The 
 silk- covered wire is first baked above 100C. to dry it com- 
 pletely, and then immersed in melted ozokerit, or better, in 
 shellac varnish made up with absolute alcohol. 
 
 The so insulated wire is cut about the proper length and 
 laid double or folded once upon itself, and then rolled up on 
 a wooden mandril so as to form a circular coil of diameter 
 suitable to drop into the hollow of the brass ring. The wire 
 being wound double, its coefficient of self-induction is 
 rendered very small, This coil of wire is then wrapped over 
 with white silk and again dipped in melted ozokerit. The 
 ends of the wire are next soldered into nicks in the ends of 
 the copper rods, they having been previously pushed a little 
 way through the brass tubes for the purpose, and afterwards 
 drawn back into proper positions. The coil is then packed 
 into the circular groove, and, after adjusting the resistance to 
 the proper value, the bottom half of the ring is placed over it. 
 A thin washer of indiarubber is inserted between the flanges, 
 and the whole screwed tightly together. The resistance-coil 
 is thus enclosed in a thin ring of metal, and can be placed 
 wholly below the surface of water or ice. In order to test 
 the tightness of the joints, a little test-pipe is provided on the 
 upper surface of the ring. By placing the ring coil below 
 water and blowing into the test-pipe, the good fitting of the 
 joints can be assured. The aperture of this test-pipe is after- 
 wards closed by solder or a screw (see Fig. 8). 
 
 Apart from the insulation of the coil itself, it will be appa- 
 rent that the insulation is limited by the amount of insulation 
 resistance secured at the ebonite insulators at the top end of 
 the brass tubes. Any leakage from the copper rod over 
 these insulators to the brass tube destroys to that extent the 
 insulation of the coil. The object of making these external 
 insulators funnel-shaped is to prevent surface-creeping due 
 to condensation of moisture on them, by placing paraffin oil 
 or insulating liquid in the funnel-shaped cavity. When 
 
46 ELECTRICAL LABORATORY EQUIPMENT. 
 
 this is done, even if dew should collect on the outer 
 surface of the funnels, the inner surface is kept dry by 
 the paraffin oil placed in them, the action being the same 
 as that in the well-known Johnson and Phillips fluid 
 insulator. 
 
 The ring coils when in use are placed in rather shallow 
 zinc troughs, which can be filled with water, and are closed 
 with a wooden lid. When so placed the whole of the 
 actual coil or resistance part is down beneath the liquid at 
 one level, where the temperature can be accurately ascer- 
 tained. The insulators and point of emergence of the 
 electrodes are away up above the level of the water, and well 
 protected from any action which might permit of leakage 
 over them. The large metallic mass of the ring assists in 
 bringing the resistance-coil quickly back to the tempera- 
 ture of the surrounding water, and the coil therefore 
 "tests quickly." In all other respects these standards of 
 resistance are as compact and portable, and not more 
 -expensive to construct, than the old form of B.A. standard, 
 whilst obviating the difficulties which present themselves 
 in the use of the old form in very accurate comparisons of 
 resistance. 
 
 It is quite possible to have two or more coils of wire inside 
 the same ring, each coil having its separate pair of electrodes. 
 A useful coil of this form can be made up containing 1, 10, 
 and 100 ohms, so that comparisons can be quickly made at 
 the same temperature with these three multiples of the same 
 unit of resistance. 
 
 In an ordinary electrical laboratory the electrician will not 
 often be called upon to make and adjust the principal stan- 
 dards of resistance himself. This is an operation requiring 
 great care and patience and some skill. Suffice it to say that 
 one of the best means of making the final adjustment of 
 resistance coils to an exact value is to wind on the coil two 
 insulated wires of the same material in parallel. One of 
 these is the principal resistance wire, and the other is a 
 much longer wire of smaller section, and is the adjusting 
 wire. The principal wire is, in the first instance, cut to a 
 length which shall be greater than the resistance required. 
 The following table may serve as a rough guide in making 
 
ELECTRICAL LABORATORY EQUIPMENT. 47 
 
 resistance coils of platinum silver, but a margin should 
 always be allowed in cutting off wire : 
 
 To make a resis- Take platinum-silver wire of 
 
 tance coil of Length. Gauge in S.W.G. 
 
 1 ohm 9ft. No. 22 = 0-036in. dia. 
 
 10 ohms 42-5ft. No. 24 = 0-025in. dia. 
 
 100 ohms 133ft. No. 30 = 0-01 4in. dia. 
 
 1,000 ohms 675ft. No. 34 = 0-010in. dia. 
 
 The principal wire being roughly adjusted to a resistance 
 a little greater than the resistance desired, it is joined in 
 parallel with a wire of one-tenth its diameter and ten times 
 the length. The final adjustment is then made by lengthen- 
 ing or shortening this finer wire until the two wires in 
 parallel have exactly the required resistance. The resistance 
 wires are wound doubled or non-inductively on themselves 
 on a metallic core. The greatest care must be taken in 
 insulating the different turns of wire from each other and 
 from the . core. The wire should be double -covered with 
 white silk and never be touched with the moist hand. 
 When the coil is prepared as above described it must be 
 placed for use in a vessel of water or paraffin which is kept 
 well stirred and the temperature of which can be taken with 
 a correct thermometer. In all very accurate measurements 
 it is better to work with the coils in melting ice. The true 
 temperature of the wire is then known with a considerable 
 degree of exactness if the coil is allowed to remain for a 
 sufficient time in the melting ice to arrive exactly at 0C. 
 The source of error to be avoided is a difference in tempera- 
 ture between different parts of the resistance wire and 
 between the wire and the external bath. In making a 
 resistance measurement sufficient time must always be 
 allowed to elapse between two measurements to permit the 
 coil to reach its original and desired temperature. The only 
 method of making such a measurement with certainty as to 
 the temperature of the wire is to make the resistance 
 measurement after keeping the coils for 12 hours immersed 
 in melting ice. 
 
48 ELECTRICAL LABORATORY EQUIPMENT. 
 
 In consequence of the slight uncertainty which still exists 
 as to the true value of the various practical standards of re- 
 sistance, it has been proposed by Prof. J. Viriamu Jones that 
 the ultimate standard of resistance shall not be embodied in 
 the form of a wire, but shall be recovered when required by an 
 absolute determination (see The Electrician, Vol. XXV., p. 552; 
 also Proc. British Assoc., Leeds, 1890, " Suggestions Towards 
 the Determination of the Ohm,"). With this object he has 
 perfected the Lorenz apparatus for the absolute determination 
 of resistance. His proposal is that such an apparatus shall be 
 set up in national standardising laboratories, and that when 
 it is necessary to evaluate a secondary standard of resistance 
 this shall be done by an absolute determination of the same. 
 In the Lorenz apparatus the essential portion consists of a 
 metallic disc revolving in the interior of a carefully arranged 
 spiral coil of wire. If an electric current is sent through the 
 coil, and if the disc is set in revolution, the disc becomes the 
 seat of an electromotive force. This electromotive force may 
 be balanced against the fall of potential down a certain 
 resistance in circuit with the coil. When once the dimen- 
 sions of the apparatus have been determined, the actual 
 observations necessary to obtain the absolute value of the 
 resistance of the inserted conductor are reduced to the deter- 
 mination of the speed of revolution of the disc, and the 
 absolute value of the resistance is given as the product of a 
 calculated coefficient of mutual induction and an observed 
 number of revolutions per second. Since the things actually 
 observed are merely a speed and the absence of a current in 
 a circuit, extreme accuracy of measurement can be obtained. 
 
 These necessary measurements can be carried out with a 
 very high degree of precision, and with a well-made Lorenz 
 apparatus it is possible to determine the value of a resistance 
 of the order of an ohm with an accuracy of one part in 10,000.* 
 
 * For a full description of the Lorenz apparatus the reader is referred to a 
 lecture given by Prof. J. V. Jones at the Royal Institution, May 24, 1895, 
 see The Electrician, Vol. XXXV., pp. 231 and 253 ; also the Proceedings of 
 the Royal Institution, Vol. XIV., p. 601. Also to an account of " A Deter- 
 
ELECTRICAL LABORATORY EQUIPMENT. 49 
 
 5. Current-Carrying Standard Resistances. In addi- 
 tion to resistance coils, which are intended to be used merely 
 with very small currents passing through them, the electrical 
 laboratory must be provided with a graduated series of 
 resistances capable of carrying or passing large currents and 
 for use in measurements in which the fall in potential down 
 a conductor of known resistance is made to yield a know- 
 ledge of the current passing through a conductor in series 
 with the resistance. 
 
 These resistances are called Current Resistances, or some- 
 times Mho Standards. Eesistances of the above kind are 
 now made by instrument makers in the form of thick 
 
 FIG. 9. Standard O't Ohm Resistance to carry 10 amperes. 
 
 manganin wires in well- ventilated brass cases (see Fig. 9), 
 and in the form of manganin strip soldered to end blocks 
 (see Figs. 10 and 11), or in the shape of tubes of manganin 
 with end terminals (see Fig. 12). The great aim in the con- 
 struction of these resistances for large currents is to afford 
 
 urination of the Ohm made in Testing .the Lorenz Apparatus of the McGill 
 University, Montreal," Profs. Ayrton and Jones, see The Electrician, Vol. XL., 
 p. 150, 1897. These experiments seemed to show that the Board of Trade 
 standard ohm is between two and three parts in 10,000 larger than the true 
 ohm. In other words, it is 0'02 per cent, greater than 10 9 centimetres per 
 second. (See Prof. Ayrton on " Our Knowledge of the Value of a Resistance," 
 The Electrician, Vol. XL., pp. 133 and 149.) See also Chapter II., RESISTANCE 
 MEASUREMENT. 
 
50 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 sufficient surface to carry off the heat generated by the 
 current, either by air convection or by radiation. 
 
 With the object of obtaining great current-carrying 
 capacity, some makers, such as Mr. Crompton, make these 
 
 FIG. 10. Bare Metal Strip Resistance for Currents up to 1,500 amperes. 
 
 FIG. 11. Metal Strip O'l Ohm Resistance for Currents up to 15 amperes. 
 
 standards in the form of tubes of manganin through which 
 water can be passed, and by this means they construct 
 standards of resistances capable of carrying without sensible 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 51 
 
 heating very large currents. In Fig. 12 is shown a tubular 
 resistance made to carry 1,500 amperes. The resistance is 
 O'OOl of an ohm. Hence the fall in potential down it at full 
 
 FIG. 12. Crompton Water-Tube Low-Resistance Standard. 
 
52 ELECTRICAL LABORATORY EQUIPMENT. 
 
 load is 1-5 volts. The water used for cooling is circulated 
 through the pipe by a rubber hose, and the current density 
 in the metal rises to 13,000 to 20,000 amperes per square 
 inch without risk. The potential measuring connections are 
 attached to terminals on clamps which are fixed at such 
 distances as to define exactly the resistance required. 
 
 These current-carrying resistances are always provided with 
 two pairs of terminals, one pair called the current terminals, 
 by which the current is led in and out, and another pair 
 called the potential terminals, between which the resistance 
 has its stated value. 
 
 A most essential possession in an electrical laboratory or 
 testing room is a set of low resistances of the following 
 capacity : 
 
 1. One-ohm resistance, carrying one ampere. 
 
 2. One-tenth of an ohm resistance, carrying 10 amperes. 
 
 3. One-hundredth of an ohm resistance, carrying 100 
 
 amperes. 
 
 4. One-thousandth of an ohm resistance, carrying 1,000 
 
 amperes. 
 
 These resistances should be of manganin strip or wire, 
 the surface being gilt to prevent oxidation and the surface 
 of such sufficient area that the resistances do not become 
 heated beyond 60C. when kept in circuit for some time. 
 
 In using them the electrician may either take their value 
 for granted from the reputation of the maker, or, if possible, 
 and far better, get them checked by some authority. In 
 default he may proceed ab initio, and construct for himself 
 low-resistance standards by means of the resistance standards 
 prepared for use in Wheatstone bridge measurements. 
 
 The method which may be adopted of creating a standard 
 of low resistance, which shall have approximately a defined 
 value, is as follows : Let 1, 2, 3, &c. (Fig. 13), be mercury 
 cups, connected, as shown, by resistance coils r v r 2 , &c, Let 
 there be an even number of mercury cups on each side, and 
 therefore an odd number of resistance coils, Arranged in 
 
ELECTRICAL LABORATORY EQUIPMENT. 53 
 
 this way, the coils r v r 2 , &c., are in series. If r be the resis- 
 tance of each coil such as r lt and there be n coils, the total 
 resistance in series will be n r. Let two copper combs, A and 
 B, made of very thick high-conductivity copper rod, be pro- 
 vided with claws, which enable them to connect together the 
 mercury cups on each side when dipped into them. Suppose 
 the cups 1, 3, 5, &c., connected on one side, and the cups 
 2, 4, 6, &c., on the other, then the coils r 1} r 2 , &c., will now be 
 in parallel between A and B, and the joint resistance between 
 
 A and B will be . The mercury cups must be made of 
 copper amalgamated in the interior, and the ends of the comb 
 
 FIG. 13. 
 
 terminals be pressed down very strongly on the bottom of 
 these cups when the resistances are thrown into parallel. 
 
 If E be the joint resistance of the n coils in series, then ^ 
 
 fi 
 
 will be the joint resistance in parallel. If, however, the 
 resistance of each coil is different, then, if &i,& 2 , &c., be 
 the conductivities of each coil in mhos that is to say, 
 the reciprocal of its resistance measured in ohms the 
 total conductivity K, when arranged in parallel, will be 
 = K, or the total parallel mho conductivity is 
 
54 ELECTRICAL LABORATORY EQUIPMENT. 
 
 the sum of the separate mho conductivities of each coil. 
 Suppose that a current is passed through such resistances in 
 parallel, it distributes itself between the coils, and, if we 
 know the conductivity of each coil, and can measure the 
 difference of potentials between A and B, we have at once 
 the means of calculating the current. 
 
 Moreover, we can discover whether the initial resistance 
 of the combined resistance has appreciably changed by the 
 heat due to the passage of the current, for, by raising the forks 
 out from the mercury cups, the n resistances, which were a 
 moment ago in parallel, are now in series, and the actual 
 change in resistance of the n in series is n 2 times the actual 
 change in resistance of the n in parallel. We get, therefore, 
 a resistance of considerable, or, at least, not very small magni- 
 tude to determine, and by performing the operation of 
 throwing the coils into series and measuring their resistance 
 on a bridge we can determine within a small amount any 
 change in resistance due to heat generated in any time in the 
 conductors. Hence, generally speaking, the method consists 
 in providing an arrangement by which resistances can be 
 arranged in parallel and traversed by the current to be 
 measured, and then thrown into series to determine what 
 change, if any, the conductor has experienced in resistance, 
 and calculating from this change, when measured in series, 
 the change when arranged in parallel. 
 
 Accordingly, the procedure is as follows : Suppose it is 
 desired to construct a resistance of one-tenth of an ohm and 
 capable of carrying ten amperes. The first step is to 
 measure on the Wheatstone bridge, as subsequently ex- 
 plained, the resistance of a series of wires, and to make them 
 exactly equal. For this purpose select platinoid wire No. 18 
 S.W.G. and measure the resistance of any length of this wire 
 on the bridge. Then calculate the length of the wire, which 
 will have a resistance of slightly more than one ohm. 
 Prepare in this way ten similar wires. Each platinoid wire 
 is then silver soldered to a square nut of well tinned copper, 
 
ELECTRICAL LABORATORY EQUIPMENT. 55 
 
 which is drilled with a central hole. The resistance of each 
 wire is then made exactly the same by rubbing down with 
 glass-paper all the wires until they are exactly equal in 
 resistance to each other and to the highest in resistance of 
 the ten. This process needs much care and patience. The 
 ten wires having been made absolutely equal in resistance 
 at the same temperature, the true resistance of each one is 
 determined. The ten wires are then joined in parallel by 
 passing a screw through the holes in the ten terminal nuts, 
 and by heating these tinned blocks to the melting point of 
 tin, they are compressed and soldered together into one mass. 
 We have then a resistance of one-tenth of an ohm con- 
 structed of ten one-ohm wires in parallel. A potential wire 
 or terminal is then soldered to the terminal blocks as near 
 as possible to the place of contact of the resistance wires and 
 the terminal blocks. 
 
 A more careful comparison must then be made between 
 this one-tenth ohm standard and a one-ohm standard coil by 
 means of a low resistance bridge or potentiometer, as sub- 
 sequently described, and the nearest value determined for the 
 resistance at a known temperature of the one-tenth ohm 
 standard. A much more tedious process of the same nature 
 would result in the construction of a one-hundredth of an 
 ohm standard. When once original standards of low resis- 
 tance have been standardised or measured by means of the 
 Lorenz apparatus, it is comparatively an easy matter to copy 
 or reproduce them.* 
 
 The minimum outfit of carefully standardised resistances 
 which any electrical laboratory should possess is as follows : 
 
 1. A 100-ohm standard. 
 
 2. A ten-ohm standard. 
 
 3. A one-ohm standard. 
 
 the above to be coils suitable for comparison on a 
 
 * For determinations of the value of low resistances by the Lorenz apparatus 
 see Prof. J. Viriamu Jones " On Standards of Low Resistance," The Electrician, 
 Vol. XXXI., p. 620. 
 
56 ELECTRICAL LABORATORY EQUIPMENT. 
 
 Wheatstone Bridge, but not necessarily adapted for carrying 
 large currents. In addition should be provided : 
 
 4. A one-ohm standard, capable of carrying one ampere. 
 
 5. A one-tenth of an ohm standard, for carrying up to ten 
 
 amperes. 
 
 6. A one-hundredth of an ohm standard, capable of carrying 
 
 up to 100 amperes. 
 
 7. A one-thousandth of an ohm standard, capable of carry- 
 
 ing up to 1,000 amperes. 
 
 The last four coils or strips must be suitable for measurement 
 of current by the fall of potential method, and have potential 
 terminals attached to them. 
 
 In addition to resistances of the above kind, for much 
 work, especially on insulators, it is necessary that the 
 laboratory should possess certain high resistance standards 
 A standard wire resistance megohm is, however, a somewhat 
 expensive article. Many cheap substitutes have been pro- 
 posed in the form of carbon or other admixtures of semi- 
 conductors. For really careful work nothing, however, is 
 satisfactory except a high resistance wire standard, preferably 
 of manganin in the form of ten coils each having a resistance 
 of 100,000 ohms. In the case of these high resistance 
 standards the insulation of the separate coils and of their 
 terminals becomes a very important matter. The coil 
 terminals must be carried on tall corrugated ebonite pillars, 
 and these must be placed a considerable distance apart on an 
 ebonite base. A standard megohm box of this kind must be 
 carefully protected from light and dust. Exposure to light 
 destroys the surface insulation of ebonite.* The coils 
 themselves must be insulated with well-baked solid shellac, 
 and be suspended or carried on glass rods, also varnished. 
 or covered with well-baked shellac. 
 
 * The action of light and air oxidises the sulphur in the ebonite and 
 produces a conducting layer, probably of sulphuric acid. This can be 
 removed by washing with a dilute solution of soda, then thoroughly drying 
 the surface and rubbing with a clean rag moistened with perfectly dry 
 paraffin oil. 
 
ELECTRICAL LABORATORY EQUIPMENT. 57 
 
 6. The Recovery of the Standard or Unit Electric 
 Current. We proceed, in the next place, to consider the 
 means and instruments necessary to recover the standard 
 electric current, and to compare currents with the autho- 
 rised unit of electric current, called the ampere. The 
 practical and legal definition of the ampere or unit of 
 current is based upon the power of the current to cause 
 electrolytic decomposition in a standard electrolyte, such as 
 a neutral solution of the nitrate of silver when electrolysed 
 with a silver anode and a platinum cathode. The British 
 Board of Trade have issued a specification for the electrolytic 
 measurement of unvarying electric currents, and the arrange- 
 ment of apparatus and process is as follows : 
 
 BRITISH BOARD OF TRADE SPECIFICATION FOR MEASURING ELECTRIC 
 
 CURRENT. 
 
 In the following specification the term silver voltameter means the 
 arrangement of apparatus by means of -which an electric current is passed 
 through a solution of nitrate of silver in water. The silver voltameter 
 measures the total electrical quantity which has passed during the time of 
 the experiment, and by noting this time the time average of the current, or 
 if the current has been kept constant, the current itself can be deduced. 
 
 In employing the silver voltameter to measure currents of about one 
 ampere the following arrangements should be adopted. The cathode on 
 which the silver is to be deposited should take the form of a platinum bowl 
 not less than 10cm. in diameter, and from 4cm. to 5cm. in depth. 
 
 The anode should be a plate of pure silver some 30 sq. cm. in area and 2mm. 
 or 3mm. in thickness. 
 
 This is supported horizontally in the liquid near the top of the solution by 
 a platinum wire passed through holes in the plate at opposite corners. To 
 prevent the disintegrated silver which is formed on the anode from falling 
 on to the cathode, the anode should be wrapped round with pure filter paper, 
 secured at the back with sealing wax. 
 
 The liquid should consist of a neutral solution of pure silver nitrate, 
 containing about 15 parts by weight of the nitrate to 85 parts of water. 
 
 The resistance of the voltameter changes somewhat as the current passes. 
 To prevent these changes having too great an effect on the current, some 
 resistance besides that of the voltameter should be inserted in the circuit. 
 The total metallic resistance of the circuit should not be less than 10 ohms. 
 
 Method of Making a Measurement. 
 
 The platinum bowl is washed with nitric acid and distilled water, dried by 
 heat, and then left to cool in a desiccator. When thoroughly dry it is weighed 
 carefully. 
 
58 ELECTRICAL LABORATORY EQUIPMENT. 
 
 It is nearly filled with the solution, and connected to the rest of the circuit 
 by being placed on a clean copper support to which a binding screw is attached. 
 This copper support must be insulated. 
 
 The anode is then immersed in the solution so as to be well covered by it and 
 supported hi that position ; the connections to the rest of the circuit are made. 
 
 Contact is made at the key, noting the time of contact. The current is 
 allowed to pass for not less than half-an-hour, and the time at which contact 
 is broken is observed. Care must be taken that the clock used is keeping 
 correct time during this interval. 
 
 The solution is now removed from the bowl, and the deposit is washed with 
 distilled water and left to soak for at least six hours. It is then rinsed 
 successively with distilled water and absolute alcohol and dried in a hot-air 
 bath at a temperature of about 160C. After cooling in a desiccator it is 
 weighed again. The gain in weight gives the silver deposited. 
 
 To find the current in amperes, this weight, expressed in grammes, must be 
 divided by the number of seconds during which the current has been passed, 
 and by O'OOlllS. 
 
 There seems reason to believe that the above officially- 
 adopted value of the electrochemical equivalent of silver is 
 about one part in a thousand too small, if the ampere so denned 
 is to represent one-tenth of the absolute C.G.S. unit of current. 
 
 A careful discussion of the different values obtained for the 
 mechanical equivalent of heat (=J= Joule's equivalent) has 
 shown that the best results obtained by the heating of water 
 electrically are in excess of the best results obtained by 
 mechanical friction methods by about one part in 400. Thus 
 at 191 by the Paris nitrogen thermometer the values of J 
 are as follows per degree Fahr. : 
 
 By Mechanical Methods. 
 
 Joule 774 foot-pounds. 
 
 Rowland .. .. 776*1 
 
 By Electrical Methods. 
 
 Griffiths 7791 foot-pounds. 
 
 Schuster & Gannon 778'5 
 
 More recent determinations of the electro-chemical equiva- 
 lent of silver gives the value 0*0011192 grammes per ampere- 
 second (see Electrical Review, September 30, 1898) and the 
 adoption of this constant instead of 0*001118 removes nearly 
 all difference between the value of J when determined 
 mechanically and electrically. 
 
 The result of the measurement carried out as above specified 
 will be the time-average of the current if during the interval 
 the current has varied. 
 
ELECTRICAL LABORATORY EQUIPMENT. 59 
 
 Iii determining by this method the constant of an instru- 
 ment the current shall be kept as nearly constant as possible, 
 and the readings of the instrument observed at frequent 
 intervals of time. These observations give a curve from 
 which the reading corresponding to the mean current (time- 
 average of the current) can be found. The current, as 
 calculated by the voltameter, corresponds to this reading. 
 
 The every-day practical measurement of current is best 
 performed by some instrument which gives not merely the 
 time-average, but the precise value at any instant. Such in- 
 struments are called amperemeters or ammeters. Of the many 
 principles employed in the construction of amperemeters 
 none is so well adapted to the construction of a standard 
 instrument as the utilisation of the fact that forces of 
 attraction and repulsion exist between conductors carrying 
 electric currents. These instruments, which are variously 
 called electro-dynamometers, current balances or ampere 
 balances, may all be said to be modifications of the electro- 
 dynamometer, which was first described by Weber in his 
 " Electro-dynamische Maasbestimmungen " (Leipsic, 1846). 
 The principle on which these instruments act was made known, 
 however, twenty-five years previously. On September 25, 1820, 
 Ampere announced to the Academy of Sciences in France 
 that he had discovered the existence of forces of attraction 
 and repulsion between conductors of non-magnetic material 
 traversed by electric currents. The experiments of Ampere 
 and the subsequent elaborate researches of Weber (W. Weber, 
 " Electro-dynamische Maasbestimmungen," Thl. I., s. 10, 
 1846, Auszug in Pogg. Annal., Bd. LXXIIL, s. 193) estab- 
 lished the fact that, if there be a fixed and a movable 
 conductor in the neighbourhood of each other, traversed by 
 the same electric current, there will in general be a 
 mechanical stress brought into existence, which will tend 
 to displace the movable conductor and to bring it into a 
 position relatively to the fixed conductor in which the 
 mechanical stress between them is zero. The mutual force 
 
60 ELECTRICAL LABORATORY EQUIPMENT. 
 
 or stress between these mutually influencing portions of the 
 same circuit is, in any given position, proportional to the 
 square of the strength of the current traversing the two 
 portions of the circuit. In the ampere balances invented by 
 Lord Kelvin this stress is measured by comparing it with or 
 balancing it against the weight of certain standard masses ; 
 in other words, the electro-dynamic stress between electric 
 circuits is compared with the gravitation stress on a given 
 mass. 
 
 The great difficulty which has hitherto presented itself to 
 all who have attempted to design instruments on the electro- 
 dynamometer principle for any but very small currents has 
 been that of getting the current into and out of the movable 
 conductor. The device on which most experimentalists have 
 fallen back is that adopted by Ampere himself, viz., to use 
 mercury cups as a means of constructing a flexible and 
 conducting joint. The use of mercury is open to many 
 objections. The surface gradually becomes oxidised, the 
 cups must be filled and emptied each time the instrument 
 has to be transported, and the joint with impure mercury is 
 by no means exceedingly flexible. The great novelty in the 
 ampere balances of Lord Kelvin was the invention of a joint 
 or electric coupling which is excessively flexible, and at the 
 same time capable of being constructed so as to carry with 
 safety any current desired. This was accomplished by the 
 introduction of a device which may be called a metallic 
 ligament. The general principle of its construction, and the 
 mode of rendering a circuit freely movable, yet accessible 
 to a large current, may be described as follows : Let A A 
 (Fig. 14) be a pair of semi-cylindrical fixed trunnions, which 
 are carried on some form of supporting frame and held with 
 the flat sides downwards. Let B B be two similar trunnions, 
 which project out from the sides of two strips, connecting 
 together a pair of rings C C. The pair of rings and the 
 connecting strips constitute the circuit which is to be 
 rendered movable. A current entering by the trunnion 
 
ELECTRICAL LABORATORY EQUIPMENT. 61 
 
 -f B flows round the two halves of the circuit, as shown by 
 the arrows, and emerges at the trunnion B. In Fig. 14 
 the current is shown, for simplicity, dividing round the 
 two rings. The circuit should in reality be shown so 
 that the current goes round both rings in series in figure 
 of eight fashion. This is the case in all but the kilo- and 
 hecto-ampere balances, in which the current divides round 
 the ring, as shown in Fig. 14. To the upper surface of the 
 upper trunnion are soldered a very large number of exceed- 
 ingly fine copper wires (No. 60 B.W.G.), which are laid close 
 together. These wires are also soldered to the under surface 
 of the lower trunnion. The movable circuit C C thus hangs 
 from the upper trunnion by two ligaments, which appear like 
 thin strips, but which are really composed of an immense 
 
 number of very fine wires. In Fig. 14 these ligaments are 
 intentionally drawn much longer in proportion to the rest of 
 the figure than they really are in the instrument, the object 
 being to render the mode of suspension clear. This method 
 of suspension enables the conductor C C to vibrate freely 
 like a balance by a motion which is partly a bending of the 
 flexible ligaments, and partly a sort of rolling and unrolling 
 of the lower trunnion on the ligament attached to it. By 
 this ingenious method not only can a heavy copper con- 
 ducting circuit of the shape shown be suspended as freely as 
 the beam of a good balance, but at the same time a very 
 large current density can be permitted in the flexible liga- 
 ment, since its great radiating surface, and the freedom with 
 
62 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 which heat is taken out of it by conduction into the mass of 
 the trunnions, allows a proportionately very large current 
 to be transmitted. If, then, the trunnions A and B are the 
 electrodes, the method above described affords the means of 
 passing a very large current into the circuit C C, which yet 
 at the same time retains within certain narrow limits great 
 freedom of movement. Let such a suspended conductor be 
 arranged so as to have a circular conducting circuit of 
 annular form, briefly called an ampere ring, placed above and 
 below each of the movable rings of the balanced arm. Let 
 the connections be made as shown diagrammatically in 
 Fig. 15, in which it will be seen that the current entering by 
 the 4- electrode flows in series through all four fixed 
 
 FIG. 15. 
 
 ampere rings F, and through the two movable ampere 
 rings M. An examination of the direction of current flow in 
 each ring will then show that, in consequence of Ampere's 
 law (parallel currents in same direction attract, in opposite 
 direction repel), forces of attraction and repulsion will be 
 brought into play between each fixed ring and the movable 
 rings, which tend to lift one ring M and depress the other, 
 and tilt over the balance arm to which they are attached. 
 The amperian forces thus exert a couple on the movable 
 part. To bring back the movable part to its initial position, 
 which we may suppose to be half-way between each fixed 
 ring, an equal and opposite mechanical couple must be 
 applied. We shall in what follows call the movable part 
 
ELECTRICAL LABORATORY EQUIPMENT. 63 
 
 of the conducting circuit the balance coils, and the other 
 portion of the circuit the fixed coils. The operation of 
 weighing an electric current consists, therefore, in bringing 
 first of all the balance coils into a definite sighted position 
 between the fixed coils, then passing the current, and 
 bringing back the balance coils into the sighted position 
 against the displacing electro-dynamic forces by applying to 
 the balanced part a couple produced by a standard weight. 
 The restoring couple is applied as follows : Attached to the 
 balanced part or movable portion is a stiff metal bar, 
 turned up at the bottom edge so as to form a sort of long 
 shelf. This shelf or tray extends the whole length of the 
 movable beam, and moves or tilts with it when the balanced 
 part is displaced (see Fig. 16). At one end of the balanced part 
 is a small V-shaped tray, in which a weight is placed. A 
 standard weight is then placed at the opposite end of the shelf. 
 This weight is of such form as to slide along the shelf 
 easily. When placed at the zero position on the shelf it 
 exactly balances the counterpoise in the V-trough, and the 
 balanced part should be in equilibrium when no current is 
 passing. If it is not so, then a small adjustment can be 
 made by means of a metal flag on the beam similar to that 
 on a gravimetric balance, so as to alter slightly the position 
 of the centre of gravity of the balanced part. If the sliding 
 weight on the shelf is moved along towards the middle the 
 equilibrium is disturbed and a couple brought to bear upon 
 the balanced part, which is proportional to the displacement 
 of the sliding weight from its zero position. If a current is 
 passed through the circuit, and the sliding weight displaced, 
 so as to restore the balance to its sighted position, the current 
 strength is proportional to the square root of the distance by 
 which the sliding weight has to be shifted in order to restore 
 equilibrium. The shifting of this weight is performed by a 
 very ingenious piece of mechanism, which will be understood 
 from the enlarged view (Fig. 17). On the base board of the 
 instrument, and just underneath the shelf on which the 
 
64 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 65 
 
 weight slides, is placed a little metal block, which carries a 
 stout vertical wire extending a little above the shelf carried 
 on the balanced beam. From the top of this wire is carried 
 a pendent wire, which hangs down through a notch in the 
 weight which slides on the shelf. This block, carrying the 
 pendant, is pulled along the railway by a silk cord. When 
 pulled it drags with it the weight on the shelf ; but when 
 the string is released the pendant returns to its vertical 
 position and disengages itself automatically from the weight, 
 leaving the balance free to tilt according to the direction of 
 the forces acting upon it. By this means the weight can be 
 shifted along until a balance is obtained, whilst at the same 
 time the whole balance is covered with a glass case to protect 
 it from currents of air. 
 
 FIG. 17. Shifting- Weight Apparatus of Kelvin Ampere Balance. 
 
 With each current balance four sliding weights and four 
 corresponding counterpoises are provided ; the weights being 
 in the ratio of 1 : 4: 16 : 64. Thus if with the ampere balance 
 the lightest weight on the sliding tray in a certain position 
 corresponds to a current of half an ampere through the 
 instrument, the next weight at the same place corresponds 
 to one ampere, and with the third weight on it the current 
 is two amperes. The upper edge of the shelf on which 
 the weights slide is graduated into equal divisions, and 
 
66 ELECTRICAL LABORATORY EQUIPMENT. 
 
 the weight is provided with a sharp tongue of metal, in 
 order that its position on the shelf may be readily and 
 accurately determined. For the purpose of avoiding con- 
 tinual reference to square root tables, another fixed scale 
 is placed behind the shelf, called the inspectional scale. On 
 the upper edge of the shelf, along which the graduations are 
 made, a small notch is cut at those divisions whose numerical 
 denominations are exact squares ; thus, corresponding to 
 divisions 1, 4, 9, 16, 25, 36, &c., on the scale engraved on the 
 shelf are cut little notches in its upper edge. The inspec- 
 tional scale is fixed close behind this, and yet not touching, 
 and at those points on it exactly behind the notches are 
 engraved numbers which are twice the square roots of the 
 corresponding numbers on the shelf; thus, corresponding to 
 1, 4, 9, 16, 25, &c., on the shelf, the numbers 2, 4, 6, 8, &c., 
 are engraved on the inspectional scale. Since the current 
 passing through the balance when equilibrium is obtained 
 with a given weight is proportional to the square root of the 
 couple due to this weight upon the balance, it follows that 
 the current strength when equilibrium is obtained is pro- 
 portional to the product of the square root of weight used, 
 and the square root of the distance of this weight from 
 its zero position ; but the inspectional scale is so graduated 
 as to show at a glance the square root of the distance of the 
 weight from its zero position, and hence the numbers on the 
 inspectional scale indicate half-amperes, amperes, or double 
 amperes, according to the weight used. 
 
 In using these and all other gravity instruments it should be remembered 
 that the acceleration of gravity, and therefore also the weight of a given mass, 
 varies with latitude and with the height above the earth's surface. If M is 
 the mass of a body and g is the acceleration of gravity, then its weight 
 W=Ma, and 
 
 ^=980-6056-2-5028 Cos 2\ - O'OOOOOSA, 
 
 where \ latitude and A = height above sea level in centimetres. 
 
 If, then, an ampere-balance is set to read correctly at Glasgow, it will need a 
 correction to be applied if used in other places. The weight of each weight, 
 and therefore the corresponding current, will vary proportionately with 
 gravity. 
 
ELECTRICAL LABORATORY EQUIPMENT. 67 
 
 The following table shows for eaeh type of instrument the 
 value per division of the inspectional scale corresponding to 
 each of the four pairs of weights : 
 
 I. II. III. IV. 
 
 Centi-amperes Deci-amperes Amperes per Amperes per 
 per division. per division. division. division. 
 
 1st pair of weights 0'25 0'25 0'25 T5 
 
 2nd 0-50 0-5 0'5 3'0 
 
 3rd 1-0 I'O 1-0 6-0 
 
 4th 2-0 2-0 2-0 12-0 
 
 The fixed inspectional scale shows approximately enough 
 for many purposes the strength of the current ; the notches 
 in the top of the aluminium sliding scale or shelf show the 
 precise position of the weight corresponding to each of the 
 numbered divisions on the inspectional scale, and practically 
 annuls error of parallax due to position of the eye. When 
 the pointer on the weight is not exactly below one of the 
 notches corresponding to integral divisions of the inspectional 
 scale, the proportion of the space on each side to the space 
 between two divisions may be estimated inspectionally with 
 accuracy enough for all practical purposes. Thus, we may 
 readily read off 34'2 or 34' 7 by estimation, with little chance 
 of being wrong by 1/0 in the decimal place. But when the 
 utmost accuracy is required, the reading on the fine scale of 
 equal divisions must be taken, and the strength of the 
 current estimated by aid of a table of square roots supplied 
 with each instrument. 
 
 These general principles being understood, we proceed to 
 describe the details of the several types of instruments 
 adapted for various ranges of useful measurement. The 
 range of each instrument is from 1 to 100 or 1 to 25 times, 
 the smallest current for which its sensibility suffices. The 
 ranges of the different types of instrument regularly made 
 are : 
 
 The Centi-ampere balance from 1 to 100 centi-amperes. 
 Deci-ampere 1 to 100 deci-amperes. 
 
 Ampere 
 Deca- ampere 
 ' Hecto-ampere 
 , , Kilo-ampere 
 
 1 to 100 amperes. 
 1 to 100 
 6 to 600 
 100 to 2,500 
 
 F2 
 
68 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 Fig. 16 shows the general appearance of the centi-arnpere, 
 deci-ampere and ampere balances, and Fig. 18 that of the 
 standard kilo-ampere balance. In these instruments the 
 outer diameters of the fixed coils are slightly greater, and the 
 inner diameters slightly less than those of the movable rings 
 attached to the balance arms. The position of the movable 
 rings when in equilibrium and equi-distant from the fixed 
 ones above and below it, is a position of minimum force, and 
 the sighted position, for the sake of stability, is above it, at 
 one end of the beam and below it at the other, in each case 
 being nearer to the repelling than to the attracting ring by 
 such an amount as to give about T 2 a per cent, more than the 
 
 FIG. 18. Kelvin Kilo-ampere Balance. 
 
 minimum force. In order to adapt these balances for alter- 
 nating currents, a special mode of arranging the conducting 
 circuit has to be adopted. In the balances intended for 
 alternate currents (which may be used also for direct 
 currents) of from five amperes to 250 amperes, the main 
 current through each circle, whether consisting of one turn 
 or of more than one turn, is carried by a wire rope, of which 
 each component strand is insulated by silk covering or 
 otherwise from its neighbour, in order to prevent the 
 inductive action from altering the distribution of the currents 
 across the transverse section of the conductor ; whilst to- 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 69 
 
70 'ELECTRICAL LABORATORY EQUIPMENT. 
 
 avoid induced currents in these parts the coil frames and base- 
 board are constructed of slate. The hecto-ampere (see Fig. 19) 
 and kilo-ampere balances are slightly different in arrangement 
 from the foregoing. In the last instrument the whole 
 current to be measured is passed through a single fixed ring 
 and then divides through the two halves of a movable ring, 
 which are urged, one up and the other down, by the resulting 
 attractive and repulsive forces. 
 
 For the British Board of Trade Electrical Laboratory Lord 
 Kelvin designed a special form of ampere balance for 
 recovering or defining a current of one ampere, of which 
 the following is the official description : 
 
 CONSTRUCTION AND USE OF THE PRINCIPAL INSTRUMENT FOR 
 DETERMINING THE STANDARD OF ELECTRICAL CURRENT. 
 
 The complete instrument is shown in perspective in Fig. 20,* 
 and the details and connections in Figs. 21 and 22. It is 
 constructed as follows : 
 
 Balance and Supports. A sensitive balance, suitable for 
 the accurate determination of weights up to five kilogrammes 
 with a beam 16in. in length between the knife edges from 
 which the scale pans are hung, is fixed on an upper hori- 
 zontal platform of marble, supported on four marble columns 
 at a height of 2ft. 3in. above a similar platform fixed on a 
 suitable stone pier, bedded solidly in a mass of concrete, and 
 kept clear from contact with the wooden floor of the 
 laboratory. 
 
 Marble Cylinder. On the lower platform is placed on 
 three supports, details of which are given below, a cylinder 
 of white statuary marble, partly hollow (see Fig. 20). 
 
 The cylinder is thoroughly impregnated with paraffin wax. 
 A block of ebonite e (Fig. 21) is fixed on one side of the 
 cylinder, and serves as a terminal board. 
 
 Fixed Coils. Two circular grooves are cut completely round 
 the cylinder, in which are wound coils of No. 18 standard 
 
 * This illustration and many others used in this book are taken from The 
 Electrician by permission of the Proprietors. 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 71 
 
 wire gauge (012cm. diameter), insulated with two coverings 
 of white silk. The wire was passed through a bath of shellac 
 
 FIG. 20. The Board of Trade Standard Ampere Balance, showing the Weight 
 raised from the Scale Pan by the Lifting Gear. 
 
 and alcohol as it was wound on the marble, and each layer 
 was well coated with the same material when in its place. 
 Each coil has 16 turns per layer and 16 layers of wire. 
 
72 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 The coils are both wound in the same direction, and the 
 outer ends are strained tight and secured to terminals 1 1 
 (Fig. 21). 
 
 The inner ends are passed through the marble and secured 
 to bolts in connection with terminals i i (Fig. 21). 
 
 Sighting Holes. Between the grooves on the marble 
 cylinder, at points equi-distant from each other, are bored 
 
 FIG. 21. Elevation and Part Section of Marble Cylinder of Board of Trade Standard 
 
 Ampere Balance. 
 
 through the marble three sighting holes, one of which is 
 shown at h (Fig. 21). These holes are closed on the inside 
 by glass, the exact centres being indicated by the intersection 
 of two straight lines engraved in the glass, and also by the 
 angle of a quadrant of tinfoil affixed to the glass. 
 
ELECTRICAL LABORATORY EQUIPMENT. 73 
 
 Suspended Coil, Suspending Wires, &c. A circular coil, 
 shown in sectional elevation at c (Fig. 21), and of the 
 dimensions given, is suspended from one end of the beam of 
 the balance by means of three gilded phosphor bronze wires 
 0'086cm. diameter, w w w (Fig. 21). These wires pass 
 through an aperture in the upper marble platform. 
 
 The wire in this coil is the same as in the fixed coils, and 
 is similarly insulated and varnished. There are 18 turns of 
 wire in each layer and 18 layers. Each complete layer was 
 allowed 24 hours to dry alter being coated with shellac 
 varnish before the next layer was put on. 
 
 The coil is covered with a taping of silk ribbon, closely 
 laid on to overlap, and varnished with shellac in alcohol, four 
 coats, each being allowed to thoroughly dry before applying 
 the next one. 
 
 The ends of the coil are brought out near each other on 
 the upper surface at I (Fig. 21). A considerable length of 
 wire is left for each end, and is formed into a spiral, and then 
 projected horizontally to the centre of the coil, where the 
 stiff wires terminate, and flexible connections are made by 
 three silk-covered silver wires, No. 40 S.W.G., from each to 
 the posts p (Fig. 21), which are connected to terminals nn. 
 
 Three ebonite blocks I (Fig. 21) are fitted over the coil, as 
 shown, and secured by a lashing of silk thread, the suspend- 
 ing wires being attached to brass eyelets screwed into the 
 ebonite. 
 
 At d d d (Fig. 21) are shown ivory cranks for effecting the 
 vertical adjustment of the suspended coil. 
 
 The attachment of the suspending wires to the balance is 
 effected by ivory rings, which are hooked on to a three-legged 
 fitting, this being hooked to the stirrup, hung on the knife 
 edge of the beam (see Fig. 21). 
 
 The scale pan is also hung from this stirrup, as shown in 
 Fig. 21. 
 
 On the upper part of each ebonite piece &, facing the 
 sighting hole h, is fixed a mirror M, the centre being fixed by 
 
74 ELECTRICAL LABORATORY EQUIPMENT. 
 
 the intersection of cross lines and by the angle of a quadrant 
 of tinfoil. 
 
 Adjustments. The proper adjustment of position of the 
 suspended coil is indicated by the coincidence of the angles 
 of the tinfoil quadrants on the mirrors in, and the glass back 
 of holes A, when the eye is so held that no reflected image 
 can be observed. 
 
 Eccentric Movement for Horizontal Adjustment. A means 
 of fine horizontal adjustment is provided in the supports of 
 the marble cylinder, which are three short slate cylinders, 
 k k k (Fig. 21), having projections from their upper and 
 lower surfaces, the upper projection being eccentric and 
 fitting in a hole in the bottom of the marble cylinder, and 
 the lower projection being concentric and fitting in a radial 
 groove in the marble slab. 
 
 The Weight. The iridio-platinum weight shown in Fig. 20' 
 can be lowered into the scale pan, and released from the 
 outside of the case by a system of levers. 
 
 The weight is accurately 33*55 grammes. 
 
 Enclosure. The marble cylinder is enclosed by means of 
 three sheets of plate glass, which slide in grooves cut in the 
 marble platforms, and when in position are in contact with 
 the sides of the three marble columns adjacent to the 
 cylinder, these sides being coated with baize, the plan of 
 this, enclosure being an equilateral triangle with the axis 
 of the marble cylinder at its centre. The planes of the 
 three glass sheets are respectively parallel with those of 
 the glass at the back of the sighting hole viewed through 
 them. 
 
 The balance is enclosed within a case of mahogany and 
 glass (see Fig. 20), and arrangements are made as indicated 
 for manipulating the rider weights of the balance and the 
 ampere weight from the outside of this case. 
 
 The whole enclosure is fairly dust-tight, and sufficiently 
 air-tight to prevent any disturbance of the weighing opera- 
 tions by currents of air. 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 75- 
 
 Connections. The connections to the reversing switch Z 
 (Fig. 22) are brought outside the enclosure by means of rods 
 passing through the marble column adjacent to the ebonite 
 block. Fig. 22 shows these connections, and the direction of 
 the current through the various parts of the apparatus, the 
 lower arrows over the fixed coils showing the alteration of 
 direction caused by operating the switch. 
 
 Fixed Coil 
 
 FIG. 22. 
 
 Auxiliary Current Balance. 
 
 In the construction of the standard ampere balance, the 
 chief object aimed at has been the securing of the greatest 
 possible constancy and precision of determination. 
 
 On account of the slow period of vibration of the beam r 
 however, the use of an auxiliary instrument has been found 
 advantageous. 
 
 This is a special form of Lord Kelvin's current balance 
 instrument arranged to balance with a current of one ampere 
 passing through the coils when a certain weight is applied to 
 one end of the beam, equilibrium being also maintained 
 when, with no current passing, this same weight is applied 
 to the other end of the beam. 
 
76 ELECTRICAL LABOR AT ORT EQUIPMENT. 
 
 Use of the Instrument. The standard balance, auxiliary 
 'balance, and the instruments to be standardised are con- 
 nected in circuit with a sufficient number of accumulators 
 and an adjustable resistance, part of which is capable of 
 continuous variation. The whole circuit is arranged so that 
 a current of approximately one ampere will pass on comple- 
 tion of the circuit. 
 
 This current is allowed to pass continuously for at least 
 one hour, being directed through the coils of the standard, so 
 as to increase the force of gravity on the suspended coil, and 
 the counterweight in the right hand pan being adjusted from 
 time to time. 
 
 At the end of this preliminary period the current is 
 stopped for a short time to take a reading of the zero of the 
 auxiliary balance, and apply a correction by means of the 
 rider weight, if necessary. The current is then again put on, 
 3,nd as rapidly as possible regulated by means of the adjust- 
 able resistance to exactly the value of one ampere, as 
 indicated by the auxiliary balance. 
 
 The counterweight in the right hand pan standard balance 
 is also exactly adjusted. 
 
 The switch Z (Fig. 22) is then operated to reverse the 
 -current in the fixed coils, and at the same time the weight is 
 lowered into the left-hand scale pan. 
 
 The balance should then still be maintained when the 
 current, after adjustment, if requisite, is exactly one ampere 
 by the auxiliary balance. 
 
 The above-described laboratory forms of Kelvin ampere 
 balances are made in two types. They are constructed in 
 one form with a sliding weight and scale so as to enable 
 any constant current to have its ampere value determined, or 
 they are constructed with fixed weights so adjusted that on 
 gradually varying the current the balance tips over at certain 
 fixed standard currents, say, one ampere or ten amperes, &c. 
 
 In this last mode of use of the balances there is no sliding 
 weight and tray but the balances have to be employed in 
 
ELECTRICAL LABORATORY EQUIPMENT. 7* 
 
 connection with a carbon rheostat or some means for con- 
 tinuously varying the current strength with extreme precision. 
 In the case of a primary standard laboratory balance it is- 
 better to have it arranged in the second manner so that by 
 its means the observer may weigh out, as it were, an ampere 
 or ten amperes rather than determine the true value of a, 
 non-integral current. 
 
 In this last manner the standard ampere balance (see 
 Fig. 23) of the Board of Trade is used, and it is desirable, 
 where extreme accuracy is required, that the laboratory 
 should be provided with a one-ampere fixed standard balance 
 of the above-mentioned description. 
 
 FIG. 23. Standard One-ampere Kelvin Balance as made for the Board ofr 
 Trade Electrical Laboratory. 
 
 Deferring, for the present, details of the standardisation of 
 these ampere balances, we may say that the electrical 
 laboratory should be provided, at the very least, with two- 
 standard Kelvin ampere balances, the most useful being the 
 deci-ampere balance weighing from one-tenth to ten amperes-, 
 and a deca-ampere balance weighing from one to a hundred 
 amperes. 
 
 These balances should be carefully set up on level stone 
 shelves of such height that an observer seated on a stool can. 
 comfortably read the scale and manipulate the rider. 
 
78 ELECTRICAL LABORATORY EQUIPMENT. 
 
 After setting up the deci-ampere balance it should be most 
 carefully standardised by a silver voltameter, using the 
 process described in the Board of Trade specification. After- 
 wards the balance should not be moved or touched except to 
 regulate the position of the equilibrium flag before each 
 weighing. A comparison should then be made between the 
 . standard Clark or Weston cell and the balance as follows : 
 Pass through the ampere balance and a tenth of an ohm 
 standard coil a current of about six or seven amperes and 
 regulate this current to perfect steadiness. Then measure 
 with the potentiometer the potential difference between the 
 
 terminals of the standard resistance and calculate from this 
 the value of the current. The current as read by the 
 
 . ampere balance and the current as determined by the stan- 
 dard cell and resistance should agree within one-tenth of 1 
 jper cent., or to one part in a thousand. 
 
 If any refined or careful measurements are to be made the 
 
 director of the laboratory should spare no pains to make sure 
 that he is in possession of the means of recovering or pro- 
 ducing the ohm, the volt and the ampere in his own 
 laboratory, and that these should be in exact agreement as 
 far as possible with the Board of Trade standards and with 
 
 each other. 
 
 It is desirable that the special appliances which form the 
 primary electrical standards of the laboratory the standard 
 ohm, the standard Cadmium or Weston cell or the standard 
 Clark cell and the standard deci-ampere balance shall not 
 be used for every-day work, but kept for special verification 
 purposes. 
 
 The laboratory being in the above-described manner pro- 
 vided with means for making the three fundamental com- 
 parisons of length, mass and time by means of a standard 
 metre, standard gramme or kilogramme weights and chrono- 
 meter must also be provided in the best possible manner 
 with the appliances for making the three principal electrical 
 measurements of resistance, electromotive force and current 
 
ELECTRICAL LABORATORY EQUIPMENT. 79 
 
 by comparison with the standard ohm, standard cell or 
 voltage and standard current. Before describing the stan- 
 dards of electromotive force it is necessary to mention certain 
 current regulating devices which are essential requisites. 
 
 7. The Regulation of Current. One of the most 
 frequently required operations in the electrical laboratory is 
 that of the regulation of a current by means of resistances. 
 
 Each working bench or table should be provided with 
 terminals between which a constant potential difference of 
 100 volts is maintained. From these terminals, however, 
 have to be taken currents of the desired strength. This is 
 best done by providing the laboratory with an outfit of 
 regulating resistances which, when placed in series with 
 any apparatus and across the main terminals, can permit 
 only the desired current to flow. 
 
 After many trials and experiments the author devised the 
 following form of working resistance, which is exceedingly 
 useful in a laboratory :* Each .element of the resistance is 
 called a cage (see Fig. 24), and is made in the following 
 manner. A brass rod about 3ft. long carries on it two 
 porcelain head-pieces or discs having porcelain pin projec- 
 tions on their upper surfaces. One of these is fixed to the 
 rod and the other is movable, but is pushed outwards by 
 a strong spiral spring. To a terminal wire attached to the 
 fixed head-piece is soldered one end of a fine wire of 
 platinoid, reostene or any high-resistance wire. This wire 
 is generally about No. 32 gauge. The movable head-piece 
 is pressed in a little way, and the resistance wire is then 
 laid backwards and forwards over the pin projections on the 
 head-pieces so as to form a zigzag conductor; the end of 
 the resistance wire being then finally connected to another 
 terminal wire passing through the fixed head-piece. When 
 the cage is so made the movable head-piece is released and 
 the spiral spring forces it out, and thus keeps the resistance 
 
 * See The Electrician, Vol. XXXVI., p. 476. 
 
80 ) 
 
 FIG. 24. Inductionless Ventilated 
 Kesistance Ccages (Fleming). 
 
ELECTRICAL LABORATORY EQUIPMENT. 81 
 
 wire always tight, even although it expands on heating. By a 
 proper selection of the resistance wire a perfectly ventilated 
 and practically non-inductive resistance may be made in this 
 manner, having a resistance of 100 ohms or more which, will 
 carry safely, without undue heating, a current of one ampere. 
 A series of these cages can then be fixed in a wood frame 
 placed on castors, with all the several resistances connected 
 in parallel between two omnibus wires ; each resistance 
 being provided with its own switch. It will then be seen 
 that the whole resistance frame can be put across the 100- 
 volt terminals, joined in series with a switch and with any 
 apparatus to be traversed by the current, and that the current 
 
 FIG. 25. Paul's Carbon Plate Rheostat. 
 
 which passes through the circuit can then be regulated by 
 the number of cages which are switched on in parallel. 
 When currents of less than one ampere are required these 
 can be obtained by joining cages in series. In this case 
 each cage can be coupled with a switch in parallel with 
 it, so that when the switch is on, the cage resistance is cut 
 out of circuit. 
 
 In addition to a set of the above cages it is necessary to 
 possess several carbon rheostats. One of the most convenient 
 forms of this regulating resistance consists of plates of 
 hard battery carbon or graphite roughened on the surface 
 and about Sin. square (see Fig. 25). A series of about 30 to 
 
82 ELECTRICAL LABORATORY EQUIPMENT. 
 
 50 of these plates are placed in an iron frame and prevented 
 from touching the guide rods by porcelain or fibre insulators. 
 The carbon plates can be more or less squeezed by a strong 
 screw. Metal plates with screw terminals can be slipped in 
 between any carbon plates, and, by means of the pressure 
 applied, a very gradual variation can be made in the inter- 
 posed carbon resistance. It is essential that the carbon 
 plates shall be hard but not smooth, and the best plates are 
 those cut out of gas-oven graphite. 
 
 FIG. 26. Kelvin Wire Rheostat. 
 
 The above resistances are a great convenience in the 
 laboratory. They can be used to carry large currents up to 
 50 or 100 amperes, but they have not a very great range ot 
 resistance variation. 
 
 For the gradual variation of resistance Lord Kelvin's form 
 of wire rheostat, in which a platinoid wire is wound off a 
 metal cylinder on to a marble or porcelain cylinder, will be 
 found convenient (see Fig. 26). In this appliance the 
 resistance wire is kept tight by means of a clock spring 
 in the interior of the metal cylinder, which always acts so 
 as to keep a little tension on the resistance wire. 
 
 For many purposes a form of rheostat devised by Mr. 
 Shelford Bid well is useful. This consists of a slate or 
 
ELECTRICAL LABORATORY EQUIPMENT. 83 
 
 porcelain cylinder on which a platinoid wire is wound in a 
 helical groove, one end of the resistance wire being insulated 
 and the other fixed to a metal plate which forms the carrier 
 for the cylinder. The cylinder is centred on a long screwed 
 shaft, the screw on which is cut to the same pitch as the 
 helical groove on the cylinder. This screw rod works in 
 tapped bearings. A fixed spring contact presses against the 
 platinoid wire, and the other end of the platinoid wire is in 
 metallic contact with one screw bearing. As the cylinder is 
 turned round a greater or less length of platinoid wire is 
 interposed between this spring terminal and the fixed terminal. 
 
 This form of rheostat is substantial and works well if the 
 wire and contact are kept clean. The contact spring should 
 be tipped with platinoid. It is a good plan to keep these 
 rheostats in boxes with glass lids, the winch handle alone 
 protruding, so that dust does not fall on the resistance wire 
 or contacts. If it does, the resistance is apt to vary in a 
 capricious manner as the handle is turned. 
 
 For some cases incandescent lamps can be used for regu- 
 lating resistances. It is useful to have some boards on 
 which are mounted half-a-dozen key sockets, wired up in 
 parallel between two brass terminal screws. If incandescent 
 lamps are placed in these sockets the resistance between the 
 terminals can be decreased by steps by switching on lamps. 
 If the light given out by the lamps is objectionable it can be 
 shielded off by dropping over each lamp an asbestos card- 
 board hood or cylinder like a canister, the top of which is 
 pierced with small holes for ventilation. Incandescent lamps 
 as resistances, owing to the light and heat given out by them, 
 are not nearly so convenient as the resistance cages above 
 described. 
 
 For the regulation of currents for dynamos and motors 
 many forms of rheostat have been introduced. One con- 
 venient form, as designed by the Author for use in the 
 electrical laboratory at University College, London, consists in 
 suspending from porcelain insulators placed against the wall 
 
 o2 
 
84 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 of the dynamo room long wires of nickel steel or eureka. 
 These wires are kept tight when expanded by heat by means 
 of a spiral bell spring attached to the extremity of the wire. 
 The wires are electrically connected in parallel as required by 
 means of a parallelising switch (see Fig. 27). The length of 
 each wire is adjusted so that the current through it, when the 
 difference of potential of its extremities is 100 volts, does not 
 
 FIG. 27. University College Dynamo Rheostats. 
 
 exceed that value which will make it too hot to touch with the 
 hand. The total resistance between the terminals is then 
 reduced, step by step by adding resistance wires in parallel. 
 It is much better thus to reduce resistance by equal steps by 
 adding equal resistances in parallel than to increase it by 
 adding equal resistances in series. In the former case the 
 current increases by equal increments per step, and in the 
 latter it decreases in harmonic ratio per step of resistance. 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 85 
 
 In cases where large currents have to be regulated or 
 varied continuously liquid resistances may be sometimes 
 advantageously employed. One useful form is Lyon's 
 Liquid Eesistance (see Fig. 28). This consists of two zinc 
 
 FIG. 28. Lyon Liquid Rheostat. 
 
 cones fitting each other, which are immersed in a strong 
 solution of zinc sulphate, and by means of a screw or lever 
 the distance of these metal cones can be varied from perfect 
 metallic contact to a position in which a considerable length 
 
86 ELECTRICAL LABORATORY EQUIPMENT. 
 
 of electrolyte is interposed between them. The resistance 
 can thus be gradually varied. If continuous currents are 
 employed with it, the direction of the current through the 
 resistance should be changed every few minutes by a current 
 reverser. and the current density or amperes per square foot 
 of zinc cone surface should not exceed the limit at which 
 zinc begins to be deposited in irregular crystals or trees on 
 the cathode cone. 
 
 The subject of power absorbing resistances will be con- 
 sidered in the chapters dealing with dynamo and transformer 
 testing.* 
 
 8. The Practical Standard of Electromotive Force. 
 
 The practical unit of electromotive force is equal to the 
 terminal difference of potential produced when a current of 
 one ampere flows through a resistance of one ohm. The 
 most satisfactory method of recovering a known difference of 
 potential say, of one volt is to pass a current of one 
 ampere, measured by a standard ampere balance, through a 
 suitable resistance of one ohm. There are, however, many 
 cases in which this is not a convenient method of recovering 
 a known difference of potential. Hence attention has been 
 directed to the construction of a standard of electromotive 
 force which shall produce directly a known difference of 
 potential between two terminals. Experience shows that, 
 although the ultimate standard of electromotive force must 
 be recovered by the passage of a known current through a 
 
 * The following references to papers or information on liquid resistances 
 and power absorbing resistances may be found useful : " Lyon's Liquid 
 Resistances," The Electrician, Vol. XXVI., p. 759. " Water Rheostats," G. T. 
 Hanchett, The Electrician, Vol. XXXVII., p. 833. " Water Rheostats," The 
 Electrician, Vol. XL., p. 696, contains useful facts and figures ; see also 
 Science Abstracts, Vol. I., p. 356. " Water Resistance for Alternator Testing," 
 The Electrician, Vol. XLI., p. 279. "Motor Starting Resistances," Pochin, 
 The Electrician, Vol. XXXIX., p. 38. "Commercial Forms of Electricial 
 Resistances," L. B. Atkinson, The Electrician, Vol. XL., p. 863. " Current 
 
 p. 
 
 Commercial Resistances," D. K. Morris, The Electrician, Vol. XXXIII., pp. 
 605, 627, 667. 
 
ELECTRICAL LABORATORY EQUIPMENT. 87 
 
 known resistance, yet the adoption of a voltaic or electro- 
 chemical standard of electromotive force, by the use of a 
 standard voltaic cell, has considerable practical convenience. 
 Great attention, therefore, has been given of late years to 
 the minute details of the construction of certain voltaic cell 
 standards of electromotive force. Experience has shown 
 that a very convenient standard of electromotive force is 
 obtained by the use of some modification of the mercury-zinc 
 cell, which was first proposed by Mr. Latimer Clark as a 
 standard of electromotive force, and made in 1873.* The 
 elements of this cell are mercury, mercurous sulphate, zinc 
 sulphate and zinc. Since the above date other forms of 
 voltaic cells have been proposed as standards of electromotive 
 force. The various species and modifications of standard 
 mercury cell in use at present are as follows : 
 
 (".) THE ORIGINAL FORM OF CLARK CELL. 
 
 (ii.) THE MUIRHKAD FORM OF CLARK CELL. 
 (in.} THE RAYLEIGH H FORM OF CLARK CELL. 
 
 (iv.) THE CARHART FORM OF CLARK CELL. 
 
 (v.) THE BOARD OF TRADE FORM OF CLARK CELL. 
 
 (vi.) THE REICHSANSTALT FORM OF CLARK CELL. 
 (vii.) THE CALLENDAR FORM OF CLARK CELL. 
 (viii.) THE WESTON CADMIUM CELL. 
 
 (ix.) THE REICHSANSTALT H FORM OF CADMIUM CELL. 
 
 (x.) THE HELMHOLTZ CALOMEL CELL. 
 
 These cells are not employed as current generators, but 
 merely as standards of electromotive force by using them as 
 subsequently to be described. A few words of description 
 may be given of each of these cells. 
 
 (i.) The Original Clark Cell. The original form of Clark 
 cell, suggested by Mr. Latimer Clark in 1873 as a standard 
 of electromotive force, consisted of a glass cup or beaker in 
 the bottom of which is placed some pure mercury. Into this 
 mercury a platinum wire dips, which is sheathed throughout 
 its length with glass or gutta perch a except at the extreme 
 
 * See Telegraphic Journal, Vol. I., p 9. 
 
88 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 end where it dips into the mercury. Above the mercury 
 rests a paste formed of mercurous sulphate mixed with zinc 
 sulphate. Above the paste there is a saturated solution of 
 zinc sulphate, and in this latter is dipped a rod of pure zinc. 
 The zinc has a platinum wire soldered to it, and the two 
 wires connecting the zinc and mercury are brought up to 
 insulated terminals (see Fig. 29). 
 
 (ii.) The Muirhead- Clark Cell. In the above original 
 form the Clark cell is not very portable and cannot be 
 turned upside down without producing a change in its 
 
 Marine Glue 
 
 Glass Tube 
 
 Platinum Wire 
 
 Glass Cell 
 
 Zinc Sulphate Paste 
 
 Mercury 
 
 FIG. 29. Original form of Clark Cell. 
 
 electromotive force by bringing the mercury in contact 
 with the zinc and thus contaminating the mercury. An 
 improved form of cell was therefore devised by Dr. Muirhead, 
 in which this difficulty is overcome. 
 
 In the Muirhead cell there is no large free mass of 
 fluid mercury. The end of the platinum wire is coiled into 
 a spiral, and this platinum is well amalgamated, and when 
 dipped in mercury it retains a globule of mercury within 
 the spiral by capillary attraction, and this is so adherent 
 that it is not easily detached. The spiral of amalgamated 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 89 
 
 platinum is buried in the mercurous paste (see Fig. 29) ; 
 above this is placed the saturated solution of zinc sulphate, 
 and in this latter a zinc rod. 
 
 A Muirhead cell, if properly sealed, can be sent by parcels 
 post, or otherwise carried about without injury to its 
 electromotive force. 
 
 (Hi.) The Rayleigh H form of Clark Cell. Lord Eayleigh 
 investigated in 1885 with great care the causes of the 
 differences in electromotive force between Clark cells set up 
 
 Marine Glue 
 
 Zinc Sulphate 
 
 Mercurous Sulphate 
 
 Glass Tube 
 Platinum Wire 
 
 Platinum Spiral 
 
 FIG. 30. Muirhead form of Clark Cell. 
 
 by various persons using apparently the same quality of 
 materials and equal care. 
 
 He came to the conclusion that the greatest source of 
 error was due to variations in the density of the zinc 
 sulphate solution. The electromotive force of the cell 
 depends upon the concentration of the zinc sulphate solution. 
 If the solution is not a saturated solution the electro- 
 motive force of the cell is too high. In some cases the 
 zinc sulphate solution may be super-saturated, especialty 
 
90 ELECTRICAL LABORATORY EQUIPMENT. 
 
 when the cells have been heated during or after charging. 
 Lord Kayleigh summarises the sources of variation of 
 E.M.F. in Clark cells as follows : The E.M.F. may be 
 too high (1) because the mercurous paste is acid ; (2) because 
 the paste is not saturated with zinc sulphate. The first 
 fault tends to cure itself, and is rarely found after cells are a 
 month old. The second is the usual cause of variation. If 
 the E.M.F. is too low it may be (1) because the cell has 
 become dry, in which case the drop in voltage will be pro- 
 gressive; (2) the solution is super-saturated with zinc 
 sulphate ; or (3) the mercury is impure. It follows that to 
 secure the correct or normal E.M.F. the mercury used should 
 
 FIG. 31. Lord Rayleigh's H form of Clark Cell. 
 
 B Amalgam of Zinc. C Pure Mercury. D Mercurous Sulphate. E Saturated Solution 
 of Zinc Sulphate. F Corks. 
 
 be free from other metals. It must, therefore, be distilled at 
 a low temperature in vacuo. Next, the zinc sulphate solu- 
 tion must be at all temperatures saturated, and hence solid 
 crystals of zinc sulphate must be present in the cell. 
 Thirdly, the cell must be hermetically sealed with marine 
 glue to prevent evaporation ; and, fourthly, the cell must not 
 be heated during manufacture. The zinc sulphate must be 
 rendered neutral by adding a little carbonate of zinc. 
 
 Lord Eayleigh devised a convenient form of cell called the 
 H form of cell. This cell consists of a pair of test-tube- 
 shaped glass vessels connected by a horizontal tube or channel 
 (see Fig. 31). In one side tube is placed some pure mercury, 
 
ELECTRICAL LABORATORY EQUIPMENT. 91 
 
 and in the other an amalgam of mercury and zinc. Platinum 
 wires sealed through the glass make contact with the metals.. 
 Over the pure mercury is put a paste made of mercurous 
 sulphate and zinc sulphate. The cell is filled up to above 
 the level of the horizontal tube with a saturated solution of 
 zinc sulphate, and the open ends are closed with corks sealed 
 over with marine glue. This H form of cell is very con- 
 venient for many experimental purposes. 
 
 s^Rgatisi ' 
 
 Zinc Sulphate 
 
 Asbestos Wad llulummmummim ^ 
 
 Mercurous Sulphate 
 
 Platinum Wire -A^afiBfiiF 
 
 Mercury 
 
 FIG. 32. Carhart Clark Cell. 
 
 Lord Eayleigh found the electromotive force of the K 
 form of cell to be 1-434 volts at 15C.* and the temperature 
 coefficient to be O08 per cent, per degree, or the E.M.F. in 
 volts at tfC.=E|, to be given by the formula 
 E,=1434 {1-0-00077 (<-15)}. 
 
 A more exact expression for the temperature correction 
 is obtained if the simple coefficient '0007 7 is replaced by 
 the quantity 0'00078 + 0'000017 ($15). If the electro- 
 chemical equivalent of silver is taken as 0'001119 instead of 
 0-001118, then the E.M.F. of the Clark cell becomes 14327 
 volts at 15C. and not 14342. 
 
 * The electromotive force of the H form of Clark cell, as determined by 
 K. Kahle and W. Wien, ie 1-4488 volts at 0C., or 1*4322 volts at 15C. The 
 Board of Trade value is 1-434 volts at 15C. 
 
92 ELECTRICAL LABORATORY EQUIPMENT. 
 
 (iv.) The Carhart-Clark Cell. In this cell the zinc is 
 made in the form of a plunger or piston (see Fig. 32), and 
 the shank or piston rod is covered with glass. In between 
 the bottom of the zinc and the mercurous paste is interposed 
 a wad of asbestos and the cell is sealed. 
 
 (>.) The Board of Trade form of Clark Cell. The British 
 Board of Trade Electrical Department have issued a specifi- 
 cation for the preparation of standard Clark cells, which is a 
 little elaborate and enters into great detail as to their mode 
 of manufacture. The following is the Board of Trade specifi- 
 cation for the preparation of a Clark cell : 
 
 ON THE PREPARATION OF THE CLARK CELL. 
 
 Definition of the Cell. 
 
 The cell consists of zinc or an amalgam of zinc with mercury and of 
 mercury in a neutral saturated solution of zinc sulphate and mercurous 
 sulphate in water, prepared with mercurous sulphate in excess. 
 
 Preparation of the Materials. 
 
 1. The Mercury. To secure purity it should be first treated with acid in 
 the usual manner, and subsequently distilled in vacuo. 
 
 2. The Zinc. Take a portion of a rod of pure redistilled zinc, solder to one 
 end a piece of copper wire, clean the whole with glass paper or a steel 
 burnisher, carefully removing any loose pieces of the zinc. Just before 
 making up the cell dip the zinc into dilute sulphuric acid, wash with distilled 
 water, and dry with a clean cloth or filter paper. 
 
 3. The Mercurous Sulphate. Take mercurous sulphate, purchased as pure, 
 mix with it a small quantity of pure mercury, and wash the whole thoroughly 
 with cold distilled water by agitation in a bottle ; drain off the water, and 
 repeat the process at least twice. After the last washing drain off as much of 
 the water as possible. 
 
 4. The Zinc Sulphate Solution. Prepare a neutral saturated solution of 
 pure (" pure re-crystallised ") zinc sulphate by mixing in a flask distilled water 
 with nearly twice its weight of crystals of pure zinc sulphate, and adding 
 zinc oxide in the proportion of about 2 per cent, by weight of the zinc 
 sulphate crystals to neutralise any free acid. The crystals should be dissolved 
 with the aid of gentle heat, but the temperature to which the solution is 
 raised should not exceed 30C. Mercurous sulphate treated as described in 3 
 should be added in the proportion of about 12 per cent, by weight of the zinc 
 sulphate crystals to neutralise any free zinc oxide remaining, and the solution 
 filtered, while still warm, into a stock bottle. Crystals should form as it 
 cools. 
 
 5. The Mercurous Sulphate and Zinc Sulphate Paste. Mix the washed 
 mercurous sulphate with the zinc sulphate solution, adding sufficient crystals 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 93 
 
 of zinc sulphate from the stock bottle to insure saturation, and a small 
 quantity of pure mercury. Shake these up well together to form a paste of 
 the consistence of cream. Heat the paste, but not above a temperature of 
 30C. Keep the paste for an hour at this temperature, agitating it from time 
 to time, then allow it to cool ; continue to shake it occasionally while it is 
 cooling. Crystals of zinc sulphate should then be distinctly visible, and 
 should be distributed throughout the mass ; if this is not the case add more 
 crystals from the stock bottle, and repeat the whole process. 
 
 This method insures the formation of a saturated solution of zinc and 
 mercurous sulphates in water. 
 
 To set up the Cell. 
 
 The cell may conveniently be set up in a small test-tube of about 2cm 
 diameter and 4cm. or 5cm. deep (sec Fig. 33). Place the mercury in the bottom 
 
 Mercury 
 
 FIG. 33. Board of Trade form of Clark Cell. 
 
 of this tube, filling it to a depth of, say, O'Scm. Cut a cork about 0'5cm. thick 
 to fit the tube ; at one side of the cork bore a hole through which the zinc rod 
 can pass tightly ; at the other side bore another hole for the glass tube which 
 covers the platinum wire ; at the edge of the cork cut a nick through which 
 the air can pass when the cork is pushed into the tube. Wash the cork 
 thoroughly with warm water, and leave it to soak in water for some hour& 
 before use. Pass the zinc rod about 1cm. through the cork. 
 
 Contact is made with the mercury by means of a platinum wire about 
 No. 22 gauge. This is protected from contact with the other materials of the 
 cell by being sealed into a glass tube. The ends of the wire project from the 
 ends of the tube ; one end forms the terminal, the other end and a portion of 
 the glass tube dip into the mercury. 
 
.94 ELECTRICAL LABORATORY EQUIPMENT. 
 
 Clean the glass tube and platinum wire carefully, then heat the exposed end 
 of the platinum red hot and insert it in the mercury in the test-tube, taking 
 care that the whole of the exposed platinum is covered. 
 
 Shake up the paste and introduce it without contact with the upper part 
 of the walls of the test-tube, filling the tube above the mercury to a depth of 
 ^rather more than 1cm. 
 
 Then insert the cork and zinc rod, passing the glass tube through the hole 
 .prepared for it. Push the cork gently down until its lower surface is nearly 
 in contact with the liquid. The air will thus be nearly all expelled, and the 
 -cell should be left in this condition for at least 24 hours before sealing, which 
 should be done as follows : 
 
 Melt some marine glue until it is fluid enough to pour by its own weight, 
 and pour it into the test-tube above the cork, using sufficient to cover com- 
 pletely the zinc and soldering. The glass tube containing the platinum wire 
 should project some way above the top of the marine glue. 
 
 The cell may be sealed in a more permanent manner by coating the marine 
 .glue, when it is set, with a solution of sodium silicate, and leaving it to 
 harden. 
 
 The cell thus set up may be mounted in any desirable manner. It is con- 
 venient to arrange the mounting so that the cell may be immersed in a water 
 bath up to the level of, say, the upper surface of the cork. Its temperature 
 can then be determined more accurately than is possible when the cell is 
 in air. 
 
 In using the cell sudden variations of temperature should as far as possible 
 be avoided. 
 
 The form of the vessel containing the cell may be varied. In the H form 
 the zinc is replaced by an amalgam of 10 parts by weight of zinc to 90 of 
 onercury. The other materials should be prepared as already described. 
 Contact is made with the amalgam in one leg of the cell, and with the 
 mercury in the other, by means of platinum wires sealed through the glass. 
 
 The cell resulting from operations carried out in accord- 
 ance with the above specification has been criticised 
 considerably, and it has been stated that in consequence of 
 diffusion-lag there is always some delay in the change of 
 saturation of the zinc sulphate solution when the temperature 
 changes. Hence it is said that it is not possible to obtain 
 the true electromotive force of the cell to a greater accuracy 
 than O'l per cent, by applying the ordinary temperature 
 correction.* 
 
 (vi.) The Reichsanstalt form of Clark Cell. A specification 
 for the preparation of a modification of the H form of Clark 
 
 * See Prof. Ayrton and Mr. Cooper, Proc. Roy. Soc., Lond., Dec., 1895. ' 
 Also Mr. Cooper " On the Permanency of the Board of Trade Clark Cell," 
 The Electrician, Vol. XL., p. 748. 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 95 
 
 cell has been issued in Germany on the basis of the experience 
 gained at the Physikalisch-Technische Reichsanstalt in Berlin. 
 The following are the details of these instructions as given by 
 Dr. K. Kahle* : 
 
 Definition and Properties of the Cell. 
 
 The cell contains mercury as the positive electrode, amalgamated zinc as the 
 negative electrode, and as electrolyte a concentrated solution o zinc sulphate 
 and mercurous sulphate. Its E.M.F. is 1-4328 Internationa 1 volts at 15C. 
 and between 10C. and 25C. decreases by O'OOllS volt with i n increase of 
 temperature of Ideg. 
 
 Construction of the Cell. 
 
 The vessel used for the cell consists, as shown in Fig. 34, of two vertical 
 branches closed at the bottom, and joined at the top into a neck closed by a 
 
 FIG. 34. Eeichsanstalt form of Clark Cell. 
 
 ground-glass stopper. The diameter of the branches should be at least 2cm. 
 and their length 3cm. The neck of the vessel should be 1'Scm. wide, and at 
 least 2cm. long. Platinum wires about 0'4mm. thick are fused into the 
 bottom of both branches. 
 
 The vessel is filled in a manner depending upon whether the cell is to be 
 used at the place of construction or is to be transported. 
 
 * See The Electrician, Vol. XXXI., p. 265-6. 
 
96 ELECTRICAL LABORATORY EQUIPMENT. 
 
 In the former case pure mercury is poured into one branch, and into the other 
 amalgam of about 90 parts mercury and 10 parts zinc, which is fluid when 
 hot and solidifies on cooling. The platinum wires must be completely covered 
 by the mercury and the amalgam respectively. Upon the mercury is poured 
 a layer of paste 1cm. deep, made by rubbing together mercurous sulphate, 
 mercury, zinc sulphate crystals, and concentrated solution of zinc sulphate. 
 This paste and the amalgam are then both covered with a layer 1cm. deep of 
 zinc sulphate crystals, and finally the whole vessel is filled with concentrated 
 zinc sulphate solution until the stopper on being introduced just touches the 
 surface. Care should, however, be taken that the vessel contains a small air- 
 bubble, since that prevents it bursting in the case of a great rise of tempera- 
 ture. At the final closing of the vessel the glass stopper is brushed over at its 
 upper edge with shellac dissolved in alcohol and then firmly inserted. 
 
 If the cell is to be portable, a circular electrolytically-amalgamated piece 
 of platinum foil, about 1cm. long and O'lmm. thick, takes the place of the 
 mercury, and is firmly attached to the platinum wire introduced through the 
 bottom. Zinc amalgam forms, as before, the negative electrode, and is 
 covered with a layer of zinc sulphate crystals 1cm. deep. The rest of the 
 vessel is filled up to the stopper with mercurous sulphate paste. The final 
 closing is affected as already described. 
 
 Preparation of the Materials to be Used in the Cell. 
 
 Mercury. All mercury to be used in the cell should be purified by the 
 ordinary processes, and distilled in vacuo. 
 
 Zinc. The commercial pure zinc may be employed. To prepare te 
 amalgam, add one part zinc to nine parts mercury, and keep both in a 
 porcelain dish at lOOdeg., stirring gently until the zinc is completely dissolved 
 in the mercury. 
 
 Sulphate. Before use, test the commercial zinc sulphate for acid with litmus 
 and for iron with potassium sulpho-cyanide. If it is sufficiently pure it may 
 be at once re-crystallised in the way detailed below. If it contains appreciable 
 traces of free acid, equal parts of the zinc sulphate and distilled water are 
 boiled with zinc filings in a suitably formed porcelain dish until no further gas- 
 is given off at the zinc, and the solution shows after cooling a white, or, in the 
 presence of ferric hydrate, a brownish precipitate of zinc hydrate. If the 
 solution is free from iron it may be filtered off after standing for two days. 
 Otherwise it is again heated to 60C. or 80C.,and electrolysed for six hours by a 
 current not exceeding 0'2 amperes introduced by two pieces of platinum foil 
 of about 50 sq. cm. surface suspended in the liquid. The liquid having cooled 
 over night, litmus is again employed to test whether any acid has been formed 
 during electrolysis. In that case the boiling with zinc filings must be repeated, 
 and the solution again electrolysed by weak currents. During this whole 
 treatment care has to be taken that the concentration of the solution remains 
 approximately constant. It is, therefore, well to cover the vessel containing 
 the solution with a glass plate, so that but little water vapour can escape. As 
 soon as the solution is sufficiently free from acid and iron it is filtered off. To 
 each litre of the filtrate about 50gr. of mercurous sulphate, free from acid, are 
 
ELECTRICAL LABORATORY EQUIPMENT. 97 
 
 added and well stirred. The mercury salt will in general assume a yellow 
 colour after long standing. If the solution has stood for a day, and a portion 
 of it, on being shaken up with more mercurous sulphate, does not turn per- 
 ceptibly yellow, the solution may be filtered off and concentrated in a flat 
 porcelain dish over a water bath. Here we must take care that the crystals 
 do not form at too high a temperature, as otherwise they easily lose a portion 
 of their water of crystallisation. To secure this the flame under the water- 
 bath is extinguished, and the dish left in position covered with a glass plate. 
 If after further cooling no crystals are separated, further concentration is 
 necessary. If the heating was too protracted, and the crystals were formed 
 under unfavourable conditions, a little water must be added and the whole 
 warmed until everything is redissolved. The concentrated solution is- 
 poured off, and either further evaporated or kept for future use. The last 
 traces of the solution are removed from the crystals by letting the dish stand 
 for some time in a slanting position. It is not advisable to sharply dry the 
 crystals, as they thereby lose water of crystallisation. For the same reason 
 they must be kept in a closed vessel. 
 
 Sulphate of Mercury. The mercurous sulphate used must not be coloured 
 yellow by a basic salt. If that should be the case, stir up one part of the salt 
 with two parts distilled water, and add, constantly stirring, so much of a 
 solution of one part mercuric sulphate to 1,000 parts of water as is necessary 
 to make the colour disappear. Then pour off the liquid and wash the paste 
 several times with distilled water, but without thereby causing another yellow 
 colouration. If the sulphate is white to begin with, and only shows a faint 
 yellow colouration after considerable time on shaking up with distilled water ; . 
 it may be used at once. If this colouration is not shown on shaking up with 
 water, the salt must be washed out several times with distilled water until the 
 first traces of yellow colouration appear. If the salt had to be wetted for 
 cleaning, the water should be driven off as much as possible by mechanical 
 means. If dried by heat the yellow colouration will reappear. In order not 
 to have to keep the wet salt only so much salt should be treated by the above 
 process as is necessary for the purpose in hand. 
 
 To prepare the paste, two parts of the sulphate should be added to one part 
 of mercury. If the sulphate was dry, it should be stirred up with a paste 
 made of zinc sulphate crystals and concentrated zinc sulphate solution until 
 the whole forms a stiff mass everywhere permeated by zinc sulphate crystals 
 and small globules of mercury. But if the sulphate was wet, only zinc 
 sulphate crystals should be added, taking care, however, that they are in 
 excess, and are not dissolved even after prolonged standing. Here, also, the 
 mercury must permeate the paste in small globules. It is well to crush the 
 zinc sulphate crystals a little before using, so that the paste may be more 
 easily manipulated later on. 
 
 Details of Construction. 
 
 For the preparation of cells containing mercury as the positive electrode 
 the following details should be attended to : Before introducing the hot zinc 
 amalgam place the glass vessel, well cleaned and carefully dried, in a hot 
 water bath. Then pass a suitable thin-walled glass tube through the neck. 
 
08 ELECTRICAL LABORATORY EQUIPMENT. 
 
 of the vessel on to the bottom of the branch \vhich is to contain the amalgam. 
 The tube ought to be as wide as is consistent with the dimensions of the 
 vessel. It is intended to protect the rest of the vessel from contamination. 
 The amalgam is introduced by means of a glass tube about 10cm. long drawn 
 out into a point, the other end being provided with an indiarubber tube about 
 3cm. long closed by a short glass rod. The point of the tube is inserted below 
 the surface of the liquid amalgam heated in a dish, and a portion of the 
 amalgam is sucked into the tube by compressing and releasing the india- 
 rubber. The point is then quickly freed from external impurities derived from 
 the surface of the amalgam, introduced into the cell through the wide tube, 
 and emptied by pressure on the indiarubber. The point ought to be so fine 
 that the amalgam does not issue except on pressing the rubber. The process 
 is continued until the branch contains the required quantity of amalgam. 
 The vessel is then taken out of the water-bath. After cooling the amalgam 
 should adhere firmly to the bottom of the vessel and exhibit a bright metallic 
 surface. 
 
 To introduce the mercury and the paste a suitable funnel with a long tube 
 is used. The paste should not touch the upper walls of the vessel, but may 
 be pushed in with a glass rod if too stiff to flow. 
 
 Before pouring in the zinc sulphate solution the paste and the zinc amalgam 
 should be covered with zinc sulphate crystals, as these prevent a creeping up 
 of the paste after wetting with the solution. In filling, the zinc sulphate 
 crystals and the paste should not contain large air-bubbles. These may be 
 removed by knocking. 
 
 If the cell is to contain amalgamated platinum foil as the positive electrode, 
 the amalgamation may be performed as follows : The cell vessel is first filled 
 with aqua regia and heated in a sand-bath until a rapid development of gas 
 takes place at the platinum. Then rinse with water, pour mercury into the 
 branch intended to contain the zinc amalgam, and fill the entire vessel with a 
 concentrated solution of mercurous nitrate containing a little nitric acid. 
 Then connect the mercury with the positive and the platinum foil with the 
 negative pole of a battery, and send a current of about 0'5 ampere through 
 the solution until the platinum foil is covered over with firmly-attached 
 mercury globules. The whole process lasts about five minutes. Finally the 
 vessel is thoroughly rinsed with distilled water until not a trace of the 
 nitrate remains. 
 
 The zinc amalgam is introduced with the precautions mentioned. After 
 cooling, it is covered with zinc sulphate crystals, to which concentrated zinc 
 sulphate is added after filling until the whole forms a paste. The vessel should 
 stand for two days, so that the crystals are closed up and form a layer 
 impervious to the paste. Then the whole vessel is filled up with the latter. 
 
 The following points should be specially borne in mind in the construction : 
 
 1. The mercury intended to serve as positive electrode must be kept rigidly 
 free from contamination by more positive metals. Special care should be 
 taken that no portion of the zinc amalgam comes into contact with the 
 mercury. 
 
 2. The cell should always be so arranged that at all temperatures the whole 
 electrically active surface of the electrodes is in contact with zinc sulphate 
 
ELECTRICAL LABORATORY EQUIPMENT. 99 
 
 solution concentrated for the temperature in question. Hence during the 
 process of filling, crystals should be added in such quantity as to ensure their 
 presence in excess even at the highest temperatures which the cell may attain. 
 
 3. The zinc sulphate used must not contain free acid. For one thing, the 
 E.M.F. of the cell is affected by it, and, on the other hand, the circuit of the 
 cell may be broken by hydrogen developed at the zinc. For the gas produced 
 cannot escape through the zinc sulphate crystals, but collects underneath 
 them, and finally pushes them up, thereby interrupting the connection 
 between the zinc and the zinc sulphate. 
 
 For easy and safe handling the cell is included in a metal case, which may 
 be closed and placed in a petroleum bath. Its lid is provided with two bind- 
 ing screws, each of which is joined to one of the electrodes ; the bottom is 
 perforated, so that the cell is surrounded by the petroleum. To determine 
 the temperature of the cell, a thermometer must be enclosed in the case whose 
 scale can be read from outside. The best plan is to fuse a thermometer into 
 the glass stopper, as shown in the figure, so that the bulb penetrates as far as 
 possible into the cell and the scale projects through the lid. 
 
 The great objection which has been raised to the form of 
 Clark cell constructed in accordance with the Board of Trade 
 specification, in which the zinc rod is surrounded throughout 
 the whole or part of its length by clear solution of zinc 
 sulphate, is that there is a source of possible error or 
 uncertainty in its use due to the fact that changes of tem- 
 perature and consequent changes in the state of saturation of 
 the zinc sulphate are not propagated immediately through 
 the cell. If the temperature of the cell is raised, more zinc 
 sulphate must be dissolved to keep the solution saturated at 
 that temperature, and this saturated solution is not diffused 
 immediately to all parts of the tube. The existence of this 
 diffusion -lag has been proved, by the experiments of Lord 
 Rayleigh, Prof. Carhart, Prof. Ayrton, Mr. Cooper and others, 
 undoubtedly to be a source of error. 
 
 The remedy proposed by Lord Eayleigh for this diffusion 
 lag was the H form of cell. 
 
 The remedy suggested by Prof. Carhart was to use a cell 
 containing a solution saturated at 0C. 
 
 (mi.) The Callendar- Clark Cell. Prof. Callendar and Mr. 
 Barnes have proposed a remedy for diffusion lag as follows : 
 The cell is made up in a rather thin and long test-tube, and 
 has two glass-covered platinum wires or electrodes ; the ends 
 
100 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 of the platinum wires protruding from the sealed ends of the 
 glass tubes (see Fig. 35). In the bottom of the tube is placed 
 a small button of a 10 per cent, amalgam of zinc and mercury, 
 and in this is immersed one electrode. Over this a layer of 
 moist crystals of zinc sulphate ; on the top of the zinc sulphate 
 a layer of mercurous sulphate paste, in which the end of the 
 second amalgamated platinum wire is buried. The cell is 
 sealed with marine glue in the usual manner. The cell is 
 thus an inverted narrow pattern of the Board of Trade cell. 
 
 Mercury 
 
 External 
 
 Cups 
 
 FIG 35. Callendar form of Clark Cell. 
 
 The inventors state that diffusion lag is absent, and that 
 changes of E.M.F. follow immediately all changes of 
 temperature between 0C. and 40 C. 
 
 The large temperature variation of the Clark cell led 
 inventors to search for a modification with a less temperature 
 coefficient. This was found, in 1891, by Mr. Weston in the 
 arrangement known as the cadmium cell. In this cell the 
 elements are mercury, mercurous sulphate, cadmium sulphate 
 and cadmium. The combination has a temperature variation 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 101 
 
 very much less than that of the corresponding zinc combina- 
 tion. The cadmium sulphate being much more equally 
 soluble at all ordinary temperatures than the zinc sulphate, 
 diffusion-lag does not occur. The only difficulty is that the 
 E.M.F. varies with the proportions of the metals in the 
 cadmium-mercury amalgam used. Hence it is best to 
 employ the H form of cell, in which the cadmium is kept 
 out of contact with the mercurous sulphate. Mr. Weston 
 makes the cell as follows : 
 
 (viii.) The Weston Cadmium Cell. The considerable varia- 
 tion in the solubility of zinc sulphate in water at different 
 
 FIG. 36. Weston Cadmium Standard Cell. 
 
 temperatures led Mr. E. Weston, in 1891, to suggest the use 
 of cadmium sulphate instead of zinc sulphate (U.S. Patent 
 No. 22,482 of 1891). The cadmium salt has nearly the same 
 solubility at all temperatures. The cadmium cell is made up 
 in the Kayleigh H-form, as shown in Fig. 36. In one side- 
 vessel is placed a little pure mercury, entirely covered with 
 a layer of mercurous sulphate. In the bottom of the other 
 
102 
 
 ELECTEICAL LABORATORY EQUIPMENT. 
 
 limb is placed an amalgam of cadmium, and the tube is filled 
 up with a saturated solution of cadmium sulphate. The cell 
 is then sealed. Platinum wires sealed through the glass at 
 the bottom of the side tubes enable connection to be made 
 between the mercury and the cadmium amalgam and the cell 
 terminals. 
 
 Mr. Weston states in his patent specification that the 
 electromotive force of this cell is 1*019 volts, and its tem- 
 perature coefficient is O'Ol per cent, per degree centigrade. 
 
 Cadmium Amalgam Mercury 
 
 FIG. 37. Keichsanstalt form of Cadmium Standard Cell. 
 
 A valuable feature, therefore, of the cadmium cell is its 
 small temperature coefficient; this may be made by using 
 proper proportions of cadmium and mercury to be as low as 
 0*004 per cent, per degree centigrade instead of 08 as in 
 the case of the Clark cell. 
 
 Special attention has been paid to the details of the 
 construction of this cell at the Physikalisch-Technische 
 Keichsanstalt in Berlin, and the following are the instruc- 
 tions for its manufacture as laid down by Prof. W. Jaeger: 
 
 (ix.) The Beiclisanstalt Cadmium Cell. This cell is made 
 up in the Kayleigh H-form (see Fig. 37). The two legs of 
 
ELECTRICAL LABORATORY EQUIPMENT. 103 
 
 the side vessels are provided with platinum wires sealed 
 through the glass at the lower ends. The negative element 
 consists of a cadmium amalgam one part of cadmium to six 
 parts of mercury. Over this is placed a layer of pulverised 
 crystals of cadmium sulphate to ensure saturation. The 
 positive element is formed of pure mercury, over which is 
 placed a paste formed by the trituration of mercurous 
 sulphate with metallic mercury and a concentrated solution 
 of cadmium sulphate in which are crystals of the salt. This 
 paste must not be too thin, but must form a stiff pulp. The 
 remainder of the cell is filled up with a saturated solution of 
 cadmium sulphate. The tubes are then closed by a layer of 
 melted paraffin poured on, then a thin washer of cork, and, 
 lastly, the cell is closed with melted sealing wax. 
 
 A more portable cell may be made like the Muirhead- 
 Clark cell with an amalgamated platinum spiral instead of 
 liquid mercury. The electromotive force E 4 of the cadmium 
 cell in the H-form at C. is given by the formula, 
 
 E,=E 20 [3-8 X 10~ 5 (t- 20) - 0-065 X 10" 5 (t - 20) 2 ], 
 where E 20 =the electromotive force at 20C. in volts and is 
 1*019 volts. The above applies to cells in which the 
 amalgam contains from 7 to 14 per cent, of cadmium. 
 
 In making the cell the following precautions must be 
 employed : 
 
 Amalgamation of the Platinum Wire. After the platinum wires are sealed 
 through the glass place a little aqua regia in the cell legs until bubbles of gas 
 arise from the platinum. Then throw this out and replace it by a solution of 
 mercurous nitrate, and, using another piece of platinum as an anode, deposit 
 mercury upon the platinum electrolytically. The platinum may also be 
 amalgamated by making it white hot in a Bunsen flame, and plunging it 
 whilst hot in the mercury. 
 
 Preparation of the Cadmium Amalgam. Dissolve one part of pure cadmium 
 in six parts of pure mercury, and whilst warm and fluid place it in one limb 
 of the H cell and warm it to ensure perfect contact with the platinum. 
 
 Cadmium Sulphate Solution. Digest a saturated solution of cadmium 
 sulphate with cadmium hydroxide to remove free acid, but be careful not to 
 raise the temperature above 70C. Then digest it still further with mercurous 
 sulphate until no more precipitation occurs. The cadmium sulphate solution, 
 must be saturated and have free crystals of the salt in it. 
 
104 ELECTRICAL LABORATORY EQUIPMENT. 
 
 Mercurous Sulphate. This must be free from acid, and made neutral by 
 triturating with finely divided mercury. In making the paste so much cadmium 
 sulphate must be added that a saturated solution of that salt is formed and is 
 present in the cell. 
 
 The cell has the electromotive force above stated if the amalgam of cadmium 
 has from 6 to 13 parts of mercury to 1 of cadmium. 
 
 The German investigators seem to have a great preference for the H form 
 of cell, but it is clear that a narrow tubular cell of the Board of Trade form 
 not only more quickly comes to the temperature of the water bath hi which 
 it is placed, but is more certain to be wholly at one temperature. 
 
 (#.) The Helmholtz Calomel Cell. It was proposed by 
 Yon Helmholtz to employ a cell, the elements of which are 
 mercury, mercurous chloride or calomel, zinc chloride and 
 .zinc, as a standard of electromotive force (see " Sitzber. der 
 Akad. der Wiss," Berlin, 1882, p. 26). 
 
 This cell can be adjusted to have an electromotive force of 
 exactly one volt by the use of a solution of zinc chloride 
 of a certain density, viz., T380 at 15C. Its temperature 
 coefficient of electromotive force is small, being only 1 part 
 in 10,000 per degree centigrade, whereas that of the Clark 
 sulphate cell is 8 parts in 10,000 per degree centigrade. Its 
 electromotive force varies, however, with the state of satura- 
 tion of the solution of zinc chloride, and as evaporation 
 from the cell tends to increase the density of the zinc chloride 
 solution it is not so definite and permanent as a standard as 
 the zinc sulphate or cadmium sulphate form of cell, unless 
 hermetically and permanently sealed. According to Mr. W. 
 Hibbert (The Electrician, Vol. XXXVII, p. 320), the cell 
 rapidly recovers its normal electromotive force if short- 
 circuited. 
 
 The Standard Daniell Cell. In addition to the above- 
 described mercury-zinc or mercury-cadmium standard cells, 
 the Daniell cell or copper, copper-sulphate, zinc sulphate, 
 .zinc cell has been used as a standard of electromotive force. 
 Although not a rival in uniformity of electromotive force to 
 the Clark or cadmium cell, it has the advantage that its 
 temperature coefficient within the range of ordinary labora- 
 tory temperatures is practically zero. Its electromotive 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 105 
 
 force is, however, a function of the density of the solutions 
 used. 
 
 The Author described, in 1885,* a convenient form of stan- 
 dard Daniell cell as follows : A glass u-tube is prepared 
 
 FIG. 38. Fleming Standard Daniell Cell. 
 
 having side bulb reservoirs and taps as shown in Tig. 38. 
 The whole apparatus can be made out of glass by a skilful 
 
 * See Phil. Mag., August, 1885. 
 
106 ELECTRICAL LABORATORY EQUIPMENT. 
 
 glass-blower. It is then fixed up against a board. In this 
 U-tube a Daniell cell is formed by inserting rods of amalga- 
 mated zinc and of freshly electrotyped copper in the two 
 limbs, which are respectively filled up with solutions of zinc 
 sulphate and copper sulphate. 
 
 The solutions required are made by dissolving the purest re-crystallised 
 sulphate of copper and sulphate of zinc in distilled water. 
 
 For the zinc solution, take 55'5 parts by weight of crystals of zinc sulphate 
 (ZnS0 4 , 7 OH 2 ), and dissolve in 44'5 parts by weight of distilled water ; and 
 the resulting solution should have a specific gravity of 1*200 at about 20C 
 For the sulphate of copper solution, take 16*5 parts by weight of pure crystals 
 of copper sulphate (CuS0 4 , 5 OH 2 ), and dissolve in 83*5 parts by weight of 
 water ; and the resulting solution should have a specific gravity of I'lOO at 
 20C. If not exact, adjust to these densities precisely. 
 
 These solutions should be kept in stock bottles and the reservoirs of the cell 
 filled up when required. 
 
 The operation of filling is as follows : Open the tap A 
 and fill the whole U-tube with the denser zinc sulphate 
 solution ; then insert the zinc rod, and fit it tightly by the 
 rubber cork P. On opening the tap C the level of the liquid 
 will begin to fall in the right hand limb, but be retained in 
 the closed one. As the level commences to sink in the 
 right hand limb, by opening the tap B copper sulphate 
 solution can be allowed to flow in gently to replace it ; and 
 this operation can be so conducted that the level of demar- 
 cation of the two liquids remains quite sharp, and gradually 
 sinks to the level of the tap C. When this is the case, all 
 taps are closed and the copper rod inserted in the right hand 
 limb. 
 
 It is impossible to stop diffusion from gradually mixing 
 the liquids at the surface of contact; but whenever the 
 surface of contact ceases to be sharply defined, the mixed 
 liquid at the level of the tap C can be drawn off, and fresh 
 solutions supplied from the reservoirs above. 
 
 A freshly electrotyped copper rod is always to be used. 
 The copper surface must have a clean salmon colour free 
 from brown spots of oxide. 
 
 * See Phil. Mag., August, 1885. 
 
ELECTRICAL LABORATORY EQUIPMENT. 107 
 
 The cell freshly prepared has then an electromotive force 
 on open circuit of TO 72 volts. 
 
 The use of this Daniell cell enables an approximate 
 recovery to be made of the unit of electromotive force, but it 
 is neither so convenient nor permanent as the improved forms 
 of Clark or cadmium cell. 
 
 Every electrical laboratory or testing room should be 
 provided with a number of specimens of the above-described 
 standard cells, either Muirhead-Clark cells, Weston cadmium 
 cells, or the Eeichsanstalt pattern of cadmium cells will be 
 found to be most trustworthy. These should be numbered 
 or lettered and careful comparison made at observed tem- 
 peratures of their relative electromotive forces from time to 
 time, and the values entered under date in the laboratory 
 book. Occasionally comparisons of these with the other volt 
 standards should be made by methods to be described, and 
 with the results of electromotive force determinations by the 
 ampere balance as presently to be discussed. With care and 
 vigilance the laboratory need never be uncertain in its 
 recovery of the standard of electromotive force by more than 
 one part, or at most five parts, in 10,000. 
 
 The standard cells should have thermometers placed in 
 the brass cases containing them or, better still, be immersed 
 in water when using them, and in taking careful observa- 
 tions sufficient time should always be allowed to elapse 
 before taking the voltage readings to enable the cell to take 
 the same temperature as that indicated by the thermometer, 
 assuming them to be under circumstances in which the final 
 temperature of both cell and thermometer will ultimately be 
 the same. 
 
 9. The Literature of the Mercury Standard Cell. 
 
 As it is impossible to transcribe in these pages the detailed 
 results of all the very numerous researches which have been 
 made during the last fifteen years on the standard Clark, 
 Weston and Helmholtz mercury cells, we shall give here 
 references to some of the principal investigations, and leave 
 
108 ELECTRICAL LABORATORY EQUIPMENT. 
 
 the reader desirous of more information to consult the 
 original papers : 
 
 (a) Investigations on the Absolute Electromotive Force of 
 
 Standard Cells. 
 
 LATKIER CLARK. " On a Voltaic Standard of Electromotive 
 Force." Telegraphic Journal, Vol. I., p. 9 ; or Proc. Roy. 
 Soc., Lond., 1872. 
 
 LORD BAYLEIGH and MRS. SIDGWICK. " On the Absolute Electro- 
 motive Force of Clark Cells." Phil. Trans. Roy. Soc., 
 Lond., 1884, Part II., p. 411. 
 
 LORD RAYLEIGH. ' On the Clark Cell as a Standard of Electro- 
 motive Force." Phil. Trans. Roy. Soc., Lond., 1885, Part 
 II., p. 781. 
 
 R. T. GLAZEBROOK and S. SKINNER. " On the Clark Cell as a 
 Standard of Electromotive Force." Phil. Trans. Roy. Soc., 
 Lond., 1892, Vol. CLXXXIIL, pp. 567-628. 
 The authors conclude that the E.M.F. is 1/434 volts at 15C., confirming the 
 
 value given by Lord Rayleigh. 
 
 C. LIMB. " On the Determination of the Electromotive Force of 
 the Clark Cell in Absolute Measure." Journal cle Physique, 
 1896 ; also The Electrician, Vol. XXXVII., p. 138. 
 
 The E.M.F. of the cell was balanced against an E.M.F. produced by the 
 rotation of a magnet inside a coil of wire. The value obtained for the E.M.F. 
 of the cell is 1'4535 volts at 0C. 
 
 H. S. CARHART and K. E. GUTHE. Physical Revietv, Nov., 1899, 
 
 p. 288 ; also Science Abstracts, March, 1900, No. 646. 
 The E.M.F. of the Kahle form of H-cell was determined by balancing it 
 against a fall of potential down a resistance due to known current. Result 
 found was 1*4333 volts at 15C. 
 
 (b) Modifications of the Clark Cell. 
 
 H. S. CARHART. " An Improved Standard Clark Cell with Low 
 Temperature Coefficient." Phil. Mag., 1890 ; The Electri- 
 cian, Vol. XXIV., p. 271. 
 
 The author constructed a cell with low temperature coefficient 
 E t = E 15 [1 - 0-000387(< - 15) + 0'0000005( - 15) 2 ], 
 
 where E* = electromotive force in volts at tC. The above paper was criticised 
 by Lord Rayleigh (The Electrician, 1890, Vol. XXIV., p. 285) who, suggests 
 that the low coefficient found by Carhart was due to the zinc sulphate not 
 being saturated. He gives a diagram of his H form of cell. 
 
ELECTRICAL LABORATORY EQUIPMENT. 100 
 
 H. S. CAEHART. " A Portable Clark Cell." Electrical World,. 
 1895 ; or The Electrician, Vol. XXXV., p. 844. 
 
 He describes the cell shown in Fig. 32. He uses a solution of sulphate of 
 zinc saturated at 0C. 
 
 E. WESTON. "The Cadmium Standard Cell." Electrical 
 Engineer (New York), 1893 ; also The Electrician, Vol. XXX.,. 
 p. 741. 
 He describes fully his mercury-cadmium sulphate cell. 
 
 H. L. CALLENDAR and H. T. BARNES. " On a Simple Modifica- 
 tion of the Board of Trade Standard Clark Cell." Proc. 
 British Assoc., 1897, Toronto ; also The Electrician^ 
 Vol. XXXIX., p. 638 ; also Vol. XL., p. 165. 
 In this pattern of cell, called the " inverted " cell, the zinc amalgam lies at 
 the bottom of the test-tube, and an amalgamated platinum \vire forms the 
 other element. 
 
 For correspondence on this form of cell see The Electrician, 
 Vol. XXXIX. (K. Kahle), p. 869 (H. L. Callendar), p. 869. 
 
 W. JAEGER. " The Keichsanstalt Type of Cadmium Standard 
 Cell." Electrotechnische Zeitschrift, October 21, 1897 ; also 
 The Electrician, Vol. XL., p. 9. 
 
 This is an important paper, and describes in great detail the construction' 
 of a standard H form of cadmium cell. 
 
 W. HIBBERT. " On the Helmholtz or Calomel Cell." The Elec- 
 trician, Vol. XXXVII., p. 320 ; also ibid., Vol. XXXVIII., 
 p. 177 ; also ibid., Vol. XLL, p. 317. 
 
 In this cell zinc chloride and mercurous chloride replace the sulphate salts. 
 of the Clark cell. It can be made to have an E.M.F. of exactly one volt, and 
 a negligible temperature coefficient. 
 
 (c) Specifications for preparing Clark and Western Cells. 
 " The British Board of Trade Specification for Clark Cells." 
 The Electrician, Vol. XXVII., p. 99; also Ibid., Vol. 
 XXXIIL, p. 518. 
 
 K. KAHLE. " Instructions for Preparing Clark Standard Cells : 
 the Reichsanstalt Specification." Zeitschrift fur Instru- 
 mentenkunde, 1893 ; also The Electrician, Vol. XXXI., p. 265. 
 
 \V. JAEGER. " The Reichsanstalt Specification for Preparing 
 Cadmium Cells." Electrotechnische Zeitschrift, October 21, 
 1897 ; also The Electrician, Vol. XL., p. 9. 
 
110 ELECTRICAL LABORATORY EQUIPMENT. 
 
 (d) On Temperature Variations of Standard Cells. 
 W. E. AYRTON and W. B. COOPER. " The Variation of E.M.F. 
 of Clark Cells with Temperature." Proc. Eoy. Soc., Lond., 
 1897, Vol. L1X. ; also The Electrician, Vol. XXXVIII., 
 p. 303. 
 
 An exhaustive examination of the effect of temperature on the Board of 
 Trade Clark cell. The authors give numerous curves. 
 
 W. HIBBERT. "The Temperature Coefficient of the Calomel 
 Cell." The Electrician, Vol. XXXVI1L, p. 177. 
 
 F. S. SPIERS, F. TWYMAN and W. L. WATERS. " Variations in 
 the Electromotive Force of the H form of Clark Cells with 
 Temperature." Proc. Phys. Soc. Lond., Vol. XVI., p. 38; 
 also Phil. Mag., 1898, Vol. XLV., p. 285. 
 
 A. DEARLOVE. " Note on the Temperature Coefficient of the 
 
 Cadmium Standard Cell." The Electrician, Vol. XXXI., 
 
 p. 645. 
 
 A very full and detailed account of experiments on the Weston cell. The 
 .author advocates a cell of Muirhead type made with cadmium salts and 
 cadmium. 
 A. CAMPBELL. " A Self-acting Temperature Compensation for 
 
 Standard Cells." Proc. Phys. Soc., Lond., Vol. XVI., p. 34 ; 
 
 also The Electrician, Vol. XXXV., p. 601. 
 
 W. JAEGER and K. KAHLE. "A Comparison of the Clark and 
 Weston Cells as regards Temperature Coefficient." See 
 Wied. Ann., No. 8, 1898; also The Electrician, Vol. XLL, 
 p. 642. 
 
 The authors have examined 68 cells (27 Clark cells and 41 Weston cells) 
 constructed since 1891. They have been tested at intervals of about a year 
 and the maximum difference observed between the Clark cells was 0'14 
 millivolt and between the Weston cells 0*18 millivolt, which last in two years 
 decreased to 0'08 millivolt. The cadmium cells should only be used between 
 20C. and 70C. The E.M.F.'s are- 
 Clark cells (H form)=l-4328 international volts at 15C. 
 Weston cell =1-0186 volts at 20C. 
 The ratio of 
 
 Clark at 0C. to Weston at 20 3 C. = T42277 
 Clark at 15C. to Weston at 20C. = 1 '40663. 
 The temperature correcting factors are 
 
 for Clark cell = 1 - 0'00119 (t- 15) - O'OOOOO? (t - 15) 3 
 for Weston cell = 1 - 0'000038 (* - 20) - 0'00000065 (t - 20) 2 , 
 .and these factors, by multiplication with the value of the E.M.F. at 15C. or 
 20C, respectively, give the value of the E.M.F. of each cell at t 
 
ELECTRICAL LABORATORY EQUIPMENT. Ill 
 
 K. KAHLE. " On the Clark Cell." The Electrician, Vol. XXIX., 
 p. 516 ; also Proc. Brit. Assoc., 1892, Edinburgh. 
 
 This paper contains a valuable table giving the temperature coefficient of 
 different types of H-form Clark cell. The mean value of the temperature 
 coefficient (a) of the H form of cell according to the author is given by 
 
 a =0-000783 + 0-000017(4 - 15) 
 and the E.M.F. at t = E.M.F. at 15 X [1 + a(t - 15)]. 
 
 The above author strongly advocates the use of the H form of cell. He 
 says he has set up about 60 H-form cells and has found no difficulty, when 
 using pure materials, in keeping the differences of E.M.F. of the various cells 
 to less than one ten-thousandth of a volt. He gives the following table 
 showing the temperature coefficient (a) for various forms of Clark cell : 
 
 Form of Cell. 
 
 Temperature Coefficient. 
 
 H-cell set up in Lord 
 Rayleigh's manner 
 
 H-cell, the paste covering both 
 electrodes 
 
 The Reicheanstalt form of H-cell, 
 paste covering both electrodes 
 
 + 0-C00812 + 0-000013 (t - 15) 
 
 -f 0-000774 + 0-000020 (t - 15) 
 
 + 0-000791 + 0-000017 (t - 15) 
 
 The electromotive force of the H form of cell appears to be about 4 parts in 
 10,000 less than that of the Board of Trade or original form when taken 
 at 15"C. 
 
 (e) Various Investigations. 
 
 J. SWINBURNE. " On the Causes of Variation of Clark Cells." 
 The Electrician, Vol. XXVII., p. 500; also Brit. Assoc. 
 Eeport, 1891, Cardiff. 
 
 S. SKINNER. "The Clark Cell when Producing a Current." 
 Proc. Phys. Soc., Lond., Vol. XIII., p. 218 ; The Electrician, 
 Vol. XXXIII., p. 644. 
 
 W. E. COOPER. " The Permanency of Board of Trade Clark 
 Cells." The Electrician, Vol. XL., p. 748 ; or Science 
 Abstracts, Vol. I., p. 492. 
 
 The author has tested a number of Clark cells set up according to the 
 Board of Trade specification, and finds, after 3 years, the mean differences or 
 mean errors in E.M.F. amount to 1 part in 700 or even 1 in 500. Time 
 introduces a progressive variation in E.M.F., the E.M.F. steadily falling. 
 
 IV. JAEGER. " On Cadmium Cells." Ann. Phys. Chem., 1898, 
 65, 1, p. 106 ; or Science Abstracts, Vol. I., p. 493. 
 
112 ELECTRICAL LABORATORY EQUIPMENT. 
 
 T. WULF. "The Clark Cell on Closed Circuits." Science 
 
 Abstracts, Vol. L, p. 340. 
 
 . After repeatedly short-circuiting cells through 50 ohms the E.M.F. was not 
 permanently affected. 
 W. C. FISHER, " The Recovery of Clark Cells after Sending a 
 
 Current." The Electrician, Vol. XXXVI., p. 647. 
 The author finds repeated short-circuiting produces no permanent injury 
 to the cell. 
 W. JAEGER. " On Change in the Zinc Sulphate in Clark Cells." 
 
 Ann. Phys. Chem., 1897, 63, 1, pp. 354-365. 
 
 KOHNSTAMM and COHEN. " The Weston Standard Cell." The 
 
 Electrician, Vol. XLL, p. 381. 
 J. HENDERSON. " On Cadmium Standard Cells." Phil. Mag., 
 
 Vol. 48, July, 1899, p. 152. 
 
 For various correspondence on the subject of the Clark cell 
 see The Electrician, Vols. XXXIX. and XL., for 1897 and 1898. 
 
 10. Mechanical Standards of Electromotive Force. 
 Voltmeters. In addition to the standard cells or electro- 
 chemical standards of electromotive force, an electrical 
 laboratory must be provided with mechanical standards 
 for the measurement of potential difference or electromotive 
 force. These instruments are called voltmeters, and are 
 each constructed to be suitable for a certain range of 
 voltage or potential difference applied to their terminals. 
 These appliances are roughly distinguished into low and 
 high voltage voltmeters, according as they are designed 
 to read over ranges of from 500 volts downwards or from 
 500 volts upwards. Some of these types of instruments 
 are adapted only for ordinary or not very accurate 
 measurements. These are called working voltmeters. Others, 
 for very careful work, are called standard voltmeters. If 
 the instrument shows by a scale deflection or pointer 
 indication directly the value in volts of the potential differ- 
 ence of its terminals it is called a direct-reading voltmeter. 
 
 For the British Board of Trade electrical laboratory a 
 mechanical standard of electromotive force was designed 
 by Lord Kelvin, which, as a standard of voltage, is considered 
 
ELECTRICAL LABORATORY EQUIPMENT. 113 
 
 to be more permanent than an electro-chemical standard 
 consisting of a battery of standard cells. This mechanical 
 standard consists of an idiostatic electrostatic voltmeter, 
 in which the difference of potential between a series of 
 fixed metallic surfaces and a series of metallic plates 
 suspended by a torsion wire, is made to exert a mechanical 
 torque twisting the suspending wire, carrying one set of 
 plates through a certain angle against the torsional rigidity 
 of the wire. The description of this principal Board of Trade 
 100-volt standard is as follows : 
 
 CONSTRUCTION AND USE OF THE BOARD OF TRADE ONE HUNDRED VOLTS 
 STANDARD OF ELECTROMOTIVE FORCE OR VOLTAGE. 
 
 The instrument is shown in plan and sectional elevation on the accompanying 
 diagrams (see Figs. 39 and 40). It consists of : 
 
 Suspended Vanes. (a) An arrangement of 10 parallel paddle-shaped vanes,, 
 in form similar to the moving portion of Lord Kelvin's Quadrant Electrometer, 
 fitted on an axis passing through the centre of gravity of each vane and 
 separated by distance pieces to a distance of nine millimetres apart. 
 
 Concave Mirror. (6) On the same axis is fixed the aluminium frame of a con- 
 cave mirror 19 millimetres in diameter and about 61 millimetres focal length,, 
 which is held in the frame by means of three light phosphor bronze springs. 
 
 Suspending Wire. (c) This arrangement is suspended by means of a wire 
 0'05 millimetre in diameter and 18 centimetres in length, formed of an alloy 
 of 10 parts of indium to 90 parts of platinum, attached to the end of the 
 axis above the mirror so that the axis hangs in a vertical line. 
 
 Horizontal Adjustment of Position of Vanes. (d) The upper extremity of 
 the suspending wire is fixed to the centre of a circular brass plate having 
 teeth cut in the circumference, into which a tangent screw is geared so as to 
 enable the end of the wire to be rotated in the horizontal plane for the hori- 
 zontal adjustment of the vanes. 
 
 Vertical Adjustment of Vanes. (e) The vertical adjustment of the position, 
 of the vanes is accomplished by the raising or lowering of the platform on 
 which the circular brass plate mentioned above is pivoted by means of three 
 screws for raising and three for lowering. These screws regulate the distance 
 of the platform above a similar platform fixed by means of three supports to 
 the framework of the instrument. 
 
 Quadrants. (/) The vanes are suspended so as to slightly enter at the 
 zero position of the instrument into the spaces between two sets of 11 thin 
 polished brass plates shaped as quadrants of a circle, which are fixed horizon- 
 tally one above another to a vertical support. These two sets of plates are 
 in metallic connection, and are carefully insulated from the framework of the 
 instrument. 
 
 Vibration Checking Arrangement. (g) In order to reduce the vibration of 
 the suspended system, and the time which must elapse before an accurate 
 
114 
 
 ELECTRICAL LABORATORY EQUIPMENT 
 
 CM 
 
 CO 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 115 
 
 N 
 
 m 
 
116 ELECTRICAL LABORATORY EQUIPMENT. 
 
 observation can be taken, a thin horizontal brass disc is suspended in refined 
 mineral oil contained within a glass vessel, by means of a wire attached to 
 the lower portion of the axis of suspension of the vanes. 
 
 Outer Case. (h) The suspended system and quadrants, with their supports, 
 are enclosed in a brass case having in front of the mirror a rectangular 
 window of parallel- worked glass. A hole is cut in this case for the insertion 
 of a key fitting the squared arbor of the tangent screw (d). 
 
 Terminals. (z) The terminals, by means of which connection is obtained 
 with the vanes and quadrants, are fixed on a thick piece of polished ebonite 
 projecting beyond the brass cover h. One terminal is in connection with the 
 metal framework, the other is entirely insulated ; and a tongue of brass or 
 switch connected by means of a brass rod with the two sets of quadrants 
 can be turned so as to make contact either with the insulated or with the 
 uninsulated terminal. 
 
 Framework and Supports. (&) The arrangement described above, forming 
 the electrical portion of the instrument, is mounted near the apex of a frame- 
 work of brass in the form of a circular arc which rests by means of three feet 
 on a horizontal slab of polished marble supported on a large block of Portland 
 stone on a concrete foundation. A screw thread is cut on the feet for 
 accurate levelling of the framework, to which two spirit levels are attached. 
 
 Eyepiece and Cross Wire. (I) On a support attached to the centre of the 
 curved portion of the framework is fixed the observing portion, consisting of 
 a magnifying eyepiece in front and in the focus of which is stretched a vertical 
 copper wire 0'06mm. in diameter. 
 
 Fiducial Marks. (m) At each end of the arc is erected a vertical support, 
 to which is fixed a tablet of brass with the surface facing towards the mirror 
 platinised. On each of these faces is engraved a vertical line. These lines 
 form the fiducial marks ; that on the left of the observer giving the zero 
 position, and that on the right the correct position for 100 volts pressure. 
 The distances from the mirror (b) of these tablets and of the sighting wire (I) 
 is adjusted so that the image of the line on the tablet, when the mirror is at 
 the proper angle, coincides with the sighting wire. 
 
 USK OF THE INSTRUMENT. 
 
 Adjustments. The instrument must be in accurate adjustment as regards 
 level and position of the suspended system. The vertical adjustment of the 
 latter is obtained by trial. The vanes should be at equal distances from the 
 quadrants above and below, this position giving minimum sensibility. The 
 horizontal adjustment of the suspended system is obtained when the image of 
 the zero fiducial mark produced by the mirror (6) exactly coincides witli the 
 sighting wire (I), the switch (t) being turned so as to connect the quadrants 
 with the metal framework of the instrument. (The levelling of the framework 
 and vertical adjustment of the suspended portion of the instrument were 
 carefully attended to when the instrument was first set up, and these adjust- 
 ments have since that time remained constant. The horizontal adjustment of 
 the suspended system requires occasional attention from time to time. ) 
 
 Headings. Arrangements should be made for obtaining a pressure which 
 can be continuously varied from about 98 to 102 volts. This pressure is 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 117 
 
 applied to the 100-volt standard, and to the instruments to be compared with 
 it, and is adjusted until the image of the fiducial mark indicating 100 volts 
 pressure exactly coincides with the sighting wire (I) by observation through 
 the eyepiece. This coincidence is maintained, by adjustment of the pressure, 
 if necessary, until the expiration of five minutes from the time of first 
 applying the pressure, when, if there is no visible vibration of the mirror, the 
 pressure is exactly 100 volts. 
 
 A perspective view of this absolute 100-volt standard is 
 shown in Fig. 41. 
 
 Instruments of the same design can be made for any 
 range of electromotive force, and a set of six standard 
 
 FIG. 41. Board of Trade Standard Kelvin Voltmeter. 
 
 voltmeters of the above described form, covering a range 
 from 20 to 3,200 volts, has been made for the British Board 
 of Trade Electrical Standardising Laboratory. With these 
 instruments an accuracy of standardisation can be attained 
 within 1 part in 3,000. 
 
 The possession of an absolute 100-volt standard of the 
 above kind is a great convenience when much standardising 
 of commercial voltmeters has to be carried out. 
 
 For general purposes, and as a secondary standard, a 
 convenient form of voltmeter is Lord Kelvin's Multicellular 
 
118 ELECTRICAL LABORATORY EQUIPMENT. 
 
 Electrostatic Voltmeter (see Fig. 42). In this instrument 
 there are a series of connected fixed and movable metal 
 plates as in the standard voltmeter, but the movements of 
 the movable system are indicated by the displacement of a 
 needle over a scale. The scale of the instrument is divided 
 so as to read directly in volts. If the plates forming the 
 fixed portion of the instrument and the movable plates are 
 not made of the same metal there will be a small difference 
 or discrepancy amounting to a fraction of a volt between the 
 
 FIG. 42. Lord Kelvin's Multicellular Electrostatic Voltmeter. 
 
 readings of the instrument taken with continuous potentials, 
 when the fixed plates are positive and the movable negative, 
 and when they are reversed in sign of potential. This is due 
 to the contact difference of potential of the metals. In this 
 case any statement of the instrumental reading must be 
 accompanied by a statement as to the nature of the relative 
 sign of electrification of the movable plates. 
 
 11. The Instrumental Outfit of an Electrical Labor- 
 atory. The majority of the measurements made in the 
 
ELECTRICAL LA BORA TOR T EQ UIPMENT. 119 
 
 electrical laboratory resolve themselves ultimately into one or 
 more of the following five measurements : 
 
 (i.) The measurement of the value or strength of an 
 electric current, or else proving the absence of a current, in 
 some circuit. 
 
 (ii.) The measurement of a potential difference or of an 
 electromotive force, or else proving the absence of a potential 
 difference. 
 
 (iii.) The measurement of a resistance or its reciprocal 
 conductance. 
 
 (iv.) The measurement of the time integral of a current 
 or of an electric quantity. 
 
 (v.) The measurement of the rate of expenditure or dissi- 
 pation of electric energy in a circuit, or of electric power 
 taken up in it. 
 
 To describe all the instruments in detail which have beer* 
 invented for the above measurements would be to transfer 
 these pages the contents of a library of trade catalogues ana 
 circulars. We shall limit ourselves here to mentioning the 
 general results of experience as to the most trustworthy and 
 convenient appliances for performing the above electrical 
 measurements which should be provided in a well-equipped 
 electrical laboratory or testing room. 
 
 12. Current - Measuring Instruments. The most fre- 
 quently recurring and fundamental of all electrical measuring 
 processes is the operation of determining the presence, or 
 proving the absence, of an electric current in a circuit. If 
 present, its strength or magnitude generally has to be deter- 
 mined in terms of the standard or unit current called the 
 ampere. An instrument which merely shows the presence or 
 absence of a current in a circuit is called a detector or 
 galvanoscope. If it gives, in addition, a means of comparing 
 the relative value of two currents, it is called a galvanometer. 
 If it shows by its indications the ampere-value of the current 
 it is called an amperemeter or ammeter. 
 
120 ELECTRICAL LABORATORY EQUIPMENT. 
 
 By far the most numerous class of instruments in use as 
 galvanoscopes, galvanometers and ammeters depend for their 
 operation on the fact that a magnetic flux exists round a 
 'Conductor, conveying, as we say, an electric current. This 
 flux can be detected and measured by the mechanical force or 
 torque acting either upon a magnet placed near the conductor, 
 or upon a small mass of iron ; or upon another movable 
 conductor traversed by the same current. Another class of 
 instruments depends upon the heating effect produced by a 
 current in a conductor and the measurement of the linear 
 expansion of the conductor due to this heating. 
 
 We may, then, classify the current measuring or detecting 
 instruments required in the laboratory as follows, depending 
 upon the principle employed in their construction : 
 
 I. Galvanoscopes or Detectors. 
 
 (a) Simple linesman's or laboratory detector, or magnetic needle 
 suspended in a coil of wire. 
 
 (6) Pole-testing paper or solution. 
 
 II. Galvanometers or Current Measurers. 
 
 (a) Movable needle galvanometers with coil fixed and suspended 
 magnetic needle, either simple or astatic, e.g., Kelvin mirror galvanometer, 
 or ordinary needle or mirror instruments of high or low resistance such 
 as Wiedemann's galvanometer. 
 
 (6) Movable coil galvanometers, in which a coil traversed by the 
 current to be measured is suspended between the poles of a strong fixed 
 magnet, e.g., Kelvin recorder pattern galvanometer or d'Areonval gal- 
 vanometer, as modified by Holden, Ayrton and Mather, and Crompton. 
 
 (c) Tangent galvanometers, in which the suspended magnetic needle 
 has a magnetic length very small compared with the diameter of a 
 large fixed coil or coils, e.g., the Post Office pattern, or ordinary single- 
 coil tangent galvanometer ; the Helmholtz, or two-coil tangent galvano- 
 meter ; the three-coil tangent galvanometer. 
 
 III. Amperemeters 
 
 (a) Electrodynamic instruments, in which the forces acting between 
 conductors conveying currents are utilised as an ammeter principle, e.g., 
 Kelvin ampere balances, Siemens dynamometer, Weber's electrodynamo- 
 meter, as modified by Siemens ; Pellat's absolute electrodynamo- 
 meter, &c. 
 
 (6) Electromagnetic instruments, in which the mechanical force 
 between a magnet and a conductor conveying a current, or between a 
 
ELECTRIC A L LA BORA TOR Y EQ UIPMENT. 121 
 
 mass of soft iron and a conductor conveying a current is utilised as an 
 ammeter principle. 'These are variously designed as follows : 
 
 (i.) Movable coil instruments, e.g. : Kelvin recorder pattern of ammeter, 
 
 d' Arson val and Weston ammeters, and similar instruments. 
 (ii.) Movable soft iron instruments, e.g.: Ayrton and Perry, Nalder, 
 Evershed, Dobrowolsky, Thomson, and most ordinary trade 
 ammeters. 
 
 (c) Electrothermal instruments, in which the heating property of the 
 current is utilised, e.g. : Hartmanu and Braun ammeters, Cardew, Holden 
 and other hot-wire instruments. 
 
 (d) Electrochemical instruments, in which the time-average of a 
 current is measured by an operation of electrolysis. This method of 
 current measurement is the ultimate process of determination, and 
 defines the current quantity in terms of the unit current by the operation 
 on which the official definition of unit current is based. Instruments for 
 electrochemical measurement of current quantity are called voltameters, 
 The chief electrolytic processes are those in which a solution of a silver salt, 
 or of a copper salt, or etae dilute sulphuric acid, are employed as electrolytes. 
 
 (e) Electro-optic insi ruments, by which a current can be measured by 
 measuring the optical n-tation produced in the plane of polarised light 
 by its magnetic field acting on a standard substance of which the Verdet 
 constant is known. If a tube with glass ends, and fitted with bisulphide 
 of carbon, is placed in the interior of a solenoid, a current passing through 
 the helix exerts a magneto-rotary effect on a ray of plane polarised light 
 passing along the tube in the direction of the axis of the helix. Such an 
 arrangement may be calibrated as an amperemeter, but it is only suitable 
 for a^very limited class of work. 
 
 (/) Electrostatic instruments. A current can be measured most 
 accurately by the measurement of the electrostatic fall in potential down 
 a conductor conveying the current. If a current is passed through 
 a known resistance, and if an electrostatic voltmeter or electrometer 
 is applied to measure the fall of potential down it, we have at once 
 a measure given of the strength of the current. 
 
 This last method in its various modifications is by far 
 the most practical and useful method of current measure- 
 ment. 
 
 The resistance through which the current to be measured 
 flows is not necessarily placed in the immediate neighbour- 
 hood of the potential-measuring apparatus. This last may 
 be either an electrostatic voltmeter, as described in the next 
 .section, or else an electromagnetic voltmeter effecting the 
 same purpose. 
 
 Further details will be given in the sections devoted to 
 current measurement. 
 
122 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 In addition to simple detectors, now and then required, by 
 far the most convenient form of galvanometer for all ordinary 
 work in the testing room and electrical laboratory are the 
 movable coil galvanometers. These consist of a fixed permanent 
 magnet having suspended between its poles a small light coil 
 of insulated wire. The current to be detected or measured 
 
 FIG. 43. Holden-Pitkin Movable Coil Galvanometer. 
 
 passes through the coil, entering and leaving, through the 
 suspending wires which may be arranged either bifilarly, 
 as in the Crompton pattern of galvanometer, or attached to 
 the top and bottom of the coil, as in the Holden-Pitkin 
 pattern. The movable coil galvanometer has two great 
 advantages in use : Firstly, it is not much affected by the 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 123 
 
 passage of currents in neighbouring wires or stray magnetic 
 fields, and hence may be used in places where an ordinary 
 
 . 44. Coil and Core of Holden-Pitkin Galvanometer. 
 
 Fio. 45. Ayrton-Mather Movable Coil Galvanometer. 
 
124 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 movable needle galvanometer would be useless; secondly, 
 the L coil can be very quickly brought to rest by short- 
 circuiting the terminals. Hence the galvanometer is or may 
 be made very dead-beat or damped. In the form designed 
 
 FIG. 46. Crompton Movable Coil Galvanometer. 
 
 by Holden and made by Pitkin (see Figs. 43 and 44), or 
 that designed by Ayrton and Mather and made by Paul 
 (see Fig. 45), or that designed and made by Crompton 
 (see Figs. 46, 47, and 48), the movable coil galvanometer is 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 125 
 
 by far the most practical and useful form of galvanometer 
 for an electrical testing laboratory. It was originally designed 
 
 FIG. 47. 
 
 by Lord Kelvin for cable signalling, although now often 
 called the d'Arsonval form of galvanometer. 
 
 FIG. 48. 
 
 The varieties of electromagnetic galvanometer which have 
 been designed are innumerable. In all of them the current 
 
126 ELECTRICAL LABORATORY EQUIPMENT. 
 
 in a conductor is measured by the measurement of the 
 mechanical action of the associated magnetic field either on 
 
 (a) Another magnet, 
 (&) A mass of soft iron, 
 
 (c) Another movable conductor carrying the same 
 current. 
 
 The magnetic force may produce, in either (a), (5) or (c), a 
 rotation or torque, or a forcive or bodily displacement. In 
 the first case a uniform field is required, in the second a 
 non-uniform field. Hence we may classify the fields as : 
 
 (A) Uniform for rotational deflection, 
 
 (B) Non-uniform for translational displacement. 
 
 Then the principal currents or current to be measured may 
 be in the fixed or the movable part of the instrument. 
 Hence we have a further classification into : 
 
 (a) Fixed coil galvanometers. 
 OS) Movable coil galvanometers. 
 
 Lastly, some arrangement, or control, is necessary to bring 
 back the displaced portion, whether magnet, soft iron or coil, 
 to its original zero position when the current is stopped. 
 This may be achieved by the aid of another magnetic field, or 
 the elasticity of a spring or torsion of a wire, or by the 
 weight or inertia of the moved mass. Hence we classify 
 according to the control into : 
 
 I. Magnetic control, 
 II. Elastic control, 
 
 III. Gravity control, 
 
 IV. Inertia control. 
 
 We can, therefore, symbolise any given type of galvano- 
 meter by an expression of four symbols denoting the classes 
 in which it is placed. Thus the ordinary mirror Kelvin 
 galvanometer is represented by the symbol (aAaL). The 
 d'Arsonval or recorder type of galvanometer by the symbol 
 
ELECTRICAL LABORATORY EQUIPMENT. 127 
 
 (a A fill.). The above method of classification of galvano- 
 meters is that due to Prof. G. F. FitzGerald.* 
 
 In appraising a galvanometer, or evaluating its applica- 
 bility for any purpose, we have to take into account five 
 qualities which, when numerically expressed, may be called 
 the five specific constants of the galvanometer. These quali- 
 ties are : 
 
 (i.) The periodic time of the movable system, or time 
 of one complete small oscillation when the 
 movable part is disturbed and then left to 
 itself. 
 
 (ii.) The logarithmic decrement corresponding to different, 
 or some known, amplitudes of swing, i.e., the 
 logarithm (Napierian) of the ratio of the amplitude 
 of one excursion on one side to the next one on 
 the other side of the zero point* 
 (iii.) The sensitiveness, both ballistic and deflectional. 
 (iv.) The internal resistance, or coil resistance, 
 (v.) The zero-keeping quality, or degree of precision, 
 with which the movable part returns exactly to 
 the original zero position when disturbed and left 
 to itself again. 
 
 If the needle or coil of a galvanometer is disturbed, it 
 comes to rest after one or more vibrations. The time of one 
 complete vibration, or interval between passing the zero 
 point in the same direction, is called the periodic time. These 
 swings of the needle or coil are resisted by the air or other 
 causes of friction, and the amplitude of the excursions 
 gradually diminishes. If the amplitude of each swing is 
 measured, it will generally be found that successive ampli- 
 tudes decrease nearly in a. geometric progression. Hence, in 
 this case, the logarithm of one excursion bears a nearly 
 constant ratio to the logarithm of the next one. This ratio 
 is called the logarithmic decrement of the galvanometer. The 
 logarithms taken are generally Napierian. The logarithmic 
 
 * See The Electrician, Vol. XXXVIIL, p. 715. 
 
128 ELECTRIC A L LABOR A TOR Y EQ UIPMEN2. 
 
 decrement usually varies with the amplitude of the swing, 
 owing to the fact that the retardation experienced by the 
 coil or needle depends to some extent on the velocity with 
 which it leaves its zero position. 
 
 If a small constant current, say a micro-ampere, is passed 
 through the galvanometer coil, it will cause a certain steady 
 deflection of the movable needle or coil. These deflections 
 are nearly always read by means of a mirror and scale. A 
 concave mirror attached to the galvanometer needle, or coil, as 
 the case may be, has a ray of light thrown upon it and a sharp 
 image of an illuminated wire or incandescent lamp filament is 
 by it thrown upon a scale. The scale is generally placed one 
 metre or 1,000 millimetres from the mirror. 
 
 The sensitiveness or deflectional constant of a galvanometer 
 may be denned as the scale deflection in millimetres pro- 
 duced by a current of one micro-ampere passing through 
 the galvanometer coil, the scale being at one metre distance 
 from the mirror. It may also be stated in terms of the 
 potential difference in micro-volts, which must be applied 
 to the terminals of the galvanometer to produce this same 
 unit deflection, or as the deflection in millimetres, at metre 
 distance of scale, per micro-volt on the terminals. The sensi- 
 tiveness of a galvanometer must always be controlled by the 
 possession of good zero-keeping quality. By this is meant 
 that when the current is stopped the galvanometer needle 
 or coil returns again to a fixed and constant zero position. 
 It is easy to give a galvanometer a spurious sensitiveness, 
 but if the zero position of the movable portion is not constant, 
 the value of the galvanometer for quantitative purposes is 
 very small. 
 
 A galvanometer with a very large logarithmic decrement 
 is called a dead-beat galvanometer. One with a very small 
 logarithmic decrement is called a ballistic galvanometer. The 
 ballistic constant of a galvanometer is defined as the reciprocal 
 of the " throw " or excursion of the needle or coil when one 
 micro-coulomb of electric quantity is discharged through it. 
 
ELECTRICAL LABORATORY EQUIPMENT. 129 1 
 
 The electrical laboratory should be provided with a collec- 
 tion of movable coil dead-beat, and movable coil ballistic 
 galvanometers of various resistances, some large, 500 or 1,000 
 ohms or more, and some of low resistances, such as 0*5, 5 
 or 10 ohms. It is desirable also to have at least one very 
 sensitive Kelvin mirror astatic movable needle galvanometer 
 of 6,000 to 10,000 ohms resistance. 
 
 Generally speaking, tangent galvanometers and needle 
 instruments are more suitable for a physical laboratory 
 than for an electro-technical laboratory, the disturbances 
 caused by the presence of large electric currents rendering 
 it most difficult to use the movable needle deflectional 
 instruments. As regards ammeters, for ordinary working 
 purposes the most convenient are those which, like the 
 Weston ammeters, are movable-coil instruments. These 
 instruments are very dead-beat, and have equal or nearly 
 equal scale divisions per ampere or per milliampere. These 
 instruments are, however, only available for continuous 
 currents. 
 
 For use with alternating currents, some form of hot-wire 
 ammeter, such as that of Hartmann and Braun, is very^ 
 useful. Its indications are entirely independent of the 
 frequency of the alternations, and the instruments are also 
 very dead-beat. 
 
 For many purposes the Siemens dynamometer is an 
 invaluable laboratory instrument (see Fig. 49). It consists 
 of a fixed coil or coils, and a suspended coil which embraces 
 the fixed coil, and the normal position of which is with 
 its plane or axis at right angles to the plane or axis of 
 the fixed coil. The movable coil is hung by a few fibres 
 of floss silk, and its position is controlled by a spiral spring, 
 the lower end of which is attached to the movable coil and 
 the upper end to a torsion-head. The current is led into and 
 out of the movable coil by means of mercury cups. The 
 wires forming the fixed and movable coils should always 
 be brought to separate terminals. The instrument can then 
 
130 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 be used for several purposes. If the coils are joined in 
 series, and a current, either alternating or continuous, sent 
 through them, forces are brought into existence which 
 cause the movable coil to be acted upon by a couple or 
 torque, and to be twisted round. If, then, a contrary twist 
 is given to the torsion-head and the movable coil brought 
 back to its zero position, the angular twist required to 
 effect this is proportional to the square of the strength 
 of the current. The dynamometer can thus be calibrated 
 
 FIG. 49. Siemens Electrodynamometer. 
 
 to measure current strength. If the current is unvarying, 
 the square root of the torsion or scale reading gives, when 
 multiplied by a constant, the current strength. If the 
 current is alternating and periodic it gives the square 
 root of the mean of the squares of the equi-distant 
 instantaneous values during the period or the root-mean- 
 square (RM.S.) value of the current, provided that the 
 periodic time of the current is small compared with the 
 periodic time of a free oscillation of the movable coil. If 
 
ELECTRICAL LABORATORY EQUIPMENT. 131 
 
 different currents are sent through the two coils the 
 instrumental readings can be made to give the mean 
 value of the product of their maximum values multiplied 
 by their power-factor or cosine of the angle of phase 
 difference, if the currents are simply periodic. 
 
 13. Yoltage Measuring Instruments Any of the 
 
 above galvanometers or amperemeters, if wound with 
 wire of sufficiently high resistance, becomes an instrument 
 which may be used for the determination of the steady 
 potential difference between two points. For the current 
 through any current-measuring instrument is proportional 
 to the steady potential difference between its terminals, 
 and inversely as the resistance of the instrument. Hence, 
 if the resistance of the instrument is so high (say, 1,000 
 to 20,000 ohms) that the current it takes off, when placed 
 as a shunt circuit between two points on any other circuit, 
 open or closed, does not disturb sensibly the potential 
 difference between those points, the indications of the 
 instrument are proportional to the original potential differ- 
 ence between those points. 
 
 For many laboratory purposes electromagnetic voltmeters^ 
 as they are called, of the above type will be found convenient. 
 
 There are, however, many measurements in which it is 
 desirable that no current shall be taken off between the 
 points, the potential difference (P.D.) of which is required. 
 Also it is often necessary to use the same instrument for 
 continuous and for alternating currents. In these cases the 
 best voltage-measuring instruments to employ are the electro- 
 static voltmeters. These, are now made to measure voltages 
 varying from 1 volt up to 40,000 volts or more. Their 
 general principle is as follows : 
 
 Let there be two sets of plates or metallic surfaces, one 
 fixed and the other suspended, so as to be capable of moving 
 in between the fixed surfaces. Let the normal position of the 
 movable plate be just outside the fixed one. The two sets 
 
132 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 of plates are insulated from each other, and thus form a con- 
 denser or Leyden jar having a certain capacity. If we 
 produce a certain potential difference between these plates, 
 this P.D. brings into existence forces of attraction between the 
 plates proportional to the square of the difference of potential, 
 
 FIG. 50. Kelvin Multicellular Electrostatic Voltmeter. 
 
 and therefore independent of its sign. This force draws 
 the movable plates in between the fixed ones, so as to 
 increase the capacity of the condenser formed by the two 
 plates or sets of plates. If this force is resisted, either by 
 the torsion of a suspending wire or by gravity, we have 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 133 
 
 an'arrangement called an electrostatic voltmeter, which can be 
 calibrated to show difference of potential, either the steady 
 value or the root-mean-square value, according as the pressure 
 is uniform or periodic. 
 
 Voltmeters of this form have been designed by Lord 
 Kelvin, Prof. Ayrton, and others. Of these the most 
 
 FIG. 51. Kelvin Electrostatic Voltmeter. 
 
 convenienOo-rm f or the electrical engineering laboratory are 
 thThorizontal and vertical pattern of multicellular electro- 
 static voltmeters, as designed by Lord Kelvin for measuring 
 electrical potential difference from 50 to 150 or 250 volts (see 
 Fig. 50) ; high-pressure electrostatic voltmeters, as designed 
 by Lord Kelvin (see Fig. 51) and by Prof. Ayrton for high 
 
134 ELECTRICAL LABORATORY EQUIPMENT. 
 
 pressures from 1,000 to 2,500 volts; and the low-pressure 
 electrostatic voltmeters of Prof. Ayrton, for pressures from 
 2 to 50 volts, are also exceedingly useful instruments. 
 
 These electrostatic voltmeters are also available as current- 
 measuring instruments. If a current is sent through a 
 resistance, and the fall of potential down the resistance is- 
 measured by a correct electrostatic voltmeter, the current 
 through the resistance becomes known. This method of 
 current-measuring is convenient in measuring small alter- 
 nating currents, such as the magnetising current of a 
 transformer. 
 
 Electrothermal voltmeters, such as those of Cardew r 
 Holden, and Hartmann and Braun, are at times required 
 when dealing with alternating currents. They are, however, 
 less generally useful than the electrostatic instruments 
 because they take up much more power to operate them. 
 
 As regards the method of standardising all the above 
 instruments, and obtaining measurements of current and 
 potential difference by means of the potentiometer method, 
 the details of these processes will be discussed in a later 
 section of this treatise. 
 
 The instrument called the potentiometer is of the greatest 
 utility in the electrical laboratory, and a good potentiometer 
 is one of the fundamental requisites of an electrical testing 
 room. In its simplest form it consists of a uniform wire 
 stretched over a scale divided into 2,000 parts. This wire 
 has its extremities connected to a couple of secondary cells 
 (see Fig. 52), and an interpolated resistance inserted in the 
 circuit. By varying this resistance it is possible to adjust 
 the current in the wire so that the fall of potential down 
 a length of the wire equal to 2,000 scale divisions is just 
 2 volts. This is achieved by placing a Clark cell and a 
 sensitive galvanometer .as a shunt on the wire, and making 
 contact at two scale divisions 011 the wire the interval 
 between which corresponds numerically to the electromotive 
 force value of the Clark cell. Thus, suppose the cell has an 
 
ELECTRICAL LABORATORY EQUIPMENT. 135 
 
 electromotive force of 1434 volts at 15C., then two sliding 
 contacts on the galvanometer and standard cell circuit are 
 set to make contact at the zero and at the 1,434th scale 
 division. When this is done the resistance in series with the 
 two-cell secondary battery is altered until the galvanometer 
 indicates no current. In order that it shall be possible to do 
 this, the positive pole of the Clark cell must be connected 
 with that end of the potentiometer wire to which is joined the 
 positive pole of the secondary cells, called the working 
 battery. When this adjustment is made, the potentiometer 
 is said to be set. If, then, it is desired to measure any other 
 potential difference, say that due to the passage of a current 
 
 FIG. 52. 
 
 through a low resistance, wires called potential wires are 
 brought from the ends of this resistance, and in one of these 
 circuits a galvanometer is inserted. One potential wire viz., 
 that attached to the highest potential point is joined to that 
 end of the slide wire in connection with the positive pole of 
 the working battery. The other potential wire is attached to 
 a slider making a variable contact on the slide wire. The 
 slider is then moved until the galvanometer indicates no 
 current. This can be always done if the fall in potential 
 down the resistance is less than that down the slide wire. The 
 reading on the slide wire, as shown by the position of 
 the slider, gives at once the potential difference in volts 
 between the potential wires. 
 
136 ELECTRICAL LABORATORY EQUIPMENT. 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 137 
 
 The practical potentiometer takes one of two forms. It 
 may be, as described, a simple slide wire potentiometer, or 
 the slide wire may be in part or in whole replaced by coils 
 of wire arranged in series, as in the potentiometers of 
 Crompton, Fleming, Nalder, Wulf, and others. 
 
 The electrical laboratory should be provided with one 
 or two potentiometers.* One should be a simple slide wire 
 instrument for rough work, the other a standard instrument 
 for exact work, made entirely with carefully adjusted coils of 
 wire. 
 
 If- 
 
 Secondary Battery, 
 do SO 80 70 60 60 40 ( 
 
 3 30 20 10 a 4 * 
 
 a 10 17 i 
 
 B SCALE 
 ( I 100 volts. 
 
 Galvanometer 
 
 1 -> 
 
 
 R High Resistance. 
 
 I () MWWVW 
 
 AdjuKtahU 
 
 FIG. 53A. Crompton Potentiometer Connections. 
 
 The Crompton potentiometer is shown in Fig. 53, and the 
 connections in Fig. 53A. The external appearance of the 
 Nalder potentiometer is shown in Fig. 54. In the former 
 (the Crompton) instrument the slide wire consists of 14 coils 
 placed inside the case of the instrument, and a slide wire 
 equal in resistance to one of these coils stretched over a scale 
 outside the box. In series with these coils is a circular 
 rheostat for adjusting the potentiometer current. There is 
 a double pole six-way switch, which enables any one of six 
 
 * The arrangement now called the potentiometer was first described by 
 Poggendorff, Poggendor/'s Annalen, Vol. LIV., page 161, 1841. The method of 
 making the potentiometer direct reading, so as to give the potential difference 
 without calculation, is due to the Author, and was first described in Industries, 
 July and August, 1886. 
 
138 ELECTRICAL LABORATORY EQUIPMENT. 
 
 test circuits to be placed in series with a galvanometer and 
 in shunt with any portion of the slide wire. The galvano- 
 meter circuit has one end attached to a sliding contact 
 which moves over the slide wire. The other end can be 
 attached to the junction between any one of the 14 coils in 
 series with it. When the potentiometer is " set," the current 
 through the slide wire is such as to make the fall in potential 
 down the whole wire 1*5 volts. The scale is divided into 
 
 FIG. 54. Nalder's Potentiometer. 
 
 1,000 parts, and each slide wire unit represents one-ten- 
 thousandth of a volt. 
 
 In the Nalder instrument the whole of the slide wire 
 consists of coils placed within the box containing the instru- 
 ment, and contact is made with the junction between these 
 coils by means of a circular revolving arm. 
 
 In Fig. 55 is shown a diagram of the connections of 
 the instrument as depicted in Fig. 54. Eeferring to the 
 second figure, it may be seen that a secondary battery 
 is joined on to the terminals F, and sends a current 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 139* 
 
140 ELECTRICAL LABORATORY EQUIPMENT. 
 
 through the resistances connected with the dials C and D, 
 and then through adjusting resistances K and H. The 
 dial D has 100 equal coil resistances in it, the whole 
 set being equal to the resistance of one coil in C. The 
 dial K contains 19 equal small wire resistances, and the 
 resistance H is a carbon resistance for fine adjustment. 
 A standard cell is joined up to A A, and a galvanometer 
 to the terminals marked galv. If the cell has a voltage 
 14412 volts, the arm of dial C is set to 144 and that 
 of D to 12. The resistances H and K are then adjusted 
 so that the galvanometer shows no current, and the 
 potentiometer is then " set." The voltage to be measured 
 is connected to the terminals B B if below 1*6 volts, and if 
 above that to the terminals marked volts, in Fig. 55, which 
 are bridged by a wire of high resistance. A fraction of 
 this potential difference, either J, T ^, TOO, or 3^, is then 
 measured, according as the switch M is on the contact 
 marked 3, 10, 100, or 300, 
 
 In practice it is found that potentiometers in which 
 the contact with the galvanometer circuit is made either 
 by rubbing or pin contacts, or by a slide contact moving over 
 a wire, give trouble owing to imperfect contacts due to 
 the deposition of dust on the contact surfaces and on 
 the wire, and time is wasted in getting the necessary 
 adjustments made. These defects led the Author to design 
 a form of potentiometer in which there is no slide wire 
 and no rubbing or pin contacts, but in which the whole 
 of the potentiometer wire or resistance is represented by 
 coils of wire contained in a case. The galvanometer circuit 
 containing the electromotive force to be measured is brought 
 to two terminals, which are in connection with two bars 
 or rings of brass, by means of plugs fitting into holes 
 bored out partly in these bars or rings and partly in 
 adjacent metal blocks. It is possible to insert any required 
 portion of the whole potentiometer wire resistance, within 
 limits, in between the galvanometer terminals, whilst at the 
 
ELECTRICAL LABORATORY EQUIPMENT. 141 
 
 same time resistance is~ added or subtracted from a main 
 current circuit, on which the galvanometer circuit is a shunt, 
 in such fashion that a constant current flows through the 
 main potentiometer circuit. This compensating resistance is 
 added or removed by plugs, as in the case of a plug pattern 
 Wheatstone bridge. Fuller details of the use of the instru- 
 ment will be given in a later section of this work. 
 
 Generally speaking, the most convenient ammeters for 
 laboratory use are those which depend upon the measure- 
 ment of the fall of potential down a low resistance. The 
 ammeter then consists of two parts : 
 
 (L) A suitable resistance, which carries practically the 
 whole of the current, and which may even be 
 removed a considerable distance from the re- 
 mainder of the instrument. 
 
 (ii.) A potential measuring part, which consists of some 
 form of movable coil galvanometer of high 
 resistance, or for special tests may be a potentio- 
 meter. 
 
 The galvanometer will generally take the form of a 
 permanent and well-aged magnet for producing a field 
 in which is suspended a light high resistance coil, with 
 pointer attached, moving on jewelled centres, and also- 
 a steel spiral controlling spring to keep the coil in a 
 normal position, and against which the electromagnetic 
 force acts (see Fig. 56). These instruments have the 
 advantage that the scale divisions are usually very nearly 
 equidistant. There is no blank part or non-readable portion 
 of the scale, and they are also very dead-beat. In Fig. 56 is 
 shown part of the mechanism of a Siemens and Halske volt- 
 meter constructed on the above principle. Part of the 
 magnet is removed to show the coil. The coil consists of an 
 insulated wire wound on a copper frame to damp the move- 
 ments. The coil has attached to it an index needle, and its 
 displacement is resisted by a steel spiral spring. The 
 
142 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 resistance traversed by the current to be measured may be 
 contained in the case of the instrument, or it may be entirely 
 
 FIG. 56. 
 
 separate and used B outside. In Figs. 57 and 58 are shown the 
 -details and mode of use of an Arnoux-Chauvin dead-beat 
 
 FIG. 57. 
 
 ammeter and shunt constructed on the above principles, 
 consisting of a high resistance movable-coil galvanometer 
 
ELECTRICAL LABORATORY EQUIPMENT. 143 
 
 with equi-divisional scale used as an ammeter by measuring 
 the fall in potential down a low resistance shunt of known 
 value. 
 
 Instruments of the above-described type are much 
 employed in the laboratory as ammeters and voltmeters 
 for the measurements of continuous currents and potential 
 differences. A series of very convenient and portable 
 
 FIG 58 
 
 instruments of the above kind have been devised by Mr. 
 Weston. These are remarkable for the almost exact 
 equality of distance of the scale divisions. They are made 
 for various ranges of work, such as ammeters to measure 
 from to 15 amperes, O'O to 100 amperes, milliamperemeters 
 and voltmeters. 
 
144 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 The three most convenient "Weston instruments for general 
 laboratory work are the ammeter, reading from zero to 15 
 amperes ; the milliammeter, reading from zero to 1*5 
 amperes by hundredths of an ampere ; and the voltmeter, 
 which reads from zero to 150 volts on one pair of terminals 
 and from zero to 15 volts on another pair. 
 
 Instruments of a similar kind are made by many other 
 manufacturers. 
 
 13. Resistance-Measuring Instruments. The com- 
 parison of conductors in regard to the quality called their 
 electrical resistance is generally conducted by means of 
 
 FIG. 59. Wheatstone's Bridge, arrangement of Circuits. 
 
 instruments technically termed bridges or Wheatstone's 
 bridges, provided the resistances to be compared are neither 
 of them very large or very small in magnitude. In its 
 simplest form the arrangement called a Wheatstone bridge 
 consists of six conductors joining four points. In one of 
 these circuits is placed a source of electromotive force such 
 as a battery, and in one other circuit, called the conjugate 
 circuit, is placed a galvanoscope for detecting the presence or 
 absence of a current. 
 
 The circuit arrangement is depicted in Fig. 59. When the 
 resistance of the circuits is so adjusted that closing the battery 
 circuit (B) does not produce any permanent current in the 
 conjugate galvanometer circuit (G), the " bridge " is said to be 
 
ELECTRICAL LABORATORY EQUIPMENT. 145 
 
 balanced. To effect the balancing, two of the resistances 
 (P and Q) are adjusted to a certain ratio, and these are called 
 the ratio arms of the bridge. Of the other pair of resistances 
 or arms of the bridge, one is a standard of resistance (S) and 
 the other (E) is the resistance to be compared. The balance 
 is obtained either by altering the ratio arms or by altering the 
 value of the resistance of the standard or measuring arm. 
 The bridge may be employed in one of two ways : 
 (i.) To obtain the ratio of two resistances, 
 (ii.) To obtain the difference of two resistances. 
 The first method is the one generally employed in ordinary 
 work, and may be called the Wheatstone method. The 
 second is that used in very exact work, and is due to Prof. 
 G. Carey Foster. 
 
 The ordinary bridge, as a laboratory instrument, takes one 
 of two forms : 
 
 (i.) The Slide Wire Bridge, in which the ratio arms can 
 be continuously varied, and the standard of 
 resistance generally remains unchanged, 
 (ii.) The fixed coil pattern, or Plug Bridge, in which the 
 ratio arms can only be given certain decimal 
 ratios, but the standard or comparison resistance 
 can be varied within wide limits by adding fixed 
 resistances in series. 
 
 The complete theory of the bridge will be considered in 
 Chapter II. under the head of KESISTANCE MEASUREMENT ; 
 but meanwhile we may state the simple principles of the 
 bridge as follows : 
 
 First, let it be assumed that the bridge is balanced. Then 
 it is clear that, starting from point a, the voltage or fall in 
 potential down P and E is the same, because the points b and 
 d are, by supposition, at equal potentials, as they must be if 
 no current flows through the galvanometer. Similarly the 
 potential fall down Q and S is equal. Call these potential falls 
 Vp, V Q , V B , V s . Then also, since no current flows through 
 the b d circuit or galvanometer circuit, we must have equality 
 
146 ELECTRICAL LABORATORY EQUIPMENT. 
 
 in the currents in P and Q and in those in E and S. Call 
 these currents C P , C Q , CR, C s , and the resistances of the arms 
 P, Q, E, S. Then we have 
 
 also C P =:C Q and C R =C S . 
 
 But, by Ohm's law, . P =P,-- Q =Q, R =E,-^ S =S. 
 
 Hence J=? or E=rS^. 
 
 Q S Q 
 
 If the bridge is not balanced that is, if the current 
 through the galvanometer circuit is not zero, but has a value 
 C, then it will be subsequently shown that the galvano- 
 meter current can be calculated from the expression 
 
 where E is the electromotive force of the battery and 
 
 . E+S)+r(P+E Q + S) 
 
 i 
 
 E being the resistance of the battery circuit, and r that of 
 the galvanometer circuit.* 
 
 The practical forms of bridge required in the electrical 
 laboratory are as follows : 
 
 I. A standard slide wire bridge, for the careful comparison 
 of standard coils with other nearly equal resistance coils. 
 
 II. A simple form of plug bridge, for approximate measure- 
 ments of resistance. 
 
 III. A well-constructed form of dial plug bridge, for 
 accurate work. 
 
 IV. A differential bridge, for exact comparisons between 
 standard coils. 
 
 V. A low-resistance bridge, for very small resistances. 
 
 * For the method of dealing with problems of networks of conductors see 
 2, Chap. IT., where the reader is referred to a Paper by the Author in the 
 Phil. Mag., August, 1885 ; also Proc. Phys. Soc. London, Vol. VIL, 1885. 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 147 
 
 The simplest form of (I.) or slide wire bridge consists of a 
 stout mahogany board, on which is strained a gilt manganiii 
 or platinum-silver wire, the wire being uniformly stretched 
 between heavy terminal pieces of copper. The ends of this 
 wire are united by a parallel bar of copper in which are two 
 gaps, one to be closed by the standard resistance (S) and the 
 other by the resistance (E) to be measured. These resistances 
 are inserted either by means of good terminal screws or by 
 the use of mercury cups. In the practical construction of a 
 slide wire bridge one of the difficulties consists in keeping 
 
 FIG. 60. Simple Slide Wire Resistance Bridge. 
 
 the slide wire tight and yet in allowing it to expand or 
 contract. The arrangement of the simple slide wire bridge 
 is shown in Fig. 60. The slide wire is attached to thick end 
 blocks of copper drawn back by springs which keep the 
 wire just tight enough without overstraining it. By cali- 
 brating the wire, as explained in the next section, the 
 resistance of these copper terminal blocks can be deter- 
 mined in terms of the resistance of a centimetre of length of 
 the wire. Over the slide wire moves a slider (c) having a knife- 
 edge contact and key, and parallel with the slide wire is a 
 divided scale equal in length to the slide wire. The battery, 
 
 L2 
 
148 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 consisting of two or three dry cells, is connected to the end& 
 of the slide wire through a contact key, and the galvanometer 
 is connected to a terminal between the standard resistance 
 and resistance to be measured and the knife contact of the 
 slides. The galvanometer used with the bridge is preferably 
 one of the movable coil dead-beat type. The battery may 
 consist of three dry cells. The operation of measurement 
 consists in finding the point at which the slider must make 
 contact with the wire so that no current passes through the 
 galvanometer. The ratio arms of the bridge are then the 
 sections into which the slider divides the slide wire, and 
 the value of the resistance (R) being tested is equal to> 
 
 FIG. 61. Double-gap Slide Wire Bridge. 
 
 the comparison resistance (S) multiplied by the ratio (P : Q'); 
 of the slide wire sections. Increased sensitiveness is given, 
 to this bridge by making double gaps in the copper bar and 
 adding two more coils or resistances to the ends of the slide 
 wire. These coils are then extensions of the slide wire, and the 
 slide wire becomes only a portion of the ratio arm resistance. 
 Thus, let the resistances of these added coils (see Fig. 58) 
 be A and B, and let x and y be the lengths of the sections, 
 into which the slide wire is divided by the contact piece (c) 
 when the balance is obtained. Then, if R is the resistance 
 being measured and S is the standard resistance, we have 
 
ELECTRICAL LABORATORY EQUIPMENT. U9 
 
 A displacement of the slide of one millimetre along the slide 
 wire corresponds then to a much less difference between E 
 and S than would be the case if the coils A and B were not 
 present. This extension enables us to compare together very 
 accurately two coils by measuring the difference between the 
 resistances of the two coils by a method due to Prof. Gr. 
 Carey Foster, and also to calibrate the wire or determine the 
 resistance of the slide wire per unit of length. 
 
 Let the bridge be first balanced with coils A and B (as 
 .shown in Fig. 61). 
 
 Then let the position of the coils A and B be interchanged 
 .and a fresh balancing position be found at a distance x r 
 divisions of the slide wire from the left hand end. 
 
 Let p be the resistance of the length of x divisions of the 
 .slide wire, and let W be the resistance of the whole slide 
 wire a b. 
 
 Let p' be the resistance of the length of the x' divisions of 
 the slide wire. 
 
 Then corresponding to the two cases we have resistance 
 -equations 
 
 R:S=B+/>':A+W P'. 
 
 A+p B + W-p 
 
 Hence lT - -.= . ^ T - M 
 
 B+p' A+W p 
 
 or 
 
 B+W p~A+W-p' 
 "Therefore it follows that 
 
 A-B-W+2p_B-A W+2p' 
 A + B+W B+A+W 
 
 or A-B=p' p. 
 
 In other words, the difference of the two resistances A and B 
 is equal to the resistance of that length of the slide wire 
 included between the x' and x divisions at which the balance 
 is found on the slide wire in the two experiments. 
 
150 ELECTRICAL LABORATORY EQUIPMENT. 
 
 If, then, the wire is of uniform resistance per unit of length, 
 and if this resistance per centimetre is known, the difference 
 between the resistances A and B is known. 
 
 The slide wire can be calibrated or tested for uniformity 
 as follows : 
 
 In place of the resistances K and S substitute another 
 slide wire and another contact slider piece, so that the ratio 
 arms of the bridge can be varied at pleasure. Then by moving 
 the second slider the balancing position on the slide wire a b 
 can be brought to any required position for any two given 
 coils A and B. For A and B select two coils of wire having 
 a very small difference in resistance, and proceed as above 
 described to find the length x'x of the bridge wire which 
 has a resistance equal to A B. Then move the second slider 
 a little, so as to change the ratio of K : S, and find again in 
 another place on the slide wire a b the length x'x equal in 
 resistance to A B. If this length x' x is not equal to the 
 same number of slide wire divisions in all parts of the wire> 
 the wire is non-uniform in resistance. It is possible, by 
 moving the second slider, to regularly inspect and measure 
 the resistance per centimetre of the slide wire; but the 
 process of applying the necessary correction for non-uni- 
 formity of slide wire is so troublesome in practice that it is 
 better to reject the slide wire if non-uniform and obtain 
 another and better wire. 
 
 If, then, we obtain a slide wire the resistance of which 
 per centimetre is uniform and is known, we can at once 
 determine the difference in resistance between any resis- 
 tance coil and a standard resistance not differing from it 
 in resistance by a greater amount than the resistance of the 
 whole slide wire. 
 
 The Author designed in 1880 a special form of slide wire 
 bridge for making such difference measurements very quickly, 
 and this has been found especially convenient in comparing 
 together standard coils and others intended for standards.* 
 
 * This bridge is still employed at the Cavendish Laboratory, Cambridge, in 
 the comparison of standard coils. 
 
ELECTRICAL LABORATORY EQUIPMENT. 151 
 
 Following is a description of this form of standard comparison 
 bridge : 
 
 Description of the Resistance Balance. A circular disc of 
 mahogany 18in. in diameter and about lin. thick (/, Figs. 62 
 and 6:3) stands upon three short feet, L. Upon this, and con- 
 centric with it, is screwed down a disc of ebonite 14in. in 
 diameter and fin. thick (e). This ebonite disc has a semi- 
 circular groove turned in its circumference. The circular 
 wooden base extends on one side into a narrow rectangle,/, 
 4in. wide and of the same thickness as the disc. To this are 
 connected two other rectangular pieces Ji, i, which are joined 
 together by slotted brass bars y, (Fig. 62) underneath, in 
 such a manner as to permit the two intervals to be made 
 wider or narrower at pleasure. This promontory is of wood, 
 of the same material and thickness as the disc/, and is sup- 
 ported and levelled by three levelling-screws, n, n', n". 
 Through the centre of the ebonite disc passes a brass centre- 
 pin 1) D' (Fig. 62), on which is centred a brass arm, H H', 
 capable of revolving just clear of the disc. Beneath the 
 arm, and soldered to it, is a short brass spring x } which 
 depends vertically downwards. This spring carries at its 
 extremity a small prism of platimmi-iridiuin with one edge 
 vertical and turned inwards. In the groove turned in the 
 disc e is stretched a platinum-iridium wire about /oin. 
 in diameter. The wire extends round about f f of the 
 circumference, and is about 39in. long ; and the groove is of 
 such a size that the wire lies with exactly half its thickness 
 embedded in it. This wire is represented by the thick black 
 line A C A' in Fig. 62. The ends of this wire are soldered to 
 copper strips k, k. On the wood rectangles /, h, i is fastened 
 an arrangement of longitudinal copper strips k, k, which 
 connect together eight transverse square copper bars in the 
 manner shown in Fig. 62. On the ends of these transverse 
 bars are fixed vertical copper pins j^in. i n diameter and fin. 
 high. On these pins are slipped short lengths of india- 
 rubber tube, which extend beyond the pins so that they form 
 
152 ELECTRICAL LABORATORY EQUIPMENT. 
 
 j 
 
 1 
 o 
 
 to 
 
 a 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 153 
 
 small cups about lin. deep, p' (see Fig. 62). The top of the 
 copper pin is well amalgamated with mercury, and forms the 
 bottom of the cup. These cups are filled about a quarter full 
 of mercury. On the longitudinal strips of copper are fixed 
 three binding screws B, B', G ; and a fourth (G') simply goes 
 through the wood, and is connected by a wire t underneath 
 the baseboard with the centre-pin D, and is therefore in 
 metallic connection with the spring x. The battery is connected 
 with the terminals B, B', and the galvanometer with the 
 terminals G, G'. To the arm H H' is adapted a trigger, T, 
 of such shape that when the button iv, which is of ebonite, 
 
 FIG. 63. 
 
 is pressed down, the spring x, carrying the platinum-indium 
 knife-edge, is bent inwards until it touches the wire strained 
 round the circumference of e. The arm caries a vernier, N,, 
 which travels round sunk in a shallow groove in the face 
 of the ebonite disc ; and the ebonite is graduated on the 
 face on the margin of the groove. The graduations are cut 
 into the ebonite, and then rubbed over with powered chalk 
 mixed with gum and water. This gives a graduation very 
 legible and pleasant to look at. The length of the wire is 
 just one thousand divisions ; and the vernier enables these 
 to be divided into tenths. The zero of graduation is so 
 
lf>4 ELECTRICAL LABORATORY EQUIPMENT. 
 
 placed that, when the pointer of the vernier reads zero, the 
 knife-edge on the spring x is exactly opposite the extremity 
 of the platinuiii-iridium wire. 
 
 It is thus clear that the revolving arm carrying its knife- 
 edge can be moved round so that, on pressing the trigger 
 button w, the knife-edge makes contact at any point of this- 
 wire, and thus connects this point with the terminal G'. 
 
 This part of the arrangement answers to the sliding block 
 and piston-contact piece of the ordinary divided-metre bridge. 
 
 Method of using the Balance. Let now two resistance 
 coils of about equal resistance be provided, and let the coil 
 terminals of one coil be placed in the mercury cups p and r, 
 and those of the other be placed in q r and &'. And let two- 
 more coils be taken of not very unequal resistance which it is 
 desired to compare with each other ; let the terminals of one 
 be placed in the mercury cups a and c } and those of the other 
 in b f and d'. It will then be seen that, if a battery be 
 connected with B B' and a galvanometer with G G', that we 
 have the usual Wheatstone bridge arrangements (see Fig. 64 
 for a diagram of the connections). Two quart Leclanche cells- 
 are best suited for ordinary use. If a more powerful battery 
 is used, there is danger of heating the platinum-indium wire,, 
 and so expanding it that it may slip down out of its groove. 
 
 The coils in the intervals between the cups p and r and q r 
 and s f form two branches; and the coil in the interval 
 between a and c, together with the resistance of the platinum- 
 iridium wire round to the place where the spring x touches- 
 it, forms the third branch, whilst the coil in the interval V d' f 
 together with the remainder of the wire, forms the fourth. 
 The " bridge " wire consists of the arm H H' and the wire 
 under the baseboard, together with the galvanometer inserted 
 between G and G'. By moving round the arm H H' and 
 pressing the button u\ we can find a position where there is 
 no current through the galvanometer. The copper strips 
 kk are made of copper so thick that their resistance is 
 practically nothing. Having established a balance between 
 
ELECT RICA L L A DORA TOR Y EQ U1PMENT. 
 
 155 
 
 the conductors and read the vernier, the next operation is to* 
 lift up the legs of the coil which were inserted in the cups a 
 and c and drop them into the cups b and d. Likewise a 
 similar change is effected on the other side; the terminals 
 of the coil inserted in I' and d r are changed to a' and c'. 
 An examination of the connections as shown in Fig. 64 will 
 show that the result of the operation is as if the coils had 
 changed places whilst preserving their former connection, 
 Now let the arm be moved round and a fresh position of 
 equilibrium found by pressing the trigger and reading the 
 vernier. A little consideration will show that the difference 
 
 COIL 
 
 FIG. 64. 
 
 of these readings gives the difference between the resistances 
 of the coils in terms of a length of the bridge wire ; for the 
 amount by which one coil exceeds the other in resistance is- 
 equal to the resistance of that part of the bridge wire included 
 between the two readings.* In order to render this method 
 of determining the difference of the two coils practicable, the 
 platinum-iridium wire must be exceedingly uniform in 
 
 * This method of obtaining the difference of two resistances in terms of a 
 length of the calibrated bridge wire was suggested by Prof. G. C. Foster, F.R.S., 
 in a Paper read before the Society of Telegraph Engineers, May 8, 1872. 
 In this Paper is given an account of the method of calibrating a wire. It is 
 obvious, without any further proof, that if the coil placed in a and c exceeds- 
 in resistance that placed in 6 and d, then on exchanging them, since the united 
 resistance of coils and bridge wire remains the same, that the contact knife- 
 edge must be moved back along the bridge wire by a length exactly equal in 
 resistance to the excess of one coil over the other. 
 
156 ELECTRICAL LABORATORY EQUIPMENT. 
 
 resistance, or else a table of calibration will have to be 
 made. Great pains were taken to procure a length of wire 
 as uniform in size and resistance as possible ; and considerable 
 care was taken, in laying the wire in its groove, not to strain 
 it in any way. It lies evenly in its groove, just sufficient 
 tension being put upon it to keep it in its place. The whole 
 resistance of the wire from end to end is not far from 
 oV of an ohm at about 15C. 
 
 The wire was carefully calibrated by measuring the difference 
 in the resistance of two pieces of thick brass wire of such lengths 
 that the difference of their resistances was about equal to 
 that of thirty divisions of the bridge wire : and this difference 
 was measured at about a hundred different equidistant 
 positions all along the bridge wire, and found to be so nearly 
 the same that no table of calibration was deemed requisite. 
 To protect the bridge wire from injuries, as well as to preserve 
 it from being heated by radiation from surrounding bodies, a 
 wooden ring vv is fastened down on the baseboard. The 
 ring is IJin. wide and fin. deep, and its internal 
 diameter is lin. greater than that of the ebonite disc. The 
 wire, therefore, lies hidden away on the side of a square- 
 sectioned circular tube ; and, furthermore, a shield of 
 cardboard faced with tinfoil lies upon the face of the disc e, 
 extending just beyond the ring. An aperture is cut in this 
 shield to permit the passage of the trigger, as well as to allow 
 the vernier to be read. By this means the wire is not only 
 out of sight, but out of reach of all radiation as well as 
 mechanical injury. 
 
 Arrangements for determining the Temperature Variation 
 Coefficients of Coils. To determine the temperature variation 
 coefficient of any given coil we proceed as follows : Three 
 other coils are provided, two of them nearly equal in resistance, 
 which we will call 1 and 2. A third coil, 3, must be taken, 
 whose resistance is nearly equal to that of 4, the coil whose 
 variation coefficient is desired (see Fig. 62). The terminals of 
 3 are inserted in the mercury cups a and c, those of 4 in V and 
 
ELECTRICAL LABORATORY EQUIPMENT. 157 
 
 d', those of 1 in p and r, and those of 2 in q r and s'. Now the 
 operation to be conducted is to keep the coils 1, 2, and 3 at a 
 fixed temperature, and to keep 4 successively at two known 
 temperatures differing by about 15C., and to obtain the differ- 
 ence of the resistances of 3 and 4 at these two temperatures. 
 The difference of these differences, divided by the difference of 
 the temperatures, is the mean coefficient of variation of resist- 
 ance between these temperatures. The chief difficulty to be 
 contended with is that of keeping the temperature of the coils 
 constant during the operation, and of ascertaining what that 
 temperature is ; for, as Prof. Chrystal has remarked in his 
 report (Brit. Assoc. Report, 1876), it is not easy to tell whether 
 the temperature of the water in which the coil rests is identi- 
 cally the same as that of the wire, since the latter is embedded 
 in a mass of slowly conducting paraffin. To reduce as far as 
 possible the difficulty of keeping the coils at a constant tem- 
 perature, they are placed in water vessels made of zinc (see 
 Fig. 65). These water boxes are composed of two cylindrical 
 vessels an outer case 9iu. high and 8in. in diameter, and an 
 inner one of lesser size ; the two are connected at the top, so 
 that they form a sort of jar with hollow sides and double 
 bottom. This interspace forms an air-jacket. Around the 
 inside vessel near the top is a row of small holes ; and two 
 tubes communicate at the bottom one with the inner vessel 
 and the other with the annular interspace. The top is closed 
 by a wooden lid with apertures for thermometer and stirrer. 
 Water can be made to flow from the supply pipes into the 
 inner vessel : it rises up and overflows through the holes, and 
 drains away down the interspace and out by the other pipe. 
 The bodies of the four coils are placed in four water boxes 
 of this description; and water from the town mains being 
 sent in a continuous stream through all four water boxes, the 
 coils are rapidly brought to and maintained at a known 
 temperature. Any desired temperature can be given to one 
 coil by leading warm water from a cistern into its vessel. The 
 annular air-tilled space renders the rate of cooling very slow. 
 
158 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 Hence the coils, once at the desired temperature, can easily 
 be kept there. Fig. 63 gives a sketch of the arrangement, two 
 of the water boxes being removed to show the connections. 
 
 The advantage of the somewhat complicated arrangement of 
 copper bars will now be seen. We can, without withdrawing 
 the coils 3 and 4 from their water boxes, and without in any 
 way disturbing the other arrangements, reverse the position of 
 ihe coils 3 and 4 on the bridge, by simply lifting up the legs 
 
 FIG. 65. 
 
 half an inch and changing the mercury cups into which they 
 clip. Thus the legs of coil 3 are changed from cups a and c 
 to I and d, and those of coil 4 from V and d r to a' and c'. 
 This exchange does not occupy more than a few seconds ; and 
 hence we can obtain the two readings necessary to give the 
 difference of the resistance of the coils 3 and 4 when they are 
 .at different temperatures in a very short time. During this 
 short time the temperatures of the two coils will not change 
 perceptibly, protected as they are by an air-jacket. 
 
ELECTRICAL LABORATORY EQUIPMENT. 159 
 
 In the ordinary form of straight bridge there is considerable 
 trouble in exchanging the coils, because the water vessels 
 have to be moved and the mercury cups readjusted ; and 
 all this time the coils are cooling, so that the two 
 readings are never made under the same circumstances as 
 regards temperature. Beginning, then, with all four coils at 
 the same temperature, we take the difference between 3 and 4. 
 To get them all at the same temperature, water from the town 
 mains is allowed to circulate through the system for half an 
 hour. At the end of this time the difference of 3 and 4 is 
 taken ; and several readings are taken at small intervals of 
 time to see if the temperatures are constant. This being 
 done, the temperature of coil 4 is raised by the introduction 
 of warm water until it is about loC. above that of coil 3. It 
 is best to raise the temperature about 20C. above the other at 
 first, and keep it there for 20 minutes, and then let it fall 
 very slowly. In this way coil and water cool together, and 
 an equilibrium of temperature is established between them. 
 The diffeience between 3 and 4 is again taken; and from 
 these two readings we have, as seen above, the mean 
 variation coefficient between the two temperatures. Another 
 method, which would probably be a more accurate one for 
 obtaining the mean coefficient of variation between 0C. and 
 15C., would be to wait until the temperature of the water in 
 the town mains was about 15C., and then to keep three of 
 the coils at that temperature, and to cool the fourth by means 
 of ice to zero. If then all four were kept at 15C. and the 
 observations repeated, we should have the means of finding 
 the variation coefficient of the fourth coil between 0C. and 
 15C. Prof. Chrystal in his report threw out the suggestion that 
 resistance coils should have a thermoelectric couple attached 
 to them, one junction being buried in the heart of the paraffin 
 surrounding the wire, and the other outside. This has been 
 tried in some coils recently made, and proves a satisfactory 
 method of ascertaining the equilibrium of temperature 
 between the wire and the water. 
 
160 ELECTRICAL LABORATORY EQUIPMEXT. 
 
 Another source of error in the ordinary methods arises 
 from uncertain or variable resistances at the mercury cups. 
 It is important that the copper legs of the coil terminals 
 should press very firmly against the tops of the copper pins- 
 on which the india-rubber tube cups are fixed. To ensure 
 this, the plan adopted is to fasten on the coil legs an ebonite 
 clamp. Along the edge of the wooden promontory j h i 
 (Fig. 62) are put brass pins, m ; and by means of steel spiral 
 springs fixed to these and attached to the clamps the coil 
 legs are pressed down very firmly (see Fig. 63). The ends of 
 the pins which carry the india-rubber cups and the ends of 
 the coil legs being well amalgamated, we get, when they are 
 thus firmly pressed in contact, a very good joint, and one 
 whose resistance is small and constant. If the clamps are 
 not used, then one leg may get lifted up a little, and thus a 
 short length of mercury interposed, which leads to an error in 
 a reading. 
 
 Example of a Determination of the Variation Coefficient of 
 a Coil. In the bridge constructed on the above plan for the 
 Cavendish Laboratory, Cambridge, the whole resistance of the 
 platinum-iridium wire is very nearly O0512 of an ohm, or 
 not far from V of an ohm, at about 15C. As the whole 
 length can be divided by the vernier into 10,000 parts, this 
 gives as the value of y^ of a division ^W^rro of an ohm. 
 
 The unit in the following example is y 1 ^ of a division. To 
 secure the greatest accuracy of measurements a sensitive low- 
 resistance galvanometer must be used. The image of a 
 wire strained across a slit is reflected on a scale in the usual 
 way, and read at a distance by means of a telescope. The 
 galvanometer should give an indication, when used with pre- 
 cautions, due to a difference of one-tenth of a division when 
 comparing two ohm coils. But as the temperature can hardly 
 be measured with certainty to within less than ^ of a degree, 
 this alone renders such refinement of reading nugatory, in the 
 absence of better methods of ascertaining with certainty the 
 real temperature of the wire. 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 161 
 
 An example may be here given of the use of this bridge in 
 comparing two resistance coils. Call them F and K. Let K 
 be the coil whose variation coefficient is required. 
 
 I. Difference of Resistance of Coils F and K at 11C. 
 
 Bridge Readings. 
 
 Difference. 
 
 Exp i 
 
 5000 
 
 4955 
 4954 
 4955 
 
 45 
 46 
 45 
 
 
 5000 
 
 
 j 5000 
 
 
 
 The first column gives the number of experiment, the 
 second the reading with the coils F and K in one position on 
 the bridge, the third when F and K are reversed or have 
 exchanged places on the balance; and the fourth gives the 
 difference of their resistance at 11C. in units of the bridge 
 wire. 
 
 II. Difference of Resistance of Coils F and K at 28'2C. 
 
 
 Bridge Readings. 
 
 Difference. 
 
 Exn. i. . 
 
 5439 
 5442 
 5440 
 
 4492 
 4497 
 4490 
 
 947 
 945 
 950 
 
 Exp ii 
 
 
 
 As before, the fourth column gives the difference of F and 
 K at 2S-2C. Taking the mean difference at 28'2C. to be 
 947 units, and that at 11C. to be 45 units, we have 
 
 947 -45 
 
 --^ umts 
 
 as the mean variation coefficients between 11C. and 28C. 
 in units of bridge wire. Since the coils F and K are approxi- 
 mately ohm coils, this gives as the variation coefficient of the 
 coil K -0262 per cent. This coil was of platinum-silver wire. 
 These three determinations occupied about an hour and a half, 
 during which time many more readings were taken, all closely 
 agreeing with the above. The actual measurement of the 
 differences requires but a few moments to effect, the principal 
 
162 ELECTRICAL LABORATORY EQUIPMENT. 
 
 expenditure of time being that required to bring the coils 
 to the same temperature as the water. 
 
 In practical laboratory or testing room measurements of 
 resistance the slide wire form of bridge is not much used. 
 It is more convenient to employ one of the forms of plug 
 bridge. In this arrangement the resistances, which form 
 three arms of the bridge, consist of coils of insulated wire 
 wound on bobbins and contained in a box. These resistance 
 coils are connected in series as required. There are two 
 principal modes of effecting this junction. The top surface of 
 the box generally consists of a slab of ebonite, on which are 
 fixed brass blocks. In the series pattern or Post Office pattern 
 
 FIG. 66. Arrangement of Resistance Coils, Blocks and Plugs in a Series 
 Pattern Bridge. 
 
 of bridge the brass blocks are arranged in rows and the coils 
 connected between them, as shown in Fig. 66. Each block 
 is bored out in such a manner that a brass plug fitting into a 
 conical hole drilled partly in one block and partly in the 
 adjacent one metallically connects the blocks and short- 
 circuits the coil joined in between them. The plug is care- 
 fully ground in, so that the interconnection offers only a 
 negligible resistance. Hence, in the case of such an arrange- 
 ment of coils interconnected by blocks, the insertion or 
 withdrawal of plugs cuts out or adds resistance into the circuit 
 in which these coils are connected. 
 
 In the series form of plug bridge the ratio arms generally 
 consist of five coils having resistances respectively of 1, 10, 
 100, 1,000, and 10,000 ohms. The third or measuring arm 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 163 
 
 -consists of a series of sixteen coils having resistances of 1, 2, 
 2, 5, 10, 20, 20, 50, 100, 200, 200, 500, 1,000, 2,000, 2,000, 
 5,000 ohms. The box is usually provided with two contact 
 keys and terminals for the galvanometer, battery, arid resistance 
 to be measured. The chief objections to the series pattern of 
 plug bridge are that the withdrawal of any plug from a hole 
 tends to loosen all the rest and so creates bad contacts. Hence 
 it is necessary to be continually going over the plugs and 
 tightening them up. Moreover, plugs withdrawn are not in 
 
 1 
 FIG. 67. Arrangement of Coils in Dial Pattern Wheatstone Bridge. 
 
 tise, and are therefore in danger of being oxidised or spoilt by 
 l>eing laid about on the table or held in a damp hand. 
 
 These objections are avoided in the form commonly called the 
 dial pattern of bridge. In this form the measuring arm of the 
 bridge consists of a series of decimal coils viz., nine 1-ohni 
 coils, nine 10-ohm coils, nine 100-ohm coils, &c. These coils are 
 connected between ten blocks fixed on the upper surface of 
 the box. These blocks are arranged round a central block (see 
 Tig. 67). Ten conical holes are bored out in between the 
 
164 ELECTRICAL LABORATORY EQUIPMENT. 
 
 central block and the outside blocks, and only a single plug is 
 employed. As the plug is moved from hole to hole it puts in 
 series between the first outside block and the central block any 
 resistance from zero to 9 ohms, zero to 90 ohms, and so on, 
 A set of three, four, or five of these coils and dials are arranged 
 in and on the box, and serve to set in series units, tens, 
 hundreds, &c., of ohms, the different dials being intercon- 
 nected, the central block of one dial being connected to the 
 
 FIG. 68. Standard Bar pattern Wheatstone Bridge. 
 
 first outside block of the next. Manufacturers often arrange 
 the blocks in a rectangular form, as in Fig. 68. In Fig. 69 is 
 shown a diagrammatic scheme of the arrangement of coils in 
 a standard Wheatstone bridge of the above kind. 
 
 In an electrical laboratory one table should be devoted to 
 a dial or bar pattern resistance bridge. The bridge should 
 be contained in a wooden box, which can be closed when 
 the apparatus is not in use to keep light and dust from 
 
EL ECTRICA L LA BORA TOR Y EQ UIPMENT. 
 
 165 
 
 the ebonite slab. The battery should consist of three or four 
 dry cells of the Leclanche type. The galvanometer should 
 be a movable coil galvanometer, having a resistance of 500 to 
 1,000 ohms. Thick flexible copper cable connectors should 
 be brought from the terminals of that arm of the bridge in 
 which the resistance to be measured is placed to two 
 mercury cups fixed on a wooden stand. In these cups can 
 be inserted the extremities of any coil or wire the resistance 
 of which is required, and this can be determined in a few 
 moments of time. Fuller details of the processes of measure- 
 ments and necessary precautions are given in Chapter II. of 
 this volume dealing with the measurement of resistance. 
 
 FIG. 69. Arrangement of Resistance Coils, Plugs and Block in Bar 
 Pattern Bridge. 
 
 The laboratory equipment must include some form of slide 
 wire bridge suitable for rough measurements, and also a 
 standard slide wire bridge for the comparison of coils by the 
 arey Foster method. 
 
 A compact form of bridge for this latter purpose is that 
 devised by F. H. Nalder, as shown in Figs. 70 and 71.* The 
 ratio arms of the bridge consist of two coils, generally 1 ohm, 
 10 ohms, 100 ohms, or 1,000 ohms, wound on one bobbin. 
 
 * See The Electrician, Vol. XXXI, p. 241, or Proc. Phys. Soc. Lond., June 1893. 
 
166 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 The bridge consists of massive bars of copper mounted on an 
 ebonite slab. In these bars are formed mercury cups, into 
 which the copper terminals of the coils are dipped. The- 
 ratio arm coils are connected in between the cups A A lr 
 B B x (see Fig. 71). The coils to be compared are connected 
 to the cups I Ij, J J r In the space between the bars is- 
 a circular disc of ebonite which carries certain copper con- 
 necting bars. When these bars are placed in one position 
 they connect the coil placed in cups A A 1 in series with the- 
 coil placed in cups I I x and that placed in cups B B x with 
 
 FIG. 70. Nalder Differential Resistance Balance.. 
 
 that placed in cups J J^. When however the copper inter- 
 connectors are lifted up and replaced in a different position 
 they exchange the places of the coils in I I x and J J r The 
 slide wire of the bridge is a very short platinoid wire, G, 
 and the instrument is provided with a n umber of these 
 slide wires of suitable resistance per centimetre for various 
 comparisons. 
 
 Bridges are also constructed for quick measurement, where 
 great accuracy is not required, in which radial arms moving, 
 round dials and making contact with studs are made to/ 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 167 
 
 throw the necessary resistance coils into the measuring arm 
 of the bridge. A bridge of this kind is useful in rapidly 
 taking the preliminary reading of the resistance of a coil to 
 be subsequently more carefully measured in a standard 
 bridge. It then answers the same purpose as the " finder " 
 on an astronomical telescope. 
 
 The special forms of low-resistance bridge will be dealt 
 with in the section on resistance measurement. 
 
 FIG. 71. Connections of Xalder Kesistance Balance. 
 
 Owing to the action of light and dust in deteriorating the 
 surface insulation of ebonite, the ordinary form of plug 
 Wheatstone bridge with lacquered brass blocks and ebonite 
 slab is not a good one to employ in the workshop. The 
 Author has therefore designed a form of workshop resistance 
 balance in which there is no exposed ebonite or metal parts. 
 
168 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 The box is made of oak, and the lid or upper surface presents 
 only a set of rows of holes (see Fig 72). Underneath the lid 
 and attached to it are a series of ebonite rings, on which are 
 arranged a row of brass blocks and a brass disc. Eesistance 
 coils of equal value viz., units, tens, or hundreds of ohms 
 are joined in between the blocks as in the dial arrangement, 
 and plugs shaped like a bradawl, placed in one of the 
 holes bored out partly in the blocks and partly in the central 
 disc, serve to throw in any required resistance between the 
 first block and the disc. The resistances forming the ratio 
 arms are in the same manner arranged to be used in series 
 with one plug only for each ratio arm. The ratio arm coils 
 are therefore O'l, 0'9, 9, 90, and 900 ohms, and these, when 
 joined in series, give 1, 10, 100, and 1,000 ohms as required. 
 
 -20- 
 
 FIG. 72. General View of the Fleming Workshop Bridge. 
 
 The resistance bobbins on which the coils are wound are 
 formed in the following manner : 
 
 Two hollow half-cylinders of thin sheet copper (Fig. 73) are 
 constructed, each having a lug, and two of these half-cylinders 
 are put together with a thin separating piece of ebonite and 
 bound together with a thin silk tape. This constitutes the 
 bobbin. The resistance wires of manganin are then cut the 
 proper length, and the two ends of the wire are soldered to 
 the two lugs of the copper half-cylinders (Fig. 74), the 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 169 
 
 remainder of the wire being wound non-inductively on the 
 bobbin and tied in position by a thin silk tape. The wire is 
 therefore so arranged that it quickly gets rid of any heat, and 
 no paraffin wax is used to overlay the wire or coils. 
 
 The measuring arm of the bridge consists of three sets of 
 coils units, tens, and hundreds each set consisting of nine 
 coils interposed between 10 brass blocks, which are arranged 
 in a cii demand carried in a sort of ebonite tray fixed on the 
 
 EBONITE SEPARATOR 
 
 COPPER - 
 HALF BOBBIN 
 
 ^.COPPER 
 HALF BOBBIN 
 
 FIG. 73. Construction of the Resistance Bobbins. 
 
 FIG. 74. Method of Winding. 
 
 underneath side of the teak lid of the box. These blocks are 
 interconnected as required with a central brass ring by means 
 of a travelling plug. A diagram of the bridge is given in 
 Fig. 75, and a section of the dials in Tig. 76. The plugs 
 resemble bradawls, except in their lower extremities, and 
 have a substantial handle ; they are kept when not required 
 in a sort of umbrella stand attached to the box, seen in the 
 
170 
 
 ELECTRICAL LABORATORY EQUIPMENT. 
 
 general view of the instrument, Fig. 72. These plugs are 
 inserted into interconnecting holes between the brass blocks, 
 
 1 
 
 &l 
 
 Q 
 
 ,3 
 
 to 
 
 5 
 l 
 
ELECTRICAL LABORATORY EQUIPMENT. 
 
 171 
 
 and the common ring through small holes bored into the lid 
 of the box. Hence the outer surface of the box exhibits only 
 sets of small holes arranged in circles and which ars marked 
 respectively units, tens, hundreds. 
 
 In order to prevent dust getting into the holes between the 
 brass blocks, there is a contrivance in the form of a self- 
 closing shutter. On the underneath side of the lid are a 
 series of circular discs of thin ebonite, which are perforated 
 by holes corresponding with the holes for the plugs in the lid 
 of the box. These circular shields move round a central 
 pivot, and by means of a spring are kept so turned that the 
 holes in the shield do not normally coincide with the holes in 
 the box lid. Hence all these box lid holes are closed as it 
 were by a small shutter, but when once opened and a plug 
 inserted in the hole the plug prevents the shutter from closing. 
 The circular shutters can be turned round by means of a 
 
 BRASS BLOCK 
 
 BRASS BLOCK 
 
 EBONITE RING 
 
 FIG. 76. Section of Dial. 
 
 common bar and finger pin protruding through the lid, so 
 that, in order to insert the first plug when commencing his 
 test, the user presses back the pin and thereby opens all the 
 shutters. But the moment all the plugs are withdrawn from 
 their hole, the shutter under the lid springs back and closes 
 all the holes belonging to that dial. 
 
 The ratio arm of the bridge is formed of a series of coils 
 which are arranged dial fashion, and which are therefore not 
 1, 10, 100, 1000 ohms as usual, but 1, 9, 90, 900. Two plugs 
 are therefore provided for the ratio arm dials, and the ratio 
 arm dial is furthermore marked in such a manner that the 
 user has no difficulty in discovering the number by which he 
 must multiply and the number by which he must divide the 
 ratio arrn resistance to get the resistance of the circuit 
 measured. The shutter closing the holes of the ratio dial is 
 
172 ELECTRICAL LABORATORY EQUIPMENT. 
 
 independent of the others, and is not provided with a finger 
 pin for opening. The spring which keeps the shutter of this 
 dial normally closed is not very strong, and the shutter is 
 easily pushed back by the point of the first plug as it is 
 inserted. 
 
 The whole of the connections are made under the lid to 
 three pairs of terminals, marked on the outside as in Fig. 72, 
 and in addition two keys are fixed under the lid, which are 
 manipulated by two little ivory buttons, like electric bell 
 pushes, protruding through the lid. There is therefore abso- 
 lutely no exposed ebonite to deteriorate in insulation, and no 
 lacquered brass, with the exception of the aforesaid six ter- 
 minals, the handles by which the bridge is carried about, and 
 the plugs. The terminals are constructed with a peculiar 
 kind of lip, which renders it easy to grip in them either a 
 single large wire like a No. 10 wire or a single small wire 
 like a No. 40. 
 
 One other point is worthy of notice. In the ordinary pat- 
 terns of plug bridges the frequent use of the plugs wears 
 them down into a shoulder, so that they no longer fit tightly 
 into the plug holes. In this workshop form of bridge the 
 plug has a semi-circular groove turned in it at such a height 
 in the plug that when in place the top of the block is just 
 on a level with the middle of the groove. This device is an 
 effective cure for " shouldering " in the plugs. 
 
 In the selection of a Wheatstone bridge for very accurate 
 work in resistance measurement it is well to have in view 
 the objections which can be raised against the ordinary form 
 of plug and coil bridge. These objections may be summarised 
 as follows : The bridge, as supplied by most makers, consists 
 of a wooden box, with an ebonite slab forming the top, on 
 which are fixed the brass blocks with conical brass plug 
 connectors. The resistance coils are in the box, and are 
 connected between the plug blocks. If platinum-silver wire, 
 or any material not having a zero temperature coefficient, 
 is used for the manufacture of the coils, then there is very 
 considerable difficulty in ascertaining the true temperature 
 of the coils when the resistance measurement is actually 
 being made. A thermometer placed with its bulb in the box 
 
ELECTRICAL LABORATORY EQUIPMENT. 173 
 
 merely gives us the temperature of the air in the box ; that 
 of the coils, perhaps embedded in paraffin or shellac, may 
 be very different, and moreover, the temperature of each 
 coil which has current passing through it may not be the 
 same. 
 
 In the next place, very great labour is involved in checking 
 the relative value of the coils, and, owing to dirt or slight 
 want of fitting of the conical plugs, the value of the resistance 
 added or removed by withdrawing or inserting a certain plug 
 may not be at all times precisely identical. In the series coil 
 or Post Office pattern of plug bridge the putting in of one 
 plug slightly displaces all the brass blocks, and the expansion 
 of the ebonite top -prevents perfect fitting of the coned 
 plugs. 
 
 The dial pattern of bridge is therefore preferable to the 
 series coil pattern, because each of the plug blocks is- 
 independent. Furthermore, the coils, as usually made r 
 cannot be annealed after being wound, and hence are liable 
 to secular changes in resistance due to strain.* 
 
 Finally, the last adjustment of balance cannot always be 
 made with integer coils, and the last decimal place in the 
 resistance measurement has to be estimated from the 
 galvanometer deflection (as described in the section on 
 resistance measurement). 
 
 To meet the above objections a form of standard bridge has 
 been designed by Messrs. Callendar and Griffiths, of which a 
 description is given in Chapter II. f 
 
 14. Electric Quantity-Measuring Instruments. 
 Ballistic Galvanometers. The passage of a certain electric- 
 discharge or quantity of electricity through a circuit, 
 
 * For a good summary of all that can be said against the ordinary form of 
 plug resistance bridge the reader is referred to a series of articles on 
 "The Electrical Measurement of Temperature," by Mr. G. M. Clark, in. 
 The Electrician, Vol. XXXVIII., p. 274, 1897. 
 
 f See also Tlie Electrician, Vol. XXXVIII., p. 747, 1897. 
 
174 ELECTRICAL LABORATORY EQUIPMENT. 
 
 reckoned as the time-integral of a varying electric current 
 having finite limits, is measured practically either by a 
 ballistic galvanometer, if the whole discharge is over in 
 a second or less, or, if the discharge endures for a very 
 considerable time, it is measured by some form of ampere- 
 hour meter. For a certain class of magnetic work the 
 ballistic galvanometer is a necessary appliance. The most 
 practical and useful form of this instrument is a movable 
 coil fixed magnet galvanometer. The movable coil may be 
 either a narrow, shuttle-shaped coil, as in the instruments 
 designed by Ayrton and Mather, or a circular, ring-shaped 
 coil, as in the ballistic galvanometer of Cronipton. 
 
 Deferring at present a detailed discussion of the principles 
 of the ballistic galvanometer, we may here merely state that 
 the elementary theory of this instrument is as follows : If 
 through the coil of the galvanometer an electric discharge or 
 very brief current is permitted to take place, the magnetic 
 field due to the discharge causes an impulsive torque or 
 couple to act upon the movable portion of the instrument, 
 whether the latter is the magnet or the coil. // the discharge 
 is all concluded before the movable portion has been sensibly 
 displaced from its zero position, then the following conditions 
 hold good : 
 
 Let I denote the moment of inertia of the movable portion of 
 the galvanometer. 
 
 Let pO denote the control or torque brought into existence 
 to restore that part to its original position when displaced 
 through an angle 6. 
 
 Let o> be the angular velocity of the moving portion at 
 any time t after the displacement begins. 
 
 If, in the first place, we neglect the retarding effect of 
 friction, we may say that the equation of motion of the 
 moving system at the time t is expressed by the equation 
 
 which is the analytical statement of the fact that the rate 
 
ELECTRICAL LABORATORY EQUIPMENT. 175 
 
 at which the angular momentum of the moving system is being 
 destroyed at any instant is proportional to the angular dis- 
 placement of the movable portion. 
 
 Since o> = , 
 
 at 
 
 we have lff+ M = 
 
 at* 
 
 as the equation of motion of the coil when we neglect 
 frictional retardation of all kinds. 
 
 From the above equation it is easily shown that the 
 duration (T) of one complete oscillation of the movable 
 system is given by the equation 
 
 -2* /?. 
 
 V M 
 
 Suppose the coil at rest in the field of the controlling 
 magnet, and let a discharge be made through the. coil, which 
 is all completed before the impulse sensibly overcomes the 
 inertia of the coil and gives it an angular displacement or 
 " throw." If B is the induction density or field strength due 
 to the fixed magnet at the place where the coil is situated, 
 and if i is the coil current at any time t after the beginning 
 of the discharge, then, assuming the coil has not sensibly 
 moved from its zero position, and neglecting as small the 
 reaction of the coil current on the fixed magnetic field, we 
 may say that the coil is experiencing a torque or couple 
 represented by CBt, where C is some constant depending on 
 the form of the coil. 
 
 Hence, as above, if o> is the angular momentum of the coil 
 at that instant, 
 
 4 = 
 
 dt 
 
 or Ida = 
 
 where I is the moment of inertia of the coil. The product 
 idt is numerically equal to the small quantity of electricity 
 
176 ELECTRICAL LABORATORY EQUIPMENT. 
 
 dq which has passed through the coil in the element of time dt- 
 Hence 
 
 Suppose time reckoned from the instant when the discharge 
 begins, and that the discharge is complete before the coil has 
 experienced any appreciable change in position. The result of 
 the passage of the whole quantity Q of the discharge through 
 the coil will be to apply to it an impulsive torque which will 
 cause it to leave its zero position with a definite velocity 12, 
 Under the above conditions we can integrate the last equation, 
 and omitting the constant of integration, write 
 
 (1) 
 
 The angular energy with which the coil leaves its zero position 
 is equal to JI12 2 . 
 
 If the impulsive torque gives the coil a twist through an 
 angle 0, and if /m is the torque due to the suspension, whether 
 bifilar or unifilar, per unit angle, then ju.9 is the restoring 
 or opposing torque due to the suspension brought into 
 existence by the displacement through an angle 0. Hence 
 the potential energy of the coil system at the end of its swing 
 is equal to J/x$ 2 , or to half the product of the torque /mO and an- 
 gular displacement 0. Accordingly, we must have an equation 
 between the kinetic energy imparted to the coil and its 
 potential energy when at the position of final displacement, or 
 
 iK 2 =M>- ........ (2) 
 
 Combining together equations (1) and (2), we arrive at_the 
 equation 
 
 or, Q = G0. 
 
 The above equation shows that, under the limitation assumed, 
 the angular excursion of the coil is proportional to the whole 
 quantity of electricity which has passed through the galvano- 
 meter. 
 
ELECTRICAL LABORATORY EQUIPMENT. 177 
 
 If to the coil is attached a mirror in the usual manner, and 
 the lamp and scale is placed at a distance of say one or two 
 metres so that the angular deflection of the coil does not exceed 
 5 deg. or 10 deg., the corresponding excursion or displacement 
 of the spot of light upon the scale will be proportional to the 
 total quantity of electricity which has passed through the coil. 
 
 The ballistic constant (G) of the galvanometer is the number 
 by which the scale deflection in millimetres or centimetres 
 must be multiplied in order to obtain the total quantity of 
 electricity in microcoulombs which produced that observed 
 deflection. 
 
 In the chapter on the Measurement of " Electric Quantity " 
 instructions will be given for the proper standardisation of 
 the galvanometer. In the meantime, a few of the qualities 
 which should be possessed by a ballistic galvanometer may 
 be discussed. 
 
 The movable magnetic needle ballistic galvanometer is a 
 most troublesome instrument to use, owing to the needle dis- 
 turbances created by outside currents and magnetic fields. 
 The most practical form of ballistic galvanometer for the 
 electrical testing room or laboratory is a movable coil galvano- 
 meter with fixed magnet. This galvanometer must have its 
 coil wound on a non-conducting frame, and may be either a 
 narrow coil i.e., a coil of long or shuttle-shaped form, as in 
 the Ayrton-Mather galvanometer shown in Fig. 45, page 123 
 or a circular bifilar suspended coil, as in the Crompton- 
 d'Arsonval galvanometer shown in Tig. 46, page 124. In 
 either case, if the galvanometer is to be used for ballistic pur- 
 poses, as little "damping" must be present as possible. Hence 
 the coil must not be wound on a closed metallic frame, and 
 preferably not surrounding a soft iron core. On the other 
 hand, when used simply as a deflectional instrument it is 
 desirable to secure as much damping of the coil as possible. 
 In this last case winding the coil on a metallic frame is an 
 advantage, because the eddy currents set up in the frame by 
 its movement in a strong field retard the movement and bring 
 
178 ELECTRICAL LABORATORY EQUIPMENT. 
 
 the coil to rest without unnecessary vibrations when the 
 current through it is stopped. 
 
 When, however, the galvanometer is to be used for ballistic 
 purposes, then it should be as little damped as possible. The 
 free period of vibration of the coil in this case, when 
 disturbed, should not be less than five seconds, and for many 
 purposes preferably 15 seconds at least. It is quite useless to 
 employ for many experiments a ballistic galvanometer having 
 a smaller free period of vibration, since then the fundamental 
 requirement for ballistic work is not fulfilled. The galvano- 
 meter should, however, have a damping arrangement by which 
 a small, properly-timed current may be sent through the galvano- 
 meter coil to bring it to rest when its excursion has been made, 
 and thus save unnecessary loss of time in experiments. This 
 may be achieved by the use of a shunt circuit (consisting of 
 a small dry cell), a very high resistance (consisting of a slip 
 of vulcanised fibre rubbed over with plumbago), and a contact 
 key, all joined in across the galvanometer terminals. By 
 making suitably timed taps on the key the galvanometer coil 
 can have small currents sent through it which will bring it 
 at once to rest. In the case of low resistance ballistic 
 galvanometers, merely short-circuiting the terminals of the 
 galvanometer by closing a key in that circuit is sufficient to 
 destroy at once the vibration of the coil and bring it to rest. 
 
 Each ballistic galvanometer used in the laboratory should 
 be set up on a very steady stone shelf or pillar, and the usual 
 lamp and scale adapted to it. In this connection it may be 
 pointed out that by far the most convenient scales to use for 
 galvanometer purposes are the semi-transparent celluloid 
 scales. These are divided into millimetres, and should be 
 set up on a firm stand at a distance of one metre or 
 1,000 millimetres from the mirror. The source of light 
 should be an incandescent lamp with a simple horseshoe 
 filament. Over this may be placed an asbestos hood with a 
 slit in it, so that only the image of one side of the filament 
 is thrown upon the scale. The galvanometer should be 
 
ELECTRICAL LABORA TOR Y EQ UIPMENT. 179 
 
 provided with a concave mirror of one metre focus. It is 
 then easy to so place the incandescent lamp that the sharp 
 image of one leg of the filament is thrown upon the semi- 
 transparent scale. The scale must have a lateral movement, 
 so that it can be moved parallel to itself and perpendicular 
 to the direction of the ray of light reflected from the mirror 
 when the galvanometer coil is in its zero, or undeflected, 
 position. The scale deflection of the sharp line of light upon 
 the screen, measured in millimetres and divided by 1,000, 
 gives very approximately the tangent of twice the angle of 
 deflection of the galvanometer coil ; and this may be taken to 
 be proportional to the coil deflection when that angle does 
 not exceed 10 deg. 
 
 The testing room should be provided with at least two 
 ballistic galvanometers, one having a resistance of about 
 20 ohms and the other a resistance of 500 to 1,000 ohms or 
 more. This latter galvanometer should have a time of free 
 vibration of its movable coil of at least 12 to 15 seconds. 
 
 The correction to be applied to the excursion of the coil 
 to allow for air friction or other retarding forces which tend 
 to diminish the deflection, as well as other precautions in the 
 use of the ballistic galvanometer, will be given in a later 
 chapter. 
 
 In connection with the standardisation of this instrument 
 it is useful to possess an apparatus called a graded condenser 
 as well as a standard half-microfarad condenser. These last 
 instruments are virtually Leyden jars, consisting of insulating 
 sheets of mica or of paraffined paper coated on both sides 
 with tinfoil, but so as to leave a margin of uncoated surface. 
 A collection of these elements is assembled together, so that 
 all the tinfoil coatings on one set of sides are in metallic 
 connection and all the corresponding opposite side coatings 
 also in connection. 
 
 The construction of a standard condenser is a matter 
 requiring some experience, and it need only here be said that 
 it is not worth while to purchase one from any except a 
 
 N2 
 
180 ELECTRIC A L LABOR A TOR Y EQ UIPMENT. 
 
 manufacturer of repute. A standard half -microfarad con- 
 denser is, however, a necessary article. Two or three other 
 condensers should be also obtained, having a capacity of 
 about one microfarad each. Also a graded condenser, 
 divided into microfarads and fractions of microfarads such as 
 01, 0-2, 0-2, 0-5, 1-0, 2-0, 2-0, and o'O, is a very useful appliance. 
 All these condensers should have been tested with 1,000 volts 
 on their terminals by the maker, so that no risk may be 
 incurred in using them on 100-volt circuits. The proper 
 charge and discharge keys for use with the condensers can 
 be procured as required. 
 
 In connection with the measurement of electric quantity, 
 in those cases in which the duration of the discharge is 
 considerable (as in secondary battery tests) it is exceedingly 
 desirable to have at hand an ampere-hour meter which will 
 automatically record the total quantity which has passed 
 through it in coulombs or microcoulombs, and at the same 
 time show the variations of current. Of these instruments 
 the most useful is the graphical recording ampere-hour 
 meter. In this instrument a drum covered with paper is 
 rotated by a clock train at a uniform rate, say once in 24 
 hours. A pen moving over the surface of the drum is 
 displaced by some mechanism which acts as an ampere meter. 
 In the Holden ampere-hour meter this current-measuring 
 part is constructed by utilising the expansion produced in a 
 series of fine wires placed in parallel. A lever arrangement 
 enables the " sag " of these wires, when heated, to displace 
 the pen over the drum by an amount depending on the 
 current through the wires. If, then, the pen is variably 
 displaced as the drum revolves, we have a curve described 011 
 the paper which shows, by the value of its ordinates at each 
 moment, the ampere value of the current. If the displace- 
 ment of the pen is exactly proportional to the current, and if 
 the speed of the drum is uniform, then the area of the curve 
 described by the pen is proportional to the whole quantity in 
 ampere-hours which has passed through the instrument. In 
 
ELECTRICAL LABORATORY EQUIPMENT. 181 
 
 ^secondary cell testing the possession of a correct graphic 
 recording ampere-hour meter of the above kind saves much 
 itime and many tedious observations. 
 
 Bemarks on the subject of ampere-hour meters generally 
 for use in the commercial supply of electric current will be 
 reserved for the section dealing with meter testing. 
 
 15. Instruments for the Measurement of Electric 
 Power. Wattmeters. In many pieces of testing work, 
 particularly in certain alternating-current measurements, it 
 is necessary to be able to measure at one operation the 
 power, or mean power, given to an electrical circuit, which 
 may be called the power circuit. This measurement is made 
 by means of a wattmeter. 
 
 In its most general form a wattmeter consists of two coils 
 of wire, one of which is fixed and is called the current coil 
 .and the other of which is movable and is called the pressure 
 coil. The circuit in which the power to be taken up is to be 
 measured is joined up with the wattmeter, so that the current 
 passing through the circuit is that passing through the 
 current coil. The pressure coil is then joined up so (i.) that 
 one terminal is connected to the entrance end of the current 
 coil and the other to the exit end of the power circuit, or 
 (ii.) so that the pressure coil is connected to the ends of the 
 power circuit. 
 
 It will be seen that, if the pressure coil is joined up in the 
 first manner, the voltage on the pressure coil is that due to 
 the fall in volts down the current coil as well as that in the 
 power circuit. If, on the other hand, it is joined up in the 
 second way, then the current in the current coil is not 
 simply that in the power circuit, but takes account also of 
 the current in the pressure coil. 
 
 In dealing with the particular measurements in which the 
 wattmeter is employed we shall point out how it should be 
 used. Meanwhile, it may here be stated that if the pressure 
 coil is held in a position either with its plane parallel to that 
 
182 ELECTRICAL LABORATORY EQUIPMENT. 
 
 of the current coil or embracing it, and with its plane at right 
 angles to it, then, when connected up with the power circuit 
 there will be found to be a mechanical force or torque 
 between the coils. The restraining force required to hold the 
 coils in any definite relative position in which the electro- 
 dynamic force between them is not zero is proportional to the 
 mean product of the values of the currents passing through 
 the coils. If one current is the current through the power 
 circuit, and the other current is proportional to the potential 
 difference between the ends of the power circuit, then their 
 mean product is proportional to the mean power taken up in 
 the power circuit. The controlling condition, however, is 
 that the free time of vibration of the movable coil of the 
 wattmeter must be large compared with the periodic time of 
 the currents, if these are periodic. 
 
 The wattmeters used in the testing laboratory generally 
 take one or two forms. In the Siemens form the movable 
 coil embraces the fixed coil (see Fig. 77). The movable coil 
 is suspended by a few fibres of floss silk, and has attached to 
 it one end of a spiral steel torsion spring. The other end of 
 this spring is fixed to a torsion head, with an indicating arm 
 moving over a circular divided scale. The movable coil 
 carries a pointer, by which it can be brought into a recognised 
 and fixed position. The arm attached to the torsion head 
 can be moved independently of the head, and clamped when 
 desired by a clamping screw. The current enters and leaves 
 the movable pressure circuit by means of mercury cups, into 
 which dip the amalgamated ends of the movable coil. The 
 instrument is provided with four terminals, two of which 
 are the extremities of the fixed coil and two are the terminals 
 of the movable coil. 
 
 The other form of wattmeter is that of Lord Kelvin r 
 which is similar in general construction to an ampere balance. 
 The circuit formed by the coils of the suspended or balance 
 arm is, however, brought to a separate pair of terminals. 
 The circuit formed by the fixed coils is separate from that of 
 
ELECTRICAL LABORATORY EQUIPMENT. 183 
 
 FIG. 77.- Siemens Wattmeter. 
 
184 ELECTRICAL LABORATORY EQUIPMENT. 
 
 the movable ones. One of these forms the pressure circuit 
 and the other the current circuit of the wattmeter. 
 
 Another form of wattmeter is that in which the pressure 
 coil is suspended by a bifilar wire suspension. In this case 
 the current enters and leaves the movable coil by the 
 suspension wires. This form is well adapted for a deflectional 
 instrument in which the deflections of the movable coil are 
 read by a mirror and scale. 
 
 In the selection of a wattmeter for use in the testing 
 laboratory, especially if it is to be used with alternating 
 currents, it is necessary to be guided by the following 
 facts : 
 
 For use with alternating currents there must be no metal 
 work near the fixed or movable coils. Instrument makers 
 are far too fond of lacquered brass. They put brass covers 
 and shields round wattmeters, and carry the coils on brass 
 pillars and supports. The result is that eddy currents are set 
 up in these metal portions, which react upon the currents in 
 the movable coil and destroy the correctness of the indications 
 of the instrument. An alternating-current wattmeter should, 
 as far as possible, be constructed of hard, well-seasoned 
 wood and ebonite, with the exception of wire circuits and 
 terminals. 
 
 A useful form of the instrument is made by providing with 
 separate terminals to its two circuits the ordinary and cheap 
 form of Siemens electro-dynamometer. 
 
 If the wattmeter is being used with continuous currents, 
 then it is necessary to so place it that the magnetic axis of the 
 movable coil is in the direction of the earth's horizontal 
 magnetic field at the place where it is used. If this is not 
 done, the terrestrial force will exercise a deflecting action on 
 that coil. Hence the wattmeter should be used on a rotating 
 turn-table, which enables it to be rotated in azimuth without 
 disturbing the level of the instrument. 
 
 In dealing with the special uses of the instrument the 
 various precautions attending its use will be pointed out. 
 
ELECTRICAL LABORATORY EQUIPMENT, 185 
 
 16. General Hints on the Outfit of a Testing Labora- 
 tory. In concluding this chapter a few general hints may 
 be given as to the equipment of an electrical testing 
 laboratory. 
 
 In most cases where this has to be done by the inexperi- 
 enced, the general desire seems to be to provide a number of 
 glass door apparatus cases, and to stock the shelves as far as 
 possible with the beautiful creations in ebonite and lacquered 
 brass of the electrical instrument maker. Hence it is that 
 in so many colleges and technical institutions we find a large 
 collection of expensive apparatus, very little of which is of 
 real use in research or commercial work. 
 
 The guiding principle in equipping an electrical testing 
 room should be to buy at first as little as possible, unless and 
 until the purpose of the laboratory is very clearly defined. 
 The instruments that are bought as standard instruments 
 should be very carefully selected, and, as far as possible, 
 made to careful specifications. An odd lot of galvanometers 
 bridges, resistance coils, keys, c., should not be bought. 
 
 The main purpose of the laboratory having been defined, 
 whether for teaching, research, commercial testing, or stan- 
 dardising, the first provision should be in the conveniences 
 for generating and distributing the currents. Bound the 
 laboratory should run several ciicuits, with means for bringing 
 the potential difference at any place to the standard volt- 
 meters and potentiometer. The principal resistance bridge, 
 the principal potentiometer, the ballistic galvanometers, the 
 ampere balances, standard voltmeters, and low resistance 
 bridge should each be set up complete on its own table, 
 with everything required for that measurement screwed 
 down to the table. There should be no moving about of 
 galvanometers and keys from one place to the other. The 
 .small local currents required should be obtained from dry cells 
 of Leclanche type, or from small 2-cell secondary batteries. 
 
 The set of apparatus on each table, when not in use, may 
 be kept free from dust by having a black cloth thrown over 
 
186 ELECTRICAL LABORATORY EQUIPMENT. 
 
 it. It stands there, however, ready for use, and the resistance 
 of a bit of wire or coil or the checking of a voltmeter can be 
 carried out at a moment's notice without loss of time. 
 
 In many laboratories there is an enormous waste of time in 
 collecting together out of cases, setting up, and connecting 
 apparatus for the simplest measurement. There is also a 
 great amount of capital sunk in apparatus pretty to look at 
 but perfectly useless for real work. 
 
 Ample provision should be made, by wire resistances and 
 carbon resistances, for regulating currents. Galvanometers 
 should, as far as possible, be movable coil galvanometers, so 
 that they are not disturbed by the presence of currents in 
 neighbouring wires. These may be kept covered over when 
 not in use with cardboard boxes or hoods. 
 
 No attempt has been made in the sections of the present 
 chapter to indicate all the apparatus necessary, as that must 
 depend on the purpose of the laboratory. In the following 
 chapters instructions will be given for carrying out the chief 
 electric and magnetic measurements. 
 
 As an illustration of the equipment required in an elec- 
 trical standardising laboratory, we may conclude this chapter 
 by a brief description of the arrangements in the British Board 
 of Trade Electrical Laboratory at No. 8, Kichmond- terrace, 
 Whitehall, London.* This laboratory was established in 
 consequence of a deputation, comprising most of the pro- 
 minent members of the electrical profession, to the Board of 
 Trade in 1889, for the purpose of urging the necessity of the 
 establishment of such an institution. A scheme was sub- 
 mitted by this deputation for the establishment and working 
 of a standardising laboratory, and this scheme has been kept 
 in view as far as was consistent with the amount of money 
 procurable from the Treasury : 
 
 The first suggestion for the establishment of a Government electrical 
 standardising laboratory was given in a Paper read by the Author in 
 November, 1885, to the Institution of Electrical Engineers (then called the 
 
 * See The Electrician, October 5 and 12, 1894, Vol. XXXIII., pp. 665, 693. 
 
ELECTRICAL LABORATORY EQUIPMENT. 187 
 
 Society of Telegraph Engineers and Electricians). This Paper was entitled 
 "On the Necessity for a Standardising Laboratory for Electrical Test 
 Instruments." The discussion on the Paper led to the formation of a 
 committee to further this object, and four years later the suggestions of the 
 Author were realised. 
 
 The laboratory exists for three purposes : First, to obtain and preserve 
 standards for the measurement of electrical quantities ; second, for giving 
 the standard measurements of those quantities ; and third, to enable the 
 Electrical Adviser of the Board of Trade to make such tests of instruments 
 and material as may be necessary in the performance of his duties. No 
 scientific work outside these purposes can be undertaken. 
 
 Six rooms are in occupation in the basement of No. 8, Richmond-terrace, 
 Whitehall, London. One of these is occupied by the gas engine and dynamos, 
 used solely for charging accumulators ; another by the accumulators, from 
 which all the power used in making electrical measurements is obtained. 
 These two rooms are outside the main building. The rooms within the main 
 building are, first, the room containing the standards for current and pressure 
 and the necessary adjuncts ; second, the room containing the transforming 
 machinery, where the power derived from the accumulators is transformed as 
 required ; third, the room occupied by the standards of resistance and the 
 Clark cells used as sub-standards, this room being used exclusively for 
 measurements connected with resistance and the comparison of electromotive 
 forces ; and, fourth, the verification room, where commercial instruments 
 sent for the purpose are verified. Beyond the verification room is fitted a 
 small chemical laboratory. 
 
 The general arrangement of the laboratory is shown in the plai in Fig. 78, 
 and consists of the various rooms already enumerated. The accumulators in 
 use consist of a battery of four large 61-plate Crompton-Howell cells, which 
 are generally used two in parallel for the direct production of large currents, 
 and 108 11-L E.P.S. cells. The large cells can supply currents of any 
 amount up to 2,000 amperes for a short time, and are charged in series at 
 the rate of 200 amperes. The E.P.S. cells are used for running the trans- 
 forming machinery and for supplying continuous pressure up to 200 volts. 
 The discharge rate is never allowed to exceed 22 amperes even for short 
 periods. Current from the large cells is brought into the room containing 
 the standards of current by mains consisting of flat copper strips, the lead and 
 return being sandwiched together to avoid magnetic disturbance. A break is 
 provided just outside this room for the insertion of regulating resistances, 
 which for the most part consist of carbon rods with suitable terminals. The 
 use of carbon in this connection has this great advantage in addition to that 
 of handiness, that as the resistance diminishes with increase of temperature, 
 the fall of current which would otherwise take place from the slight polari- 
 sation of the cells and the warming of the metallic circuit can be completely 
 obviated by choosing suitable lengths and cross sections of carbon. Great 
 steadiness of even the largest currents for ample time has thus been obtained. 
 Fine adjustments of current are secured by the use of rheostats formed of 
 carbon plates under variable pressure inserted either in the main circuit or as 
 a shunt to the measuring instruments. 
 
188 
 
 ELECTRIC A L LA BORA TOR Y EQ UIPMENT. 
 
ELECTRICAL LABORATORY EQUIPMENT. 189 
 
 A large electric balance (A, Fig. 78), made under Lord Kelvin's supervision, 
 is fixed immediately at the point of entry of the above- mentipned large 
 mains. This instrument can read up to 10,000 amperes. Round two sides 
 of the current and pressure standards room is fixed a concentric main of 
 the same pattern as those used by the London Electric Supply Corporation 
 for trunk mains from Deptford. The outer conductor is cut across at 
 intervals, and large terminals clamped on at each side of these breaks, to 
 which the current-measuring instruments are attached, while copper bars are 
 provided for short-circuiting every instrument. The inner conductor is only 
 exposed at the two ends, where it can be similarly connected to the outer 
 conductor either through an instrument or by means of a short-circuiting 
 strap. A complete anti-induction circuit is thus provided for current. A 
 shelf of enamelled slate is carried on corbels let into the external wall of 
 the building underneath the concentric main, as a support for the current- 
 measuring instruments. The ampere standard B is placed upon a stone 
 pedestal near the centre of the room, and the auxiliary ampere balance O 
 upon a similar adjacent support. The volt standard D, which really 
 measures 100 volts, or one hekto-volt, occupies a third stone pedestal in the 
 centre of the room. Another instrument of the same pattern is placed at E. 
 On the shelves round the wall of the room are five sub-standard Kelvin 
 balances of the following ranges : 1 to 5 amperes (F, Fig. 78), 5 to 30 (G), 30 
 to 120 (H), 100 to 600 (K), and 500 to 2,500 (L). The first two of these 
 have aluminium beams. A composite watt-balance is placed at M. One of 
 the remaining walls R is occupied by various pressure-measuring instruments 
 for low pressures, and the fourth wall partly by pressure-measuring 
 instruments for high pressures Q and partly by a switchboard P for 
 regulating the transforming machinery. A highly insulated platform is 
 provided for standing on when manipulating the high - pressure instru- 
 ments. On this board are a pair of Cardew voltmeters, supplemented by 
 twelve resistance tubes. Each of these is practically a complete Cardew 
 voltmeter, but without hand movement and dial. Each contains the usual 
 wires and pulleys, under exactly the same " live " condition as in a working 
 voltmeter. By means of these resistances, which can, of course, be 
 independently checked and mutually compared, differences of potential up to 
 2,150 volts can be measured. A "chain" of voltmeters that is to say, a 
 set of instruments, the range of each one overlapping two others, as with the 
 sub-standard ampere balances are placed in this room. 
 
 The chief work which has been done in this room is the comparison of the 
 three standards of current, electromotive force, and resistance. The standard 
 ampere, as obtained by many repeated determinations by the silver volta- 
 meter, was passed through the ampere standard, the auxiliary balance, and 
 through a resistance of 100 ohms, and gave a difference of potential of 
 ICO volts, which was observed on the volt standard. This 100-ohm resistance 
 is made of manganin, and is maintained at a constant temperature by oil 
 circulated by a small electric motor, and by the circulation of water in an 
 outer jacket. This 100-ohm resistance was compared with the ohm standard, 
 the value of which was accepted from the British Association determinations. 
 The volt was thus deduced from the correlation of the ampere and the ohm. 
 
190 ELECTRICAL LABORATORY EQUIPMENT. 
 
 The scale of the volt standard is long enough to include the pressures due to 
 69, 70, and 71 Clark cells, and by direct comparison the value of the cell was 
 thus determined. The work of carrying out this triple comparison occupied 
 many months. 
 
 A current of about 0*8 ampere is kept continually passing through the 
 ampere standard to keep it warm and dry. The period of a complete swing 
 of the standard of current is about half a minute, and hence the need for an 
 auxiliary balance, to act as the " finder " of a telescope. 
 
 The machinery for "gen era ting the required currents consists of a continuous- 
 current motor and an alternator with shafts in line and both keyed to a 
 common pulley, while a continuous-current high-pressure dynamo can be run 
 from this pulley by means of belting. By varying the exciting currents of 
 these different machines a very delicate adjustment of the transformed 
 current or pressure is obtained. There are, in addition, various alternating- 
 current transformers for giving a range of current up to 500 amperes and of 
 pressure up to 10,000 volts. 
 
 The room containing the standard of resistance and Clark cells is a small 
 room arranged to be kept at a uniform temperature of 16C. In this room 
 is a Carey Foster bridge, and a Kelvin reflecting galvanometer with a 
 transparent scale. 
 
 The verification room is fitted with a concentric main running around 
 three sides, elate shelves for the support of instruments ; and a large fireclay 
 oven 2ft. Sin. wide, 2ft. 6in. deep, and 3ft. high, with plate glass front 
 perforated with holes for leads, is heated by gas, for testing instruments at 
 various temperatures. It has been run to a very high temperature, but it is 
 not proposed to use it for more than 30 C. This room is fitted up with 
 secondary standards for the measurement of current and pressure up to the 
 limits of instruments in common use. In this room calibration and tests of 
 meters have been carried out. This work has nothing to do with the 
 calibration and sealing of actual house meters, which is carried out by the 
 London County Council, but relates to the approval of the patterns. In this 
 room the deci-ampere, deka-ampere, and hekto-ampere Kelvin balances are 
 fixed. 
 
 In the verification of instruments in this laboratory definite 
 methods are employed for defining the inaccuracy. For 
 instance, if an instrument reading to 100 volts is sent for 
 verification at certain points, say 90, 95, and 100, the readings 
 of those instruments when pressures of those amounts are 
 applied are given, and not the true values of the scale indica- 
 tions 90, 95, and 100 on the instrument. It is obvious that 
 where a large number of instruments have to be checked, 
 this method results in economy of time and power. 
 
CHAPTER II. 
 
 THE MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 1. The Comparison of Electrical Resistances. The 
 
 electrical resistance of a conductor may be defined as that 
 physical quality of it in virtue of which energy is dissipated 
 in it when an electric current flows along it. This amounts 
 to saying that a fall of electrical potential accompanies the 
 flow of a steady unvarying current along a conductor. The 
 ratio between the numerical values of the fall or drop in 
 potential (P.D.) down a conductor and the current (C) in it 
 is a measure of the electrical resistance of that conductor, if 
 the current is an unvarying or continuous current. 
 
 The energy dissipated in the conductor, measured by the 
 product of the values of the potential fall and the current, 
 takes the form of heat, and raises the temperature of the 
 conductor. This temperature change affects the physical 
 state of the conductor and alters the ratio of potential fall 
 to current, and hence changes the numerical value of the 
 resistance. If, however, the heat is so rapidly removed that 
 change in temperature is not allowed to occur in the 
 conductor, or if a correction is made equivalent to making 
 allowance for this change in temperature, then it has been 
 found that the ratio between the fall in electric potential 
 down the conductor and the electric current in it remains 
 the same for the same conductor whether the current is large 
 or small. This interdependence, or rather exact pro- 
 portionality of potential fall to current strength, in the case 
 of conductors traversed by steady currents is called Ohm's 
 Law. 
 
192 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 Ohm's law is not a mere truism : it is the expression of a physical fact, and 1 
 our confidence in the general truth of the statement is an induction from the 
 results of experiment in particular instances. Ohm's law states the exact pro- 
 portionality of the current when unvarying to the unvarying electromotive 
 force producing it. This is not a necessary truth. The electromotive force 
 E required to produce a current C in a conductor might, for instance, have- 
 been a function of the current C of the form 
 
 Only odd powers of C could have occurred in the expression, because, as the 
 current reverses its direction when the electromotive force is reversed, the 
 right hand side of the expansion representing E in terms of C must change 
 sign with C. 
 
 Suppose we consider as important only the first two terms, and write the 
 expression for E in the form 
 
 E = RC(1-K) 2 ). 
 
 It has been experimentally shown by Chrystal and Saunders (see British 
 Association Report, Glasgow, 1876) that in the case of copper A is a quantity 
 less than 10~ 12 , assuming all proper corrections for temperature made. It 
 has been also shown by FitzGerald and Trouton* that in the case of a solution- 
 of sulphate of copper h in the above formula is less than 3 x 10~ 6 , the 
 maximum current used being 10 amperes per square centimetre. Similar 
 verifications have been made by Beetzt for zinc sulphate solution, by 
 F. KohlrauschJ for dilute sulphuric acid employing electromotive forces- 
 between O'l and 1 volt, and by E. Cohn for solutions of sulphuric acid and 
 sulphate of copper, using alternating currents of low (100 M and high 
 (25,000 a.) frequency. 
 
 Hence there is a certain mass of experimental proof that the electromotive 
 force is proportional simply to the first power of the current when it reaches 
 a steady value. 
 
 Although no d priori reasoning would suffice to establish this law as a 
 general truth, yet, as remarked by "W. N. Shaw (B. A. Report on " Electrolysis," 
 1890), Ohm's law evidently belongs to that class of physical law which, though 
 in the first instance discovered empirically, expresses in numeral relations 
 necessary consequences of the nature of the physical quantities involved. 
 J. Hopkinson has suggested (Phil. Trans. R.S., 1877, p. 614) that the law 
 asserts the superposition of the effects of electromotive force in bodies in 
 which conduction is not complicated by any residual effects, and may there- 
 fore be regarded as a special instance of the general law of superposition. 
 
 Although, therefore, demonstrated experimentally only in the case of a few 
 metallic and electrolytic conductors, no facts have been found which are 
 inconsistent with a conviction of its universal truth as regards metals. It is T 
 
 * B. A. Report, 1888, p. 341 ; 1886, p. 312 ; 1887, p. 345, 
 t Pogg. Ann., 125, 1865, p. 126 ; 117, 1867, p. 15. 
 J Pogg. Ann., 138, 1869, pp. 280, 370. 
 Wied. Ann., 21, 1884, p. 646. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 193 
 
 however, not true in the case of every conductor. According to Braun,* it is 
 not true for psilomelane, iron pyrites, and copper pyrites. Quincket states 
 that some liquids of high resistance, such as ether, carbon bisulphide, turpen- 
 tine oil, and benzene are disobedient for electromotive forces of 30,000 volts 
 and upwards. He also refers to a similar departure from Ohm's law in the 
 case of thin layers of gutta-percha, sulphur, paraffin, and shellac for small 
 electromotive forces. 
 
 In the case of liquids, when a departure from Ohm's law shows itself 
 evidence of chemical decomposition also appears. Actual or initial chemical 
 decomposition may, in all cases, be at the root of the deviations from exact 
 obedience to Ohm's law so far found. It has been asserted that the conduc- 
 tivity of a plumbago line or pencil mark drawn on ground glass does not 
 follow Ohm's law, and it is well known that the conduction current through 
 gases is not proportional to the total electromotive force acting.! 
 
 Assuming the Volt (equal to 10 8 absolute C.G-.S. electro- 
 magnetic units) as the practical unit of potential difference, 
 and the Ampere (equal to lO' 1 absolute C.G.S. electromagnetic 
 units) the practical unit of current, the practical unit of 
 resistance is the Ohm (equal to 10 9 absolute C.G.S. units). 
 For the denomination of very large or very small resistances 
 the terms Megohm or Microhm are used, denoting respectively 
 one million ohms and one-millionth part of an ohm. A 
 resistance measured or appropriately reckoned in megohms 
 is called a high resistance; one conveniently expressed in 
 microhms is called a low resistance. An extra high resistance 
 can be measured in mega-megohms or billions of ohms. 
 Hence methods of resistance measurement are correspond- 
 ingly described as methods for the measurement of ordinary 
 or moderate, of low, and of high resistances. 
 
 We shall, in the following pages, deal separately with 
 the methods for the measurement of electrical resistance in 
 the three cases: (i) when the resulting value is most 
 conveniently expressed in ohms ; (ii) when the result is best 
 expressed in microhms ; and (iii) when the result is most 
 suitably expressed in megohms. 
 
 Each range of resistance measurement has its own most 
 appropriate methods. Processes in which the numerical 
 
 * Pogg. Ann., 153, 1874, p. 556. 
 t Wicd. Ann., 28, 1886, p. 542. 
 Maxwell, " Electricity and Magnetism," 2nd ed Vol. ., p. 463, 370. 
 
194 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 value of a resistance is determined by comparing it with a 
 known standard resistance are called comparison methods. 
 Measurements in which the value of a resistance is 
 determined by immediate reference to the fundamental 
 measurements of length, mass, and time are called absolute 
 metlwds. 
 
 2, Networks of Conductors. In the generality of cases 
 the conductor whose electrical resistance has to be determined 
 takes the form of a wire, strip, or rod of metal of uniform 
 cross-section, or a column of a liquid conductor of similar 
 form. A number of wires or conductors, so joined together 
 that their ends meet in certain common points, is called a 
 network of conductors. A network of conductors has a 
 common or resultant electrical resistance, which can be 
 expressed as a function of the separate or individual resist- 
 ances of the members forming the network. 
 
 As the majority of methods for the measurement of the resistances of wires 
 involve arrangements of networks, it will be useful to indicate the best 
 method of calculating the resultant resistance of a network from its con- 
 stituent resistances, and also the method of calculating the current flowing 
 through any constituent branch by the application of a known electromotive 
 force to the network. 
 
 The following method of calculating the resultant resistance 
 of a network of conductors was given by the Author in a 
 Paper read before the Physical Society of London, June 27, 
 1885 (see Phil. Mag., Sept., 1885, or Proc. Phys. Soc., London, 
 Vol. VIL, 1885) : 
 
 If at any two points in the network connection is made with a source of 
 electromotive force by conductors called respectively the anode and cathode con- 
 ductor, then, after a short period, depending on the self and mutual induction 
 coefficients of the various conductors, the total quantity of electricity arriving 
 by the anode will distribute itself throughout the network and settle down 
 into a steady flow. When this is the case, there is a certain definite difference 
 of potential between the anode or source-point and the cithode or sink-point, 
 and there is also a certain definite and constant strength of current in the anode 
 conductor and in every mesh or branch of the network. Call a and 7 the poten- 
 tials of these source and sink-points, and x the strength of the current in the 
 anode lead (that is, the whole quantity of electricity flowing per second 
 through the network), then (y a}/x measures the resistance of the network. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 195 
 
 We can imagine the network replaced by a single linear conductor or wire of 
 such sort that if the anode and cathode conductors are applied to its ends the 
 difference of potentials at the ends of this simple conductor and the strength 
 of the current flowing through it have the same numerical values, y, a, and x. 
 The resistance of this single conductor is then the same as that of the complex 
 network. 
 
 The resistance of the network is obviously some function of the resistances 
 of the separate conductors or wires which compose it, and is capable of being 
 calculated from them. Experimentally, the resistance of a complicated net- 
 work would best be determined by the measurement of the current-strength 
 in the anode lead and the difference of potential between the source and the 
 sink. Theoretically, it is interesting to examine the law of distribution of 
 currents in a network, and to reduce to a function of the separate resistances 
 the total resistance of the whole network between any two points. 
 
 In his treatise on "Electricity and Magnetism " Clerk Maxwell has treated 
 the general case to determine the differences of potentials and the currents in 
 a linear system of n points connected together in pairs by ^n(n 1) linear 
 conductors,* and has shown how to form the linear equations, the solution of 
 which gives the condition of the network when given electromotive forces 
 acting along some or all of the branches have established steady currents in 
 them. 
 
 The usual method of obtaining a solution for the distribution of currents is 
 the application of Ohm's law round the several circuits of the network, 
 controlled by the condition of continuity that there is no creation nor 
 destruction of electricity at the junctions. 
 
 Since the publication of the first edition of his treatise, Maxwell reduced 
 these two sets of equations to one set by the simple device of regarding the 
 real currents in the meshes of the network as the differences of imaginary 
 currents round each cycle or mesh of the network, all directed in the same 
 direction, and thus obtained by the application of Ohm's law a single set of 
 linear equations, the solution of which gives the required currents in each 
 branch. Maxwell's method is as followsf : If we have p points in space and 
 join them together by lines, the least number of lines which will connect all 
 the points together is p-1. If we add one line more we make a closed 
 circuit somewhere in the system that is to say, a portion of space is enclosed 
 and forms a cell, cycle, or mesh. Every fresh line added then makes a fresh 
 mesh, and hence, if there are I lines altogether joining p points, the number 
 of cycles or cells will be k = l-(p -1). Let such,a system of points and lines 
 represent conducting wires joining fixed points and forming a conducting 
 network. Let a symbol be affixed to each point which represents the electrical 
 potential at that point, and also a symbol affixed to each line representing the 
 
 * Maxwell's "Electricity and Magnetism," 2nd edition, Vol. I., p. 374,: 
 and 2826. 
 
 f This method was first given by Clerk Maxwell in his last course of 
 University lectures. It is alluded to in the second edition of his larger 
 treatise and in the Appendix of his smaller treatise by their respective editors, 
 Prof. W. D. Niven and Dr. W. Garnett, to whom it was communicated by the 
 present Author. 
 
 o2 
 
19G MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 electrical resistance of the conductor represented by it. In such a diagram of 
 conductors the form is a matter of indifference so long as the connections are 
 not disturbed and lines are not made to cross unless the conductors they 
 represent are in contact at that point. 
 
 Consider a network (Fig. 1) formed by joining nine points by thirteen 
 conductors. Then there will be 13 - (9 - 1) = 5 cycles or cells. Let an electro- 
 motive force E act in one branch B, and give rise to a distribution of currents 
 in the network. Take a, /3, 7, 5, &c., to represent the potentials at the points, 
 and A, B, C, D, &c., the electrical resistances of the conductors joining these 
 points, and consider that round each cycle or circuit an imaginary current 
 flows, all such currents flowing in the same direction of rotation. 
 
 A circuit is considered to be circumnavigated positively if we move round it 
 so as to keep the boundary on the right hand. Hence, going round an area A 
 in the direction of the arrow is positive as regards the inside if we walk inside 
 
 the boundary-line, and negative as regards external space B if we walk in the 
 same direction round the outside. We shall consider a current as positive 
 when it flows round a cycle in the opposite direction to the hands of a watch, 
 Keturning then to the network, we consider that round each cycle an imagi- 
 nary current flows in the positive direction. The real currents in the 
 conductors are the differences of these in adjacent cycles or meshep, and the 
 imaginary currents will necessarily fulfil the condition of continuity, because 
 any point is merely a place through which imaginary currents flow, and at 
 which therefore there can be no accumulation nor disappearance of electricity. 
 Let x, y, z, &c., denote these imaginary like-directed currents. Then x- y 
 denotes the real current in the branch I, and similarly x-z that in branch H. 
 Then a-, y, z, &c., may be called the cyclic symbols of these areas. The cyclic 
 symbol of external space is taken as zero ; hence the real current in branch B 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 197 
 
 Let an electromotive force act in the branch B. Let the internal resistance 
 of the source of electromotive force be included in the quantity B, representing 
 the resistance of the branch A. Then apply Ohm's law to the cycle x formed 
 by the conductors B, I, H, and we have 
 
 E-Bx = 7-a. 
 
 In this case x is the actual current flowing in the resistance B, and the poten- 
 tial at the ends of B is equal to the effective electromotive force acting in it, 
 less the product of the resistance of the conductor multiplied by the current 
 flowing in it. For the conductor I we have similarly 
 
 Hence x - y represents the actual current in I : it is the difference of the 
 imaginary currents flowing round the x and y cycles in the positive direction. 
 And for the conductor H we have also 
 
 Add together these three equations, 
 
 and we have, as the result of going round the cycle x, formed of conductors 
 B, I. and H, 
 
 /I- 2 H, ..... . . (1) 
 
 <a, , 7 having disappeared in virtue of these opposite signs. 
 
 The above equation (1) is called the equation of the x cycle, and we see 
 that it is formed by writing as coefficient of the cyclic symbol x the sum of all 
 the resistances which bound that cycle and subtracting the cyclic symbol of 
 -each neighbouring cycle multiplied respectively by the common bounding 
 resistance as coefficient, and equating this result to the effective electromotive 
 force acting in the cycle, written as positive or negative acjording as it acts 
 with or against the imaginary current in the cycle. This statement may be 
 called Maxwell's rule for the formation of the cycle or mesh equations. 
 
 Since there are k cycles or meshes, we can in this way form k independent 
 equations, and by the solution of these determine the k independent variables, 
 , y, z, &c. The value of the current in any branch is then obtained by simply 
 taking the difference of these variables belonging to the adjacent meshes, of 
 which the conductor or branch considered is the common boundary. 
 
 The rule for forming the cycle equations, as given above, is merely a modi- 
 fication of the two statements concerning current networks generally known 
 as KirchhofFs Laws or Corollaries. These laws are usually stated as follows : 
 
 (i.) In any network of conductors conveying steady electric currents the 
 algebraic sum of all the currents meeting at a common point is zero, or 
 
 S(C) = 0. 
 
 In applying the above rule the current magnitude or value must be considered 
 as algebraically positive if it flows to the common point, as negative if it flows 
 Jrom, it. 
 
198 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 (ii.) In any mesh of a network of conductors conveying steady currents, the- 
 sum of the products of the resistance of each conductor bounding the mesh 
 and the current conveyed by it, is equal to the sum of all the electromotive- 
 forces acting round the mesh, or 
 
 2(CR) = 2(E). 
 
 If we assume the existence of imaginary cycle electric currents, all circu- 
 lating round the several meshes of the network in the same direction, it is 
 obvious that this in itself implies the truth of (i.) ; and the second law (ii.)' 
 follows at once from an application of Ohm's law and the additive property 
 of electromotive forces. 
 
 Let us now consider the most general case possible, in which we have a 
 network composed of linear conductors sufficiently far apart to have no- 
 sensible mutual induction, and let there be electromotive fotces acting in 
 each branch or conductor. Let the system be considered to have arrived at< 
 
 FIG. 2. 
 
 the steady condition. Let x, y, z, &c., be the cyclic symbols or measure of the- 
 imaginary current circulating counter-clockwise round each mesh. Let 
 A, B, C, &c. (Fig. 2) be the resistances, and e 1} c. 2 , e 3 , &c., the electromotive forces 
 acting in each branch. These are reckoned positive when they tend to force 
 a current round the mesh counter-clockwise, and negative when they act in. 
 the opposite direction. Then the equation to the x cycle will be 
 
 The symbols of all the cycles are written down, putting in those of z, u, and 
 w with zero coefficients, as they are not adjacent cycles to that of x. We 
 shall have four equations similar to the above for the other cycles, y, z, w t 
 and u. These equations involving only first powers of the variables x, y, z, &c., 
 are called linear equations, and the student of physics is constantly met by 
 the necessity for quickly obtaining the solution of such simultaneous linear 
 equations, so as to evaluate the variables in terms of the constants. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 199 
 
 In order that it may be possible to obtain a solution for the n variables in 
 n simultaneous linear equations, certain conditions must be satisfied, and these 
 conditions are determined by the relation between the constants. 
 
 The solution of linear equations is best effected by means of the method of 
 determinants, and a small knowledge of this department of higher algebra is 
 exceedingly useful to the student of electrical physics. The following elemen- 
 tary principles may be here explained : 
 
 Consider the two linear equations 
 
 l , ......... (i.) 
 
 2 .......... (ii.) 
 
 Multiply (i.) by 6 2 and (ii.) by b l} and subtract the results. We obtain 
 
 (a t b n azb t ) x = Ci& 2 C 2^i- 
 
 This result is symbolically written in the form 
 
 c, ft, 
 
 C 2 63 
 
 02 63 
 
 The solution of the equations expresses the value of x as the quotient of two 
 expressions called determinants. 
 
 A determinant may therefore be defined as an algebraical expression 
 which consists of the sum (algebraic) of a number of terms denoted by letters 
 or other signs, each of which is a product of certain elements. Into each 
 product or term every element enters only once, and the elements can be 
 arranged in a square or rectangular form consisting of columns and rows such 
 that every product is formed by taking one element progressively from every 
 row and every column once and multiplying together. 
 
 stands for the expression ay - b x, the minus sign occurring 
 
 Thus 
 
 
 before the product b x because the order of operation or sign of the term must 
 always be positive when the selection of elements proceeds forward i.e., 
 from first row to second row, &c., or from first column to second column, &c. ; 
 and negative when the order of selection is reversed that is, from the second 
 row to the first row, or second column to the first column. 
 
 It can be similarly shown that if there are n linear equations of the type 
 
 
 
200 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 the solution for any variable a, is capable of being expressed as the quotient 
 of two determinants, thus : 
 
 p t 0-2 .... a n 
 
 Pn 
 
 a 2 
 
 a n 
 6. 
 
 The diflference between the determinants which form the numerator and 
 denominator in the solution for x n results from writing as numerator the 
 determinant of the n equations having the column p } , p z . . . p n substituted 
 for its nth column, and then writing down as denominator the determinant of 
 the n equations simply. For example, the solution of the three linear equations 
 ax + b +cz = d, 
 
 d b c 
 d } 6, c, 
 d z 6 2 c 2 
 
 with similar expressions for y and z, differing only in having as numerators 
 respectively the determinants 
 
 and 
 
 a b d 
 
 a, &, d, 
 
 a 2 6 2 d% 
 the denominator being in each case the same. 
 
 In each case the evaluation of these determinants is easy : a simple sym- 
 metrical process of taking products, according to the rule 
 a b c 
 
 g h i 
 
 suffices to give the equivalent of the three-row determinant in an ordinary 
 algebraic form. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 201 
 
 The properties of determinants enable us also very easily to evaluate a 
 numerical determinant of any order. The process consists in a gradual reduc- 
 tion in the order of the determinant by such transformations as will render 
 all the elements of the first row or column zero except the first. The deter- 
 minant is then reduced to the product of its leading elements and the 
 corresponding minor. The minor of any determinant is one formed from it 
 by omitting all the^elements in one row and one column and closing up all the 
 rest of the elements into one determinant. A repetition of this process lowers 
 the determinant one degree at each stage ; and finally, when it is resolved into a 
 numerical two-row determinant, a simple cross multiplication gives its value. 
 
 The process of evaluation of a numerical determinant is dependent on four 
 principles : 
 
 (1) That the value of a determinant is not altered if rows are changed into 
 columns, or columns into rows. 
 
 (2) The interchange of two rows or two columns reverses the sign of the 
 determinant. 
 
 (3) If every constituent in any row or column be multiplied by the same 
 factor, then the determinant is multiplied by that factor. 
 
 . (4) A determinant is not altered if we add to each constituent of any row or 
 column the corresponding constituents of any other row or column multiplied 
 respectively by an identical factor, positive or negative. 
 
 For example, suppose that the solution of a series of network equations 
 with numerical coefficients of resistance yields the determinant 
 
 5316 
 7892 
 2143 
 10 7 5 7 
 
 we proceed to operate on this as follows : Subtract the second column from 
 the first and write the remainder as a new first column, we get 
 
 2316 
 
 -1 
 1 
 3 
 
 Subtract the third row from the first and put the remainder as a new first 
 row, also add the third row to the second for a new second row, and we get 
 
 12-33 
 
 9 13 5 
 
 1143 
 
 3 7 5 7 | 
 
 Again, subtract the first row from the third for a new third, and subtract 
 three times the first row from the fourth row for a new fourth row, and we have 
 
 12-33 
 
 9 13 5 
 
 0-170 
 
 1 14 -2 
 
202 MEASUREMENT OF ELECTRICAL RESISTANCE, 
 
 which is equivalent to the third order determinant 
 
 9 13 5 
 -170 
 
 1 14 -2 
 And a similar series of operations reduces this to 
 
 76 5 
 
 21 -2 
 
 which is equal to 
 
 -76x2-5x21=-257. 
 
 Accordingly, a series of simple subtractions and multiplications will effect 
 the evaluation of any numerical determinant, and enable us to solve a series of 
 linear network equations for the currents in all the branches when the 
 numerical values of the resistances of the conductors are given. 
 
 The linear current equations as written above give as solutions the values 
 of the cyclic symbols or imaginary currents round each mesh. To obtain the 
 actual current in any branch we should have to obtain the values of the cyclic 
 symbols or imaginary currents, for the adjacent meshes of which the given 
 branch is a common boundary, and then take their difference. Maxwell 
 ingeniously saves labour in this operation by taking as the symbol for one 
 
 B 
 FIG. 3. 
 
 mesh say x + y, and for an adjacent mesh y (Fig. 3), and then the real current 
 in the branch AB is *. 
 
 x + y-y=x. 
 
 And the simple rearrangement and solution of the network equation gives at 
 once as value for x the current in the resistance AB, which is the common 
 partition of the two meshes. 
 
 Keturning to the case when there is only one impressed electromotive force 
 in one branch, we see that in forming the cycle equations only one will be 
 equated to an electromotive force viz., the equation for the mesh containing 
 the impressed electromotive force in one of its branches. All the other equa- 
 tions will be equated to zero ; and accordingly the equation for the current in 
 any conductor will be of the form 
 
 EA rt _.i . 
 
 where A n is a determinant of the ?ith order, and A n _i is a first minor of this. 
 Referring to Fig. 1, we see that, by writing down the five equations of the 
 cycles x, y, z, u, w, we obtain equations by which to calculate the currents in 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 203- 
 any of the thirteen branches, and the current in branch B will be 
 
 where A n is the determinant formed of the coefficients of the five equations, 
 and A ft _i is the first minor corresponding to the coefficient of x in the equa- 
 tion of the sc-cycle. 
 
 We also saw that if 7 and a are the potentials at the ends of the branch B, 
 E-Bz = 7-a. 
 
 Consider that part of the network which remains if the conductor B is 
 removed, and let us imagine that a current x continues to be forced into it at 
 7 and drained out at a. The total resistance of that part of' the network, not 
 counting B, is 
 
 J~y-. 
 
 ~ x > 
 
 V 
 
 but this is equal to -- B. 
 
 Since the resistance of B may be anything, let it be zero ; then the total 
 resistance of the network between 7 and a will be 
 
 E 
 
 but 
 
 JB=0, 
 
 where the suffix and bracket denote that after the determinants are formed 
 from the cycle equations, according to Maxwell's rule, then in them B is put 
 equal to zero. 
 
 If we denote the determinant of all the w-cycle equations under the condi- 
 tion of B = by d n , and by d n -\ the first minor of this latttr, or the minor of 
 its leading element corresponding to the coefficient of x with the resistance of 
 the circuit containing the effective electromotive force put equal to zero, we 
 have for the total resit tance R of the network between the points at which the 
 current enters and leaves the expression 
 
 R= *-. 
 
 rf n -i 
 
 Since, then, as we have seen, the linear equations for the cycles can always 
 be solved by evaluating the determinants, it follows that in all cases, no 
 matter how complicated, the resistance of any network can be calculated by 
 simple arithmetic processes from the given resistances of the branches or 
 conductors which compose it. We have therefore here an interesting exten- 
 sion of Maxwell's method of calculating the currents in a network and the 
 potentials at the junctions to a method of calculating the combined resistance 
 of a number of conductors forming a network ; which method consists, as seen 
 above, in forming a certain determinant whose elements are formed of the 
 separate resistances of the branches, and dividing this determinant by another 
 of an order next below viz., the first minor of its leading elements ; and we 
 find that the resistance between any two points of any network of conductor?, 
 however complicated, is expressible as the quotient of a certain determinant 
 by another formed from it. 
 
'204 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 We shall proceed to illustrate this method by a few examples. 
 
 1. Find the resistance between the points 1 and 3 (Fig. 4) of a network 
 
 FIG. 4. 
 
 consisting of five conductors, whose resistances are A, B, C, D, E, joining four 
 points, 1, 2, 3, and 4. 
 
 Connect 1 and 3 by an imaginary conductor of zero resistance, and having 
 an electromotive force, e, supposed to act in it. Let x, y, z denote the cycles 
 or imaginary like-directed currents in the three meshes so formed, and write 
 down the current equations, according to Maxwell, for these three cycles 
 (A+B)as -Ay -Ez = e, 
 
 -Ax + (A + E + D)y -Ez = 0, 
 -Ex -Ey + (B + C + E)s=0. 
 
 Then, by what has been shown above, the resistance R between the points 1 
 and 3 of the network is given by the expression 
 
 (A + B), -A, -B 
 
 -A, (A + E + D), -E 
 
 -B, -E, (B + C + E) 
 
 (A + E + D), -E 
 
 -E, (B + C + E) 
 In dealing with numerical cases we need 110 longer introduce any notice of 
 imaginary electromotive forces, but proceed according to the following 
 rule : 
 
 TO DETERMINE THE RESISTANCE OF A NETWORK OF CONDUCTORS 
 BETWEEN ANY TWO POINTS ON THE NETWORK. Join these two points by 
 <i line whose resistance is supposed zero, and give symbols to the meshes of the 
 network so formed, calling the additional mesh produced by this added zero 
 conductor the added mesh. Then write doivn a determinant whose dexter 
 diagonal has for elements the sum of the resistances which bound each mesh t 
 beginning with the added mesh; and for the other elements of each row the 
 resistances, having the minus sign prefixed, which separate this mesh respectively 
 from adjacent meshes, zeros being placed for elements corresponding to non- 
 adjacent meshes. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 205 
 
 More explicitly, if we denote by x, y, z, &c., the meshes, x being the added 
 mesh, and by SR^, 2R y , 2R 3 , &c., the sum of the resistances which bound each 
 cycle, then these will be the elements along the dexter diagonal of the 
 determinant And if x and y are adjacent meshes, and Z R^ represents the 
 resistance of the common boundary, then - x R y will be the 'element in the 
 a;th row and yth column, and also in the 7/th row and xth column ; but if x 
 and z are non-adjacent meshes, then will be the element in the ceth row and 
 2th column, and also in the zth row and xth column. Having formed th:& 
 determinant, which we call the network determinant, we divide it by the first 
 minor of its leading element ; and the quotient is the resistance of the net- 
 work between the two points, joined by the zero-conductor forming the added 
 mesh. It is seen that, owing to the mode of formation of the network 
 equations, the network determinant is a symmetrical determinant that is r 
 one half of the determinant is the reflection, as it were, of the other half in 
 the diagonal considered as a mirror. 
 
 As a means of comparing the results of this method with other known 
 results, let ua take the exceedingly simple case of three conductors joining 
 two points in so-called multiple arc 
 
 Let 1, 2, and 3 (Fig. 5) be th three conductors joining two points A and B - r 
 
 FIG. 5. 
 
 heir respective resistances be r v r^, r$ ; then join A, B by a dotted line so 
 as to make one added mesh, and let the resistance of this added circuit be- 
 zero. Then, without writing down the equations to the cycles, we see that 
 the network determinant is 
 
 d n = r, -r, I 
 
 -r l r, + r. 2 - r. 2 
 \ -r 2 r 2 + r 3 \ 
 
 The elements r,, r,4 r- 2 , r 2 + r 3 of the dexter diagonal are the sums of the 
 resistances which bound each mesh, x, y. and z, taking the added mesh x first. 
 The other elements of the first row are the resistances, with minus sign pre- 
 fixed, which separate the mesh x from mesh y and mesh z ; or are common to x 
 and y and x and z viz., r } and zero, because x and z are non-adjacent. And r 
 similarly, if m and n are any two meehes, then the element in the nth row and 
 with column is the resistance separating or common to the two meshes ; and 
 the element in the nth row and with column is identical with that in the mth 
 row and nth column ; zero being placed as an element if these meshes, m and 
 n, have no common boundary or circuit. 
 
206 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 The above determinant is easily evaluated. By adding the first row to the 
 second for a new second row, and this second row to the third for a new third 
 row, we transform the determinant easily into 
 
 r, -r 
 r 2 - r 2 
 r 3 
 -which is equal to r\r z rz. 
 
 The first minor of the leading term of the network determinant is 
 
 which is equal to r,r 2 + r 2 r 3 + r s r } ; 
 
 and hence the resistance of the network between A and B is 
 
 d n - 
 
 which is a known result. In these simple cases the above general rule is of 
 -course a less easy method of finding the combined resistance than the direct 
 application of Kirchhoff's corollaries of Ohm's law ; but whereas the general 
 
 FIG. 6. 
 
 method is alike applicable to the most complicated as well as to the most 
 pimple cases, the simple direct method requires twice as many equations, and 
 <loes not determine the direction as well as magnitude of the current in each 
 branch.* 
 
 As a simple numerical example we may take the case of a crossed square of 
 wires. Let twelve conductors join nine points (Fig. 6) so as to form a square 
 
 * The joint resistance of two conductors in parallel may be obtained by the 
 following single geometrical construction : Draw two straight lines perpen- 
 dicular to a common base line and at any distance apart. Set off on each 
 lengths proportional to the two resistances respectively. Join the top of each 
 line so set off with the base of the other line by a straight line, and from the 
 point where these diagonals cross drop a perpendicular on the common base 
 line. The length of the last perpendicular will represent to scale the joint 
 resistance of the two conductors. We leave the proof as an exercise to the 
 .student. (See The Electrician, Vol. XXVIII., p. 167.) 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 207 
 
 divided into four squares, or a four-mesh network of conductors. Let the 
 resistance of each branch, as ab, be unity. It is required to find the combined 
 resistance between A and B. Number the meshes 2, 3, 4, 5 ; 1 being the 
 .added mesh formed by joining A B by a dotted line, making an additional 
 fifth mesh, the resistance of this additional ideal conductor being zero. Then 
 the network determinant is 
 
 4 
 
 -1 
 
 -2 
 
 -1 
 
 
 
 - 1 
 
 4 
 
 -1 
 
 
 
 -1 
 
 2 
 
 _ ^ 
 
 4 
 
 -1 
 
 ^<K 
 
 -1 
 
 
 
 -1 
 
 4 
 
 -i 
 
 
 
 -1 
 
 
 
 -1 
 
 4 
 
 The dexter diagonal has for each element 4 viz., the sum of the four 
 resistances, each to unity, which form each mesh or cell. And all the other 
 figures, say in the nth row, are the resistances (with minus sign prefixed) 
 separating the nth mesh from all other meshes, zero being placed in the 
 column corresponding to any mesh which has no common conductor or branch 
 with this wth mesh. The order in which the columns stand and also the rows 
 correspond to the order in which the meshes are numbered in Fig. 6. 
 
 FIG. 7. 
 
 The numerical value of this determinant is easily found to be 288 = 3 x 96 = c n . 
 'Now if we take the first minor of its leading element, we get a determinant 
 formed of the elements included in the dotted rectangle ; and taking this as a 
 separate determinant and evaluating it, we have its value 
 
 d n -i = 192 = 2x96; 
 
 hence the resist nice of the network between the points A and B is 
 d n 288 . 
 
 One more simple numerical case may be taken and compared with the 
 results of known methods. 
 
 Let a hexagon of conductors be taken (Fig. 7) having crossed diagonals all 
 meeting in the centre. Let the resistance of each side, as ab, be unity, and 
 
208 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 also let the resistance of each semidiagonal, as Oa. be unity. Then required 
 the combined resistance of this network of 12 conductors between the points 
 A and B diametrically opposite. Join the points A and B by a dotted line of 
 zero resistance, making an added mesh 1. Mark the other meshes 2, 3, 4, 5 r 
 6, 7. Then by forming the network equations it is easily seen that the net- 
 work determinant d n is 
 
 3-1-1-1 
 -1 3-1 0-1 
 -1 -I 3-1 
 -1 0-1 3 0-1 
 
 0-0003-10 
 
 0000-13-1 
 
 0-1 0-1 3 =d n . 
 
 The value of this determinant is 256. 
 
 The first minor of the leading element of d n is d n -i 
 
 = 3-10-100 
 -13-1000 
 
 0-1 3 0-1 
 -1003-10 
 
 0-1 3-1 
 
 0-1 0-1 3 
 
 The value of this last is 320. 
 
 Hence the resistance of the network between the points A and B is 
 
 R _ 
 
 " 
 
 32u 5' 
 
 FIG. 8. 
 
 We can easily verify this result in the above symmetrical case, for the 
 hexagonal framework in Fig. 7 is traversed symmetrically by the current 
 flowing through it ; and hence no disturbance of the distribution of currents 
 will take place by separating it, as in Fig. 8. We break the connection 
 between the semi-diagonal conductors a, b and the mean diagonal A B, whilst- 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 209 
 
 keeping them in contact with each other, the resistance of each branch still 
 remaining unity. It is then easily seen that the hexagon so arranged must 
 offer exactly the same resistance between the points A and B as in its original 
 form. 
 
 The combined resistance of a, b, and /, each equal to unity, between the points 
 C D is f , and the combined resistance of this with e and g in series is 2f ; and 
 hence the total resistance of the whole network between A and B is equal to 
 that of three conductors in multiple arc whose resistances are respectively 2f . 
 2, and 2f , which is equal to 
 
 1 _4 
 1 . J. _1 5' 
 2f 2 2| 
 the same result as obtained above. 
 
 These numerical examples show conclusively that, in cases in which the 
 resistance of a network can be obtained by simple direct methods, the results 
 coincide, as should be the case, with those obtained by the employment of the 
 general method ; but at the same time the general method is capable of 
 conducting easily to a solution in the most unsymmetrical cases. The general 
 rule will, for instance, just as easily give the determinants when the selected 
 points between which the resistance is required are not symmetrically placed, 
 but are say adjacent angles of the hexagon, in which case no such simple 
 direct method as employed above can be used. 
 
 A little practice will enable the student to apply the above 
 rules to very complicated cases of networks of conductors, and 
 to calculate the resultant resistance between any two points 
 of a network. 
 
 3. The Wheatstone-Kirchhoff Bridge. Slide Wire 
 Form. The arrangement or network of conductors called 
 Wheatstone's bridge has already been briefly explained in 
 principle (see 13, Chap. I.). It consists essentially of six 
 conductors joining four points (see Fig. 59, Chap. I.). In one 
 of these circuits is placed a source of electromotive force, and 
 in the other a galvanometer. In the laboratory the actual 
 apparatus takes many different forms. In its most simple 
 modification it is known usually in England as the slide 
 wire bridge, or, as Continental writers call it, the Wheatstone- 
 Kirchhoff bridge. In this form its most important portion 
 is a uniform straight metallic wire of platinum-indium alloy, 
 platinum-silver alloy, manganin (which must be surface-gilt), 
 or platinoid, This wire is stretched over a scale between 
 
lUO MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 terminal blocks of copper, and may conveniently be one or 
 two metres in length. The scale in contiguity to it may be 
 either of boxwood, ebonite, or metal, and it should be divided 
 into centimetres and millimetres. The slide wire must be very 
 carefully selected, and its uniformity in electrical resistance per 
 centimetre of length tested as described in 5 of this chapter. 
 
 In the construction of a high-class instrument it is desirable 
 to employ a wire drawn of an alloy formed of 90 per cent, 
 platinum and 10 per cent, iridium. This alloy is very hard 
 and non-oxidisable by exposure to the air. An alloy of 
 platinum-silver may also be adopted having a composition of 
 66'6 per cent, silver and 33*3 per cent, platinum. 
 
 In cheaper instruments a German-silver or platinoid wire 
 is generally used, but both these last alloys tarnish slightly 
 when exposed to air. Manganin can be preserved from 
 atmospheric action only by being gilt on the surface. The 
 gilding must necessarily not be very thick, and in con- 
 sequence is somewhat easily rubbed off the manganin. The 
 extremities of the wire are screwed or clamped to massive 
 terminal blocks of high-conductivity copper. 
 
 If the wire is soldered to the terminals, care must be taken 
 that the solder does not affect the composition of the alloy at 
 the extreme ends of the wire. Thus, for instance, manganin 
 should not be soldered with any solder containing zinc, and 
 platinum alloys should not be soldered with any solder 
 containing lead. 
 
 The instrument must be provided with a travelling block or 
 slider, such that an electrical contact may be made with the 
 wire at any point by pressing a contact key. This contact 
 must be made by a knife-edge, and it is desirable that the 
 pressure of the finger should not apply the knife-edge directly 
 to the slide wire, but merely release a spring. Thus, in 
 Fig. 9, iow' is a portion of the slide wire, and EE' is a part 
 of the sliding block, K a knife-edge carried on the extremity 
 of a spring x t and P a finger-piece or trigger. A pressure 
 applied to P will release the knife-edge and permit it to make 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 211 
 
 contact with the wire. It is easily seen that the pressure of 
 the knife-edge on the wire is determined by the elasticity 
 spring x carrying it, but not by the pressure of the linger 
 on the finger-piece. The object of employing the above 
 device is to prevent any undue pressure on the knife-edge 
 causing "nicks" or deformations in the slide wire if contact is 
 repeatedly made at one place on the wire. The knife-edge 
 should consist of a piece of the same alloy used for the slide 
 wire itself, carefully shaped to a wedge shape and soldered to 
 a metallic carrier spring. The block holding the contact 
 knife-edge should be capable of being traversed easily to and 
 fro along the base-board in such a way that the knife-edge 
 can make contact with the slide wire at any point in its 
 length, and the exact position is observed and recorded by an 
 indicating point, or vernier, moving over the divided scale. 
 
 FIG. 9. 
 
 The " bridge " arrangement is then completed, as shown in 
 Fig. 10, in which the third and fourth arms of the bridge 
 consist respectively of a variable standard resistance S and 
 the resistance E to be measured. A battery, B, consisting 
 of two or three dry cells, is connected to the ends of the slide 
 wire, and a movable coil galvanometer, G, between the knife- 
 edge on the slider block and the junction between the third 
 and fourth arms. Keys K x and K 2 are inserted in the battery 
 and galvanometer circuits respectively. The comparison 
 resistance may best be a dial or series plug pattern resistance 
 box. The resistance unplugged or inserted into the third arm 
 of the bridge should be as nearly as possible equal to the 
 
'212 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 resistance to be measured. Under these conditions, if the 
 slider is moved along the wire and trial contacts made with 
 the knife-edge at various places, a point, C, will be found at 
 which the galvanometer G- indicates no current when- the 
 knife-edge contact is made. The ratio of the resistance being 
 measured to that of the standard is then the same as that 
 of the resistances or lengths of the two sections Into which 
 the knife-edge divides the slide wire. Hence, if S is the 
 value of the standard in ohms and E that of the resistance 
 being measured, and if P and Q are the resistances or the 
 
 I V.,i|in.,iiiflniiii:.ir ,;. -.. ,-,.i,t ii..|.-..i'., .....fX,.- ; - ,. .,,. nTTTi! **j 
 
 ^^^t- ^^^ 
 
 3 
 
 B 
 
 ^OJ-^ 
 
 FIG. 10. 
 
 lengths of the uniform slide wire sections on the respectively 
 adjacent sides of the bridge arrangement, we have, when the 
 galvanometer current is zero, 
 
 P:Q = R:S, 
 
 or 
 
 If the electrical resistances of various lengths of the slide 
 wire are exactly proportional to those lengths, if the total 
 length of the slide wire is 1,000 millimetres, and the slide 
 wire reading at the knife-edge contact when the bridge is 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 213 
 
 balanced is at x millimetres from one end of the wire, then 
 we have 
 
 P : Q = : 1,000 as. 
 
 Hence B - 
 
 Accordingly, we can determine the value of the unknown 
 resistance II in terms of the value of a known standard, S, 
 and the ratio of the lengths of the two sections of the slide 
 wire when the balance is obtained. 
 
 4. The Plug Pattern Resistance Bridge. In practice it 
 is generally much more convenient to employ a plug pattern 
 Wheatstone bridge for the measurement of resistances. In 
 this case the resistances which form the three arms of the 
 
 FIG. 11. Sectional View of Blocks, Bobbins and Coil in Series Pattern Plug 
 
 Bridge. 
 
 bridge are formed by adding in series the resistances of fixed 
 coils of wire contained in a box. This addition is effected -by 
 the insertion of coned metallic plugs into holes bored out 
 partly in one block of metal and partly in another adjacent 
 one. 
 
 The resistance coils may be arranged either in series or in 
 parallel, and the plugs may be arranged so as to short- circuit 
 coils or to interconnect the junction between any coil of the 
 series and a common or omnibus bar alongside the coils. In 
 Fig. 11 is shown the series system of short-circuiting arrange- 
 ment of plugs and blocks interconnected by resistance coils. 
 In this case we have a series of bobbins of insulated wire of 
 
214 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 various resistances, and one or more coils can be short- 
 circuited and cut out of series by the insertion of plugs 
 between the metal interconnecting blocks. In the second 
 arrangement (Fig. 12) the coils are also arranged in series, but 
 a junction can be effected between any interconnecting block 
 and a parallel common or omnibus bar, so that the resistance 
 between the bar and one end of the coil series can be varied 
 by steps. In this latter case it is customary to employ a 
 series of nine or ten coils of exactly equal value say ten 
 units, ten tens, or ten hundreds. The plug may be stepped 
 along from hole to hole, and thus insert a resistance of one, 
 
 FIG. 12. 
 
 two, three, four, &c., units, tens, or hundreds of ohms between 
 the end or terminal block and the common bar or block 
 alongside. In some cases the blocks are arranged for this 
 second pattern in a circle or dial (see Fig. 13), and in other 
 cases in a row or rows (see Fig. 14) so connected that the 
 resistances are joined in parallel and not in series, when one 
 or more plugs are inserted. 
 
 A " bridge " is constructed of a series of coils arranged so 
 as to form the two ratio arms of the bridge by having a 
 terminal placed in some position in the series, and another 
 sciic-s of resistances forming the measuring arm. These 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 215 
 
 resistances may be arranged as follows : In the so-called 
 " Post Office " pattern of Wheatstone bridge the ratio arms 
 are each formed of a series of coils of 1,000, 100, 10, and 1 ohms 
 
 1 
 
 FIG. 13. Arrangement of Blocks and Colls in Dial Pattern Resistance Box. 
 
 resistance arranged in the series fashion. The measuring arm 
 is then made of a series of coils (generally of 1, 2, 3, 4, 10, 20, 
 30, 40, 100, 200, 300, 400, 1,000, 2,000, 3,000, 4,000 ohms in 
 
 FIG. 14. Arrangement of Resistances in a Conductivity Box. 
 
 series) ; and terminals for the battery, galvanometer, and 
 resistance to be measured, together with a contact key in the 
 battery and one in the galvanometer circuit, arc also added. 
 
216 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 The block pieces are of brass, generally mounted on an ebonite 
 slab, which forms the top of the box. The arrangement of circuits 
 in a series coil bridge is shown in Fig. 16, and the external 
 appearance in Fig. 15. The particular design illustrated is 
 that of Messrs. Nalder Bros, and Co.* 
 
 In using this bridge the operator connects the resistance 
 to be measured to the terminals marked L arid L, the 
 galvanometer to the terminals G G, and a battery of 
 three or four dry cells to the terminals 13 and I>. He 
 then removes one of the plugs from the one ratio arm 
 
 FIG. 15. Series Plug Pattern Wheatstoue Bridge. 
 
 series and one from the other ratio arm series. In so doing 
 it is desirable to have some notion of the value of the 
 resistance to be measured, and in general it is well, unless 
 the unknown resistance is suspected to be very large or very 
 small, to begin by a ratio of equality that is, the two ratio 
 arms are made 1 and 1, or 10 and 10, or 1,000 and 1,000 
 ohms by removing the plugs from the holes marked 1, 10, or 
 1,000 on each side. This done, the observer removes plugs 
 from the other or measuring arm series until, on pressing first 
 
 * See The Electrician, Vol. XLL, p. 596. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 217 
 
 the battery key and afterwards the galvanometer key, the 
 galvanometer indicates no current. The bridge is then said 
 to be balanced. It will generally happen that with integer 
 value coils of the three arms it is not possible to secure 
 a perfect or absolute balance. For instance, if the ratio arms 
 are 10 and 10 ohms, then with 230 ohms resistance un- 
 plugged on the measuring arm, the galvanometer may show a 
 small current in one direction through it, whereas with 231 
 ohms unplugged the galvanometer may show a small deflec- 
 tion in the opposite direction. 
 
 NAl OCR BROS CO. UONOON 
 
 
 
 Q:O;CCP:O:Q 
 
 ^\^*+*l*J -x-v-r'O*' .^%^^*WV^.> lM ^^tWV J xx-^x.*V ^s*^/^^ 
 
 FIG. 16. Arrangement of Circuits in Series Plug Pattern Wheatstone Bridge. 
 
 A further approximation to the true value of the unknown 
 resistance may be obtained as follows : If the galvanometer- 
 is one reading by a mirror and scale, note the small 
 steady scale deflection of the galvanometer when the 
 galvanometer and battery key are both held down and 
 the lower of the two measuring arm resistances is 
 unplugged. Thus, for instance, suppose that, with 230 ohms 
 out in the measuring arm, the steady scale deflection of 
 the galvanometer is 10 millimetres to the left. This small 
 deflection of the spot of light or indicating needle is propor- 
 tional to the galvanometer or bridge current under those 
 
218 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 conditions. Suppose, then, that the measuring arm is made 
 231 ohms and the galvanometer deflection is changed to 15 
 scale divisions to the right. We may deduce the true value 
 of the measuring arm resistance, which would exactly balance 
 this unknown resistance being measured, by a simple calcula- 
 tion. Since a change of one unit in the measuring arm 
 resistance changes the galvanometer deflection from +15 to 
 10, it is clear that, since the whole scale deflection change 
 is 25 divisions for the whole change from 230 to 231 ohms in 
 the measuring arm resistance, a value of the measuring arm 
 
 of 230 -f ohms, or of 2304 ohms, would exactly balance 
 
 the unknown resistance being measured. Hence, if the ratio 
 arms are 10 and 10, the resistance being measured is 2304 
 ohms. The above-described method, called taking right and 
 left galvanometer deflections, enables us to make an initial 
 approximation to the value of the unknown resistance. 
 
 When this is done a different ratio may be selected for the 
 ratio arm* The ratio may, for instance, be made 10 to 1 by 
 removing the plugs corresponding to 1,000 and 100 ohms in 
 the two ratio arms. Balancing again, suppose we find that 
 a value of 2,304 ohms unplugged out of the measuring arm 
 makes a scale deflection of one division to the left, and with 
 2,305 ohms unplugged in the measuring arm we obtain a scale 
 deflection of two divisions to the right ; then similar reasoning 
 shows that the exact balancing resistance would be 2,304*33 ohms. 
 Hence the resistance being measured is 230433 ohms. 
 
 In using a series pattern plug bridge the following pre- 
 cautions must not be neglected : 
 
 (i.) The plugs when not in use should never be laid on the 
 table, or be held in a hot hand, but should be placed in the lid of 
 the bridge box, which is generally lined with velvet or cloth. 
 
 (ii.) The greatest care should be taken to prevent the plugs 
 becoming permanently soiled, oxidised, or amalgamated with 
 mercury. If necessary to clean a plug, only a very careful 
 application of the finest glass-paper should be made. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 219 
 
 (Hi.) In putting the plug into a hole, give it a slight twist 
 to make it seat itself accurately in the coned hole, and, if the 
 box is a series plug pattern box, after each rearrangement of 
 plugs go over the other plugs in the same manner again to 
 see that there are no loose plugs. The plugs should, however, 
 not be put into the holes so violently that there is risk of 
 twisting off the heads in getting them out again. 
 
 (iv.) The ebonite slab carrying the brass blocks should be kept 
 carefully dusted, and the bridge when not in use should be put 
 away in its box with all the plugs loosely placed in their holes. 
 
 The advantage of the dial pattern of bridge (see Fig. 13) 
 is that there is only one plug to each decimal series of coils. 
 A resistance of to 9 ohms is introduced into the measuring 
 arm by merely moving the plug to the holes marked to 
 9 in the dial or group or row of blocks marked units. 
 A resistance of to 90 ohms or to 900 ohms is intro- 
 duced by placing a plug in one or other of the holes in the 
 block group marked tens or hundreds, and so on. 
 
 In using a dial pattern bridge to measure an unknown 
 resistance, set off first a ratio of 1 to 1 in the ratio arms, and 
 then systematically increase the measuring arm resistance by 
 changing the unit plug ; then move the ten ohm plug, next the 
 hundred ohm plug, from hole to hole progressively until a 
 resistance is found such that the galvanometer is deflected 
 one way for the lower and the opposite way for the higher. 
 Thus, suppose that with a ratio arm of 100 and 100 ohms we 
 find a resistance of 500 ohms in the balancing arm makes the 
 galvanometer needle fly to the left and 600 ohms makes it fly 
 to the right, we may try next increasing regularly from 500 
 to 600 by tens. If then we find left and right deflections for 
 550 and 560 ohms, we proceed to increase by units; and when 
 we find small left and right deflections for 553 and 554 ohms 
 we adopt the deflectional method and unequal ratio arms 
 already explained to determine the next decimal place or places. 
 
 In measuring any inductive resistance it is essential to 
 cluac the battery circuit of the bridge before the galvanometer 
 
220 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 circuit, in order to permit the currents in the various 
 branches to become steady. This is achieved without thought 
 by the employment of a double key (see Fig. 17), which closes 
 first the battery circuit B B, and afterwards the galvanometer 
 circuit G G. 
 
 In making careful measurements it is necessary to apply a 
 correction to the bridge reading for the temperature variation 
 of its own coils, and also for any error there may be in the 
 actual coil resistances. 
 
 The possessor of a plug pattern bridge should not take for 
 granted that it is correct, but should proceed to check its 
 readings as follows : A standard 1-ohm coil should be 
 connected to the bridge, using very thick copper rods or 
 strips of copper and mercury cups to make the connection. 
 
 FIG. 17. Wheatstone Bridge Combined Battery and Galvanometer Key. 
 
 The bridge reading should then be taken, using various ratio 
 arms say 1 to 1 ohm, 10 to 1 ohm. 1,000 to 100 ohms. If 
 the bridge is properly adjusted each of these readings, when 
 reduced, should give a value of unity for the known standard 
 1-ohm resistance. The maker of the bridge generally marks 
 on it the temperature at which it is correct in its readings, 
 and he will always furnish the purchaser with a statement of 
 the nature of the wire used for the coils and its temperature 
 coefficient. Thus, if the bridge coils are made of platinum- 
 silver wire, the temperature coefficient of which at about 
 15C. is 0'026 per cent, per degree, and if the bridge is 
 correct at 15C., then it follows that, if the bridge coils at the 
 moment of reading are at a temperature tG., the true value 
 of one unit of the bridge reading is 1+0 < 00026( 15) ohms. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 221 
 
 The real difficulty is the uncertainty as to the actual 
 temperature of the wire of the bridge coils at the moment of 
 measurement. A thermometer placed in the box containing 
 the coils merely gives the temperature of the air round the 
 coils, and if these have become internally heated by currents 
 passing through them, the actual temperature of the wire 
 may be, and probably is, very different from that of the air 
 outside them. To avoid this uncertainty, it is necessary that 
 bridges intended for very accurate work should be made up 
 with manganin wire properly aged, and that the coils of wire 
 should be wound on brass or copper tubes merely having one 
 layer of silk tape laid over it. The box containing all the 
 coils should be filled with an insulating oil which can be kept 
 stirred. In this manner it is possible to maintain the coils at 
 a temperature near to that at which the manganin has a zero 
 temperature coefficient, and at this temperature the coils 
 should be adjusted to be correct. 
 
 In the case of the measurements made in an electro- 
 technical laboratory, it will not often happen that a degree of 
 refinement is necessary in the resistance measurements which 
 will make it worth while to apply the above correction for the 
 temperature of the bridge coils. For very accurate work, 
 however, it has been proposed to employ coils of bare wire 
 wound on mica- frames.* The coils after winding are annealed 
 by passing a strong current through them. When in use they 
 are kept immersed in a fluid insulating oil which is well 
 stirred. 
 
 We may conclude this section with a description of a 
 standard form of Wheatstone bridge for very accurate 
 resistance measurements which has been designed by Prof. 
 H. L. Callendar and Mr. E. H. Griffiths.f 
 
 * See Mr. F. W. Burstall, " On the Use of Bare Wire for Resistance Coils." 
 Proc. Phys. Soc., Vol. XIV., p. 286. 
 
 f The following paragraphs describing the Callendar and Griffiths bridge are 
 taken by permission verbatim from a series of articles in The Electrician for 
 1898 by Mr. G. M. Clark, entitled " On the Measurement of Temperature : 
 an Application of the Measurement e>f Resistance." (The Electrician, 
 Vol. XXXVIII., p. 747.) 
 
222 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 A general view in its case is given in Fig. 18, and a view of 
 the top of the box in Fig. 19. It will be seen that, besides a 
 
 FIG. 18. Callendar ind Griffith's Resistance Bridge. 
 
 set of coils, the box has a bridge wire in addition. One arm 
 of the bridge is formed by the resistance to be measured and 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 223 
 
224 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 part of the bridge wire, the rest of the bridge wire and the 
 necessary coils forming the other arm. As the back coils of 
 the bridge are equal, a pair of compensating leads (equal in 
 resistance to those leading to the resistance to be tested) may 
 also be introduced into this arm. It is therefore not 
 necessary to make separate measurements for the leads. 
 When the resistance to be tested is short-circuited, the bridge 
 should be in balance with the contact at the centre of the 
 bridge wire. Thus, by short-circuiting the bridge by the four 
 connectors shown at the right of Fig. 18, the zero of the bridge 
 can be readily tested at any time. 
 
 The coils of the bridge are thirteen in number. Eleven of 
 these form the ordinary working coils of the bridge. These 
 are arranged on the binary scale. The smallest coil, marked 
 A, has a resistance of 5 box units. The unit of the box is 
 0*01 ohm. The other coils are respectively 10, 20, &c., of 
 such units. The largest coil, L, is 5,120 units. Thus the 
 whole resistance of the box is a little over 100 ohms. Since 
 the back coils are equal, this is also the greatest resistance 
 that can be measured with the box. The other two coils are 
 marked respectively Cal. and <. The coil Cal. has a resistance 
 of approximately the box unit, arid is used in the calibration 
 of the bridge wire. The coil < has a resistance of 100 box 
 units, and is useful for the adjustment of platinum thermo- 
 meters. For if these are constructed so that their funda- 
 mental interval is 100 box units, then the calculation of the 
 platinum temperature is greatly simplified.* 
 
 A movement of two centimetres on the bridge wire corres- 
 ponds to the box unit. As it is easy to read this movement 
 by means of a vernier to ^mm., the least count of the bridge 
 is joW^ f the box unit, or O'OOOOl ohm. The contact 
 maker seen on the bridge wire is of a special design to permit 
 of this fine adjustment. It also, by its construction, renders 
 injury to the bridge wire impossible. 
 
 In calibrating the bridge wire all that is required is a rough 
 adjustable resistance, whose value need not be known. Having 
 adjusted this until the bridge is in balance with the slider at 
 one end of the scale, the plug Cal. is removed and the slider 
 moved until a fresh balance is obtained. The plug is then 
 replaced and the external resistance adjusted until the balance 
 
 * For pt = 100(R - RoVRi - R : and F. I. = RI - R = 100, then pt = H- R . If 
 the F. I. is not exactly 100, but differs only by a small quantity, then pt can 
 be found by the usual methods of making small corrections, 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 225 
 
 is again attained at, or sufficiently near to, the same place 
 in the bridge wire, and the process is repeated until the whole 
 bridge wire has been traversed. We have thus a series of 
 steps on the bridge wire, each equal in resistance to one box 
 unit. The length of these steps has been read off on the scale, 
 so that if there are any errors in the scale, these have been 
 introduced into the calibration, and are therefore of no 
 consequence. 
 
 In the calibration of the coils a somewhat similar process is 
 followed. As each coil only differs from the sum of all that 
 precede it by five box units, a balance obtained with any one 
 coil can also be obtained with the preceding coils, together 
 with a length of bridge wire. Thus every coil in the box 
 can be readily determined in terms of the bridge wire. By 
 using different combinations of coils to measure any resis- 
 tance, there is a perpetual check on the calibration of the 
 whole box. Any change which takes place in the value of 
 any of the coils can be readily detected. It is, however, very 
 improbable that much will take place. These coils are of 
 naked platinum silver, and are wound on mica frames. By 
 lifting the box out of its case all the coils can be seen, and are 
 easily accessible. Coils so formed can be very thoroughly 
 annealed by passing a strong current through them, sufficient 
 to raise them to a red heat, after the coil has been wound. 
 They are thus entirely free from all strain. The bare wire 
 coils are immersed in a bath of non- volatile hydrocarbon oil 
 of high insulating power. This oil can be stirred, and there is 
 no doubt that the temperature indicated by a thermometer in 
 the oil is also the temperature of the coils themselves. The 
 temperature of the box can be rapidly raised or lowered if 
 necessary ; and as the coils follow these changes, the tempera- 
 ture coefficient of the coils can very readily be found. 
 
 The back coils of the bridge also consist of two naked 
 platinum silver coils wound together on the same rnica frame. 
 There is thus no chance of the two being at different tempera- 
 tures. A short length of wire on the top of the box joins the 
 two ends of these coils, and on this length is the galvanometer 
 contact. If the back coils are not equal the galvanometer 
 contact can be adjusted till equality in the back arms is 
 obtained. The galvanometer contact is a potential one only, 
 so that resistance through the contact is of no importance. 
 
 The top of the box is formed of white marble. This has 
 high insulating properties, and is not open to the same 
 
 Q 
 
226 
 
 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 objections as ebonite. Separate brasses are used for each plug, 
 so that the movement of one plug in no way affects the rest. 
 Each block and plug is also marked with its distinguishing 
 letter and value, so that in case of wear either can be refitted. 
 As no part of the plug is wider than the top of the plug hole, 
 no shoulder can be worn on the taper, and the wear is reduced 
 to a minimum. The contact resistance of these plugs is found 
 to be very constant. When not in use, the plugs are placed 
 in a spring rack lined with wash-leather, so that they are 
 always kept thoroughly cleaned. 
 
 The box case is constructed of a double copper box with 
 asbestos lining between. Thus the inner surface of this must 
 be at a very uniform temperature throughout. The top of the 
 box is protected by a glass case similar to a balance case. The 
 
 FIG. 20. 
 
 front of this is made to slide up or down. This serves the 
 purpose not only of keeping the instrument free from dirt and 
 dust, but also adds very considerably to the uniform distribu- 
 tion of temperature throughout the box. The terminals are 
 brought through the side of the case. 
 
 The bridge wire is connected in such a manner that its ten- 
 sion is not affected by changes in temperature. The coefficient 
 of expansion of platinum-silver is intermediate between that 
 of steel and brass. The rectangular framework carrying the 
 bridge wire has its two longer sides one of steel and the other 
 of brass. By placing the bridge wire in the correct position 
 it will suffer no further strain, no matter what temperature 
 changes it may be subjected to. These bars further tend 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 227 
 
 to protect the bridge wire, so that there is but little danger of 
 differences in temperature existing in the bridge wire. Along- 
 side the bridge wire proper is stretched a second wire, on 
 which the galvanometer contact is made. 
 
 This contact is made through the contact maker, which is 
 shown in section in Fig. 20 and in plan in Fig. 21. ABA' is a 
 brass framework, which slides between the steel and brass 
 bars. A second block, FEE'H, is within the brass framework. 
 Springs at A and A' press the brass frame against the steel 
 bar, and springs at E and E' press the inner block against the 
 brass bar. Thus if the screw S is turned the inner block is 
 alone moved, for the pressure of the inner block against the 
 brass bar is that of the springs at E and E' only, whereas the 
 
 ilimimi mmiiiiii 
 
 Brass Bar 
 
 
 FIG. 21. 
 
 pressure of the framework against the steel bar is that of the 
 springs at A and A in addition. If the screw S is receded 
 instead of advanced, then the inner block is made to follow it 
 l)y long springs indicated by the dotted lines in Fig. 21. The 
 screw C clamps the bridge wire and galvanometer wire together 
 on to a short length of wire W, as shown in section in Fig. 20. 
 If it is desired to make a temporary connection only, then the 
 block G- must be pressed down. The spring MN releases the 
 bridge wire from the contact wire. If by mischance the screw 
 S is turned whilst the bridge wire is clamped by the screw C, 
 then the outer framework ABA alone moves, and it is thus 
 impossible with this form of contact maker to scrape or in any 
 way damage the bridge wire. At the same time a very sharply 
 defined contact is obtained. 
 
 Q2 
 
228 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 5. Portable Forms of Wheat stone Bridge and Testing 
 Sets. Trotter Bridge. Instrument makers have devised! 
 numerous forms of portable slide-wire and plug bridges suitable- 
 for laboratory and outdoor work. For the details of these the 
 trade circulars of the principal electrical instrument makers 
 may be consulted. In most of these arrangements the galvano- 
 meter is one with a movable nearly astatic double-magnetic 
 needle carried on a jewelled centre. The vibrations of the- 
 
 FIG. 22. Portable Form of Wheatstone Bridge. 
 
 needle are arrested by a stop which raises the needle off its- 
 steel centre-suspension point when the box lid enclosing the- 
 instrument is shut. 
 
 For rapid work, where great accuracy is not required, or 
 for obtaining a preliminary measurement of the resistance of 
 a wire afterwards to be more accurately measured, some of 
 these portable bridges are very useful. The resistances are 
 thrown into circuit, not by removing plugs, which may be- 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 229 
 
 lost, but by a revolving contact arm making contact against 
 sfixed brass studs. The stud surfaces must be kept clean. 
 These instruments are arranged either for measuring ordinary 
 -and low resistance or for high resistances such as insulation. 
 (See Figs. 22 and 23.) In the latter case the battery is 
 replaced by a small continuous-current magneto machine, 
 giving a voltage of from 80 to 100 volts when the handle is 
 quickly turned. 
 
 FIG. 23. 
 
 A form of portable slide-wire bridge has been developed 
 'by Messrs. A. P. Trotter and J. Swinburne out of a simpler 
 form due to Major P. Cardew.* Two wires of nickel steel 
 .are stretched over a scale divided into equal parts. These 
 wires are connected together at one end by a bar of 
 negligible resistance. These wires are represented by the 
 lines b and a and c, d, e in Fig. 24. A length I is. set off one 
 >end of one wire, and a length c is set off the end of the 
 
 * See The Electrician, Vol. XXXVII., p. 691. 
 
230 
 
 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 other wire, so that the resistance of I is equal to that of c~ 
 The scale extends over d and e, and the scale zero is at d~ 
 The resistance to be measured is represented by the coil x. 
 A battery is joined in between the cross piece and the 
 junction a to x and a galvanometer between junctions I to a 
 and a slide which moves over the wire c, d, e and make* 
 contact at any place. 
 
 1 
 
 
 \ 
 a 
 
 t b 
 
 I 
 
 FIG. 24. 
 
 Then it is obvious that, if the bridge is balanced so that 
 the galvanometer shows no current, we have 
 
 a+b 
 
 b c+d 
 
 where the letters stand for the resistances of the segments of 
 the two wires. If b = c and a = e + d, then the above ratio- 
 
 1 1 A X 
 
 is reduced to ~ = -, 
 6 d 
 
 or 
 
 a+l 
 
 Hence the length d on the slide wire is proportional to the- 
 resistance x if a-\-b/b is a constant ratio. Accordingly, by 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 231 
 
 shifting the galvanometer con- 
 tact on the wire a b, so as to 
 give the ratio a/b any desired 
 value, we can make the ratio 
 a+b/b what we please. 
 
 When once this ratio is fixed, 
 the length of d, when the gal- 
 vanometer balance is obtained, 
 is proportional to x. Points may 
 therefore be marked off on the 
 wire a b, so that the segments 
 a and b have such values that 
 a + b/b=l or 10 or 100. If, 
 then, the resistance per unit of 
 length of the wire d e is known, 
 we have at once the value of x 
 given. 
 
 The Trotter bridge is made up- 
 in a portable form, as shown in 
 Fig. 25. 
 
 A useful implement to possess 
 in an electrical laboratory is a 
 pair of equal uniform platinum- 
 silver wires stretched parallel to 
 each other over a pair of divided 
 scales, both wires having contact 
 sliders moving over them and 
 terminal screws at each end of 
 each wire. The platinum -silver 
 wires may be replaced by plat- 
 inoid or manganin. They should 
 be about the size called No. 20 
 S.W.G. A thick strip of copper 
 should be provided for con- 
 necting across corresponding ends 
 of the two wires. 
 
 o 
 
 Q 
 
 5 s ' 
 I- 
 
 r 
 
 i 
 
 
 
232 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 6. Theory of the Wheatstone Bridge, In connection with 
 the use of the Wheatstone bridge for resistance measurement, 
 we have to consider the best arrangement of the circuits so 
 that with a given galvanometer and battery the sensitiveness 
 of the arrangement may be a maximum. The six con- 
 ductors joining four points consist of two ratio arms or 
 resistances, the standard of comparison or balancing arm, and 
 the galvanometer and battery circuits. These can be shown 
 arranged symmetrically as in Fig. 26, instead of in lozenge 
 form as in Fig. 27. 
 
 Let the three meshes of the above network be supposed to be traversed by 
 imaginary cycle currents x + y, y, and z, then the real current through the 
 galvanometer circuit is x, and that through the battery circuit is s. Forming, 
 by Maxwell's rule, the cycle equations (see page 197), we have 
 
 Gy _ -P 0, 
 
 (G + Q + S) y -G(x + y)-Qz = 0, 
 (P + Q + B) z - 
 
 where G and B are taken as the respective resistances of the battery and 
 galvanometer branch, and E is the electromotive force of the battery. 
 Rearranging these equations, we have 
 
 = E . . . . (i.) 
 
 - P 2 = .... (ii.) 
 
 - Qz=0 .... (iii.) 
 
 Hence, solving these equations for x, we obtain 
 
 E(PS-RQ) 
 
 KQ+S), -Q 
 
 -P , -<P + Q),(P+Q+B) 
 
 (P + R + G), (P+R), -P 
 -G , (Q + S), -Q 
 
 where A stands for the determinant, in the denominator with the full 
 algebraic expression of which we are not for the moment concerned. 
 
 Accordingly, if PS-RQ = 0, that is, if the relation ? = ? holds good, then 
 
 Q S 
 
 the current through the galvanometer is zero ; the bridge is then said to be 
 balanced, and x = 0. The determinant A can be written out symmetrically 
 into the expression 
 
 (iv.) 
 The full expression for the current x through the galvanometer circuit of the 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 233 
 
 .bridge, in terms of the electromotive force (E) of the battery and the 
 resistances (P, Q, R, S, B, G) of the six branches, is therefore 
 
 _ E(PS-RQ) __ 
 '~ .bG(P T Ci + R + S) + B(Q + S)(P -I- R) -i- G(R + S)(F + Q) + RS(P + Q) + PQ(R+ S) 
 The question then arises whether for given values of P, Q, R and S the current 
 .x through the galvanometer will be greater if the battery circuit is connected 
 in between the junctions where (P and R) and (Q and S) meet and the 
 galvanometer in between the junctions where (P and Q) and (R and S) meet, 
 or vice versa. 
 
 If we consider the position of the galvanometer and battery exchanged 
 that is, if we write B instead of G and G instead of B in the above expression, 
 .(iv.), and call the result A lf we have for the value of A x - A the equations 
 
 -A = (G-B)(S-P)(R-Q). 
 
 FIG. 26. 
 
 FIG. 27. 
 
 The best arrangement of the battery and galvanometer therefore is that 
 which will make x a maximum, other arrangements remaining the same ; for 
 if the balance is nearly obtained, the galvanometer should show the greatest 
 possible deflection for a small defection from the fulfilment of the relation 
 PS = RQ. It will generally happen that the value of G, the galvanometer 
 resistance, is greater than that of the battery B. 
 
 Let us suppose the four resistances arranged in consecutive order of magni- 
 tude are denoted by S. R, Q, P. That is, assume 
 
 S>R R>Q Q>P, 
 
 or else S<R R<Q Q<P ; 
 
 then (S - P) and (R - Q) are both positive quantities or both negative ones, so 
 that their product is always positive. Therefore, in the expression given 
 -above Ai-A = (G-B) (S-P) (R-Q), Aj-A must have the same sign as 
 (G B). Accordingly, if G is greater than B, Aj will be greater than A; 
 .and hence sc will be less in value when the galvanometer and battery have 
 4he positions shown in Fig. 28 than when they are exchanged. 
 
234 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 We have therefore the following rule : Assuming the galvanometer to have 
 a greater resistance than the battery, the current through the galvanometer 
 G, when it and the four resistances S, R, Q, P in order of magnitude are 
 arranged so that the galvanometer is connected in between the junctions of 
 the two greatest resistances S, R and the two least resistances Q,-P, is greater 
 than when the battery occupies that position ; or the rule may be formulated 
 in another manner, as follows : 
 
 Of the two resistances, that of the lattery and that of the galvanometer, select 
 that which is greater, and connect it to join the junction of the two greatest to- 
 thai of the two least of the four resistances forming the arms of the bridge. Let 
 the remaining appliance occupy the conjugate position. 
 
 Thus, for instance, if we have to measure a resistance of the order of say 50 
 ohms, and we decide to adopt a ratio of 1,000 to 10 for the ratio arms of the 
 bridge, then, when the balance is obtained, the resistance in the measuring 
 arm will be about 5 000 ohms. Suppose that in the quadrilateral of resistances 
 we have two large and two small, as shown in Fig. 28. 
 
 FIG. 28. 
 
 In this case the rule above given shows that if the battery circuit B has a 
 ower resistance than the galvanometer circuit G, then the galvanometer and 
 battery should be connected as shown in Fig. 28. If, however, the battery 
 has a higher resistance than the galvanometer, then their positions should be 
 exchanged. 
 
 If the equations (i.), (ii.) and (iii.) for x, y and z are solved for z instead of X T 
 we obtain the value of the current through the battery circuit, and we find, 
 by the above methods the equation 
 
 ^ I (P + R + G), (P + R)| 
 
 A 
 
 where A has the same value as in (iv.). Hence the ratio of x to z, or current 
 through galvanometer to current through battery, is 
 
 -P 
 
 -Q 
 
 (P + R + G), (P + R) 
 -G (Q + S) 
 PS- QR 
 
 S) + (P + R)(Q + S) 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 235 
 
 It has been shown independently by Mr. Oliver Heaviside 
 (Phil Mag., Vol. XLY., 1873, p. 114) and by Mr. T. Gray 
 (Phil Mag., Vol. XII, 1881, p. 283), that if K is the resist- 
 ance to be measured, and B and G, the battery and galva- 
 nometer resistances, are fixed, the maximum sensitiveness 
 is secured if the other resistances P, Q and S forming the 
 bridge arms are selected so that 
 
 , and P 2 = 
 
 (For the proof of the above formulae the reader is referred to 
 " Absolute Measurements in Electricity and Magnetism," by 
 Prof. A. Gray, Vol. T., p 332.) 
 
 7. The Matthiessen and Hockin Bridge. We have 
 already explained that the slide-wire bridge can be used so 
 as to enable us to measure the difference in resistance between 
 two coils and not their ratio. In this arrangement four coils 
 are provided and connected with the bridge wire as shown 
 in Fig. 29. 
 
 FIG. 29. 
 
 We have, also, already proved (see page 149) that if the 
 coils A and B are exchanged in position, the resistance of 
 that length of the slide wire over which the slider contact 
 has to be moved to find a second balancing position after the 
 
236 
 
 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 coils are exchanged is equal to the difference in electrical 
 resistance of the two coils. This method of resistance com- 
 parison is due to Prof. G. Carey Foster,* and is invariably 
 used when comparisons have to be made between coils of 
 nearly equal value, one being a standard and the other a 
 coil of which the resistance is required with reference to 
 the standard. 
 
 We have already also described some of the mechanical 
 devices for effecting quickly the interchange of the coils A 
 and B. The simplest device for this purpose is to form a group 
 
 00 
 
 
 1 
 
 T-^a " p~ 
 
 cl 
 
 yb 
 
 
 i 
 
 FIG. 30. 
 
 of 12 mercury cups, x, y, x', y\ 1, 2, 3, 4, 1', 2', 3', 4', which may 
 be made by holes bored out in a thick mahogany slab. These 
 mercury cups are connected, as shown in Fig. 30, by copper 
 strips about half an inch wide and one-eighth of an inch thick. 
 These strips are prevented from touching one another where 
 they cross by slips of mica inserted between them. The 
 coils to be compared are represented by A and B, and these 
 coils have their legs or terminal rods placed in mercury cups 
 x, y, x' y', which can be connected by thick copper fl -shaped 
 rods with the other cups, so that x is connected to 1, y to 3, 
 
 * See Journal of the Society of Telegraph Engineers, May 8, 1872. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 23 7 
 
 x r to 2', y' to 4', or else a; to 2, y to 4, x' to 1', ?/' to 3'. The 
 ends of the copper strips are connected up to a bridge wire- 
 and to two ratio arm coils E and S as shown. 
 
 To obtain very accurate results, all the coils A, B, E and 
 S must be placed in melting ice or in paraffin oil surrounded 
 by melting ice, to keep them at a known and constant 
 temperature. In the bottom of each mercury cup must be 
 placed an amalgamated copper dish, against which the ends of 
 the copper strips, fl-connectors, or coil terminals are placed. In 
 the Author's form of circular bridge (seepage 152) the mercury 
 cups are formed by slipping pieces of indiarubber tube on to 
 the ends of short cylinders of copper which are soldered to- 
 
 INDIA RUBBER TUBE 
 ICURY 
 
 FiG. 31. 
 
 the copper bars or strips (see Fig. 31). The ends of these- 
 cylinders being well amalgamated, the coil legs or connectors 
 are then well pressed down on them by weights or springs so 
 that a good copper-to-copper contact is made between well 
 amalgamated true copper surfaces immersed in mercury. A 
 joint such as this offers an exceedingly small and constant 
 resistance. 
 
 The process of taking a reading is then as follows : Let A 
 be a standard coil of known value at 0C. After the coils 
 have been kept immersed in ice for a sufficient time to ensure 
 that in each the whole wire is all at the temperature of 
 
238 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 melting ice, a bridge reading is taken by finding the balancing 
 point of the slider on the wire. The position of the coils 
 A and B is then exchanged and a second reading taken. The 
 resistance of that part of the slide wire between the two 
 positions of balance is equal to the difference between the 
 resistances of the known resistance A and the unknown 
 resistance B at 0C. For if E and S are the values, 
 of the resistances of the ratio arm coils, and A and B 
 the resistance of the coils the difference of which is 
 desired, and if p is the resistance of the slide wire and 
 connections at the side of A up to the point of contact of 
 the slider, whilst W is the whole resistance of the slide wire 
 and connections between A and B, we have the following 
 relation between these resistances when the bridge is 
 balanced : 
 
 S:K=A + /> :B + W-/>. 
 
 Supposing, then, the coils A and B interchanged in position 
 and that the reading p then becomes p, for a new position 
 of balance ; then : 
 
 S:E=B + p' : A+W />'. 
 
 Hence A ~B=p' p. 
 
 Accordingly, the difference in the resistances of A and B 
 becomes known when the slide wire is calibrated so that its 
 resistance per centimetre or per scale division is discovered, 
 and then, if A is a known resistance, the value of B is 
 accurately determined. 
 
 In the accurate comparison of standard coils or of unknown 
 resistances with a standard resistance, the great difficulty is 
 that of discovering the actual temperature of the wire 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 239 
 
 corresponding to a certain evaluation or measurement. The 
 passage of a current, however small, through a wire heats it 
 and changes its resistance ; hence the very accurate comparison 
 of resistances is not easy to make unless the coils can be kept 
 immersed in crushed and melting ice for long periods of 
 time, or else can be placed in tanks containing a large 
 quantity of water or oil in a state of motion and at the 
 temperature of the air around them. 
 
 There are several methods by which this constancy of 
 temperature can be secured. If the supply of water to the 
 laboratory is from a constant town supply, it will generally 
 be found that, if a current of this town water is kept flowing 
 through a tank, after a time the temperature will be main- 
 tained at a nearly constant value, or at least within narrow 
 limits. The coils to be compared can be both immersed in 
 such a tank. Another way is to place both coils in a vessel 
 h'lled with an insulating oil, which is kept in motion by a 
 paddle driven by an electromotor, or by blowing air through 
 it with a bellows, or by hand stirring. In any case the 
 object must be to rapidly and thoroughly renew the layer of 
 liquid in contact with the metallic case of the resistance coil 
 or the wire itself, and it is only under these conditions that 
 we can assume that a thermometer placed in the liquid will 
 give even an approximation to the true temperature of the 
 wire. Then, after discovering the points of balance on the 
 bridge, the coils should be left for some time, and when 
 quite at the temperature of the bath should be once more 
 compared. 
 
 For the very accurate comparison of standard resistances a 
 special room should be set apart, and this room should 
 preferably be below ground, so as to be preserved nearly at a 
 constant temperature all the year round. No person should 
 be allowed in the room except the observer at the time the 
 measurements are being made. If it is necessary to place 
 the galvanometer scale at a distance, it can be read by means 
 of a telescope suitably fixed near the observer. 
 
240 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 8. The Calibration of a Slide Wire. In the use of a 
 
 standard wire bridge a preliminary operation is that of 
 the calibration of the wire to determine the true resistance 
 per centimetre length of the wire. The following method is 
 the one which is most convenient : Two resistances are 
 provided of nearly equal value at the same temperature. These 
 may be manganin wires, each having a resistance of 1 ohm 
 and soldered to suitable terminal rods. These wires should 
 be of sufficient diameter not to heat sensibly with the bridge- 
 currents. If they are not of exactly equal resistance, 
 then one of them will be greater. Let two plug resistance 
 boxes be provided, and let the terminals of these be connected 
 to the ends of the 1-ohm wires, so that when a high 
 resistance K is unplugged out of either box the resistance of 
 the 1-ohm wire and this high resistance in parallel can be 
 slightly varied. Thus, suppose the 1-ohm wire to have a 
 value of exactly 1 ohm, and that we place in parallel with, 
 it a resistance of 2,000 ohms. The joint resistance of the 
 two in parallel is 
 
 1_ _2,000_ 1_ 
 
 JL_l_ "2,001 ~ 2,001' 
 
 1^2,000 
 
 or is diminished by nearly O'OOOS of an ohm. Hence, by 
 a series of trials we can adjust the parallel low and high 
 resistances so that the combined resistances consisting of the 
 two 1-ohm coils so shunted are of exactly equal resistance. 
 The high resistance shunts must be adjusted until the two- 
 combined resistances are brought into a condition of equality 
 as shown by the fact that when placed as coils A and B and 
 exchanged on the bridge the balancing point on the slide wire 
 is not changed. 
 
 This being done, let the two equal combined resistances be 
 furthermore made different by a known small amount by 
 shunting one of them with a resistance say of 1,000 ohms. 
 We have then two resistances which differ by a known 
 small resistance. For if each of the equal combined 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 241 
 
 resistances is x ohms, the cue shunted with 1,000 ohms is 
 ,andhence their differenceis then fa+ 
 
 1,000 + 
 
 ohms. Let these two groups of coils be connected to the 
 Matthiessen and Hockin bridge as the coils A and B, and inter- 
 changed in position, the balancing point on the slide wire a b 
 (see Fig. 32) being found for each position. Let the distance 
 between the two balancing positions be y centimetres of wire. 
 We then know that the resistance of the length y of the slide 
 wire lying between the two points of balance is equal to the 
 known difference of resistance of the two coils viz., to 
 
 l ^ x } ohms. The coils P and Q in the Matthiessen 
 1,000 + n/ 
 
 FIG. 32. 
 
 and Hockin bridge are then to be replaced by a wire of 
 platinoid a'b' about equal in resistance to the resistance of 
 each of the coils A and B taken together. This wire need not 
 be specially selected for uniformity. It is preferably in the 
 form of a slide wire stretched over a board with a divided 
 scale beneath it, and having a sliding contact piece to make 
 contact with any point in its length. 
 
 The connections are then made as in Fig. 32, the ends of 
 the galvanometer circuit being connected to the sliders on the 
 wires. The observer begins by moving the contact G- on the 
 top slide wire until a place of balance, 1, is found on the bridge 
 
242 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 slide wire a b as near as possible to one end of the bridge 
 wire. Then he .interchanges the coils A and B, and finds a 
 new balancing position at 2. The resistance of the lengths 
 between points 1 and 2 on the bridge slide wire is equal to 
 the resistance A-B. Then he changes the coils A and B 
 back to their original position, and moves the contact G to G' 
 until a place of balance is found at the same point 2 on the 
 bridge slide wire. Again he interchanges A and B, and finds 
 a new place of balance at 3. The resistance of the length 
 between 2 and 3 on the bridge slide wire is also equal to the 
 resistance A B. In this way, by changing alternately the 
 position of the coils and the point of contact G, we are able to 
 mark off the whole length of the bridge slide wire into little 
 intervals of length, 1 2, 2 3, 3 4, &c., each of equal 
 electrical resistance. 
 
 We can then from these values construct a table, by using 
 proportional parts, which will give us very approximately the 
 true resistance of each centimetre in length of the slide wire, 
 and thus give us the mean resistance per unit of length or 
 centimetre of the slide wire. 
 
 This calculation should be checked by increasing the differ- 
 ence between the coils A and B by a known shunting resist- 
 ance, so that the difference A B is just a little less than the 
 resistance of the whole slide wire. The constant application 
 of corrections for inequality in the slide wire is, however, so 
 troublesome, that in building a standard Matthiessen and 
 Hockin slide wire bridge it is worth while to take some pains 
 to secure a Wire of such uniformity in resistance per unit of 
 length that the correction to be applied for inequality in 
 resistance per centimetre is practically negligible. When the 
 resistance of the wire has been thus determined, we can at 
 once employ the bridge to measure the difference between a 
 standard resistance and a coil not differing from it by more 
 than the whole resistance of the bridge wire, and this method 
 of differences is more accurate for evaluating standard coils 
 than is the method of ratios. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 243 
 
 In this manner, given a standard 1-ohm coil, a standard 
 or known value 10-ohin coil, &c., the experimentalist can fix 
 the exact value at a known temperature of other coils intended 
 to represent 1 ohm, 10 ohms, &c. 
 
 9. To Determine the Temperature Coefficient of a 
 Standard Resistance Coil. If the observer possesses a 
 resistance coil the value of which, in terms of some standard 
 of reference, is known at a stated temperature, it is essential 
 to determine the temperature coefficient (T.C.), so that the true 
 resistance of the coil may be known at any other temperature. 
 In the case of the high-resistance alloys platinum-silver, 
 manganin, platinoid, &c., used in the construction of standard 
 coils for ranges of temperature from about 0C. to 25C., it 
 may be assumed that for all practical purposes the resistance 
 (K,) of the coil or wire at any temperature tC. is related to 
 its resistance (R ) at 0C., in the manner expressed by the 
 formula 
 
 In this case a is called the temperature coefficient. It is 
 generally expressed as a percentage per degree Centigrade of 
 the resistance at 0C. or at 15C. 
 
 In the case of pure metals or alloys taken over wider 
 ranges of temperature, the relation between the resistances at 
 different temperatures is less simple, and can generally only 
 be expressed in a graphical form by a curve of resistance in 
 
 terms of temperature. If E is the value of the resistance of 
 
 jp 
 
 the conductor at any temperature C., then ^ is the rate of 
 
 ctt 
 
 1 /7"P 
 
 change with temperature, and -~ Vis the rate of change per 
 unit of resistance at that temperature. The value of the 
 expression - - may be taken as the temperature coefficient 
 
 _Lt Ctt 
 
 corresponding to that temperature tC. It is usual to state 
 the mean temperature coefficient between certain extreme 
 temperatures. Thus, the mean temperature coefficient (mean 
 
 R2 
 
244 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 T.C.) between 0C. and 25C. must be known for every 
 standard coil possessed by the laboratory. Also its true- 
 resistance at 0C. Its resistance at tC. is then at once 
 calculated by the expression 
 
 Generally speaking, instrument makers mark on a coil the 
 temperature at which it has its nominal value. Thus, a 
 1-ohm standard may be marked as u correct at 15*4C." If r 
 then, the temperature coefficient is known or given, the true 
 resistance at any other temperature can be found provided it 
 lies within the limits of practical constancy of the tempera- 
 ture coefficient. 
 
 The temperature coefficient of a standard coil is most easily 
 determined as follows: >Select two coils of nearly equal value, 
 say A and B. Place both coils in crushed melting ice 
 contained in any convenient vessel, and let the coils remain 
 in this ice until it is practically certain all parts of the wire 
 of the coil are at 0C. Place these coils on a Matthiessein 
 and Hockin bridge (which may conveniently be the Fleming 
 or Nalder form of differential^bridge), and take the difference- 
 between the resistance of these coils in terms of the resistance 
 of the bridge wire unit. Thus, suppose at 0C. we have 
 
 A B =# divisions of bridge wire. 
 
 Next keep the coil B at 0C., but immerse the coil A in tap 
 water say at t*C. or the service water temperature, and keep it 
 there until it is practically certain all parts of the wire are 
 at the same temperature. Then again take the difference in 
 resistance of A and B on the bridge, and we have 
 
 A, B =:^ divisions of bridge wire. 
 Hence, by subtraction, A t A =.yx. 
 
 ) I 'Y* 
 
 Accordingly, - - is the increment in bridge wire divisions 
 t 
 
 of the resistance of coil A when heated from 0C. to tC. If 
 p is the resistance of the bridge wire per unit of length, we 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 245 
 
 Iiave the value of the temperature coefficient (a) of the coil 
 A between 0C. and 15C. given by the expression 
 
 100 ?/ x 
 
 == r ' 3 P- 
 A t 
 
 10, To Determine the Mean Temperature Coefficient of 
 a, Metallic Alloy in the Form of a Curve. The sample of 
 the alloy should be drawn into a wire of uniform diameter 
 and as far as possible of uniform resistance per unit of 
 length. It is then required to determine the mean tempera- 
 ture coefficient of the material. This is effected in the 
 following manner: A boxwood cylinder of about 2in. (or 
 5cm.) in diameter and Sin. in length has a deep and coarse 
 
 n 
 
 n 
 
 FIG. 33. 
 
 screw thread cut on it in the lathe. This screw tlireaa ma 
 Iiave a pitch of six or eight turns per inch. The opposite 
 sides of the cylinder should have deep grooves cut in them 
 and copper rods about T \in. (or 4mm.) in diameter attached 
 to the cylinder, as shown in Fig. 33. These rods may be 
 slightly flattened where they lie against the wood cylinder, 
 and be screwed to it. The rods are bent over, as shown in 
 the diagram, to form electrodes. The alloy must be drawn 
 into the form of a wire of diameter between No. 22 and 
 Xo. 30 S.W.G., and must be wound loosely on the boxwood 
 cylinder in the grooves. The ends of the wire must be 
 
246 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 soldered to the copper terminal rods. The cylinder is then 
 to be immersed in a copper vessel containing paraffin oil 
 enclosed in another vessel which contains water. The 
 resistance coil is connected with the resistance bridge by 
 means of thick stranded copper connecting leads. In the 
 first instance the copper vessel of paraffin oil may be 
 immersed in crushed ice and kept there until the paraffin 
 and the resistance wire immersed in it has a temperature of 
 0C. as taken by a correct mercury thermometer. The 
 resistance of the wire is then observed on the bridge by 
 taking either its difference from, or ratio to, a known 
 resistance. The resistance coil is conveniently connected to 
 the bridge circuit by having its copper legs placed in 
 mercury cups, which are in connection with the bridge by 
 thick flexible leads of stranded copper. In order to eliminate 
 the resistance of the leads a copper loop must be provided, the 
 total length of which is equal to the total length of the two 
 copper terminal rods of the coil, and it must be made of a 
 sample of the same copper wire. This blank, as it is called, is 
 placed in the mercury cups and measured, and the difference 
 in measurements taken when the resistance coil is in the 
 cups and when the blank is in the cups is the resistance of 
 the wire of the resistance coil. 
 
 The measurements having been made at 0C., the next step 
 is to make them at a temperature as near as possible to 
 100C. For this purpose the outer jacket of the copper vessel 
 is filled with water, which is made to boil. The paraffin oil 
 in the inner vessel must be kept well stirred and the tempera- 
 ture taken by a correct mercury thermometer. The double 
 readings are then obtained as before. Other readings may 
 then be taken at intermediate temperatures. The chief diffi- 
 culty in obtaining good results consists in ascertaining the 
 true mean temperature of the wire at the moment when the 
 resistance measurement is made. 
 
 A very extensive series of measurements of the above kind 
 were made by the Author in conjunction with Prof. J. Dewar 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 247 
 
 in 1893, using metals of known purity and alloys of ascer^ 
 tained composition. The measurements were made between 
 200C. and + 200C., using boiling liquid oxygen to provide 
 a temperature of 182'5C., a mixture of solid carbonic acid 
 in ether to create a temperature of 78'2C., melting ice to 
 give a temperature of 0C., and boiling water under a pres- 
 sure of 760mm. to fix a temperature of 100C. By this 
 means a series of observations of resistances of the same 
 metallic wire were taken at known temperatures, and the 
 results set out in a series of curves. These curves show that 
 the resistance of a wire of a pure metal steadily diminishes as 
 the temperature falls in such a manner as to indicate that 
 at or near the absolute zero of temperature ( - 273C.) the 
 resistivity of the metal would in all probability be zero. In 
 other words, it would become a perfect conductor. Values of 
 the ordinates of these curves showing the volume resistivity 
 of different metals at fixed temperatures between 150C. and 
 -f- 150C. are given in Table Y. at the end of this chapter. 
 
 The curves of temperature resistance (temperatures being 
 the abscissae) are in the case of some metals concave upwards 
 and in other cases concave downwards. The curves of the 
 magnetic metals iron and nickel are at first concave upwards 
 and rise very rapidly. At a temperature very near to that at 
 which the metals lose their marked magnetic qualities (the 
 magnetic critical temperature) the temperature resistance 
 curve has a point of inflexion and becomes concave down- 
 wards. The temperature coefficient thereafter becomes 
 greatly diminished. In the case of iron this change tem- 
 perature is near 780C., and in the case of nickel near 340C. 
 The variation of resistance with temperature in the case of 
 iron is therefore delineated by a curve not unlike its magnetisa- 
 tion (see Fig. 34). 
 
 The following table gives the values of the absolute volume 
 resistivity of a certain specimen of annealed iron wire as 
 observed by Dr. D. K Morris.* The absolute volume 
 
 * "On the Magnetic Properties and Electrical Resistance of Iron as Dependent 
 upon Temperature." D. K. Morris, Ph.D. Phil. Mag., Sept. 1897, p. 213. 
 
248 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 resistivities (/>) in C.G.S. measure have been calculated for 
 exact centennial temperatures by interpolation from the 
 observed values as given by Dr. Morris for numerous inter- 
 mediate temperatures. The change in resistivity per degree 
 
 ( - in the neighbourhood of each century is also stated. 
 
 120,000 
 100,000 
 
 80,000 
 
 03 
 
 c5 
 60,000 
 
 | 40,000 
 20,000 
 
 
 
 
 
 
 
 
 
 
 X 
 
 ^ 
 
 
 
 
 
 / 
 
 
 
 
 
 / 
 
 f 
 
 
 
 
 / 
 
 / 
 
 
 
 
 ./ 
 
 / 
 
 
 
 
 
 / 
 
 
 
 
 
 
 2CO 400 600 800 1,000 1,100 
 
 Temp. Centigrade. 
 FIG. 34. Temperature Resistance Curve of Iron. 
 
 The temperature coefficient at any temperature (t) is obtained 
 by dividing - at that temperature by the absolute resistivity 
 (p t ) corresponding to that temperature. 
 
 Volume electrical resistivity of iron annealed at 1,150. 
 Magnetic critical temperature=77SC. 
 
 Centigrade temperature 
 t. 
 
 Volume resistivity in 
 C.G.S. units. 
 
 Change in resistivity 
 per degree Centigrade. 
 
 
 
 10,050 
 
 61 
 
 100 
 
 16,527 
 
 71 
 
 200 
 
 24,308 
 
 82 
 
 300 
 
 34,537 
 
 115 
 
 400 
 
 45,024 
 
 116 
 
 500 
 
 57,416 
 
 124 
 
 600 
 
 71,764 
 
 152 
 
 765 
 
 100,025 
 
 195 
 
 780 
 
 103,200 
 
 
 
 800 
 
 106,600 
 
 133 
 
 900 
 
 115,342 
 
 52 
 
 1,000 
 
 118,781 
 
 22 
 
 1,100 
 
 120,656 
 
 12 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 249 
 
 The temperature coefficient at 0C. is 0'0057, and it rises 
 -to a maximum value of 0*0204 at 765C. and falls again to a 
 value 0-00244 at 1,000C. 
 
 Observations on the specific heat of iron seem to show a 
 remarkable similarity in variation to that of the resistance 
 temperature coefficient. According to M. Pionchon, the 
 .specific heat of iron can be calculated for any temperature 
 between 0C. and 660C. by the formula 
 
 7, = 0-1012 + O-OOOOSO^G* + 0-0 00000164* 2 . 
 Hence we have the specific heat of iron at various 
 temperatures as follows : 
 
 Temperature. Specific heat. 
 
 0C 01012 
 
 100C 0-1079 
 
 200C 0-1176 
 
 300C 0-1306 
 
 400C 01468 
 
 500C 01665 
 
 600C 0-1892 
 
 Also it has been shown that the average specific heat of iron 
 between 750C. and 1,000C. = 0-213, 
 between 954C. 1,006C. = 0-218, and 
 between 1,050C. 1,200C. = 01988. 
 
 If the above values are set out in a curve, we find that the 
 specific heat of iron rises to a maximum and falls again in a 
 very similar manner to the temperature resistivity coefficient. 
 'These remarkable changes in the temperature coefficient and 
 in the form of the resistivity curve are doubtless connected 
 with the changes in the internal energy which go on in iron 
 ;at certain critical temperatures. 
 
 Many attempts have been made to express the relation 
 'between temperature and electrical resistivity by an algebraic 
 formula. Over moderate ranges of temperature for most 
 nnetals an expression of the form 
 
250 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 where p t is the resistivity at tC., p is the resistivity at 0C. r 
 and a and (3 are constants, will suffice to approximately 
 express the facts. 
 
 It is, however, clear, from the form of the resistance 
 temperature curve of iron given above, that no such simple- 
 formula will suffice over wide ranges. of temperature or when 
 including critical temperatures. 
 
 In some other cases, such as that of the alloy manganin,- 
 there is a well-marked maximum value of the resistivity 
 corresponding to a certain temperature, and in certain 
 specimens of bismuth a minimum value of the resistivity has 
 been found for a particular temperature. This is the case 
 also with graphitic carbon. Hence all simple algebraic 
 expressions, expressing the value of resistivity in terms of 
 temperature, can only be made conformable with the facts of 
 observation over a certain range of temperature, and such 
 expressions cannot safely be extrapolated to yield results 
 lying beyond the limits of temperature for which the formula 
 was originally constructed. 
 
 When a pure metal is fused there are always rapid and 
 generally large changes in the electrical resistivity in passing 
 from the solid to the liquid condition. Thus, when solid 
 mercury is heated up from 200C. to above +100C. it 
 melts at 40 C., and just beyond that temperature its resis- 
 tivity is increased nearly 4'1 times,* as shown in Fig. 35. 
 The temperature coefficient whilst solid is not very different 
 from that of other pure metals. 
 
 In the case of pure platinum Mr. J. Hamilton Dickson, 
 after discussing other formula?, showedf that the resistivity 
 of pure platinum could be very well represented in terms of 
 the centigrade temperature by an empirical equation of the 
 form (E + a) 2 = 
 
 * See Dewar and Fleming, " On the Electrical Resistivity of Mercury at the 
 Temperature of Liquid Air." Proc. Roy. Soc., June, 1896, Vol. LX., p. 76. 
 See also Cailletet and Bouty, Comptes Kendus, 1885, Vol. C., p. 1188, who- 
 found the ratio to be 4'08 times. 
 
 t " On Platinum Temperatures,*' by J. D. H. Dickson, M.A. Phil. Man. r 
 Dec., 1897, p. 445. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 251 
 
 where R is the resistance at the temperature C. and a, p,. 
 and b are suitably selected constants. He has found, by 
 comparison with actual observations made on a pure annealed 
 platinum wire by Profs. Fleming and Dewar over a range of 
 temperature of 200C. to +200C., that a formula of the 
 above kind can be made to express with considerable accuracy 
 the variation in resistivity of platinum between the above 
 
 -283 -200 -100 +1 
 
 
 
 
 M* 
 
 ^ 
 
 ^ 
 
 's 
 
 
 
 
 
 
 ^ 80,OOC 
 QJ 70000 
 
 
 
 
 
 
 60,000 
 
 | 50,000 
 
 1 
 5 40,0(K 
 
 | 30,000 
 J 20,000 
 10,000 
 r 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 $^ 
 
 y 
 
 
 ^,,-''' 
 
 ^ 
 
 
 
 -283 -2CO -108 
 
 Temperature in Platinum Degrees. 
 
 +100 
 
 FIG. 35. Temperature Resistance Curve of Mercury. 
 
 limits of temperature. The formula will be seen to be- 
 equivalent to the statement that the square of the resistance 
 measured from an artificial zero is simply proportional to 
 the temperature also measured from an artificial zero. In 
 the case of the magnetic metals iron, nickel, and cobalt, 
 there are remarkable changes in resistivity at the temperatures 
 at which the magnetic qualities are suddenly altered which 
 prevent any empirical formula from adequately representing 
 
252 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 the temperature change in resistance over ranges of tempera- 
 ture which include these critical points.* 
 
 11. To Determine the Specific Resistance or the Resis- 
 tivity of a Metal or Alloy. The volume-resistivity of a 
 material is defined to be the resistance of a cube of the 
 material having a side of unit length, taken between opposed 
 faces of the cube at a defined temperature. The usual mcde 
 of stating the resistivity of metals and alloys is in C.G.S. units 
 or in microhms per centimetre-cube at 0C. In the case of 
 electrolytes or conducting liquids it is expressed in ohms 
 per centimetre-cube at 18C. In the case of materials of very 
 high resistivity, commonly called insulators, it is usual to state 
 the resistivity taken at 75F. in megohms or in mega-megohms 
 that is, in millions of megohms per centimetre-cube. 
 
 To determine the volume-resistivity of a sample of a metal 
 or alloy, it is desirable to possess it in the form of a carefully 
 drawn wire of uniform circular cross-section, Owing to the 
 -difficulty of determining the diameter of very fine wires, it is 
 found more convenient to determine and define the resistivity 
 of metals and alloys by the resistance in ohms per metre- 
 gramme at 0C. that is to say, by stating the ohmic resistance 
 at 0C. of a wire of circular cross-section having a length of 
 one metre and weighing one gramme. 
 
 * For a discussion of the chief formulae which have been proposed to 
 represent the variation in the electrical resistivity of metals, and especially 
 'platinum, with temperature, the reader may consult with advantage the 
 following papers : 
 
 "On Platinum Temperatures," by J. D. Hamilton Dickson, Phil. Mag.. 
 Dec., 1897. Also 
 
 "Notes on Platinum Thermometry," by H. L. Callendar, Phil. Mag.. 
 
 Feb., 1899. 
 
 With regard- to the temperature variation in resistance of magnetic metals, 
 consult 
 
 W. Kohlrausch, Wied. Ann., Vol. XXXIII., p. 42, 
 
 J. Hopkinson, Proc. Roy. Soc., Vol. XLV., p. 457, 
 
 Le Chatelier, Comptes Rcndus, Vol. CX., p. 283, and 
 
 D. K. Morris, Phil. Mag., Sept., 1897. , 
 
 For a record of very careful work on the variation of the resistance of metals 
 with temperature, and the representation of results by a parabolic formula 
 of the type Rf/R = 1 + a U-, see Benoit, Comptes Rendus, 1873, p. 342. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 The relation between the resistance per centimetre-cube, 
 called the volume-resistivity, and the resistance per metre- 
 gramme, called the mass-resistivity, is as follows : 
 
 Consider a wire of uniform circular cross-section of s square 
 centimetres and of length I centimetres. Let the density of 
 the material be d, its electrical volume-resistivity in C.G.S. units- 
 be p, and the total resistance of the wire be E ohms. Then, 
 we have 
 
 ~~s~' 
 
 also lsd=M, 
 
 where M is the mass of the wire in grammes. 
 Hence, if M=l, we have 
 
 lsd=l, ors= . 
 Id 
 
 Hence ltfR=pPd. 
 
 If the wire has a length of one metre or 100 cms. we have 
 
 5 , 
 
 Accordingly, if p is the mass-resistivity, or resistance- 
 expressed in ohms, of a wire of circular section one metre- 
 long and weighing one gramme, we have 
 
 If the mass-resistivity is expressed in microhms per metre- 
 gramme (=10V) we have the rule : Microhms per metre- 
 gramme, divided by ten times density, is equal to resistivity per 
 centimetre-cube in C.G.S. units. Also, if the volume-resistivity 
 of the material, reckoned in microhms per centimetre-cube, is 
 denoted by />" we have 
 
 l,OOOp"=/>. 
 
 Hence 100p'=//W, <*' 
 
 Accordingly, the resistivity of a uniform wire in ohms per 
 metre-gramme is to the resistivity of the material in microhms 
 per centimetre-cube as the density is to 100. Or, again,, 
 
-254 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 since we have p" = p r =-, we see that the volume-resistivity 
 . a 
 
 can always be deduced from the mass resistivity when we 
 know the density of the material. 
 
 The mass-resistivity per metre-gramme can always be 
 -obtained b} 7 measuring the resistance and the mass of any 
 uniform sectioned wire of which the length is known. If, as 
 above, p stands for the mass-resistivity in ohms per metre- 
 gramme and p for the volume-resistivity per centimetre-cube, 
 and if E is the resistance in ohms of any uniform sectioned 
 wire of length I centimetres and mass M grammes, we then 
 .have 
 
 Also lOV =p W * d , or 10 V =pcl 
 
 , 
 M M 
 
 Hence a determination of the length (7), mass (M), density (rf), 
 and resistance (E) of any wire enables us to find the mass- 
 resistivity in ohms per metre-gramme (/o / ) and the volume- 
 resistivity in C.G-.S. units per centimetre-cube (/>) by the 
 -equations 
 
 Hence we have the following practical rules : 
 
 Given the resistance in ohms (R) of a uniform sectioned wire of length (I) 
 in centimetres and mass (M) in grammes, calculate the mass-resistivity (p'} in 
 -ohms per metre-gramme. 
 
 Answer. Multiply together 10,OCO times the mass in grammes and the 
 resistance in ohms, and divide the product by the square of the length in 
 centimetres ; the quotient is the ohmic mass-resistivity per metre -gramme.- 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 255 
 
 Example. The resistance of a column of pure mercury 106*3 centimetres in 
 length, and weighing 144521 grammes, is one ohm at 0C. ; find the mass- 
 resistivity of mercury. 
 
 Answer. 12'789 ohms per metre-gramme at 0C. 
 
 Again, given the mass -resistivity in ohms per metre-gramme (//); find the 
 volume-resistivity (/>) in C.G.S. units per centimetre-cube. 
 
 Answer. Multiply the ohmic mass-resistivity by 100,000, and divide the 
 product by the density (rf). 
 
 Example. Given that the density of mercury at 0C. is 13 '595; find 
 the volume-resistivity in C.G.S. units, knowing the mass- resistivity to be 
 12'789 ohms per metre-gramme. 
 
 Answer. 94,070 C.G.S. units per centimetre -cube at 0C. 
 
 To determine the resistivity of a metallic material in the 
 form of a wire of uniform section, we must, therefore, find the 
 total resistance, length, mass, and density of the wire. The 
 density may be taken with appropriate samples on the whole 
 wire. It is convenient to proceed in the following manner : 
 
 If the length and diameter of the wire furnished is such 
 that the total resistance is not much less than one ohm, 
 the wire may be laid in a flat circular coil the turns of which 
 are prevented from touching each other by winding the wire 
 on a suitable bobbin or frame. The ends of the wire must 
 be soldered to thick copper terminal rods or leads by which it 
 can be connected to the bridge. The wire must be immersed 
 in a bath of paraffin oil kept continually stirred. The resist- 
 ance of the wire is then carefully taken at several tempera- 
 tures. It is best to take it at the temperature of the room 
 and also at or near 0C. by cooling the paraffin oil by ice. In 
 this manner the temperature-coefficient becomes known. 
 
 Having satisfactorily ascertained the resistance of the wire 
 at known temperatures, it is cut off close to the thick 
 terminal rods, and these are soldered together and the 
 resistance of the leads determined in order that a correction 
 may be applied for lead resistance. The length of the wire 
 used has then to be determined. This must be done without 
 in the least degree stretching the wire, and is best achieved 
 by pressing the wire gently into a shallow groove made with 
 a saw in the surface of a long board. This groove holds the 
 
256 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 wire straight and enables its length to be measured with arc 
 accurate metre scale. The length and resistance having 
 been found, the wire may be cut up into sections and the- 
 density or specific gravity found in the usual way. If the 
 wire is a fine wire it may be wound up into a sort of loose- 
 ball, and the specific gravity of the whole mass determined. 
 The great difficulty which here occurs is that of the removal 
 of all the air which is entangled in, or adherent to, the wire.. 
 The best way to proceed is as follows : The hank of wire is- 
 suspended by a fine horse-hair from the beam of a delicate 
 chemical balance and the weight taken. Let this weight be 
 W grammes. The wire is then placed in distilled water and 
 well boiled, and allowed to remain in the water whilst the- 
 water cools. The wire is then weighed again in the water 
 without removing it from the water. Let the weight then be 
 
 W 
 
 W grammes. The density d is equal to . If the 
 
 wire is of such a material that it is chemically affected by 
 being boiled in water at 100C. the adherent air must be- 
 removed by gently heating the water and then placing it 
 under the receiver of an air pump and exhausting the air from* 
 around it. The water will then boil under a reduced pressure- 
 at a much lower temperature. The presence of any air- 
 bubble in contact with the wire when weighed in water will 
 render the apparent density too small. In both weighings 
 a correction must be applied by weighing the horse-hair 
 suspension alone and deducting this from the weight of the 
 mass. It is more difficult to get correct results the smaller 
 the mass of the wire. Hence the mass of the material 
 weighed should be as great as possible. The density d being 
 obtained and the mass M of the wire in grammes used for the 
 resistance measurement, as also the length I in centimetres r 
 we have the means of determining the mean cross-section s of 
 the wire for /scfcM. 
 
 M 
 
 Hence s=-.- 7 . 
 
 id 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 25? 
 
 In the case of very line circular-sectioned wires a close 
 approximation can be made to the mean diameter of the 
 wire by measuring with a microscope-micrometer the mean 
 diameter in a large number of different places and positions 
 and taking the mean of all these measurements. 
 
 Having determined in one way or other the mean diameter 
 of the wire, we have the volume-resistivity p in C.G-.S. units 
 given by the equation, 
 
 -W-, 
 s M 
 
 MK10 9 
 
 
 Tables of the volume-resistivities of various metals and alloys 
 are given at the end of the present chapter. (See Tables I., 
 II, III., IV., V. and VII.) 
 
 12. Determinations of Volume and Mass-Resistivity 
 of Metals and Alloys. Great labour has been expended on 
 the determination of the mass and volume-resistivity of 
 metals and certain standard alloys. Considerable differences 
 are, however, found in the values assigned by various 
 authorities to the volume-resistivities at 0C. of the various 
 metals. The reason for this is that exceedingly minute pro- 
 portions of impurity or other metals have an immense effect 
 upon the electrical resistivity. Some metals, such as iron, 
 have probably never yet been obtained in an absolutely 
 pure annealed condition. 
 
 The work on this subject to which reference is most often 
 made is that of Dr. A. Matthiessen, who published between 
 1860 and 1864 the results of numerous researches on elec- 
 trical conductivity recorded in the Philosophical Magazine, 
 in the Philosophical Transactions of the Eoyal Society, and the 
 Jieports of the British Association for those years. 
 
 For most electrical engineering purposes the constants of 
 greatest importance are those of the mass and volume- 
 resistivity of pure copper in its hard-drawn and annealed 
 
258 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 conditions. Matthiessen's value for the mass-resistivity of 
 pure hard-drawn copper is called Matthiessen's Standard. 
 
 Matthiessen's Standard is defined in the following state- 
 ment* : 
 
 The resistance of a wire of pure hard-drawn copper, one 
 metre long, weighing one gramme, is 0-1469 British Association 
 units at SWF. 
 
 Since the numerical value of a resistance measured in 
 standard or international ohms is, by authoritative definition, 
 equal to O9866 of the value of the same resistance stated in 
 B.A. units, the above may be modernised into the following 
 fundamental definition : 
 
 The resistance of a ivire of pure hard-drawn copper, one metre 
 long, and weighing one gramme, is '1449 3 standard ohms at 
 0C. 
 
 Since resistances are not conveniently determined at 0C., 
 but better at 60F. or 15'55 C., the definition has again been 
 re-cast in form by the Committee on Copper Conductors 
 appointed to consider this question of Copper Conductivity 
 Standards-)- as follows : 
 
 Matthiessen's standard for hard-drawn high-conductivity 
 commercial copper shall be considered to be a 'wire of pure 
 hard-drawn copper one metre long and weighing one gramme, 
 whose resistance at 60F. is 0*153858 standard ohms. 
 
 Hard-drawn copper is defined as that which will not 
 elongate more than 1 per cent, without fracture. 
 
 The conversion from B.A. units at 32F. to standard 
 ohms at 60F. is made by employing a formula given by 
 
 *Briti&h Association Report, 1864, or Phil. Mag., Vol. XXIX., May, 3865, 
 p. 362. 
 
 t The Committee on Copper Conductors was organised in 1899 by writing 
 to the General Post Office and the Institution of Electrical Engineers and 
 inviting them to send delegates to meet the representatives of eight of the 
 principal manufacturers of insulated copper cables to consider and come to an 
 arrangement as to the standard to be adopted for Copper Conductivity. 
 The sittings of the Committee were held in London. The Secretary was 
 Mr. A. H. Howard. The recommendations of the Committee have been adopted 
 by the General Post Office and the chief cable manufacturing companies. The 
 Report of the Committee is published in the Journal, of the Institution of 
 Electrical Engineers, January, 1900, p. 169. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 259 
 Matthiessen for the temperature coefficient of copper, viz. : 
 
 n_ 
 
 1-0-00215006 (* 32) + 0*00000278 (-32) 2 ' 
 
 and the rule : 
 
 Resistance in B.A.U. X -9 86 6= resistance in standard ohms. 
 Hence, we have for hard-drawn copper wire the values below 
 for the metre-gramme resistivity (p'} : 
 
 p' (at 32F.)=01469 B.A.U. 
 
 p' (at 0C.) =0-1449 standard ohms. 
 
 P r (at 60F.)=0'1539 standard ohms. 
 
 Matthiessen also measured the mass-resistivity of annealed 
 copper in the form of wire. Annealed copper may exist in 
 various states of annealing, and in this condition its resis- 
 tivity 'is less by slightly variable amounts than in the 
 hard-drawn condition. The resistivity of annealed copper 
 was measured by Matthiessen at an earlier date (Phil. 
 Trans. Roy. Soc., 1860, p. 86), and he found that it showed 
 a conductivity greater than that of hard-drawn copper 
 by about 2-26 per cent, to 2*5 per cent. Although this is 
 undoubtedly correct for carefully annealed copper, it is a 
 result which cannot be obtained in practice with ordinary 
 commercial copper wire, as this latter is unannealed, or 
 hardened somewhat by bending and winding in the process 
 of manufacturing it into covered wire. In practice it 
 is found tli at the resistance of commercial annealed copper 
 wire is about 0-9875, or \\ per cent, less than that of 
 hard-drawn wire of the same length and section. 
 
 Matthiessen, however, gave a later value for annealed 
 copper as follows : 
 
 The resistance of a wire of annealed copper one metre long 
 and weighing one gramme is 0'1440 British Association 
 units at 32F. 
 
 In modern standard units the definition reads thus : 
 
 The resistance of a wire of annealed copper one metre long 
 and iveighing one gramme is ! 1421 standard ohms at 0C. 
 
 a 
 
260 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 The ratio of the numbers 01421 to 01449 is G'98025. 
 
 This value has accordingly been accepted by the Committee 
 on Copper Conductors, and the ratio of the resistivity of soft 
 or annealed to hard-drawn copper is taken at the above 
 value, so that 
 
 The resistivity of _ Q.ggQ.?- x the resistivity of pure 
 pure annealed copper ~ ' hard-drawn copper. 
 
 Hence the Committee have formulated the definition for the 
 standard for soft or annealed copper as follows : 
 
 Matthiessen's standard for annealed high-conductivity com- 
 mercial copper shall be considered to be a wire of pure annealed 
 copper one metre long and weighing one gramme, whose resist- 
 ance at 60F. is 0150822 standard ohms. 
 
 Employing the same temperature coefficient as for hard- 
 drawn copper, we have the following values for the metre- 
 gramme resistivity of annealed copper : 
 
 P ' (at 32F.)=01440 B.A.U. 
 
 P r (at 0C.)=01421 standard ohms. 
 
 p' (at 60F.) =01508 standard ohms. 
 
 It is to be noted that this standard for annealed copper is 
 based upon an assumption as to the relative conductivities of 
 hard and annealed copper. The figures given by Matthiessen 
 for this ratio vary considerably in different Papers. See Phil. 
 Trans., 1860, p. 86 ; Phil. Trans., 1864, p. 197 ; and Phil. 
 Mag., May, 1865, p. 363; also The Electrician, Vol. XLV., 
 p. 59. 
 
 The next question with which we are concerned is the 
 equivalents of the above numbers in volume-resistivity. The 
 specific gravity of copper varies from 8'89 to 8'95, and the 
 standard value which is now accepted for high-conductivity 
 commercial copper is 8*912, corresponding to a weight of 
 5551b. per cubic foot at 60F. Hence, multiplying the values 
 for the metre-gramme resistivity by 100 and then dividing 
 by 8*912, we have the corresponding volume-resistivities in 
 
MEASUREMENT OF ELECTRTCAL RESISTANCE. 261 
 
 microhms per centimetre-cube for pure commercial hard- 
 drawn and pure annealed copper as follows : 
 
 The volume-resistivity of pure hard-drawn copper at 0C. = 
 1'626 microhms per centimetre-cube, or 1,626 C.Gr.S. units. 
 
 The volume-resistivity of pure annealed copper at 0C. = 
 1-594 microhms per centimetre-cube, or 1,594 C.G.S. units. 
 
 A table giving the resistances of annealed copper wire 
 calculated on the basis of the above value is given at the end 
 of this chapter. (See Table XIII.) 
 
 The calculation of the resistivity at any other temperature 
 (0 requires a knowledge of the temperature coefficient (T.C.J 
 for copper. Matthiessen's formula for the reduction of the 
 resistivity at tY.(p t ) to the resistivity (p 3 J at 32F. was : 
 
 P&f=Pt (1-0-00215006 (*-32) + 0-00000278 (*-32) 2 ), 
 or approximately p t =p Q (1 + 0*00387 t'), if '= Centigrade temp. 
 
 It is now known that this correcting factor is rather too 
 small, owing to the improvement in the quality of copper 
 made since Matthiessen's time. Hence the Committee on 
 Copper Conductors have recommended that the average tem- 
 perature coefficient between the temperatures 30F. and 100F. 
 shall be that value obtained by Messrs. Clark, Forde and 
 Taylor, as given in a pamphlet published by them on Feb- 
 ruary 20th, 1899, viz., 0-00238 per degree Fahr., or 0*00428 per 
 degree Centigrade*, so that for Centigrade temperatures we 
 shall have pt=pQ ^ + 0-004280, 
 
 or P6QY.=P32. x 1*06665. 
 
 Since the date when Matthiessen's work was carried out 
 the most careful research carried out on the conductivity of 
 copper is that by Mr. T. C. Fitzpatrick, described in a Paper 
 read before the British Association at Leedsf in 1890. 
 Mr. Fitzpatrick's experiments on the conductivity of hard- 
 
 * This is precisely the same mean value for the temperature coefficient of 
 annealed copper as was independently obtained by Profs. Fleming and Dewar. 
 See Phil. Mag., Sept., 1893, p. 299. Messrs. Clark, Forde and Taylor's pamphlet 
 is published by " The Electrician " Printing and Publishing Co. 
 
 t See Report B.A., Leeds, 1890 ; Appendix IIT. to the Reports of the Com- 
 mittee on Electric*! Standards for 1890 : also The Electrician, Vol. 25, p. 608, 
 1890. 
 
262 MEASUREMENT Of ELECTRICAL RESISTANCE. 
 
 drawn copper led him to confirm exactly Matthiessen's value 
 for the resistivity (per metre-gramme) of a wire of hard-drawn 
 copper wire taken at 18C., viz., O1571 ohms per metre- 
 gramme. Also, he found substantially the same percentage 
 difference as Matthiessen did between the metre-gramme 
 resistance of a hard-drawn copper wire and that of the same 
 wire when annealed and soft. 
 
 Mr. Fitzpatrick found, as others have done, great variations 
 in the specific gravity of copper, so that wires having the same 
 mass-resistivity per metre-gramme do not give the same 
 volume-resistivity per centimetre-cube at the same temperature. 
 Matthiessen therefore expressed all his results in mass-resis- 
 tivity, believing it to be more accurate and affording a better 
 definition of the real conductivity. 
 
 In addition to the determination of the conductivity of 
 copper, Matthiessen carried out very elaborate researches on 
 the electrical conductivity of different metals and alloys, 
 researches which are justly regarded as classical. At various 
 times numerous other observers have obtained values for the 
 volume-resistivities of different metals and alloys. 
 
 A table of resistances of platinoid and manganin wires of 
 various sizes is given at the end of this chapter. (See 
 Tables XII. and XIII.) 
 
 As regards the metals, with the exception of silver, copper 
 and mercury, and one or two others, such as tin and gold, 
 obtained without much difficulty in a state of chemical purity, 
 it is found that the greatest differences exist between the 
 electric conductivities as found by different observers. This 
 is due partly to the influence of minute proportions of 
 impurity, and the all but impossibility of obtaining certain 
 metals, such as iron, in a state of absolute chemical purity. 
 It is also due to differences in physical condition. Even 
 in the case of platinum and nickel, which are capable of 
 being prepared almost, if not quite, perfectly pure, the 
 greatest differences are found in the values assigned by 
 different observers to the electric conductivity. In the tables 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 263 
 
 at the end of this chapter are given Matthiessen's results for 
 the principal metals reduced to express them in terms of the 
 standard ohm; also values obtained from a very extensive 
 series of observations made in 1892 and 1893 by Fleming 
 and Dewar.* (See Table V.) 
 
 In these last-mentioned researches great care was taken to 
 obtain the metals in the highest state of chemical purity. 
 These materials were drawn into uniform wires and the 
 diameters of these wires measured by a micrometer method 
 as described in the above-mentioned papers. Hence the 
 measurement made was a volume-resistivity determination. 
 The resistances of these various wires were measured over a 
 range of temperature lying been -f 200C. and -200C., this 
 latter temperature being obtained by the use of liquid air. The 
 temperatures were measured by means of a platinum thermo- 
 meter. A table of densities (see Table I.) of the principal 
 metals is added to enable inass-resistivity to be converted to 
 volume-resistivity. 
 
 The differences which occur in the values assigned by 
 different authors and experimentalists to the volume-resistivity 
 of the various metals are in some cases very great. 
 
 It appears as if, in some metals, very considerable pro- 
 portions of impurity or changes in physical state make but 
 little difference in the electric conductivity, whereas in the 
 case of other metals very great differences are created in the 
 electric conductivity by the presence of mere traces of other 
 metals. Matthiessen showed that metallic alloys may be 
 broadly divided into two classes : 
 
 (i.) Those in which an admixture or alloy composed of them has a very much 
 higher resistivity than either or any of the constituents. To this class belong 
 alloys of copper, silver, gold, aluminium, platinum, nickel and most other metals. 
 
 (ii.) On the other hand, alloys which consist only of two or more of the 
 following metals, viz., lead, tin, zinc, and cadmium, have a conductivity which 
 is nearly the mean of those of their constituents, and may be roughly calcu- 
 lated from the proportions in which the elements are mixe l.f 
 
 In the case of alloys of these last four metals (ii.), the resultant or mean 
 conductivity C can be calculated by the formula 
 n_ c^ + caifr + &c. 
 
 v l + y. 2 + &c. : 
 
 * See Phil. May., Oct. 1892 aud Sept. 1893. t Matthiessen, B.A. Report, 1864. 
 
264 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 while Cic 2 , &c., are the specific conductivities of the constituents, and v^v-^ &c. 
 are the volumes of the respective constituents. 
 
 For alloys containing only two or more of the above-named metals, viz. 
 zinc, lead, tin and cadmium, the mean density D of the alloy is also obtain- 
 able from the densities d^, Ac., of the constituents, and their relative 
 volumes ?; 1 t > 2 , &c., by a similar formula, viz. : 
 
 Vi + V>2 + &C. 
 
 The alloys formed with metals of class (i.) with one another have a much 
 inferior conductivity to that of any of the components, but as the percentage 
 of one component rises to 100 the conductivity of the alloy rises also very 
 quickly to that of the pure metal. 
 
 Alloys of metals taken partly from class (i.) and partly from class (ii.) have 
 a specific gravity and conductivity which is always less than that of the mean. 
 If a metal of class (ii.) is alloyed with a considerable percentage of a metal 
 from class (i.) the conductivity is not much altered, but if a metal from 
 class (i.) is alloyed with a very little of a metal from class (ii.) the conductivity 
 is very much reduced. Hence we find an immense effect produced by the 
 presence of a little zinc in reducing the conductivity of pure copper, or of 
 lead in reducing that of pure silver. Accordingly large variations may be 
 expected in the determinations of resistivity in the case of chemically- 
 prepared metals which are not easily prepared pure. 
 
 The reader may be referred to the following Papers and 
 sources of information for additional knowledge on the subject 
 of resistivity measurement : 
 
 " The Specific Eesistance of Pure Copper." By Messrs. J. W. 
 Swan and Ehodin. The Electrician, Vol. XXXIII., p. 803. 
 
 As the mean of a number of determinations of the volume -resistivity made 
 with hard-drawn and annealed copper the authors find the following values 
 for the resistivity (p ) at 0C. in C.G.S. units and the temperature coefficient (a). 
 
 Hard-drawn copper p = 1603 a = 0'00408. 
 A nnealed copper p - 1563 a = 0'00416. 
 
 The density of the copper at 15C. was 8'96. 
 
 " The Electrical Conductivity of Aluminium." By Messrs. J. W. 
 Eichards and J. A. Thomson. The Electrician, Vol. XXXVIII., 
 p. 801. 
 
 The authors find the volume resistivity at to be as follows : 
 Hard-drawn aluminium p = 2684 
 Annealed aluminium p - 2659 
 
 "The Electric Conductivity of Steels." By M. Campredon. 
 The Electrician, Vol. XXVIIL, p. 845. 
 
 The author gives a useful table of the electric conductivity of steels of 
 given composition. The resistance of a wire linin. diameter and 1 kilometre 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 265 
 
 long at 15C. would be 21 ohms if of copper and 125 ohms if of iron. The 
 resistivity of steel is lower in proportion as the purity and softness is greater. 
 Manganese is the element which has the greatest effect in raising the 
 resistivity. 
 
 " The Electric Eesistance of Copper at Low Temperatures." 
 By Wroblewski. The Electrician, Vol. XXI., p. 432. 
 
 " Electric and Thermal Conductivity." By H. F. Weber. 
 The Electrician, Vol. VII., p. 6. 
 
 A remarkable connection is established between the electrical conductivity 
 (K), the thermal conductivity (H), and the specific heat per unit of volume 
 
 TT 
 
 (S). This relation is =a + 6S. where a and 6 are constants. 
 K 
 
 " Electric Conductivity and Atomic Volume." By W. P. 
 Granville. The Electrician, Vol. XXI., p. 381. 
 
 An attempt to establish a relation between these quantities. 
 
 "The Electrical Resistivity of Silicon." The Electrician, 
 Vol. XL., p. 580. 
 
 "The Conductivity of Cement and Concrete." By Dr. St. 
 Lindeck. The Electrician, Vol. XXXVI., p. 788. 
 
 Useful data on the electrical conductivity of road-making materials. 
 
 13. Determination of Low Resistances by Fall of 
 Potential. For the determination of very low resistances 
 many of the above-described bridge methods are not 
 applicable. If it is desired to measure the resistance of a 
 dynamo armature or transformer coil or short length of 
 electric lighting cable, the uncertain resistance at the contacts 
 of any conductors used in connecting the resistance to be 
 measured to other circuits would perhaps be greater than 
 the whole resistance to be measured. 
 
 In the case of such low resistances one method which may 
 be adopted is that of measuring the resistance by the fall of 
 potential down it when a known current is sent through it. 
 The resistance to be measured is joined in series with a known 
 low resistance standard, say one-tenth or one-hundredth of an 
 ohm. A suitable adjustable resistance is then added in series 
 with the two above-mentioned resistances, and a few cells of 
 
266 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 a primary or secondary battery are employed to send a 
 current through the circuit. The terminals of a high 
 resistance galvanometer, or a galvanometer having a resist- 
 ance of 1,000 or 2,000 ohms in series with it, are then 
 connected, first to the terminals of the known low resistance 
 and next to the terminals of the unknown low resistance. 
 In each case the galvanometer deflection is noted. It is 
 desirable to reduce the current in the circuit to such a value 
 that neither of these galvanometer deflections is very large. 
 The ratio of these scale deflections then gives us the ratio of 
 the unknown to the known deflection, on the assumption, 
 which must previously be justified, that the deflections of the 
 galvanometer are proportional to the current flowing through it. 
 The methods of testing the correctness of this assumption 
 in the case of the galvanometer used will be given in the 
 chapter on CURRENT MEASUREMENT. Meanwhile, assuming it 
 to be the case, let G- denote the galvanometer constant, or the 
 number by which the scale deflection of the galvanometer 
 must be multiplied to give the current in amperes flowing 
 through it. Let K^ be the galvanometer resistance, R s the 
 resistance of the known standard, and K the resistance to 
 be determined. Also let V s be the potential difference (P.D.) 
 between the terminals of the standard resistance, and V 
 that between the ends of the unknown resistance. If, then, 
 D g and D are the galvanometer scale deflections in the two 
 cases, we have, by Ohm's law, 
 
 , . and =: , 
 
 since the current in the main circuit is everywhere the same. 
 Hence, from the above equations, 
 
 D_E pp p D 
 
 TT fp 01 K=::K rf 
 
 D s li s D s 
 
 Accordingly, the value of the resistance being measured is 
 given as the product of the value of the standard resistance 
 i and the ratio of the two scale deflections D and D,. 
 
MEASUREMENT OP ELECTRICAL RESISTANCE. 267 
 
 In practically measuring, for instance, the resistance of a 
 dynamo armature, we must first give a rough guess at the 
 probable order of the resistance. Let it be ascertained to be 
 something of the order of O'Ol of an ohm. We should 
 then select as a standard resistance a resistance strip 
 having a resistance of 0*01 ohm. This may be a suitable 
 strip or strand of manganin or platinoid. The strip is then 
 joined in series with the armature by connecting it to the 
 brushes or terminals, and a few dry cells may be employed to 
 send a current through the circuit. The ends of a pair of 
 wires are then connected to the terminals of the standard 
 resistance strip, and a pair to the terminals of the armature. 
 These last ir ay preferably be pressed into contact with opposite 
 sections of the commutator by being placed under the brushes, 
 if the armature being measured is a continuous-current 
 armature. The other ends of these wires are conveniently 
 brought to a set of six mercury cups mounted on a board, 
 so that, by changing the position of a pair of copper bridge 
 pieces, either of the potential wires can quickly be brought 
 into connection with the galvanometer. 
 
 It is necessary to make both the measurements quickly 
 after one another, and to ascertain that the main current 
 has not altered in the meantime. It is best, therefore, to 
 take several readings of the values of D and D, alternately. 
 If, say, D is taken first, and we find a value D x , and then D, 
 is taken, and after an equal interval D is taken again, and 
 we find a value D 2 , the scale reading which must be taken 
 for D is half the sum of D! and D 2 , or its mean value, and it 
 may be assumed that this is the proper value corresponding 
 to D,. In any case, a large number of such readings should 
 be taken and the value ultimately accepted, for the ratio of 
 I) : D, should be the mean of a large number of observations. 
 
 An essential condition of success in this method is that the 
 galvanometer circuit shall be so high that its connection as a 
 shunt on one of the low resistances does not sensibly alter 
 the potential difference of the terminals of the latter. 
 
268 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 15. Measurement of Low Resistances by the Matthies- 
 sen and Hockin Bridge. We may employ the slide wire 
 bridge with a carefully calibrated or uniform slide wire to 
 compare together two resistances which are small, one of 
 them having a known value. Let the resistances be arranged 
 in bridge form as in Fig. 36. 
 
 Let PE be the slide wire extended electrically by the 
 resistance coils A and C, -and let a battery of a few dry 
 cells be joined up to points x and y. Let ab and'cd be 
 the low resistances to be compared joined in so as to complete 
 the four arms of the bridge. Let G be a galvanometer of high 
 or not very low resistance but great sensitiveness, and let 
 
 FIG. 36. 
 
 contact keys be inserted in the galvanometer and battery 
 circuits. The following operations are then performed : 
 
 Connect the galvanometer G in between the sliding contact 
 on the bridge wire and the point a. Find a point Q x on 
 the slide wire such that the galvanometer shows no current. 
 Then we have 
 
 xa, A+PQ, ,, xa A+PQ t 
 
 ^ = 0+02? e ^ = A+0+Pfi' 
 
 where xa stands for the resistance of the conductor between 
 points x and a, and A stands for the resistance of the 
 conductors between the points x and P, and so forth for the 
 other points. 
 
 We then connect the galvanometer in between points b and 
 the slider, and find a second position of the slider at which the 
 
 (i.) 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 269 
 
 galvanometer indicates no current. Similarly we have, 
 
 (iii) xl = A tJ Q2 > whe 
 
 xy W 
 
 Hence from (i.) and (ii.) we find 
 &==*&-*= 
 Also in the same way we find 
 
 where Q 3 Q4 are the balancing positions on the slide wire 
 when the galvanometer is connected to the points c and d 
 respectively. 
 
 Accordingly, we find the ratio of ab to Ho be 
 
 cd Q 3 Q 4 ' 
 
 In other words, assuming the uniformity of the slide wire, 
 we have 
 
 The resistance between ab _ 
 
 The resistance between cd 
 
 The length of the slide wire between Q, and Q 2 
 The length of the slide wire between Q 3 and Q, 4 
 
 It may so happen that the resistances A and C will have 
 to be changed between the readings, so as to make all the 
 balancing positions come on the. slide wire. If in the case 
 of the four readings of the resistance A takes the values A lf 
 A 2 , A 3 and A4, and the same for the resistance C, then, pro- 
 vided A 1 + C 1 = A 2 +0 2 , the four equations will take the form 
 
 l xa j 
 
 ' 
 
 ay . + xy 
 
 . -d hence <* = (A 2 -A 1 + Ql Q 2 ), 
 
 where W, as before, is the constant resistance 
 
270 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 In 'the same way we can find that 
 
 *-*?(A 4 -A,+Q,Q 4 ). 
 Hence o6_A a -A 1 +Q 1 Q 11 
 
 ^-A.-AS+QA- 
 
 If A t = Ag = A 3 = A 4 , the last equation reduces as before to 
 
 If, then, cd is a known low resistance, we obtain the value 
 of db in terms of cd and the ratio of two lengths of a uniform 
 slide wire. 
 
 The accuracy of the above method is not dependent upon 
 the absence of any variation of the battery current. It can 
 be carried out with the current supplied from public supply 
 circuits if necessary.* 
 
 15. The Kelvin Double Bridge. The Kelvin double 
 bridge is an arrangement of nine conductors joining six 
 points and having a source of electromotive force in one 
 branch and a galvanometer in another. 
 
 Let P, Q, E, S, B, G, a, b, c (Fig. 37) be the nine conductors, 
 B being the battery branch and G- the galvanometer branch 
 Let the above letters stand for the respective resistances of these 
 branches. It will be seen that if the conductor c is cut at any 
 point x the arrangement then becomes a simple Wheatstone's 
 bridge. It is always possible to find some point x in the con- 
 ductor c dividing c into two segments, a and /3, such that the 
 point x and the two points x 1 and # 2 are all at the same potential. 
 
 When this is the case we must have the relation a = -. For, 
 __ __ ft t> 
 
 * The above method was reproduced in The Electrician, July 1, 1898, 
 Vol. XLL, p. 320, as a new method due to Messrs. Miiller and Wallau. It 
 was, however, described many jears previously in Maxwell's Treatise on 
 " Electricity and Magnetism," and is due to Messrs. Matthiessen and Hockin, 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 271 
 
 under the above conditions, the current along the conductor a 
 must be the same as the current along b. Also, for the same 
 reason, we must have the relation 
 
 1 
 
 Or, since a + /3=c, the above becomes 
 
 P+- a 
 
 Q+ 
 
 B 
 
 C 
 
 If, then, we make a-f l c, we have 
 
 X 2 
 
 FIG. 37. Diagram of Kelvin Bridge. 
 
 Under this last condition the Kelvin bridge becomes 
 modified into a form called the Thomson (Kelvin) and Varley 
 
272 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 slide. This latter instrument may be described in principle 
 as follows : 
 
 Let two slide wires XY, XT' (Fig. 38) be stretched over 
 scales parallel to one another. Let a battery B be attached 
 to the terminals of one slide wire, XY, so as to create a fall 
 of potential down it. Along the wire XY a slider is arranged 
 to move having double contact edges, so as to make contact 
 at two places, nn' on XY, separated by a constant resistance 
 or length of slide wire, nn'. Let the resistance from X to n 
 be P, that from Y to n' be Q, and let nn' be c. The second 
 slide wire X'Y' must have a resistance equal to a + b=c, and 
 
 FIG. 38. Diagram showing arrangement of Conductors in Kelvin and Varley 
 
 Slide. 
 
 it has a slider m running on it and making contact at any 
 point, and thus dividing it into two sections a and ~b. A pair 
 of adjustable resistances B, and S, are connected to the points 
 X and Y, and from their common junction, t, a galvanometer 
 having a resistance G is connected in between the slider m 
 and t. The double contact slider nn' has its contacts con- 
 nected to the ends of the wire X'Y'. 
 
 In Fig. 38, showing the diagram of the above arrangement 
 of circuits, the letters denoting resistances are the same as 
 those used in Fig. 37, showing diagrammatically the form of 
 the Kelvin bridge. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 273 
 
 Iii the laboratory the practical form of this double 
 bridge is known as the Kelvin and Varley slide. In this 
 instrument (shown in Fig. 39) the slide wire XY consists of 
 101 coils of wire in series, each of 1,000 ohms. The common 
 junctions of these coils are brought to terminal pins on the 
 top board of the instrument, which is generally an ebonite 
 slab. The wire X'Y' is represented by a similar series of 
 100 coils of 20 ohms each so that the whole resistance of 
 XT' =2,000 ohms = that of two coils of XY. The double 
 contact piece nn f is represented by a double branched 
 revolving arm which as it moves round makes contact with 
 
 FIG. 39 Kelvin and Varley Slide. 
 
 a pair of studs including between them two of the 1,000 ohm 
 coils in series. This interval of 2,000 ohms corresponds with 
 the resistance c in the diagrams. 
 
 The resistances to be compared are the R and S in the 
 diagrams, and these are represented in practice by a plug 
 resistance box and the unknown resistance to be determined. 
 The revolving contact arms of the two resistance boxes, which 
 represent the wires XY and X'Y' are then moved round 
 to touch the various contact pins until positions are found 
 where the galvanometer connected in circuit as indicated 
 shows no current. 
 
274 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 If It is the unknown resistance and S is the standard or 
 resistance of the plug box, we have 
 
 E 
 S 
 
 If the point n is indicated by a scale reading N\ on the first 
 box and the point m by a scale reading N 2 on the second box 
 we have P= 1,000 K,_ ohms, 
 
 and a= 20 N 2 ohms. 
 
 Also, we have Q = 1,000 (99 - NJ, 
 and 1= 20(100-N 2 ). 
 
 Accordingly P + ? = 1,000 N x + 10 N 2 , 
 
 and Q+l =1,000 (99 -2^) + 10 (100-N 2 ) 
 
 = 100,000 -(1,000 N x +10 N 2 ); 
 E 1,000 K + lONa 
 
 QY 
 
 100,000 -(1,000 Ni + 10 
 
 FIG. 40. 
 
 The theory of the Kelvin bridge is as follows : Referring again to Fig. 37, 
 it is easy to show that the absence of a current in the galvanometer circuit 
 necessitates a certain relation between the values of the various resistances. 
 Assign letters x + y, y, z, and w to denote the imaginary cycle currents in the 
 meshes of the bridge arrangement (see Fig. 40) and consider the network so 
 formed of the nine conductors. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 275 
 
 Let imaginary currents x + y and y circulate clockwise round the circuits 
 bounded by the resistances R, G, P, a and G, &, Q, S. Then the actual current 
 through the galvanometer is x. Form, as before described, the cycle equations 
 by the method of Maxwell, and we have 
 
 ay cio = 0. 
 Re-arranging terms, we have the four equations in x, y, z, w as follows : 
 
 The solution for x (the galvanometer current) is then 
 
 (S + Q + 6), -b, -Q 
 
 (R + P + a), -a, -P 
 
 -(a + 6), (a + b + c), c 
 where D in the denominator is a determinant whose value does not concern us* 
 The above equation writes out into 
 
 x = ^(a + b + c) (RQ -SP) + c (R6 -Sa)}. 
 
 Hence the condition that the galvanometer shall show no current, or that x 
 shall be zero, is that the relations RQ = SP and R6 = Sa must simultaneously 
 hold good. If, however, c is a very small resistance, then the galvanometer 
 current will be very nearly zero if RQ = SP, even though R6 is not quite equal 
 to Sa. 
 
 Accordingly, in the Kelvin double bridge we have a double relation which 
 must hold good in order that the bridge may be balanced. We must have 
 
 - = - as a relation between the resistances P, Q, R and S, and also - =^ as a 
 Q S So 
 
 relation between the resistances a, b, R and S. 
 
 16. Modifications of the Kelvin Double Bridge for Low 
 Resistance Measurement. Practical Forms. The Kelvin 
 
 double bridge can be arranged so as to be a convenient instru- 
 ment for measuring low resistances, such as lengths of electric 
 arc light carbons or short lengths of copper cable. One form 
 which it then takes is as follows : 
 
 The resistance to be measured is clamped in between 
 massive clamps, GI C 2 , fixed on a board, and contact knife 
 edges, e 1 e 2 , arranged to press against it, intercepting any 
 required length of the conductor. A slide wire, AI A^ is 
 fastened to the same board, and on it move two sliders, ^ v%> 
 
 *2 
 
276 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 one or both of which are movable, which can make contact 
 with the wire at any position. In the centre of the board 
 are two plug resistance boxes of series pattern, having re- 
 sistances 10, 10, 100, 3,000 ohms each, and each provided 
 with two plugs. The galvanometer Gr and battery B (which, 
 should be a couple of storage cells) are connected in as shown. 
 The resistances in Fig 41 are lettered to correspond with, 
 those in Fig. 37. 
 
 In the first place, the plugs are inserted so as to make the 
 resistances E and S in the same ratio as a to b, viz., either 
 10 : 10, 10 : 100, or 10 : 1,000. The sliders ^ and v 2 are then 
 moved until the galvanometer shows no current. Calling the 
 
 FIG. 41. 
 
 ratio of K : S = a : I = n, we then have P = Qw. If the slide- 
 wire has been calibrated so that its resistance per centimetre 
 of length is known, we have at once the resistance of P in 
 terms of a certain length of slide wire, v l t- 2 . 
 
 Another form of the Kelvin bridge adapted for the purpose 
 of low resistance measurement has been devised by Mr. J. H.. 
 Beeves.* In this apparatus A and E (see Fig. 42) are two 
 massive pieces of copper, which can be joined by a plug 
 when desired. To one is connected the wire or bar EFGH of 
 which the resistance is to be determined, and to the other a. 
 
 *See Proc. Phys. Soc. Lond., Vol. XIV., p. 166. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 277 
 
 comparison wire ABCD of known resistance per unit of 
 length. A pair of contact edges K and M make contact with 
 the wire FG at two places L and N of known distance apart. 
 It is convenient to make the distance LN equal to one metre. 
 A pair of connecting wires BO, CT are soldered to the wire 
 BC intercepting a known resistance, which may be con- 
 veniently O'Ol ohm. The same board or another carries a 
 calibrated slide wire, a&, the terminals of which are con- 
 nected to anJ K. 
 
 A pair of adjustable resistances x and y are connected to 
 M and T. These last may be ordinary resistance boxes, one 
 say y, is 1,000 ohms, and the other is a series plug box 
 
 Galvo. 
 
 
 ft 
 
 x||y 
 
 ^ Battery J. 
 
 x' ^ 
 
 O, . b ' 
 
 M * ^T 
 
 ? B . II P'H [" 
 
 
 
 FIG. 42. 
 
 reading from 1 to 5,000 ohms. Between the junction of 
 x and y and the slider on the slide wire is joined in a galvano- 
 meter, and a battery is connected to the terminals I) 
 and H. If the plug P is removed so that the blocks A and E 
 .are not connected, the arrangement is an ordinary Wheatstone's 
 bridge. The slider s can be then adjusted so as to divide the 
 slide wire into two segments a and & such that the resistance 
 -a is to that of b as x is to y. This being done, the plug P is 
 inserted to connect A and E. The arrangement then becomes 
 a Kelvin double bridge. If the resistance of the wire under 
 4est between L and N" is called E, and if that of the standard 
 wire between B and C is called r, we can then further adjust 
 
278 MEASUREMENT OF ELECTRICAL RESISTANCE, 
 
 x and y so that the galvanometer shows no current. When 
 this is the case we have again 
 
 r y 
 
 If the wire under test is a copper wire, then we know from 
 the tables of wire resistances approximately the resistance of 
 one metre length of it. Calling this resistance ~R V we choose 
 x l as the value of the resistance unplugged out of the box 
 
 represented by %, so that ^ = l . If y is made 1,000 ohms, and 
 V r 
 
 Eemoving the plug and making the bridge an ordinary 
 one we find a position of the slider so that the slide wire is 
 divided into sections a and b, and when the balance is obtained 
 
 b + r y r 
 
 n "P T* 
 
 or - = ! - approximately, 
 
 where R is the true resistance of the wire between L and K". 
 Next, inserting the plug P and passing a stronger current 
 from the battery, we find a new balancing position by altering 
 
 x l to # 2 but keeping a and b the same. Then, since - = 
 
 b r 
 
 nearly, we have 
 
 R 2fe <n 3fe i 
 
 = - , or R= r very nearly. 
 r y y 
 
 In any case the value of R so obtained is much nearer to the 
 true value of the resistance of the metre length of the wire 
 than R r 
 
 If the value of x 2 is not very different from x 1 the value 
 
 r may be taken as the true value of R, but if # 2 differs 
 
 y 
 
 considerably from x^ then we must begin over again, and, 
 employing x% as the resistance in branch x, obtain a new 
 position of the slider and new values for a and b. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 279 
 
 In carrying out the test the battery employed should be 
 such that a small current can be sent from it when the bridge 
 is being employed as a simple bridge, but a much larger current 
 when as a double bridge. This is best achieved by employing 
 a couple of secondary cells in series with a resistance which 
 can be more or less short circuited as required. This 
 resistance may be a simple length of platinoid wire with 
 terminals at each end so arranged that the resistance can 
 be short-circuited by bringing the ends together. 
 
 The above method enables us to measure with great ease 
 and accuracy the resistance of a metre length of ordinary 
 copper wire of, say, No. 16 S.W.G., and deduce the volume 
 or mass-resistivity from the observations. It is, therefore, of 
 great utility when only a short sample of bare wire is obtain- 
 able. It may be employed also to measure the resistance of 
 short lengths of strand copper cable or copper rod. The 
 sensibility of the method is that an accuracy of 01 per 
 cent, can be obtained, or, in other words, by this means the 
 resistance of a yard or two of bare copper wire of No. 16 or 
 No. 14 S.W.G. can be as accurately measured as a resistance 
 of the order of an ohm or more can be measured on the 
 ordinary plug form of Wheatstone's bridge. 
 
 17. Modifications of the Ordinary Wheatstone's Bridge 
 for Low Resistance Measurement. A simple yet effective 
 bridge arrangement for measuring low resistances is that 
 devised by Mr. E. H. Housman.* The principle of the 
 method consists in making an ordinary bridge measurement 
 in two stages in such a manner that the value of a low 
 resistance standard of O'OOl or even O'OOOl of an ohm can 
 be compared with a standard one-ohm resistance with an 
 accuracy of about one-tenth per cent. This test can be 
 carried out with an ordinary plug Wheatstone's bridge, 
 using with it a movable coil mirror galvanometer of fairly 
 high sensibility, say, giving a scale deflection of 1mm. at a 
 
 * See The Electrician, Vol. XL., p. 300, December 24, 1897 
 
280 
 
 MEASUREMENT OF ELECTRICAL RESISTANCE 
 
 metre distance per microvolt at the galvanometer terminals. 
 The method requires the possession of a one-ohm standard 
 resistance, which will carry safely a current of one or two 
 amperes for a few seconds without sensible heating. For 
 this purpose a Xo. 18 bare manganin wire, wound on a 
 frame but otherwise exposed to the air, may be employed. 
 This wire resistance standard should terminate in thick copper 
 connecting rods. The standard should be very carefully 
 compared, by any of the methods already described in this 
 chapter, with an ordinary small current one-ohm standard 
 resistance of platinum-silver or manganin of known value. 
 
 Let us suppose, then, that a low-resistance standard in the 
 form of a manganin strip has to be measured, and that its 
 
 FIG. 43. Diagram of Housman Bridge Arrangement. 
 
 resistance value is something of the order of O'OOOl of an 
 ohm. This strip will be provided with current terminals in 
 the usual way and also with potential terminals. Let the 
 resistance ' of the strip to be tested be taken between the 
 potential terminals and called R 2 - It is then to be joined in 
 series with a second resistance or strip, having a resistance 
 (denoted by 11Q of about O'Ol ohm, and with the one-ohm 
 resistance standard, whose exact value will be denoted by S. 
 These three resistances must be joined up in series by stout 
 copper rods or strips, and connected to a plug resistance, 
 which may be an ordinary resistance box, as shown in Fig. 43. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 281 
 
 The first stage in the process is to measure the ratio of 
 the resistance of the O'Ol ohm strip (R,) with contacts and 
 connections plus the resistance of the strip under test 
 
 (iy to the resistance of the one-ohm standard S. Let 
 P i ~p 
 Lzlf^srek The one-ohm standard, S, should be provided 
 
 k> 
 
 with double terminals, two for current entrance and exit, 
 .and two for potential terminals, between which its resistance 
 is known. The Wheatstone bridge employed with the above 
 resistances, RI, E 2 and S is used merely as a potentiometer 
 wire, the side AB, or the ratio arms, being used as one 
 branch, and BC, or the measuring arm, being used as the 
 other branch. When this bridge arrangement is connected 
 with a galvanometer, as shown in Fig. 43, and with a single 
 storage cell, the cell sends a current of about two amperes 
 .along the circuit E 2 +Ri-f-S. Since the ratio of R 2 +R t to 
 .S is about 1 : 100, it can be determined with an accuracy 
 of 1 to 10,000 when a suitably sensitive galvanometer G is 
 employed, connected across between the terminals B and E, 
 as shown in Fig. 43. 
 
 The second stage in the process is to shift one galvanometer 
 .connection from E to F and one battery connection from 
 I) to E. The storage cell used should be one which can for 
 ;a short time send a current of 200 amperes or so without 
 injury. The arrangement in the second case is again a 
 .simple bridge, but in this last form the circuit Rj + R^ is 
 traversed by about 200 amperes No contact which was 
 included in the first stage is altered, but we can now 
 measure the ratio of E 2 to E r This is again a ratio of about 
 
 1 to 100. Hence we can find with great accuracy the ratio 
 p 
 
 ^ -^ = I. Accordingly, we have, by the first measurement, 
 
 .and by the second one =5. 
 
 Hence, 
 
282 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 The contact resistances are all eliminated. If the galvano- 
 meter is one having a resistance of 100 ohms, and giving a 
 scale deflection of 1 mm. at 1 metre distance with 1 micro- 
 volt, we can measure the ratio of R 2 to (^1 + ^2) with an 
 accuracy of 1 in 10,000. 
 
 The connections of the bridge wire or bridge circuit ABC 
 to the series of three resistance S p R^ E 2 should be made as 
 small as possible. If, for instance, Rx^O'Ol ohm, R 2 0*0001 
 ohm, then in the measurement the arm AB may be 10 ohms 
 and the arm BC may be 1,000 ohms. The fall in potential 
 down each side will be 2 volts. Hence, if a current of 
 200 amperes is flowing through Ei + R 2 =0 > 010 ohm, it is clear 
 that a change in resistance of T ^th of the '0001 ohm 
 resistance, or of '0000001 ohm, or of one-tenth of a microhm,, 
 will produce a potential change of nearly 20 microvolts on 
 the galvanometer terminals, and hence produce 20mm. scale 
 divisions deflection, which it is impossible to avoid detecting. 
 This method is therefore one which can quite easily be put 
 into practice in any laboratory possessing a good plug 
 resistance bridge and a sensitive galvanometer. 
 
 When once a low resistance strip is obtained, the value- 
 of which is accurately known at any temperature, then it is 
 easily copied and others reproduced from it. 
 
 Bridge methods, speaking generally, have a great advantage 
 over methods for the comparison of resistances which depend 
 upon the measurement of the relative value of the fall of 
 potential down conductors to be compared when traversed 
 by the same current, in that, in the case of bridge measure- 
 ments, slight variations in the value of the currents passing 
 through the network do not affect the accuracy of the 
 result.* 
 
 * See The Electrician, Vol. XLTf, p. 354, 1898, for remarks by Prof. 
 H. L. Callendar " On the Bridge Method of Comparing Low Resistances," 
 in which the advantages of bridge over potentiometer methods of com- 
 paring low resistances are upheld. For a trenchant criticism by the same 
 writer on the subject, see also The Electrician, Vol. XLI., 1898, p. 501 and. 
 p. 631. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 283- 
 
 18. Measurement of High Resistances by Direct 
 Galvanometer Deflection. The measurement of high 
 resistances, or resistances of the order of a megohm. 
 or upwards, cannot be well effected by any of the above 
 described bridge methods. The method by which it is 
 generally achieved is by observing the current which can be 
 sent through a calibrated galvanometer of great deflectional 
 sensibility, but good zero-keeping quality, by a battery of 
 high electromotive force placed in series with the galvanometer 
 and with the resistance to be measured. If the resistance to 
 be measured is placed in series with the galvanometer and 
 with a battery of small secondary cells, we have then a 
 circuit of which the resistance is made up of the resistance 
 to be measured (which may be reckoned as megohms and 
 denoted by II), the internal resistance of the cells denoted by 
 r v the resistance of the galvanometer (represented by r), and 
 that of the connections by r% these last three being measured 
 in ohms. If, then, E is the electromotive force of the battery 
 in volts, and A the current in amperes which flows through. 
 the circuit, we have 
 
 If the battery is composed of secondary cells, and the- 
 connections are of copper wire and not long, then 7*1 and r& 
 may be neglected in comparison with 10 6 B, arid we have 
 
 \= E 
 
 10 6 E+r" 
 
 Under these circumstances the galvanometer will give a 
 deflection S such that A = GS, where Gr is the galvanometer- 
 constant for steady currents. The galvanometer must, for 
 this purpose, be a highly sensitive mirror instrument, with 
 either movable needle or movable coil, placed at a distance,, 
 say, 2 metres, from a scale divided into millimetres. On the 
 scale the sharp image of a portion of an incandescent lamp 
 filament is focussed so that any deflection of the coil or 
 
284 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 needle can be carefully measured in terms of the scale 
 deflections. In the case of such a mirror galvanometer the 
 deflections will be proportional to the current flowing through 
 the galvanometer. The first step, therefore, is to determine the 
 galvanometer constant. This is best done by the employment 
 of a potentiometer. A fall of potential is created down a long 
 fine wire of high resistance laid over a divided scale, and this 
 fall of potential is adjusted by means of a Clark cell, so that 
 the fall of potential per scale division is known. For the 
 details of this process the reader is referred to the descrip- 
 tion given of the potentiometer and its uses in Chapters I., 
 III. and IV. 
 
 Suppose the potentiometer is so adjusted that we have 
 a fall in potential of O'OOl volt per scale division of the 
 scale over which the wire is laid. The terminals of the 
 galvanometer are then connected through a resistance of 
 several thousand ohms with twc points on this slide curve 
 and the distance between these points adjusted until the 
 galvanometer gives a convenient deflection. Thus, suppose 
 the galvanometer has a resistance of 6,000 ohms and we place 
 in series with it 4,000 ohms and find that when the terminals 
 are connected to two points on the slide wire separated by 
 20 scale divisions we have a galvanometer deflection of 
 40 divisions. Then we know that the potential difference on 
 the terminals of the galvanometer is 20 X O'OOl volt= 0'02 volt 
 and the resistance of the galvanometer circuit is 10,000 ohms. 
 Hence the current through it is (0-02-^-10,000) amperes. 
 
 If G is the galvanometer constant, then 
 40G = (0-02-=-10,000),. 
 
 or G = 20,000,000 = 20 X l(?' 
 
 or '05 of a microampere, per scale division. A determination 
 of G should be made for a great many different values of S 
 (the galvanometer deflection) and the mean value taken. 
 
 In the next place we must determine, by means of the 
 potentiometer, the value of the electromotive force (E) of the 
 
MEASUREMENT OF ELEOTRLCAL RESISTANCE. 285 
 
 battery. This can be done in the way described in 
 Chapter IV., in which are given methods for the 
 measurement of electromotive force. Having thus deter- 
 mined the value of G and E, and knowing the value of the 
 galvanometer resistance r, we can calculate the value of 
 E in the expression 
 
 -&-> ;., 
 
 In this test the electromotive force E should be produced 
 by a number, say, 50 to 100, of small secondary cells, so 
 that it can be measured with a good voltmeter. It may 
 even be the circuit pressure of an electric supply circuit if 
 it is sufficiently constant. 
 
 If neither potentiometer nor voltmeter is at hand, but 
 merely a battery of cells and resistance boxes of the ordinary 
 type, we may proceed as follows : 
 
 Let <j be the galvanometer resistance, and s be the resist- 
 ance of a shunt across its terminals. Then the total resistance, 
 (j v of the shunted galvanometer is 
 
 (IS 
 
 Employing one cell of the battery, send first a current 
 from it through the shunted galvanometer and a resistance, 
 r v in series with it. Let r be the internal resistance of the 
 cell and e its electromotive force. If, then, the resulting 
 galvanometer deflection is d v and if G is the galvanometer 
 constant, or the number by which the galvanometer deflection 
 must be multiplied to give the current in amperes producing 
 that deflection, then, by Ohm's law, we have 
 
 or 
 
386 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 Next alter the resistance r\ to r% and obtain a corresponding 
 scale deflection, d%, of the galvanometer ; then 
 
 or rdz+rA+dtf! ..... (ii.) 
 
 Eliminating from (i) and (ii.), we have 
 
 If the resistance r 2 is so adjusted that the second deflection 
 ,dz=%d lt then we may reduce the equation (iii.) to 
 
 r=(r 2 -2r 1 )-g v 
 
 Hence the internal resistance of the cell becomes known 
 under the conditions that it is sending a very small current. 
 
 In the next place, let a battery of n cells be joined in series 
 with the galvanometer and the large resistance to be measured 
 of which the value in megohms may be denoted by E. Let 
 -the galvanometer deflection then be d 3 . Hence we have 
 
 Gd 3 . (iv.) 
 
 Change the number of cells to n', and obtain another galvano- 
 meter deflection d^ then 
 
 Eliminating r - from (iv.) and (v.), we have 
 
 (jT 
 
 ''(d^ d 3 )r 
 
 .'Substituting in (vi.) the value found above by equation (iii.) 
 for r, we obtain the value of the resistance E. in megohms in 
 terms of the scale deflections and the resistances of the 
 galvanometer and cells. 
 
 The assumption made that each cell has the same internal 
 resistance must be tested by measuring the internal resistance 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 287 
 
 of various cells, and if they differ, as they probably will do, 
 then the mean value of all must be taken. 
 
 The method, however, cannot be regarded as affording 
 more than an approximation to the value of the high 
 resistance unless each of the cells has absolutely the same 
 internal resistance and electromotive force. This is never 
 the case in any actual battery. If, however, we employ a 
 battery, say of 50 moderately large secondary cells which 
 have been about half discharged, and in which each cell is 
 in good order, the voltage of each cell will be very nearly 
 2 volts and the internal resistance of the whole battery will be 
 negligible in comparison with that of a galvanometer having 
 a resistance of say 5,000 ohms. In this case the equations 
 become reduced as follows : 
 
 Let a single secondary cell be first applied to create a 
 current through the shunted galvanometer in series with a 
 resistance. Then, taking the same symbols as before, we have 
 
 (vii.) 
 
 Xext let the high resistance be placed in series with the 
 battery of n cells and the galvanometer be unshunted, and we 
 have 
 
 nc n 7 / ... 
 
 Hence, from (vii.) and (viii.) we obtain 
 
 lu% 
 or, if the high resistance is measured in ohms, then 
 
 . ,. , 
 
 The most satisfactory method is, however, to standardize 
 the galvanometer by the potentiometer, and then to measure 
 
288 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 by the same means the actual value of the high electromotive 
 force employed to transmit the currents through the high 
 resistance. 
 
 The apparatus therefore required for this measurement 
 consists of three parts : First, the sensitive high-resistance 
 galvanometer combining good zero-keeping quality and pro- 
 portionality of deflection to current or constancy of deflectional 
 constant over the useful range of the scale. These qualities 
 must not be taken for granted, but be carefully proved to- 
 exist. The galvanometer should have various electromotive 
 forces applied to its terminals by the potentiometer, and the- 
 ratio between the observed scale deflection and the potential 
 difference of the terminals observed. This ratio should prove 
 to be constant. In the next place, when the circuit is opened,, 
 the galvanometer needle or coil should return accurately to 
 the same zero position. If it does not, the galvanometer is no 
 use for the present purpose. In the next place a good 
 potentiometer is required by means of which to make the 
 above-described calibration and to determine the galvanometer 
 constant at any moment. In the third place a battery of 
 small secondary cells is required. This is most conveniently 
 provided in the form of a series of trays containing rows of 
 lithanode cells made up in large test tubes. For most work 
 in measuring insulation frolh 6 to 12 trays will be required,, 
 each containing 25 cells. These trays should be exceedingly 
 well insulated by being placed on ebonite legs or paraffin 
 blocks. High resistance keys are also required. The insula- 
 tion of the galvanometer itself is a matter of importance, and 
 it should be supported on three ebonite blocks in which the 
 levelling screws rest. 
 
 The above apparatus serves for the measurement of the 
 insulation resistance of cables or of highly insulating 
 materials such as indiarubber or gutta-percha, 
 
 19. Measurement of Insulation Resistance. Let it be 
 
 desired to measure the insulation resistance of the dielectric 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 289 
 
 of a cable or insulated wire. The method of procedure is as 
 follows : 
 
 A large tank is provided of sufficient capacity to contain 
 one or more coils of the wire or cable to be tested. For 
 laboratory purposes it is convenient to have a galvanised iron 
 tank about 3ft. wide, 3ft. long, and 2ft. deep, and to rest it 
 upon a wooden platform on castors for facility of movement. 
 The coil of cable is placed in the tank, and the tank filled up 
 with water. The two ends of the cable are kept well above 
 the surface of the water and must be prepared by stripping 
 
 FIG 44. Use of Price's Guard Wire. 
 
 back for some distance the plait or tape outer covering so 
 as to expose the indiarubber (I.E.) or gutta-percha (G.P.) 
 insulation. The two ends of the copper conductor are also 
 bared and twisted together. Bound the exposed length of 
 I.B. or G.P., which should be a foot or more in length, is 
 twisted a fine wire, G, called a guard wire. This should be 
 put on at about Gin. from the outer end of the insulation. 
 
 The cable then presents 'the appearance shown in Fig. 44. 
 C, C' are the exposed copper ends connected by a wire W. 
 I, I' are the exposed indiarubber or gutta-percha surfaces, the 
 
290 
 
 MEASUREMENT OP ELECTRICAL RESISTANCE. 
 
 tape or protective covering being neatly stripped off and the 
 ends connected by the guard wire G. T,T is the tape or twist- 
 covered complete cable which remains under water in the tank. 
 The connections are then made as follows : One terminal 
 of the battery is connected to the tank or to a metal plate 
 placed in the water. The other terminal is connected to one 
 terminal of the galvanometer, and the remaining terminal of 
 the galvanometer G (see Fig. 45) is connected to the copper 
 wire iv of the cable. The guard wire g short-circuits the galvano- 
 meter. It is best to insert a key in circuit with the battery 
 and to place this next to the tank. The battery and galvano- 
 meter should be well insulated by placing them on ebonite 
 
 FTG. 45. Testing Insulation of Cable. 
 
 slabs or blocks of paraffin. The use of the guard wire is as 
 follows : If any leakage of current takes place over the cleaned 
 surfaces of indiarubber, this current would, unless prevented, 
 pass through the galvanometer and be added to the true 
 conduction current or flow through the dielectric of the cable. 
 The guard wire, however, arrests the leakage current and 
 conducts it harmlessly past the galvanometer.* 
 
 * This ingenious yet simple means for annulling the effect of the leakage 
 current over the exposed dielectric ends of a cable under insulation test is 
 called Price's Guard wire, being due to Mr. W. A. Price (see Electrical Review, 
 Vol. XXXVII., p. 702, 1895). It is described also in a Paper by Mr. R. Apple- 
 yard on Dielectrics (see Proc. Phys. Soc., Lond., Vol. XIV., p. 256 ; or The 
 Electrician, Vol. XXXVII., p. 159). See also, Prof. W. E. Ayrton, " Some 
 Developments in the Use of Price's Guard Wire in Insulation Tests," Phil. 
 Mag., April, 1900, Vol. XLIX., p. 343. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 291 
 
 In making such an insulation test it will be found that if 
 the material of which the dielectric of the cable consists is 
 indiarubber, gutta-percha, okonite or any of the usual insulators, 
 the deflection of the galvanometer does not remain constant 
 when the same electromotive force is continuously applied. 
 It will be seen to decrease with the time during which the 
 battery is kept in circuit. If the cable is at all a long one, 
 then at the moment of first making contact there will, in 
 addition, be a rush of current into the cable. In the case of 
 very large cables this rush is so violent that it is better to 
 short-circuit the galvanometer for a moment whilst putting 
 -down the battery key, and then to withdraw the galvanometer 
 short-circuit i mmediately. 
 
 If we operate in. this manner we shall find that the 
 galvanometer deflection decreases from moment to moment 
 in a manner which indicates that the insulation resistance is 
 increasing with time. It is the custom to define the insula- 
 tion by stating its value in megohms after one minutes 
 electrification, naming also the electromotive force of the 
 battery and the temperature of the cable. 
 
 In the case of such materials as indiarubber and gutta- 
 percha, and probably in the case of most dielectrics, the 
 apparent insulation resistance is a function of the electro- 
 motive force and of the time during which it acts. The, 
 .apparent resistance increases with the time of application of 
 the electromotive force, and in some cases it decreases also 
 slightly as the electromotive force is increased, even if taken 
 .after the same interval. The insulation resistance decreases 
 markedly with rise of temperature. 
 
 Hence the voltage, temperature, and time of electrification 
 must always be stated, or else the numerical value of the 
 insulation resistance is a meaningless number. Thus a cable 
 may be marked as having an insulation resistance of 300 
 megohms per mile tested with 600 volts after one minute's 
 -electrification on application of the electromotive force, the 
 insulator being at a temperature of 75Fahr. Such a 
 
 u2 
 
292 . MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 statement is precise, but tlie mere statement that the insula- 
 tion resistance is 300 megohms per mile is a very imperfect 
 description of the actual insulation quality of the cable. 
 
 The relation between the strength of the current flowing 
 through a non-metallic conductor and the electromotive force 
 producing it is in general much less simple than in the case 
 of metals. 
 
 In addition to the metals and alloys formed of them, which are called 
 the metallic conductors, we have bodies such as carbon, selenium, tellurium, 
 phosphorus, certain metallic oxides and sulphides, &c. which are non-metal? r 
 and yet in certain states are electrical conductors. These are called non- 
 metallic conductors. They are generally characterised by the property of 
 existing in two or more allotropic conditions, in which their electrical 
 conductivity differs widely. Carbon exists in three forms, as diamond r 
 charcoal and graphite. In the first state it is a good insulator, in the second 
 a poor or indifferent conductor, and in the third a fairly good conductc r. 
 Selenium, also, can exist in two allotropic forms, and is remarkable from the 
 fact that light falling on it when it is in one of these forms causes a sudden 
 and considerable diminution in resistance. For the most part, the electrical 
 volume-resistivity of all these non-metallic conductors is much higher than 
 that of any of the metallic conductors. '. 
 
 The third class of conductors comprises such substances as indiarubber, 
 gutta-percha, mica, glas?, ebonite, etc. These are all substances of very high 
 electrical resistivity, and are generally called insulators. They have a volume - 
 resistivity enormously greater than any metallic or non-metallic conductor. 
 They are usually termed non-conductors, but may also be denominated a* 
 dielectric conductors. This class includes numerous solids and liquids. 
 
 The fourth class of conductors comprise the conducting liquids. These are 
 called electrolytes,. In their case the process of conduction is accompanied by 
 an evident chemical decomposition of the material, and it is described as 
 electrolytic conduction, the liquids themselves being spoken of as electrolytic 
 conductors. It is a difficult matter to give a precise answer to the question, 
 AVhat is an electrolyte 1 
 
 A fifth class may be said to comprise the gaseous conductors ; and although 
 there is some evidence that in their case the process of conduction is ele c- 
 trolytic in nature, it may be well to retain them at present in a distinct 
 sub-division. Gases at ordinary pressures are good insulators, but if subjected 
 to an electromotive force exceeding a certain limit, they pass into the 
 conductive condition. 
 
 As examples of these five classes of conductors, we may select copper,, 
 graphite, mica, melted silver chloride, or an aqueous solution of sodic 
 cliloride, and hydrochloric acid gas. 
 
 It may be that these divisions are not sharply marked. The conduction in 
 the case of glass may be electrolytic, and also in the case of gases. On the 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 293 
 
 other hand, the process of conduction may be of a' similar nature in all the 
 five sub-divisions, and even in the metallic conductors may be electrolytic. 
 
 The action of temperature on the conductivity of the substances in the 
 various classes is very different. In the case of metallic conductors, if ihey 
 are pure metals, increasing their temperature always increases their resistivity, 
 and lowering the temperature towards the absDlute zero indefinitely decreases 
 the resistivity. As regards metallic alloys, some of these, such as manganin, 
 have a maximum resistivity at a certain temperature, above which they 
 decrease in resistance as temperature rises, and below which they also decrease 
 in resistivity, but not probably indefinitely, and there is no indication, as in the 
 case of pure metals, that it would become zero at the absolute temperature.* 
 la the case of the non-metallic conductors, increase of temperature lowers the 
 resistivity. As regards graphite there is clear indication that it has a 
 minimum resistivity corresponding to a certain temperature near a dull red 
 heat.t 
 
 The class of dielectric conductors are distinguished by the 
 fact that rise in temperature always reduces their electric 
 resistivity, and this rate of decrease in some instances is very 
 marked. Thus, in the case of glass .we have an exceedingly 
 large .negative temperature co-efficient ,J as shown in the 
 following tables : 
 Volume-resistivity of Glasses in C.G.S. Units per Centimetre- 
 
 cube. 
 BOHEMIAN GLASS. FLINT GLASS. 
 
 Temp. 
 
 60C G xlO 22 
 
 100C 2 xlO 21 
 
 130C 2 xlO 20 
 
 160C. ...... 2-4 xlO 19 
 
 174C. 8-7 x 10 18 
 
 60C 1-02 xlO- 4 
 
 100C 2 xlO 2 * 
 
 120C 4-68 xlO 22 
 
 140C. 1-06 XlO 22 
 
 160C. 2-45 XlO 21 
 
 180C. 5'6 xlO 20 
 
 200C. 1-2 XlO 20 
 
 Another characteristic of some dielectric conductors is that 
 the resistivity is a function of the electromotive force with 
 
 * For a theory as to the cause of the greater average resistivity and 
 smaller temperature cc-efficient of alloys compared with that of the metals 
 composing them, see a Paper by Lord Rayleigh in The Electrician, Vol. XXXVII., 
 p. 277. 
 
 t See The Electrician, Vol. XXXVIII., p. 835, Mr. J. C. Howell, " On the 
 mductivity of Incandescent Lamp Filaments." 
 
 See Mr. Thomas Gray, Proc. Roy. Soc. Lond., January 12, 1882. 
 
294 
 
 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 which it is measured. This is shown by the results in the 
 following table, obtained by measurements made at the works 
 of Messrs. Siemens Bros. & Co.* 
 
 Resistance of Certain Dielectrics under various Electromotive 
 Forces or Voltage after One Minute's Electrification. 
 
 Dielectric. Voltage. 
 
 Kesistance. Dielectric. Voltage. 
 
 Resistance. 
 
 f 150 
 
 ... 3,468 
 
 r 150 
 
 ... 2,813 
 
 
 300 
 
 ...3,366 
 
 Lead-covered 
 
 300 
 
 ... 2,674 
 
 Gutta-percha.^ 
 
 750 
 1,050 
 
 ... 3,267 
 ... 3,117 
 
 impregnation 
 cable 
 
 750 
 1,050 
 
 ... 2,541 
 ... 2,224 
 
 
 1,500 
 
 ... 3,086 
 
 (C class). 
 
 1,500 
 
 ... 2,057 
 
 Vl,800 
 
 ... 3,021 
 
 
 d,800 
 
 ... 1,798 
 
 
 f 150 
 
 ... 8,054 ; 
 
 r 150 
 
 ... 2,602 
 
 High insula- 
 tion india- 
 
 300 
 750 
 1,050 
 
 ... 7,916 , 
 ... 7,470 
 ... 7,268 
 
 Lead-covered 
 impregnation 
 cable 
 
 300 
 750 
 1,050 
 
 ... 2,492 
 ... 2,425 
 ... 2,345 
 
 rubber. 
 
 1,500 
 
 ... 6,705 
 
 (A class). 
 
 1,500 
 
 ... 2,274 
 
 1,800 
 
 ... 6,245 
 
 
 ,1,800 
 
 ... 2,212 
 
 ( 150 
 
 ... 513 
 
 
 
 Ordinary 300 
 
 ... 462 
 
 
 
 indiar ubber. 1 750 
 
 419 
 
 
 
 U,050 ... 355 
 
 The above figures show beyond question that the resistance 
 of certain dielectrics after one minute's action of the impressed 
 electromotive force or voltage decreases as the voltage 
 increases. The same variation has been found to exist after 
 electrification for other intervals. Hence it must not be 
 hastily assumed that in the case of any dielectric the current 
 flowing through it under different electromotive forces is in a 
 constant ratio to the electromotive force. The current flow 
 in amperes or micro-amperes per volt of impressed electro- 
 motive force is not constant. The actual current flowing 
 
 * The figures were given by Mr. A. Siemens at the Institution of Electrical 
 Engineers, during a discussion on a Paper by Sir W. H. Preece on " The 
 Specification of Insulated Conductors." See Journal Inst. Elec. Eng., 
 Vol. XXL, p. 217. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 295 
 
 through a dielectric conductor at any instant after an 
 impressed electromotive force has been applied to it is a 
 complicated function of the time from closing the circuit, the 
 temperature and the impressed electromotive force, and the 
 usual custom of denominating the ratio of the electromotive 
 force (measured in volts) to the current (in amperes) through 
 the dielectric after one minute's application of that electro- 
 motive force, the ohmic resistance of the dielectric, is a 
 perfectly arbitrary or conventional proceeding. The properties 
 of dielectrics will be more fully considered in a later chapter 
 in the section dealing with capacity measurement. 
 
 Returning to the practical test of insulation, we may add 
 that it is necessary in these tests to provide a sufficient 
 electromotive force in the form of a well-insulated battery 
 In cable factories it is usual to set up in a room a battery of 
 600 to 1,200 Leclanche cells arranged in groups, in series, 
 and placed on well-insulated platforms of paraffined wood 
 standing on oil insulators. From this battery insulated wires 
 run to the testing room, so that any required electromotive 
 force up to 1,800 volts or so is available for testing purposes. 
 In a laboratory it is more convenient to employ small 
 secondary cells set up in test-tubes and arranged in trays of 
 10 cells. The most convenient form of cell is the lithanode 
 secondary cell. These cells consist of glass tubes about 1 inch 
 in diameter and' 4 inches high, and each contain two plates. 
 They should be charged when required with a small current, 
 and no greater current than one-tenth of an ampere taken 
 from them. The trays of cells should be arranged in a 
 portable cupboard and terminal wires from the various sets 
 of cells or from each cell brought out to insulated terminals 
 on the outside. 
 
 The insulation tests of ordinary indiarubber-covered cable 
 as used in electric lighting work are always made with an elec- 
 tromotive force of 300 volts to 600 volts, and the resistance 
 taken after one minute's electrification. Previously, however, 
 the cable must be allowed to lie in water for at least 24 hours, 
 
296 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 so that the final result is stated in the form of a certificate 
 appended to each coil of cable that it has been tested with 
 600 volts applied for one minute after 24 hours' soaking in 
 water. 
 
 In making a critical examination of a dielectric material 
 the cable or insulated wire must be supplied in coils of known 
 length, say, one-quarter or half-mile coils. The insulation 
 tests enable us then to state the results as so many megohms 
 per mile ,of cable. 
 
 It is to be noted that if, for instance, the test of 440 yards 
 of cable showed its dielectric to have an insulation resis- 
 tance of 4,000 megohms, then the insulation is at the rate of 
 1,000 megohms per mile. 
 
 Each coil of cable after testing should then have a certifi- 
 cate appended to it as follows : 
 
 Certificate of Insulation Test. 
 
 Length of this Coil yards or miles. 
 
 Gauge of Copper Wire .........S.W.G. 
 
 Natu re of Insulation . 
 
 Temperature of Coil when Tested 
 
 Insulation Resistance megohms 
 
 per mile at ..F. when tested 
 
 with volts after one minute's electrification 
 
 and hours' soaking in water. 
 
 Daie of test 
 
 Test made at Laboratory, by 
 
 For electric light wiring no wire should be employed which 
 has not thus been tested, and the certificates of each coil 
 of wire as used by the contractor should be demanded by 
 the clerk of works or consulting engineer. No wire should 
 be employed of less insulation than 300 megohms per mile 
 at 7oF. after 24 hours soaking in water, the test being made 
 with 600 volts and resistance taken after one minute. 
 
 In the case of dielectrics such as paper or jute impregnated 
 with oil or resins or various other dielectrics, which are not 
 in themselves waterproof, the cable must be covered with 
 a continuous sheath of lead in order to protect them. In 
 
MEASUREMENT OF ELECTRICAL RESISTANCE, 297 
 
 this case, also, a test in water is necessary in order to 
 ascertain whether the lead covering is perfect. 
 
 20. Measurement of Dielectric Resistance by Time of 
 Falling to Half Charge. A usual method of measuring the 
 insulation or dielectric resistance of a substance of very high 
 resistivity is to connect it between the earth arid a charged 
 conductor, which is otherwise perfectly insulated, and then 
 observe the time taken for the conductor to fall in potential 
 by a known fraction or, say, to half its value. 
 
 As a first simple approximation to a theory, assume that 
 .the capacity r of the perfectly insulated conductor is C, and 
 that it is charged to an initial potential V, and connected to 
 earth through a resistance, E, of large value. After a time, 
 t seconds, let the potential of the conductor be v, and after a 
 further small time, dt, let it be v dv ; then the time rate of 
 
 change of potential at that time is - -~. If the capacity of the 
 
 (JLt 
 
 conductor is C, the electric quantity in it at that instant is Cv, 
 and the time rate of change of the charge or quantity is 
 
 C^; hence, this also must be the rate of leakage or 
 
 current flow through the dielectric resistance. If K is this 
 resistance we have, if Ohm's law is obeyed, 
 
 v _ f <dv dv _ dt 
 
 iT dt' I 'V-~OK' 
 
 Hence, integrating each side of the equation, we obtain 
 
 where A is the constant of integration. If t = 0, then v = 
 where V is the initial voltage. 
 
 Hence log e - lo&V = - ^, 
 
 or 
 
298 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 If we use ordinary logarithms to the base 10, then we have 
 
 0-4343* 
 it = 
 
 where 04343 is the modulus or factor for converting 
 Napierian to ordinary logarithms. If T is the time in 
 seconds taken to fall to half potential, then V/ / z; = 2, and 
 Iog 10 2- 0-30103, and 
 
 p 04343T T _ 10T , 
 
 Cx 0-30103 "0-693C" 7C 
 
 Hence E is obtained as the quotient of a time by a capacity. 
 If C is measured in microfarads, then E will be measured or 
 given in megohms. 
 
 In the above proof two things are assumed : First 
 that the resistance strictly obeys Ohm's law, and, secondly, 
 that the capacity is constant and independent of the 
 voltage. In the case of actual dielectrics and condensers 
 neither of the above assumptions is strictly in accordance 
 with fact 
 
 In applying this method the difficulty is to find a voltmeter 
 or electrometer which is itself sufficiently well insulated. No 
 electrostatic voltmeter or electrometer is so absolutely insulated 
 that if charged and left to itself it will not lose charge, 
 neither is any condenser or body having capacity similarly 
 free from leakage. We may, however, proceed| in practice as 
 follows : A condenser or body having capacity is charged to a 
 known voltage and connected to the voltmeter. The arrange- 
 ment is then left insulated and the time of falling to half 
 charge or half potential is noted. Thus a Kelvin multicellular 
 electrostatic voltmeter, having its terminals closed by a half 
 microfarad condenser, may be placed on a sheet of ebonite 
 and charged, say, to 100 volts, and left insulated. We note 
 the time T (in seconds) taken by the voltmeter to fall to 
 50 volts. Then the internal leakage resistance E of the volt- 
 meter and condenser, taken together, can be calculated by the 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 299 
 
 10T 1 
 
 formula above given, viz., R=_ _, from which, if C = ^ 
 
 (microfarad), we find R = "^-T, where R is the insulation 
 
 resistance in megohms, T the time of falling to half charge in 
 seconds, and C the capacity in microfarads. 
 
 The insulator or dielectric whose insulation resistance is 
 required is then joined across the terminals of the voltmeter 
 and the experiment repeated. Let T' be the time in seconds 
 required then to fall to half charge. The combined insulation 
 resistance of the insulator and the voltmeter and condensev 
 
 9Q 
 
 is R' megohms when R' = ~^T'. If, then, R" is the resistance 
 
 / 
 
 per se of the substance tested, we must have ^+^7=^7;, 
 
 . It K lv 
 
 RR' 
 
 or ir=- =-7, for the total conductivity found in the second 
 
 jU-j-R 
 
 experiment must be the sum of the conductivities of the 
 body tested, and of the voltmeter and condenser taken 
 together. 
 
 The above method is only practicable and useful in those 
 cases in which the insulation resistance of the condenser and 
 voltmeter and body tested is so high that the time required in 
 any case for the charge of the system to fall to half its initial 
 value is a considerable number of seconds say 15 or 20 at 
 the very least. If the potential falls to half value in a, much 
 less time, the power of observing it accurately is much 
 diminished. 
 
 If, however, a highly insulated quadrant electrometer is 
 available, and an air condenser of considerable capacity, the 
 method may be used with success to determine the insulation 
 resistance of glass or porcelain telegraph insulators and long 
 lengths of highly insulated cable. The difficulty which 
 besets this method is that the internal leakage of the volt- 
 meter or condenser and other supports is due to films of dirt 
 or moisture. It is not certain (in fact, very doubtful) that 
 dirt or moisture films of this kind obey Ohm's law. The 
 
330 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 formula for calculating resistance by this leakage method 
 is worked out on the assumption that all the conductance 
 which takes place does so in accordance with Ohm's law 
 in other words, that the resistance is independent of the 
 voltage. This is not quite, the case for any dielectric, and 
 there is no proof that it is the case for surface films causing 
 leakage. The method, therefore, must be applied with care 
 and discrimination. 
 
 In estimating the insulating value of a dielectric it is 
 necessary to consider not only the mere insulation resistance, 
 but also the dielectric strength or voltage required to pierce 
 the insulation. This is an important matter in connection 
 with cables for high-pressure currents and porcelain insulators 
 for carrying bare high-pressure electric wires.* Any report 
 on the insulating po\ye,r of a cable or dielectric should 
 comprise the results of tests as to the average electro- 
 motive force required to pierce a known thickness of the 
 insulation. 
 
 21. Cardew's Differential Method for Measuring High 
 Resistance. This method consists in comparing together 
 the rate of leakage from the two quadrants of a quadrant 
 electrometer. The quadrants are connected respectively to the 
 
 two poles of a highly insulated battery of about 400 cells. 
 For this purpose the most convenient battery to use is a 
 form of small water battery devised by Lord Kelvin, con- 
 sisting of a large number of copper-zinc couples attached 
 to an ebonite slab, and so arranged that when dipped into 
 water the drop of liquid held by capillarity between adjacent 
 copper-zinc slips forms the exciting fluid of each couple. A 
 battery of about 500 couples of this form provides an 
 electromotive force sufficient for the test. 
 
 The terminals of the battery are connected to the two 
 quadrants of the electrometer, and the needle is connected 
 
 * See N. M. Hopkins on " Testing Insulators for High Pressure Overhead 
 Service," The Electrician, Vol. XXXVIII., p. 432. 
 
MEASUREMENT OP ELECTRICAL RESISTANCE. 301 
 
 to the .earth. The battery must be highly insulated by 
 placing it on paraffin blocks. If, then, the quadrants are 
 connected also to earth through two high resistances of equal 
 magnitude, the leakage from each, quadrant will be the same, 
 and the needle will remain at zero. If one of these resistances 
 is an adjustable one, the other may be determined in terms 
 of it. 
 
 In starting the test, the centre of the battery should be 
 earthed for one moment, which will bring the needle to zero. 
 As comparison resistances lengths of silk or string have been 
 found convenient. Thus, a white embroidery silk was found 
 to have a resistance of 250,000 megohms per inch, and a 
 green thread, partly silk, partly cotton, 10,000 megohms per 
 inch, an ordinary measuring tape 1,400 megohms per inch, 
 and a piece of wet tape 64,000 ohms per inch. These 
 materials, however, are all more or less hygroscopic. Prob- 
 ably better standards would be found by using capillary glass 
 tubes filled with liquids of definite composition, which do not 
 act upon glass. The method, however, is of great sensibility, 
 and useful for rapid qualitative comparisons of insulation 
 power. 
 
 22. The Practical Measurement of Electric Light Wiring 
 Insulation. The Ohmmeter. In measuring the insulation 
 resistance of the electric light wiring of a building, it is 
 now the custom to employ some form of Ohmmeter. The 
 principle of this instrument is as follows : Let there be 
 two coils. of wire, C, c, through one of which, C, flows a current 
 passing through a conductor, E, the resistance of which is to 
 be measured, and another coil, c, of high resistance connected to 
 the terminals of the conductor. Let these coils be placed 
 with their planes or axes at right angles, to each other.. 
 Then, in the case of each coil there will be a magnetic field 
 proportional at any point to the current flowing, through 
 it. Hence, at some common point in the field of the two COLS 
 (see Fig. 46), there will be two magnetic forces, one pro- . 
 
302 
 
 MEASUREMENT OF ELECTRICAL RESISTANCE 
 
 portioiial to the current through the conductor and one at 
 right angles to it proportional to the voltage fall down the 
 conductor. Hence the resultant magnetic force will have 
 a direction which depends upon the relative magnitude of the 
 components or their ratio to one another i.e., upon the ratio 
 of the potential fall down the conductor to the current 
 through it. In other words, the direction of this resultant 
 magnetic force will depend upon the resistance of the con- 
 ductor so connected to the coils. If, then, a small magnetic 
 needle, n s, or piece of soft iron is placed at that point, its 
 direction may be indicated on a scale, and the scale may 
 be graduated so as to show at a glance the resistance of 
 the conductor in ohms. 
 
 FIG. 46. Theory of the Ohmmeter. 
 
 In order to apply this principle to the measurement of 
 insulation resistances we require a source of high electro- 
 motive force. It is universally recognised that an insulation 
 test is entirely insufficient if made with an electromotive, force 
 loss than the working or circuit electromotive force. Hence, 
 if the electric light wiring of a building is put in for use at 
 200 volts the insulation resistance must be tested with 
 200 volts at least. 
 
 In a well-known form of ohmmeter by Evershed, the 
 electromotive force for testing is supplied by a small hand- 
 driven magneto machine, which provides the necessary 
 pressure, (see Fig. 47). One coil of the ohmmeter is connected 
 in series with the copper conductor of the insulated wire and 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 303 
 
 the armature of the magneto machine, the remaining terminal 
 of the generator being connected to a good earth by being 
 joined to gas or water pipes. When the handle of the magneto 
 machine is turned, a current at an electromotive force of 
 200 volts is operative on the dielectric of the insulated cable 
 and the series coil of the ohmmeter, and completes its circuit 
 through the earth. The other or volt coil of the ohmrneter 
 
 FIG. 47. Evershed's Ohmmeter. 
 
 has its ends connected respectively to the copper conductor 
 and the earth, or is a shunt across the series coil and magneto- 
 armature in series with that last coil. Hence, if the insula- 
 tion is perfect- when the magneto-machine handle is turned 
 at the proper speed no deflection of the needle of the 
 ohmmeter will be seen. If, however, the insulation is not 
 perfect, but if a current flows through the dielectric either 
 
304 
 
 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 uniformly or at some faulty place, the series coil has a current 
 in it and the ohmmeter needle deflects. The scale or dial of 
 the ohmmeter is divided so as to indicate directly in megohms 
 the insulation resistance. It is possible to make use of the 
 service pressure itself as a testing pressure in measuring 
 the insulation resistance of electric light wiring. This may 
 be done as follows*: 
 
 The portion of the circuit to be tested is separated from 
 the main circuit by removing the fuses. Let ABCD (see 
 Fig. 48) be the portion of the circuit to be tested, and let the 
 terminals J K be those of the dynamo or secondary battery 
 or street service which normally supplies the electric current. 
 
 w 
 
 Earth 
 
 FIG. 43. 
 
 Provide a milliampere meter or other sensitive calibrated 
 galvanometer and connect it in series with a resistance 
 between the terminals A and J. Then connect the terminal 
 K to earth through a lamp, W. The galvanometer or milli- 
 amperemeter will then show a current if there is leakage or 
 conductivity through the dielectric of the wiring system 
 ABCD, and if the galvanometer has been calibrated for 
 small currents the numerical value of this resistance may be 
 
 * The method here described is due to Dr. Oscar May. See The Electrician, 
 Vol. XXXVIII., p. 81 ; see also a critical letter, ibid., p. 128. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 305 
 
 determined knowing the voltage between the main GH and 
 the earth. 
 
 It is to be noted that the testing pressure we are really 
 here using is not the ordinary service pressure between the 
 terminals J and K, but the voltage between J and K when 
 this latter is connected to the earth through a lamp. Hence 
 the determination of this voltage must always be made at the 
 time by means of a voltmeter of sufficiently high resistance 
 (or say by an electrostatic voltmeter) not to disturb this 
 potential difference. The main GH should always be the 
 positive main, because the negative main on a public supply 
 service by continuous current is nearly always dead-earthed, 
 especially if bare copper strip carried on glass insulators 
 of certain descriptions is used as part of the distribution 
 system. 
 
 The method therefore must be applied with discrimination. 
 
 23. Insulation Rules for House Wiring. The various 
 electric lighting companies and insurance offices have 
 different regulations as to the minimum insulation resistance 
 which should be indicated on test under the working pressure 
 by electric light wiring. This is generally defined as so many 
 megohms per lamp. If, then, there are n incandescent lamps 
 (reckoned, say, in 8 c.p. lamps or their equivalent) in the 
 building, the total insulation resistance between the copper 
 conductors and the earth must not be less than this limiting 
 number divided by n. It is generally specified that these 
 tests shall be carried out with a voltage equal to double the 
 working voltage and the reading taken after not less than 
 one minute's application of the E.M.F., all lamps being in 
 and switches on. Thus, for instance, the limiting values 
 for various electric lighting corporations and fire insurance 
 companies are as follows : 
 
 For some calculations dealing with problems on the measurement of 
 insulation resistance and leakage currents from insulated conductors, and 
 especially in connection with 3- wire systems, the reader is referred to a paper 
 by Mr. A. Russell in The Electrician, Vol. XLL, p. 206 ; also Vol. XXXIV., p.7. 
 
306 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 Minimum Insulation Resistances allowed per Lamp in Installa 
 tions of Incandescent Lamps* by various Authorities. 
 
 Lightng 
 
 Glasgow Corporation ............ 60 
 
 Manchester ........................ 50 
 
 Scarborough Electric Lighting ) ^ 
 
 Company ........................ j 
 
 Brighton Corporation ............ 20 
 
 Liverpool Corporation, Phoenix ( 19 .- 
 
 Fire Office, Lloyds ............ j 
 
 Bradford Corporation ............ 10 
 
 The lead ing Insurance Companies, 
 including Guardian, Sun, North 
 British, London, Liverpool and 
 Globe, Alliance, London As- 
 surance, Royal Exchange and 
 
 others. 
 
 Leakage not to exceed 
 of total 
 
 current. = 6 megohms 
 per lamp for 100- 
 volt 8 c.p. lamps. 
 
 Institution of Electrical Engi- ) 10 megohms per ampere 
 neers latest regulations j of maximum use. 
 
 2$. Measurement of the Resistance of Liquids. 
 
 As all liquids which conduct at all do so in virtue of 
 electrolysis, special difficulties are introduced into the 
 resistance measurement of liquids by the counter electro- 
 motive force of polarisation due to the ions liberated on 
 the electrodes. The possibility, therefore, of obtaining 
 accurate information as to the resistance of a column of 
 an electrolyte depends upon the completeness with which 
 these disturbing effects of electrolysis can be eliminated. 
 One obvious method is to employ an alternating electromotive 
 force, so that in the column of liquid there is no unilateral 
 flow of electric quantity, but the electrolytic effects due to a 
 current for one moment in one direction may be annulled by 
 an equal current in the opposite direction the next instant. 
 
 * For a chart showing the regulations for insulation resistance of electric 
 light wiring enforced by various authorities see The Electrician, Vol. XXXII., 
 p. 265, 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 307 
 
 A plan due to F. Kohlrausch is to employ with an ordinary 
 Wheatstone's bridge a small induction coil instead of a 
 simple battery, and in place of the galvanometer to use a 
 telephone. The secondary currents from the induction coil, 
 which are created at each make-and-break of the primary 
 circuit, are equal in total quantity i.e., the time integrals 
 of the two secondary currents are equal. Hence, on the 
 whole, polarisation is absent. 
 
 The liquid resistance to be measured may be contained 
 in a vessel of any suitable shape forming an electrolytic cell, 
 
 ''-:::"-:^~":^;H;^ : - |. : -- ;; : ::::: : . . -..:.,,- 
 
 FIG. 49. Kohlrausch's Bridge for Liquid Resistance Measurement. 
 
 the cell having two electrodes by which it is connected with 
 the bridge circuits. These electrodes are formed of sheet 
 platinum, which should be covered with a deposit of 
 platinum black (sie below). In Fig. 49 are shown diagrams 
 of the usual arrangements. The bridge is a simple slide 
 wire bridge, and the induction coil is set in operation by a 
 few dry cells. 
 
 After connecting the electrolytic cell to the proper 
 terminals of the bridge, and setting the induction coil in 
 
 x2 
 
308 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 action, the slider is moved until no sound is heard in the 
 telephone. As this point of silence is not sharply marked, 
 but reached by slow gradations of sound, the observer will, 
 unless he possesses very sharp hearing, have some difficulty 
 in deciding exactly the point of balance. The method, in 
 fact, tests the acuteness of the observer's hearing as much as 
 it tests the resistance of the electrolytic cell. The ability to 
 distinguish an exact position of the bridge slider correspond- 
 ing to silence in the telephone depends also upon the nature 
 of the electrodes used in the electrolytic cell. If these are of 
 bright sheet platinum they must be much larger in area than 
 if covered with a deposit of platinum black. This is due to 
 the deposit on them of the products of electrolytic decomposi- 
 tion and is called the " polarisation of the electrodes." This 
 polarisation creates a counter electromotive force in the 
 circuit. It is not altogether absent even when alternating 
 currents are employed, and in this last case it operates to 
 produce an effect as if the inductance of the circuit in which 
 it exists had been increased. The point of balance on the 
 bridge when so used is often affected by the capacity and 
 inductances of the four arms of the bridge arrangement. 
 
 The platinizing of platinum electrodes with platinum black 
 is best done with the platinizing solution employed by 
 Lummer and Karlbaum for their bolometer strips, and the 
 same solution is very useful for coating platinum electrodes 
 for use in electrolytic cells. It consists of 1 part of PtCl 4 to 
 0-008 of lead acetate and 30 of water. 
 
 The solution is used as an electrolyte in an electrolytic cell 
 with platinum electrodes, the cathode or negative plate being 
 the one on which a deposit of platinum black is required. 
 The electrolysing current must be adjusted until on the 
 chemically-clean platinum cathode is deposited an adherent 
 dull platinum black deposit. To ensure wetting the electrode 
 so prepared with water they should be treated first with a 
 drop of alcohol. A thick deposit of platinum black should 
 be secured, Platinum electrodes covered with this dull 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 309 
 
 black deposit of platinum black are less easily polarisable 
 than ordinary sheet platinum and hence give better defined 
 readings when used with a telephone induction coil and 
 bridge. 
 
 If ordinary bright sheet platinum is used for electrodes, 
 these are easily polarised or covered with a deposit of 
 liberated gaseous ions, and these polarisation films, as they 
 are called, are strongly adherent to the platinum and create 
 between the electrodes a potential difference which forms a 
 counter electromotive force. Since the counter electromotive 
 force cannot exceed 2 volts to 2'5 volts, its presence is most felt 
 at or near the balancing point of the bridge, and it operates to 
 prevent the development of a sharp or well-defined condition 
 of silence in the telephone in this bridge circuit. If the 
 electrodes are covered with a deposit of platinum black they 
 are less polarisable, and hence better defined bridge readings 
 can be obtained.* 
 
 A method due to Messrs. Stroud and Hendersonf is, in 
 many respects, more satisfactory than the use of a bridge with 
 telephone and induction coil. Their method depends upon 
 inserting in the two arms of a bridge two glass tubes, T 1 , T 2 , 
 of different lengths, having terminal cups of the same size. 
 These tubes are filled with the electrolyte the resistance of 
 which is to be measured. In the terminal cups are placed 
 cylinders of sheet platinum covered with a deposit ot 
 platinum black. The two tubes form, therefore, electrolytic 
 cells identical in every way except in that one contains a 
 longer column of liquid than the other. The dimensions of 
 this column of liquid are easily obtained by measuring the 
 length and mean inner diameter of the glass tubes. These 
 electrolytic cells are arranged as the two arms of a bridge, 
 
 * See F. Kohlrausch, Annals Phys. Chew., 60, 2, pp. 315-322, 1897 ; or Science 
 Abstracts, Vol. I., p. 338. 
 
 t " On a Satisfactory Method of Measuring the Resistance of Electrolytes 
 by Continuous Currents." By Prof. W. Stroud and J. B. Henderson. Tke 
 Electrician, Vol. XXXVIIL, p. 49 ; also Proc. Phys. Soc. Lond., Vol. XV., 
 p. 13, Oct. 30, 1896, 
 
3iO MEASUREMENT OP ELECTRICAL RESISTANCE. 
 
 the shorter tube being in series with a resistance box, II (see 
 Fig. 50). The two other arms of the bridge are made up with 
 high metallic resistances, P and Q, of about 20,000 ohms each. 
 The galvanometer used must be a sensitive galvanometer of 
 high resistance, say 1,000 ohms or more. The battery, 1>, 
 should consist of a number of cells giving an electromotive 
 force of at least about 30 volts. It can conveniently consist 
 of 20 dry cells in series. 
 
 The measuring operation consists in altering the resistance 
 II until the galvanometer shows no current. When this is 
 the case, the resistance of E must be identical with that 
 
 FIG. 50. Stroud and Henderson's Bridge Arrangement for Liquid 
 Resistance Measurement. 
 
 of a column of the electrolyte equal to the difference in 
 length between the two columns forming the two cells. Since 
 the electromotive forces of polarisation are equal, and since 
 the two columns of liquid are traversed by equal currents, the 
 effects of electrolysis in the two arms of the bridges exactly 
 neutralize each other. If then the two tubes are of the same 
 diameter and graduated in centimetres along their lengths, we 
 can at once deduce the resistance of a column of the liquid of 
 known length and section, and hence determine its volume- 
 resistivity. 
 
OF ELECTRICAL RESISTANCE. 
 
 A modification of this method, due to Fitzpatrick (see 
 Brit. Assoc. Report, 1886, p. 328), which has been constantly 
 in use at the Cavendish Laboratory, Cambridge, overcomes all 
 difficulties due to polarization. It consists in employing a 
 revolving current-reverser, driven by a small water motor, 
 which rapidly reverses the direction of the battery current 
 flowing through the bridge. The direction of connection of 
 the galvanometer is reversed about the same time, but not quite 
 at the same instant, the galvanometer circuit being closed a 
 little later than the battery circuit and opened a little earlier. 
 If the galvanometer needle is made heavy, so as to have a 
 long period of vibration, these continual reversals do not 
 affect its steadiness, but the result is to eliminate altogether 
 effects due to polarization, and to make it quite as easy 
 to measure an electrolytic resistance as to measure a metallic 
 conductor. The reverser consists of a drum on which are 
 fixed brass sectors with wire brushes touching them. The 
 drum resembles a dynamo commutator, only alternate 
 segments are connected to metallic bands at each end. The 
 segments which belong to the galvanometer circuit are 
 rather less wide than those which belong to the battery 
 circuit. 
 
 In measuring the absolute value of the resistivity of an 
 electrolyte it is usual to place it in a glass containing vessel 
 or tube having platinised platinum electrodes. Once for all a 
 careful measurement is made of the resistivity of some pure 
 electrolyte, such as potassic chloride, of known concentration. 
 This is done in a rectangular or tubular vessel of such shape 
 that the dimensions of the mass of liquid and the distribution 
 of current through it are known. Afterwards any other 
 electrolyte can have its resistivity determined by being placed 
 in a cell of any form and the ratio of the resistances 
 determined when the cell is first filled with the standard 
 electrolyte and then with the electrolyte under test. 
 
 It is not unusual to express the conductivity of elec- 
 trolytes in terms of a fraction (say 10"" 8 ) of that of mercury, 
 
312 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 For many purposes, however, it is better to express it in 
 ohms or megohms per centimetre-cube. 
 
 In the tables on pp. 327, 329 are given the values of the 
 volume-resistivity of electrolytes of various kinds. The 
 aqueous solutions of the acids and many aqueous solutions of 
 salts or hydrates have a minimum resistivity corresponding to 
 a certain dilution or concentration. The temperature of the 
 electrolyte very greatly affects its conductivity. It will be 
 seen from the tables that the temperature coefficient of an 
 electrolyte is generally about three to four times greater 
 tnan that of a pure metal. 
 
 25. The Absolute Measurement of Electrical Resist- 
 ance. The determination of the value of an electrical 
 resistance in absolute measure, or its direct recovery in terms 
 of the units of length and time, is an operation not likely to 
 be conducted in an ordinary electrical testing laboratory. 
 Space cannot here be granted to review in detail all the 
 various processes which have been suggested. The student 
 desirous for information on this question may be referred for 
 full information to the following advanced treatises on 
 electricity and magnetism : 
 CLERK MAXWELL. "Treatise on Electricity and Magnetism." 
 
 Vol. II., Chap. XVIII., 2nd Ed. 
 E. MASCART and J. JOUBERT. "Electricity and Magnetism." 
 
 Translated by E. Atkinson. Vol. II., Chap. VII. 
 A. GRAY. " Absolute Measurements in Electricity and Magne- 
 tism." Vol. II., Part II., Chap. X., p. 538. 
 G. WIEDEMANN. Electricitdt, Vol. IV., p. 910. 
 
 The various methods used for the absolute measurement of 
 resistance have also been critically discussed by Lord Kayleigh, 
 Phil. Mag., Vol. XIV., 1882, and by Mr. E. J. Glazebrook, 
 B.A. Report, 1890. See also The Electrician, Vol. XXV., p. 544. 
 
 Amongst the processes there described for the absolute 
 determination of an electrical resistance is one due to 
 Lorenz which, from its simplicity, has been made the 
 starting point for the construction of an apparatus by 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 313 
 
 Prof. J. V. Jones which is likely soon to be found in the 
 possession of every well-equipped electro- physical laboratory. 
 This apparatus enables an observer to re-determine for him- 
 self in absolute measure the value of a low resistance, and 
 that with not greater expenditure of time than would be 
 incurred in making a mere comparison experiment. 
 
 The general theory of the Lorenz method of determining 
 a resistance in absolute measure may thus be described : 
 If a metallic disc is caused to rotate in the mean plane 
 of a coil concentric and co-axial with the disc, and if a 
 current passes through the coil, an electromotive force is 
 created in the disc. If brushes touch the centre and 
 circumference of the disc, and if from these connections are 
 led away to make contact with two points on the circuit, 
 which includes the coil, then it is possible to so adjust the 
 resistance between these contact places that no current flows 
 through the disc in other words, the electromotive force set 
 up in the disc may be made to exactly balance the potential 
 fall down the resistance in series with the coil. If, then, E 
 is the resistance of this conductor and C the current through 
 it and the coil, and if M is the co-efficient of mutual 
 inductance between the coil and the disc, and n the speed 
 of revolution, the electromotive force set up in the disc is 
 equal to MCw, and the fall of potential down the conductor 
 is EC. Hence, when there is equilibrium, MO/i = EC, or 
 E = M?i. The measurement of the resistance is therefore 
 reduced to the calculation of a co-efficient of inductance from 
 the measured dimensions of the coil and the disc and the 
 observation of a speed of revolution. 
 
 In Fig. 51 the points and M are the centre and circum- 
 ference of the disc, and XY is the resistance of which the 
 absolute value is to be determined. The real apparatus as 
 designed by Prof. J. Y. Jones* is represented in Fig. 52. 
 
 * For a full description of the theory and practice of the method the reader 
 is referred to Papers by Prof. J. V. Jones in The Electrician of 1890 and 1895 
 Vol. XXV., p. 552, and Vol. XXXV., pp. 231 and 253. 
 
314 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 The metallic disc is driven at a uniform speed by an electric 
 motor. Contact is made against the centre and circum- 
 
 FIG. 51. 
 
 FIG. 52. The Jones-Lorenz Apparatus for Absolute Resistance 
 Determinations. 
 
 t'erence of the disc by brushes, and these are connected 
 through a galvanometer with the ends of the resistance 
 
MEASUREMENT Otf ELECTRICAL RESISTANCE. 3 15 
 
 being measured. The axis carrying the disc carries also a 
 speed indicator, which is preferably an arrangement for 
 making an electric contact every revolution of the disc. 
 This is made to print dots on a fast-running paper tape on 
 which also series of parallel dots are printed by a standard 
 clock. The speed of the disc can then be accurately determined. 
 The coil consists of a wire wound specially in grooves in 
 a marble ring, on the outer edge of which is cut a screw- 
 groove. The calculation of the mutual inductance of the 
 coil and disc once effected becomes a constant of the 
 instrument. 
 
 For the details of the machines already designed and made 
 under the direction of Prof. J. V. Jones the reader is referred 
 to the following Papers by Prof. Jones : " Suggestions 
 towards the Determination of the Ohm in Absolute Measure," 
 a Paper read before the British Association at Leeds in 
 1890. (See also The Electrician, Vol. XXV., p. 552.) 
 
 In this Paper the details of the theory are set out. Reference is also made 
 to a Paper, by the same author, read before the Physical Society in 1888, 
 (see Phil. Mag., Jan., 1889), in which the theory of the calculation of -the 
 mutual inductance of a disc and co-axial coil of single layer is given. 
 
 Also, by the same author, a Lecture on this subject was 
 given at the Eoyal Institution, London, in May, 1895, entitled 
 " The Absolute Measurement of Electrical Resistance." (See 
 The Electrician, Vol. XXXV., p. 231.) 
 
 In this Lecture the details of an improved Lorenz apparatus are described. 
 
 A well-constructed Lorenz apparatus was made for the 
 McGill University, Montreal, and a description of the design 
 will be found hi The Electrician, Vol. XXXVIL, p. 267, as 
 well as a perspective view of the machine (see Fig. 53), A 
 careful determination of the absolute value of the Board of 
 Trade standard ohm was made by Profs. Ayrton arid Jones in 
 1897, with the above described Montreal Lorentz apparatus 
 and the results of these experiments are recorded in The 
 Electrician, Vol. XL,, pp. 149-150 (see also Science Abstracts 
 Vol. 1., p. 24). 
 
316 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 317 
 
 A Paper by Prof. Ayrton in The Electrician, Vol. XL., 
 p, 149, entitled " Our Knowledge of the Value of a Kesistance," 
 gives the facts on which are founded the opinion that the 
 Board of Trade standard ohm, which is intended to represent 
 as nearly as possible the International ohm, or a resistance of 
 106*3cms. of mercury 1 sq. mm. in section at 0C., may in fact be 
 equal to 106'33cms. or may be in error by three or four parts 
 in 10,000. Hence we cannot say that this official standard 
 ohm really represents 10 9 absolute C.G.S. units of resistance 
 with a greater accuracy than three or four parts in 10,000 or 
 0*03 per cent. The mean of nine absolute determinations of 
 the value of the Board of Trade wire standard ohm showed 
 that its real value is, in all probability, 1-00026 true ohms 
 the true ohm being 10 9 absolute C.G.S. units. 
 
 The reader desirous of information on the relative value of 
 the experimental methods which have been adopted for the 
 absolute determination of resistance and the absolute measure- 
 ment of the resistivity of mercury may be referred to two 
 important reports made by Mr. E. T. Glazebrook on behalf of 
 the Electrical Standards Committee of the British Association 
 (see Brit. Assoc. Pteports, 1890 (Leeds) and 1892 (Edinburgh); 
 also The Electrician, Vol. XXV., pp. 543 and 588, and Vol. 
 XXIX., p. 462). 
 
 Values which have been obtained by various observers for 
 the ohm in terms of the dimensions of a column of pure 
 mercury at 0C. are given in Table XV. following (p. 335). 
 
 26. Resistance of Conductors to Alternating Currents. 
 
 If a metallic conductor, in the form of a wire or rod, is 
 traversed by an alternating electric current, it is well known 
 that the current does not distribute itself uniformly over the 
 cross-section of the conductor, but concentrates itself more 
 or less at the surface. The result is to make the effective 
 resistance of the conductor greater for alternating currents 
 than for continuous, because the periodic current, so to speak, 
 makes less use of the conductor- Hence we need a correction 
 
318 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 which must be applied to the true or ohmic resistance in cal- 
 culating the resistance of a conductor to alternating currents. 
 Assuming the currents to be simply periodic and the conduc- 
 tor a round metallic rod, Lord Rayleigh in 1886 gave a 
 formula for calculating the resistance to alternating currents.* 
 Another formula and method was given by Lord Kelvin in 
 1889, f and he gave a table calculated for conductors of round 
 section of certain diameters, and for certain frequencies. 
 
 The above formulae are, however, in a form which does 
 not render them very convenient for laboratory calculation. 
 M. E. Hospitalier has, however, reduced Lord Kelvin's 
 formula to a very convenient table. 
 
 If we denote the resistance to alternating currents by R A and 
 that to continuous currents by II , then for round-sectioned 
 rods as wires the two quantities are related by the general 
 expression p _;,p 
 
 k being a numerical constant which depends upon the 
 frequency n and on the diameter d. 
 
 In the case of wires made of the same metal but of 
 different diameters k has the same value for equal values 
 of the product nd 2 . Hence we can make a table showing 
 the values of k corresponding to various values of nd 2 . 
 M. E. Hospitalier, assisted by M. A. Potier, has calculated 
 the following table, which is correct for copper having a 
 resistivity of 1,597 C.G.S. units.* 
 
 nd\ k 
 
 1-0000 
 
 20 1-0000 
 
 80 1-0001 
 
 180 1-0258 
 
 320 1-0805 
 
 500 1-1747 
 
 720 1-3180 
 
 980 1-4920 
 
 1,280 1-6778 
 
 1,620 T8628 
 
 2,000 2-0430 
 
 2,420 2-2190 
 
 2,830 2-3937 
 
 5,120 3-0956 
 
 8,000 3-7940 
 
 18,000 5-5732 
 
 22,000 7-3250 
 
 * Phil. Mag., May, 1886. See also " The Alternate Current Transformer," 
 Fleming, Vol. I., third edition, p. 294. 
 
 t Presidential address to the Institution of Electrical Engineers, 1889. 
 
 t See The Electrician, Vol. XXXII., p. 277, >r L' Industrie Electrize, 1893, 
 p. 563. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 319 
 
 As an example of its use, let us apply it to the following 
 problem : 
 
 What will be the resistance to alternating currents having 
 a frequency of 80, of a round-sectioned copper rod 2cms. in 
 diameter. Here d = 2, n = 80 ; hence nd* = 80x4 = 320. 
 
 From the above table we see that, corresponding to nd 2 = 320, 
 /j = 1*0805. Hence, if the ohmic resistance of the rod is, say, 
 3 ohms, then its resistance to the above periodic currents 
 is 3*2415 ohms. If the exact value of the product ?icf 2 
 required is not in the above table, it can be obtained by 
 interpolation or by setting out the figures in a curve. In 
 Table XVI., at the end of this chapter, are given the values 
 of the ohmic and alternating resistance for stranded copper 
 cables for a frequency of 100. For other non-magnetic metals 
 besides copper the table in the text (p. 318) may be made 
 available by employing a factor to find k equal to the values 
 for copper of nd* multiplied by 1,597/p, where p is the resis- 
 tivity in C.G.S. units. 
 
 Hence, for a round metal rod of diameter d, and made of 
 a material having double the specific resistance of copper, 
 in order to find its resistance to alternating currents of a 
 frequency n, we should have to find the value of k in the 
 
 above table corresponding to a value - , and not simply 
 
 nd 2 , as for copper. Accordingly, the higher the resistivity of 
 the material the less different is the alternating from the 
 continuous current resistance. 
 
( .320 ) 
 TABLE I Atomic Weights and Densities of Metals. 
 
 The quotient of density multiplied by 1,000 by atomic weight gives a number 
 called the atomic density, and is proportional to the number of atoms per 
 centimetre-cube. 
 
 Metal. 
 
 1 
 
 Atomic 
 
 weights. 
 a. 
 
 Density. 
 Water =1. 
 
 Atomic 
 density 
 
 Atomic 
 volume 
 
 
 1 
 
 H = l 
 
 = 16 
 
 d. 
 
 Xd/a. 
 
 = a{d. 
 
 Lithium 
 Beryllium ... 
 Sodium 
 
 Li 
 Be 
 
 Na 
 
 7 
 9-1 
 23 
 
 7 
 9-0 
 23-05 
 
 0-589- 0-598 
 1-85 
 0-974 
 
 85 
 203 
 42 
 
 11-8 
 4-86 
 23-6 
 
 Magnesium . . 
 Aluminium . . 
 Potassium ... 
 Calcium 
 
 Mg 
 Al 
 K 
 Ca 
 
 23-9 
 27-0 
 39-0 
 39-9 
 
 24-3 
 27 
 39-11 
 40 
 
 1-743 
 2-56 - 2-583 
 0-875 
 1-566- 1-584 
 
 73 
 95 
 22-5 
 39-5 
 
 13-76 
 10-56 
 44-96 
 
 25-28 
 
 Titanium . . . 
 Chromium . . . 
 Manganese. . . 
 Iron .... 
 
 Ti 
 Cr 
 Mn 
 Fe 
 
 48-0 
 52-0 
 54-8 
 55-9 
 
 48 
 52-1 
 55-1 
 56-0 
 
 6-8 ' 
 7-33 
 7-8 - 8-1 
 
 130 
 134 
 142 
 
 7-0 
 7-0 
 7-1 
 
 Nickel 
 
 Ni 
 
 58-7 
 
 58-7 
 
 8-3 - 9-0 
 
 148 
 
 6-94 
 
 Cobalt 
 
 Ho 
 
 59-4 
 
 59-5 
 
 8-5 - 8-9 
 
 148 
 
 6-94 
 
 Copper . 
 
 On 
 
 63-2 
 
 63-6 
 
 8-9 - 8-95 
 
 141 
 
 7-10 
 
 Zinc 
 
 fin 
 
 64-9 
 
 65-3 
 
 6-9 - 7-2 
 
 108 
 
 9-12 
 
 Arsenic 
 Rubidium ... 
 Strontium ... 
 Molybdenum 
 Ruthenium... 
 Ehodium . . . 
 Palladium ... 
 Silver 
 
 As 
 Rb 
 Sr 
 Mo 
 Ru 
 Rh 
 Pd 
 Ap 
 
 74-9 
 85-2 
 87-3 
 95-7 
 101-4 
 1027 
 106-2 
 107-6 
 
 75 
 
 85-5 
 87-66 
 
 103 
 106-5 
 107-92 
 
 2-54'" 
 8-6 
 110 -11-4 
 11-0 -11-2 
 11-3 -12-1 
 10-4 -10-57 
 
 29 
 89-5 
 110-5 
 108 
 110 
 97-5 
 
 12-96(?) 
 56-1 (?) 
 34-56 
 11-13 
 9-05 
 9-12 
 9-12 
 10-04 
 
 Cadmium . . . 
 Indium 
 Tin 
 
 Cd 
 In 
 
 Sn 
 
 111-7 
 113-4 
 117-3 
 
 112 
 113-7 
 119 
 
 8-54- 8-66 
 7-2 - 7-4 
 7-3 
 
 77 
 64 
 62 
 
 12-96 
 15-53 
 16-20 
 
 Antimony ... 
 CaBsium 
 
 Sb 
 
 Cs 
 
 119-6 
 132-7 
 
 120 
 132-9 
 
 6-72 
 
 1-88 
 
 56 
 14 
 
 18-16 
 70-5 
 
 Barium 
 Cerium 
 
 Ba 
 O 
 
 136-4 
 139-9 
 
 137-4 
 140-2 
 
 4-0 
 6-73 
 
 29 
 47-5 
 
 34-25 
 20'8 
 
 Tungsten . . . 
 Osmium 
 Iridium 
 
 W 
 Os 
 Tr 
 
 183-6 
 190-3 
 192-5 
 
 193-1 
 
 19-261 
 22-43 
 22-4 
 
 105 
 117 
 116 
 
 9-53 
 8-49 
 8-6 
 
 Platinum ... 
 Gold 
 
 Pt 
 
 An 
 
 194-3 
 196-8 
 
 195 
 197-3 
 
 20-3 -22-1 
 19-3 -19-5 
 
 106 
 98 
 
 9-12 
 10-04 
 
 Mercury 
 
 HP 
 
 199-8 
 
 200 
 
 13-596 
 
 68 
 
 14-56 
 
 Thallium ... 
 Lead 
 
 Tl 
 Ph 
 
 203-7 
 206-4 
 
 204 
 20695 
 
 11-8 
 11-3 -11-4 
 
 58 
 55 
 
 17-20 
 
 18-24 
 
 Bismuth 
 Thorium . . . 
 Uranium . . . 
 
 Bi 
 Th 
 U 
 
 208-0 
 232-0 
 239-8 
 
 208 
 232-6 
 
 9-8 - 9-9 
 10-97-11-23 
 18-4 
 
 47 
 
 48 
 
 77 
 
 21-34 
 20-84 
 13-03 
 
 The atomic weights under column (0 = 16) are the numbers published by 
 the American Chemical Society's committee on atomic weights (Journal 
 American Chemical Society, Vol. XVII.), revised to January, 1894. 
 
 The atomic weights under column (H = l) are those given by Professor 
 T. E. Thorp ("Manual of Inorganic Chemistry," Vol. I.). 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 321 
 
 TABLE II. 
 
 Electrical Mass-resistivity of Various Metals at 0C., or Re- 
 sistance per Metre-gramme in Standard Ohms at 0C. 
 (Matthiessen.) 
 
 Metal. 
 
 Resistance at 0C. (in 
 Standard Ohms) of a 
 wire one metre long 
 and weighing one 
 gramme. 
 
 Approximate 
 temperature co- 
 efficient near 
 20C. 
 
 Silver (annealed) 
 
 0-1523 
 0-1657 
 0-1421 
 0-1449 (Matt 
 0-4025 
 0-4094 
 0-0757 
 0-4013 
 1-9337 
 0-765 
 1-058 
 0-9618 
 2-2268 
 2-3787 
 12-8554 
 12-885 
 
 0-00377 
 
 0-00388 
 hiessen's Standard) 
 0-00365 
 
 0-00365 
 0-00387 
 0-00389 
 0-00354 
 0-00072 
 
 Silver (hard drawn) 
 Copper (annealed) 
 
 Copper (hard drawn) 
 Gold (annealed) 
 
 Gold (hard drawn) .. . 
 
 Aluminium (annealed) ... 
 Zinc (pressed) 
 
 Platinum (annealed) 
 Iron (annealed) 
 
 Xickel (annealed) 
 
 Tin (pressed) 
 
 Lead (pressed) 
 
 Antimony (pressed) 
 Bismuth (pressed) 
 
 Mercury (liquid)* 
 
 
 * Matthiessen's value (12'885) for the electrical mass-resistivity of liquid 
 mercury is too high by nearly 1 per cent. The value now accepted is 
 12*789 international standard ohms per metre-gramme at 0C. The values 
 for nickel and bismuth are also much higher than are obtainable now with 
 pure electrolytic metals. The temperature coefficients given by Matthiessen 
 are also, in all cases, smaller than those now adopted for pure metals. 
 
322 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 TABLE III. 
 
 Electrical Volume-resistivity of Various Metals at 0C., or 
 Resistance per Centimetre-cube in C.G.S. Units at 0C. 
 
 This Table is calculated from the results of experiments made by 
 Matthiessen, employing the values given by Jenkin in his Cantor Lectures 
 (Society of Arts, 1866) for the resistance in B.A. units of a uniform circular- 
 sectioned wire of the metal 1 metre long and 1 mm. in diameter taken at 0C. 
 The figures given by Jenkin have been reduced to standard ohms and C.G.S. 
 units by multiplying by - x 0'9S66 x 10 5 =77,485. 
 
 Metal. 
 
 Volume Resistivity 
 at 0C. in C.G.S. Units. 
 
 Silver (annealed) 
 
 Silver (hard drawn) . . 
 
 Copper (annealed) 
 
 Copper (hard drawn) . . 
 
 Gold (annealed) 
 
 Gold (hard drawn) 
 
 Aluminium (annealed) 
 
 Zinc (pressed) 
 
 Platinum (annealed) .. 
 
 Iron (annealed) 
 
 Nickel (annealed) 
 
 Tin (pressed) 
 
 Lead (pressed) 
 
 Antimony (pressed) 
 
 Bismuth (pressed) 
 
 Mercury (liquid) 
 
 1,502 
 
 1,629 
 
 1,594 
 
 1,630* 
 
 2,052 
 
 2,090 
 
 3,006 
 
 5,621 
 
 9,035 
 
 10,568 
 
 12,429! 
 
 13,178 
 
 19,580 
 
 35,418 
 
 130,872 
 
 94,896t 
 
 * The value (1,630) here given for hard drawn copper is about one-quarter 
 per cent, higher than the value now adopted, viz. : (1,626). The difference Is 
 due to the fact that either Jenkin or M atthiessen did not employ precisely the 
 same values as at present employed for the density of hard-drawn and annealed 
 copper in calculating the volume-resistivities from the mass-resistivities. 
 
 t Matthiessen's value for nickel is much greater than that obtained by the 
 Author, as shown in Table IV. 
 
 t Matthiessen's value for mercury is nearly 1 per cent, larger than the value 
 now adopted as the mean of the best results, viz. : 94,070. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 323 
 
 TABLE IV. 
 
 Electrical Volume-resistivity of Various Pure Metals at 0C., 
 or Resistance per Centimetre-cube at 00. in C.G.S. Units. 
 
 (Fleming and Dewar, Phil. Mag., September, 1893.) 
 
 Metal. 
 
 Resistance at 
 0C. per centi- 
 metre-cube in 
 C.G.S. Units. 
 
 Mean tempera- 
 ture coefficient 
 between 0C. 
 and 100C. 
 
 Silver (electrolytic and well) 
 annealed)* j 
 
 1,468 
 
 0-00400 ' 
 
 Copper (electrolytic and well) 
 annealed)* j 
 
 1,561 
 
 0-00428 
 
 Gold (annealed) 
 
 2,197 
 
 0-00377 
 
 Aluminium (annealed) 
 
 2,665 
 
 0-00435 ^ 
 
 Magnesium (pressed) 
 
 4,355 
 
 0-00381 
 
 Zinc 
 
 5,751 
 
 0-00406 
 
 Nickel (electrolytic)* 
 
 6,935 
 
 0-00618 
 
 Iron (annealed) 
 
 9,065 
 
 0-00625 
 
 Cadmium 
 
 10,023 
 
 0-00419 
 
 Palladium 
 
 10,219 
 
 0-00354 
 
 Platinum (annealed) 
 
 10,917 
 
 0-003669 
 
 Tin (pressed) 
 
 13,048 
 
 0-00440 
 
 Thallium (pressed) ... 
 
 17,633 
 
 0-00398 
 
 Lead (pressed) 
 
 20,380 
 
 0-00411 
 
 Bismuth (electrolytic)f 
 
 110,000 
 
 0-00433 
 
 Mercury (Pure) 
 
 94 070 
 
 0-00098 
 
 
 
 
 * The samples of silver, copper and nickel employed for these tests were 
 prepared electrolytically by Mr. J. W. Swan, F.R.S., and were exceedingly 
 pure and soft. The value for volume-resistivity of nickel as given in the 
 above table (from experiments by J. A. Fleming) is much less (by nearly 
 40 per cent.) than the value given by Matthiessen's researches. 
 
 t The electrolytic bismuth here used was prepared by Messrs. Hartmann 
 and Braun, and the resistivity taken by J. A. Fleming. The value is nearly 
 20 per cent, less than that given by Matthiessen. 
 
 Y2 
 
324 
 
 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 TABLE V. 
 
 Electrical Volume-resistivity of Pure Metals at Various 
 
 Temperatures. 
 (From experiments by Fleming and Dewar.) 
 
 Tempera- Specific Resistance in C.G.S. Units. 
 
 ture 
 
 
 
 (Centi- 
 grade). 
 
 Silver. 
 
 Copper. 
 
 Gold. 
 
 Alu- 
 minium. 
 
 Mag- 
 nesium. 
 
 Zinc. 
 
 Nickel. 
 
 - 150C. 
 
 580 
 
 515 
 
 960 
 
 900 
 
 1,625 
 
 2,270 
 
 2,400 
 
 - 100C. 
 
 890 
 
 860 
 
 1,360 1,485 
 
 2,585 
 
 3,430 3,645 
 
 - 50C. 
 
 1,195 
 
 1,210 
 
 1,770 
 
 2,075 
 
 3,485 
 
 4,585 
 
 5,130 
 
 0C. 
 
 1,468 
 
 1,561 
 
 2,197 
 
 2,665 
 
 4,355 
 
 5,751 
 
 6,935 
 
 + 50C. 
 
 1,775 
 
 1,895 
 
 2,605 
 
 3,255 
 
 5,205 
 
 6,925 
 
 8,915 
 
 + 100C. 
 
 2,070 
 
 2,215 
 
 3,030 
 
 3,845 6,010 
 
 8,115 
 
 11,210 
 
 + 150C. 
 
 2,360 
 
 2,560 
 
 3,440 
 
 4,420 ! 6,790 
 
 9,345 
 
 13,820 
 
 + 200C. 
 
 2,885 
 
 2,890 
 
 3,840 
 
 5,000 
 
 7,540 
 
 10,590 
 
 16,630 
 
 
 
 i 
 
 
 
 
 Tempera- 
 
 Specific Resistance in C.G.S. Units. 
 
 ture 
 
 
 (Centi- 
 grade). 
 
 Iron. 
 
 Cad- 
 mium. 
 
 Palla- 
 dium. 
 
 Plati- 
 num. 
 
 Tin. 
 
 Thal- 
 lium. 
 
 Lead. 
 
 -150C. 
 
 2,325 
 
 4,210 
 
 4,205 
 
 4,760 
 
 5,080 
 
 6,275 
 
 8,515 
 
 - 100C. 
 
 4,360 
 
 6,115 
 
 6.290 
 
 6,890 
 
 7,650 
 
 10,155 
 
 12,340 
 
 - 50C. 
 
 6,590 
 
 8,045 
 
 8,300 
 
 8,945 
 
 10,350 
 
 13,930 
 
 16,390 
 
 0C. 
 
 9,065 
 
 10,023 
 
 10,219 
 
 10,917 i 13,048 
 
 17,633 
 
 20,380 
 
 + 50C. 
 
 11,770 
 
 12,060 
 
 12,055 
 
 12,910 
 
 15,895 
 
 21,225 
 
 24,555 
 
 + 100C. 
 
 14,765 
 
 14,315 
 
 13,840 
 
 14,820 
 
 18,870 
 
 24,770 
 
 28,900 
 
 + 150C. 
 
 18,110 
 
 16,725 
 
 15,545 
 
 16,690 
 
 21,990 
 
 28,100 
 
 33,470 
 
 + 200C. 
 
 21,960 
 
 19,325 
 
 15,215 
 
 18,535 
 
 25,155 
 
 31,635 
 
 38,000 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 325 
 
 TABLE VI. 
 
 Electrical Conductivity of Metals at C. in Absolute and 
 Arbitrary Units. 
 
 Absolute conductivity is measured in mhos. The mho is the reciprocal of 
 the ohm, and the mho-conductivity is obtained by dividing 10 9 by the volutne- 
 resistivity in C.G.S. units. 
 
 Metal 
 
 Mho-conductivity at 0C. 
 1 mho = conductivity of a 
 centimetre-cube of 
 material having a volurne- 
 resistivity of 1 ohm. 
 
 Arbitrary conduc- 
 tivity. Annealed 
 electrolytic silver 
 = 100atOC. 
 
 Silver (electrolytic\ 
 annealed) J 
 
 681,198 
 
 100 
 
 Copper (electrolytic) 
 annealed) / 
 
 640,615 
 
 94-04 
 
 Gold (annealed) 
 
 455,166 
 
 66-81 
 
 Aluminium (annealed) 
 Sodium (pressed at) 
 20 C } 
 
 37.5,234 
 253,973 
 
 55-08 
 37-43 
 
 Magnesium 
 
 229,616 
 
 33-71 
 
 Zinc 
 
 171,381 
 
 25-16 
 
 Calcium (at 18C.) ... 
 Nickel (electrolytic) . . . 
 Potassium (at 20C.) 
 Lithium (at 20C.) ... 
 Indium 
 
 150,818 
 144,196 
 141,990 
 129,428 
 112,400 
 
 22-14 
 21-17 
 20-85 
 19-00 
 16-50 
 
 Iron 
 
 110,314 
 
 16-19 
 
 Cobalt 
 
 106,140 
 
 15-58 
 
 Oa^rninm 
 
 99,770 
 
 14-64 
 
 Palladium 
 
 97,857 
 
 14-64 
 
 Platinum 
 
 91,600 
 
 13-44 
 
 Tin 
 
 76,640 
 
 11-25 
 
 Thallium 
 
 56,712 
 
 8'32 
 
 Lead. .. 
 
 49,067 
 
 7-20 
 
 Strontium (at 18C.) 
 Arsenic 
 
 45,708 
 32,425 
 
 6-71 
 4-76 
 
 Antimony 
 
 31,471 
 
 4-62 
 
 Mercury 
 
 10,630 
 
 1-56 
 
 Bismuth . 
 
 9,091 
 
 1-33 
 
 
 
 
326 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 TABLE VII. 
 
 Volume-resistivity of Alloys of known Composition at 0C. 
 in C.G.S. Units per Centimetre-cube. 
 
 Mean temperature coefficients taken at 15C. 
 (Fleming and Dewar. ) 
 
 Alloy. 
 
 Resis- 
 tivity 
 at 0C. 
 
 Tempera- 
 ture 
 coefficient 
 at 15C. 
 
 Composition in 
 per cents. 
 
 Platinum-Silver 
 
 31 582 
 
 0-000243 
 
 Pt337, As667 
 
 Platinum- Iridium . 
 
 30,896 
 
 0-000822 
 
 Pt 807, Ir 207 
 
 Platinum-Rhodium 
 
 21,142 
 
 0-00143 
 
 Pt907,Khl07 
 
 Gold-Silver, 
 
 6,280 
 
 0-00124 
 
 Au907,Agl07 
 
 Manganese-Steel 
 
 67,148 
 
 0-00127 
 
 Mnl27,Fe807 
 
 Nickel-Steel . 
 
 29 452 
 
 0-00201 
 
 Ni 4-357 
 
 Germ an -Silver .. 
 
 29 982 
 
 0-000273 
 
 Cu, Zn Q NL 
 
 Platinoid* 
 
 41,731 
 
 0-00031 
 
 
 Manganin 
 
 46,678 
 
 o-oooo 
 
 /Cu84%,Mnl2%, 
 
 Aluminium- Silver 
 
 4 641 
 
 0-00238 
 
 I Ni4% 
 Al 947, As 67 
 
 Aluminium- Copper 
 
 2,904 
 
 0-00381 
 
 v /o' 5 **/o 
 
 Al 947, Cu 67 
 
 Copper- Aluminium ... 
 
 8,847 
 
 0-000897 
 
 Cu 977, Al 37 
 
 Copper - Nickel - Aluminium 
 Titanium- Aluminium 
 
 14,912 
 
 3,887 
 
 0-000645 
 0-00290 
 
 /Cu87%,Ni6-7%, 
 1 A16-5% 
 
 
 
 
 
 * Platinoid is an alloy first produced by Martino, the composition being 
 said to be similar to that of German silver, but with a little tungsten added. 
 It varies a good deal in composition according to manufacture, and the resis- 
 tivity of different specimens is not identical. The electrical properties of 
 platinoid were first made known by Dr. J. T. Bottomley, F.R.S., in a Paper 
 read at the Royal Society, May 5, 1885. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 TABLE VIII. 
 
 327 
 
 Electrical Volume-resistivity of Various Liquids in Ohms er 
 Centimetre-cube. 
 
 I. FUSED SALTS. 
 
 Substance. 
 
 Kesistivity. 
 
 Remarks. 
 
 Observer. 
 
 Plumbic chloride Pb 
 
 Clo 
 
 0-376 
 
 
 F. Braun 
 
 Silver chloride AgCl 
 Sodic nitrate NaN0 3 
 Zinc chloride ZnCl 9 
 
 0-392 
 0-817 
 109-3 
 
 at 600C. 
 
 W. Kohlrausch 
 F. Braun 
 F. Braun 
 
 II. AQUEOUS SOLUTION OF ACIDS.* 
 Solution having maximum conductivity at 18C. 
 
 Acid. 
 
 Resistivity. 
 
 Temperature Coefficient. 
 
 Nitric Acid N0 3 H.... 
 
 1-28 
 
 0-014 \ 
 
 Hydrochloric Acid HC1 
 Sulphuric Acid H 2 S0 4 
 Tartaric Acid C 4 H e 6 
 Acetic Acid C 2 H 4 9 ... 
 
 1-32 
 1-36 
 100-0 
 618-4 
 
 0-0155! . , 
 0-0169 as given by 
 0-0192 [G.Wieaemann. 
 0-0174J 
 
 III. AQUEOUS SOLUTIONS OF SALTS AND HYDRATES.* 
 
 Salt. 
 
 Resistivity. 
 
 Specific 
 Gravity. 
 
 Temperature Coefficient. 
 
 Potassic Hydrate KHO 
 
 1-84 
 
 
 0-0225\ 
 
 
 Potassic Iodide KI 
 
 2-29 
 
 1-70 
 
 0-014 
 
 
 Ammonic Chloride Am 
 
 
 
 
 
 Cl 
 
 2-36 
 
 1-078 
 
 00155 
 
 
 Silver Nitrate AgN0 3 ... 
 Sodic Chloride NaCl ... 
 Hydro -potassic Car- 
 
 4-48 
 4-66 
 
 2-18 
 1-201 
 
 0-0211 
 0-0234 
 
 as given 
 by G. 
 Wiedemann. 
 
 bonate KHCO S 
 
 8-54 
 
 1-15 
 
 0-0199 
 
 
 Copper sulphate CuS0 4 ! 29-37 
 
 1-208 
 
 0-0241 
 
 
 Zinc sulphate ZnS0 4 ... 
 
 21-35 
 
 1-286 
 
 t 
 
 
 * The above Table contains only the resistivity values corresponding to the 
 maximum conductivity in the case of the aqueous solutions of salts and acids. 
 
328 
 
 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 TABLE IX. 
 
 Electrical Volume-resistivity of Various Badly Conducting 
 Liquids in Megohms per Centimetre-cube. 
 
 Substance. 
 
 Resistivity in 
 megohms per c.c. 
 
 Observer. 
 
 Ethylic Alcohol 
 
 0-522 
 
 Pfeiffer. 
 
 Ethylic Ether 
 
 1-175 to 3-760 
 
 W. Kohlrausch. 
 
 Benzine 
 
 4700 
 
 
 Water 
 
 (1-446 at 14C. 
 
 Pfeiffer. 
 
 Absolutely pure water 
 approximates probably 
 to 
 
 5'222 at 18C. 
 1 25-0 at 18C. 
 
 F. Kohlrausch. 
 c Estimated value by 
 Kohlrausch and 
 I Heydweiler. 
 
 All very dilute aqueous 
 salt solutions having a 
 concentration of about 
 0-00001 of an equiva- 
 lent gramme- molecule* 
 per litre approximate to 
 
 - 1-00 at 18C. 
 
 {From results by F. 
 Kohlrausch and 
 others. 
 
 * An equivalent gramme-molecule is a weight in grammes numerically 
 equal to the chemical equivalent of the salt. For instance, one equivalent 
 gramme- molecule of sodic chloride is a mass of 58'5 grammes, since NaCl 
 = 58-5. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 329 
 
 TABLE X. 
 
 Volume-resistivity of Solutions of Copper and Zinc Sulphate of 
 Various Densities at IOC. in Ohms per Centimetre-cube. 
 
 (Ewing and MacGregor.)* 
 SULPHATE OF COPPEB. 
 
 Density. 
 
 Resistivity. 
 
 Density. 
 
 Resistivity. 
 
 1-0167 
 
 164-4 
 
 1-1386 
 
 35-0 
 
 1-0216 
 
 134-8 
 
 1-1432 
 
 34-1 
 
 1-0318 
 
 98-7 
 
 1-1679 
 
 31-7 
 
 1-0622 
 
 590 
 
 11829 
 
 30-6 
 
 1-0858 
 
 47-3 
 
 1-2051 
 
 29-3 
 
 1-1174 
 
 38-1 
 
 (saturated) 
 
 ... 
 
 SULPHATE OF ZINC. 
 
 Density. 
 
 Resistivity. Density. 
 
 II 
 
 Resistivity. 
 
 1-0140 182-9 1-2709 
 
 28-5 
 
 1-0187 140-5 1-2891 
 
 28-3 
 
 1-0278 111-1 
 
 1-2895 
 
 28-5 
 
 1-0540 
 
 638 
 
 1-2987 
 
 28-7 
 
 1-0760 
 
 50-8 
 
 1-3288 
 
 29-2 
 
 1-1019 
 
 421 
 
 1-3530 
 
 31-0 
 
 1-1582 
 
 33-7 
 
 1-4053 
 
 32-1 
 
 1-1845 
 
 321 
 
 1-4174 
 
 33-4 
 
 1-2186 
 
 303 1-4220 
 
 33-7 
 
 1-2562 29 2 
 
 1 
 
 ^saturated) 
 
 ... 
 
 * Trans. Roy. Soc., Edin., Vol. XXVII., 1873. 
 
 The resistivity values obtained by various observers for electrolytic con- 
 ductors do not agree at all well. The above values are not quite in accord 
 with other results. 
 
330 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 TABLE XI. 
 
 Electrical Volume-resistivity of Dielectrics expressed in Millions 
 of Megohms (Mega-megohms) per Centimetre- cube, and in 
 Megohms per Quadrant-cube i.e., a Cube whose side is 
 10" cms. 
 
 Substance. 
 
 Resistivity. 
 
 Temperature. 
 Cent. 
 
 Mega- 
 megohms 
 per c.c. 
 
 Megohms per 
 quadrant- 
 cube. 
 
 Bohemian Glass 
 
 61 
 84* 
 450* 
 1,020 
 
 1,630 
 
 2,280 
 9,000* 
 10,900 
 
 11,900 
 
 16,170 
 20,000 
 28,000* 
 34,000* 
 
 061 
 084 
 45 
 1-02 
 
 1-63 
 
 2-28 
 9-0 
 10-9 
 
 11*9 
 
 16-17 
 20-0 
 
 28 
 34 
 
 60 
 20 
 24 
 60 
 
 15 
 
 15 
 28 
 24 
 
 15 
 
 15 
 20 
 46 
 46 
 
 Mica 
 
 G utta-percha 
 
 Flint Glass at 60 C 
 
 Glover's Vulcanised India- 
 rubber 
 
 Siemens' ordinary pure 
 Vulcanised India-rubber 
 Shellac 
 
 India-rubber 
 
 Siemens' High Insulating 
 Fibrous Material 
 
 Siemens' Special High 
 Insulating India-rubber 
 Flint Glass at 20 C 
 
 Ebonite 
 
 Paraffin 
 
 
 The values of the resistivity of various dielectrics given in the above Table 
 can only be taken as approximate. In most cases the observers have not 
 stated the time of imposition of the electric stress. Values marked (*) are 
 those given by experiments by Profs. Ayrton and Perry : " On the Viscosity 
 of Dielectrics " (Proc. Roy. Soc., March, 1878), " after several minutes' 
 electrification." 
 
 The temperature coefficients of the resistivities of dielectric conductors are 
 very large ; in most cases far larger than those of the pure metals, and 
 the apparent resistivity is also a function of the value and of the time of 
 operation of the electromotive force. 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 331 
 
 TABLE XII. 
 
 Resistances of various sizes of Platinoid Wire. 
 (London Electric Wire Company, Ltd.) 
 
 Size. 
 
 Diameter. 
 
 Resistance (approximate). 
 
 : L.S.G. 
 
 Inch. 
 
 m/m. 
 
 Per Ib. 
 
 Per 1,000 yards. 
 
 
 
 
 Ohms. 
 
 Ohms. 
 
 8 ' 
 
 0-160 
 
 4-064 
 
 0-1241 
 
 28-852 
 
 10 
 
 0-128 
 
 3-251 
 
 0-3031 
 
 45-084 
 
 12 
 
 0-104 
 
 2-642 
 
 0-6957 
 
 68-292 
 
 14 
 
 0-080 
 
 2-032 
 
 1-9869 
 
 115-416 
 
 16 
 
 0-064 
 
 1-626 
 
 4*8520 
 
 180-338 
 
 18 
 
 0-048 
 
 1-219 
 
 15-3312 
 
 320-601 
 
 19 
 
 0-040 
 
 1-016 
 
 31-7952 
 
 461-664 
 
 20 
 
 0-036 
 
 0-914 
 
 48-4602 
 
 569-952 
 
 21 
 
 0-032 
 
 0-813 
 
 77-6480 
 
 721-368 
 
 22 
 
 0-028 
 
 0-711 
 
 132-4272 
 
 942-192 
 
 23 
 
 0-024 
 
 0-610 
 
 245-3280 
 
 1282-392 
 
 24 
 
 0-022 
 
 0-559 
 
 347-4720 
 
 1526-184 
 
 25 
 
 0-020 
 
 0-508 
 
 508-7280 
 
 1846-656 
 
 26 
 
 0-018 
 
 0-457 
 
 775-3680 
 
 2279-808 
 
 27 
 
 0-0164 
 
 0-417 
 
 1125-2160 
 
 2746-440 
 
 28 
 
 0-0148 
 
 0-876 
 
 1696-4880 
 
 3372-264 
 
 80 
 
 0-0124 
 
 0-315 
 
 8442-8000 
 
 4803-984 
 
 32 
 
 0-0108 
 
 0-274 
 
 5982-7200 
 
 6332-904 
 
 34 
 
 0-0092 
 
 0-2337 
 
 11362 
 
 8727-120 
 
 36 
 
 0-0076 
 
 0-1930 
 
 24398 
 
 12789-640 
 
 38 
 
 0-0060 
 
 0-1524 
 
 62805 
 
 20518-560 
 
 40 
 
 0-0048 
 
 0-1219 
 
 153333 
 
 32060-160 
 
 42 
 
 0-0040 
 
 0-1016 
 
 317904 
 
 46166 
 
 44 
 
 0-0032 
 
 0-0813 
 
 784280 
 
 72136 
 
 46 
 
 0-0024 
 
 0-0610 
 
 2453280 
 
 128239 
 
 47 
 
 0-0020 
 
 0-0508 
 
 5087280 
 
 184665 
 
332 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 TABLE XIII. 
 
 Resistances of various sizes of Manganin Wire. 
 (London Electric Wire Company, Ltd.) 
 
 Size. 
 
 Diameter. 
 
 Resistance (approximate). 
 
 L.S.G. 
 
 Inch. 
 
 m/m. 
 
 Per Ib. 
 
 Per 1,000 yards. 
 
 
 
 
 Ohms. 
 
 Ohms. 
 
 14 
 
 0-080 
 
 2-032 
 
 2-027 
 
 117-85 
 
 16 
 
 0-064 
 
 1-626 
 
 4-952 
 
 184-17 
 
 18 
 
 0-048 
 
 1-219 
 
 15-652 
 
 327-42 
 
 20 
 
 0-036 
 
 0-914 
 
 49-475 
 
 582-00 
 
 22 
 
 0-028 
 
 0-711 
 
 135-175 
 
 962-00 
 
 24 
 
 0-022 
 
 0-559 
 
 354-700 
 
 1560-25 
 
 26 
 
 0-018 
 
 0-457 
 
 791-475 
 
 2330-00 
 
 28 
 
 0-0148 
 
 0-376 
 
 1731-750 
 
 3442-50 
 
 30 
 
 0-0124 
 
 0-315 
 
 3514-250 
 
 4907-50 
 
 32 
 
 0-0108 
 
 0-274 
 
 6107-250 
 
 6467-50 
 
 34 
 
 0-0092 
 
 0-2337 
 
 11597-750 
 
 8912-50 
 
 36 
 
 0-0076 
 
 0-1930 
 
 24904-500 
 
 13060 
 
 38 
 
 0-0060 
 
 0-1524 
 
 64100 
 
 20955 
 
 40 
 
 0-0048 
 
 0-1219 
 
 156525 
 
 32875 
 
 42 
 
 0-0040 
 
 0-1016 
 
 324550 
 
 47150 
 
 44 
 
 00032 
 
 0-0813 
 
 792375 
 
 73675 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 333 
 
 3 il 
 
 I 
 
 I 
 
 1 
 
 OQ 
 
 111 
 
 GO i-H 
 
 s 
 
 CO <M CO t- 
 
 o 
 
 <M b- CO O CO 
 Cq^H 
 
 i-H (M CO 
 
 ^ 
 
 
 CO CO 
 OQ CO 
 
 "<H co f< 
 
 <NCOCOOOOCO<Ni-l 
 r^ (M rH 
 
 kO 
 
 00 tM O CO t^ 00 
 OCCCCt^COOS^OO 
 
 (M O "* X O CO CM rH O 
 ^ <M i 1 
 
 fI 
 
 o <M oo ^ oq 
 
 t>OCOr-(^O5<NrH^ 
 
 obrHcbcbdb4cb<irH 
 
 00 rji r- 1 
 
 co (?q -I 
 
 r> co GO o co p so 
 
 O O rH CN CO 1* 
 
 X O t- l> O 
 
 rHrHi lrHC<lGt>l>-i I 
 
 
 OrHrHCOXOOOCMOOO 
 
 O O O O ' G<1 G<l 
 (~) f^ {^} f_^ <^ ^^ ^^ 
 
 ooooooooo 
 
 as 
 
 pOOpO^-irHrHrH 
 
 OOOOOOOOO 
 
 w , 
 
 ai^ 
 
 llifH 
 
 t-O<MOOCOpppp 
 rH <M CO -T" 
 
 CO 05 O O O O 
 OrH-rHcboobciOOO 
 
 O 
 
 
( 334 ) 
 
 Ill 
 
 i i l> !> 
 
 COCDCDOOt>-CCOi i OCO 
 
 CO 
 
 i i TH co -^ T-HCMCOOCMCOOOC; 
 
 OOCOO 
 
 00 
 
 iH rH Cq TJ1 t*(M 00 <M CO D- (M Oi CO O l> CO TH 00 -* (M O CO 
 
 i ir-i T-H i i co o r-((Mcoooq^co 
 
 a a 
 
 CO"^QOOCOCOTHTHOOCO(MrHOOOOr-iOOOOOOOOC 
 
 
 o i i co a 
 
 OOOQOCOr- 
 
 ^00-^CDCOCMrHOOOOqTHOOOOOOOOOOOOOOC 
 
 O 
 
 (M rH 
 
 OOOOrHOOOOOOOOC 
 
 OOt^QO 
 
 COOOO 
 COrH . 
 
 d& 
 
 S's *>% 
 
 t CO rH CM 
 
 rH O b- 
 
 rH CD US <* t- CO ^ t- t* (M C5 05 
 
 C5 
 
 ^^ ^D ^^ ^D "* O^ CO *-O 00 T"H rH CO CO O^ *O "^^ CO CO <^ GO ^H ^^ O^ C^ ^H 1C 
 OOOOpOOOOOOOOOTH^OOrHr-iCprHnHCpO^) 
 
 ooooooooooooooooooooooooooc 
 
 g 
 
 ll 
 
 s 
 
 
 s 
 
 
 
 ooooooooooooooooooooooooooc 
 
 -2 ' 
 
 CM TH ; 
 
 CqCOTHXOrHrHrHCqCOTHOr-HrHC<lCO-HHrHCMCOTHa; 
 
 CM CO TH CM CO TH CO 00 O CM CM CO TH CO 00 O CM CO TH O 00 O TH O OO O OC 
 OOOpOOpOrHrHOOOpOrHrHOOOOT-lOOOTHC 
 
 OOOOOOOOOOOOOOOOOOOOOOOOOOC 
 
 to 
 
 OD TH CO 
 iOTHrHTHOOOCNOt^ CO CO *O CO 
 
 O 
 
 OCOr>COCOC5O5CDOOOCOTHOOO5t-b- 
 rH rHCMCOTHb-OrHCMTHt-OCOCOiOOOCNOOOOOqOOOCOG: 
 rH rHi ICQ 'rHCMrHrHCMTHOC 
 
 gH 
 
 f*l 
 
 CO TH CO <M 
 
 rHCMCO^OOOrHrHCOCOOSiO 
 
 rHt^COt--COOC5CO(7q<Nr- 
 
 THCOCOi lOOrHOOOrHO 
 
 s 
 
 ^^<M rH CJ^CM rH -~-^-^.~~^ ^ -^. 
 
 ^c^^t^i^i^^t^^^^o^Grcrcrorcrt^^^t^t^" 
 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 335 
 
 TABLE XV. 
 
 The Value of the Ohm. 
 
 Observer. 
 
 Date. 
 
 Method. 
 
 Value of 
 B.A.U. 
 in ohms. 
 
 Value of 
 100 centi- 
 metres of 
 mercury 
 in ohms. 
 
 Value of 
 ohm in 
 centi- 
 metres of 
 mercury. 
 
 Lord Rayleigh 
 Lord Rayleigh 
 G.Wiedemann 
 Mascart 
 
 1882 
 1883 
 1884 
 1884 
 1887 
 
 1887 
 1882 
 1888 
 189U 
 
 1890 
 1891 
 
 1885 
 1888 
 1890 
 
 Rotatin^ coil 
 
 0-98651 
 0-98677 
 
 0-98611 
 
 0-98644 
 0-98660 
 
 0-98665 
 0-98686 
 
 0-98634 
 
 0-94133 
 
 0-94096 
 
 0-94071 
 0-94061 
 
 0-94074 
 0-94077 
 
 0-94067 
 0-94067 
 
 0-94056 
 0-94074 
 
 0-94054 
 0-94076 
 0-94076 
 
 o 1 u t e^> 
 
 3ments 
 3d with 
 i silver > 
 s issued 
 lens or 
 
 f ) 
 
 K'6-24 
 106-21 
 106-19 
 106-33 
 
 106-32 
 106-32 
 
 106-29 
 106-27 
 
 106-32 
 106-31 
 
 106-32 
 106-30 
 
 106-33 
 106-30 
 106-28 
 10537 
 106-16 
 
 105-89 
 
 105-98 
 106-24 
 106-03 
 105-93 
 
 Lorenz method 
 
 Rotation through 180 
 Induced current . . 
 
 Rowland 
 
 Mean of several 
 methods 
 
 Kohlrausch ... 
 Glazebrook . . . j 
 
 Wuilleumeier 
 Duncan and 
 Wilkes 
 
 Damping of magnets 
 } Induced currents . . . 
 
 Lorenz 
 
 Jones 
 
 Lorenz 
 
 Strecker . . . 
 
 Mean 
 
 0-98653 
 
 f An absolute deter-' 
 mination of resist- 
 ance was not made. 
 The value 0-98656 
 has been used 
 
 Mean 
 
 Hutchinson ... 
 Salvioni 
 
 Salvioni 
 
 H.F.Weber... 
 H.F.Weber... 
 
 Roiti 
 
 1884 
 1884 
 
 1885 
 1889 
 1883 
 1885 
 
 Induced current 
 Rotating coil 
 
 ... 
 
 Mean effect of induced 
 current 
 
 / Abs 
 measur< 
 compar 
 Germar 
 wirecoi' 
 by Sien 
 Streckei 
 
 Himstedt 
 Dorn ... . 
 
 Damping of a magnet 
 Damping of a magnet 
 Lorenz method 
 
 Wild 
 
 Lorenz 
 
 
336 
 
 MEASUREMENT OF ELECTRICAL RESISTANCE. 
 
 TABLE XVI. 
 
 Table of Resistance of High Conductivity Bound Copper 
 Conductors to Alternating and Continuous Currents. 
 
 Size of stranded 
 cable. 
 
 Area in 
 square inches. 
 
 Kesistance in ohms per 1,000 yards. 
 
 To continuous 
 currents. 
 
 To alternating 
 currents. 
 Frequency 100 ^ 
 per second. 
 
 7/18 
 
 00126 
 
 1-974 
 
 1-974 
 
 7/17 
 
 0-0172 
 
 1-452 
 
 1-452 
 
 7/16 
 
 0-0225 
 
 1-108 
 
 1-108 
 
 7/15 
 
 0-0285 
 
 0-878 
 
 0-878 
 
 7/14 
 
 0-0351 
 
 0-712 
 
 0-712 
 
 19/18 
 
 0-0351 
 
 0-712 
 
 0-712 
 
 19/17 
 
 0-0477 
 
 0-524 
 
 0-524 
 
 19/16 
 
 00624 
 
 0-401 
 
 0-401 
 
 19/15 
 
 0-0789 
 
 0-318 
 
 0-318 
 
 19/14 
 
 00973 
 
 0-257 
 
 0-257 
 
 19/13 
 
 0-1289 
 
 0-194 
 
 0-195 
 
 19/12 
 
 0-1645 
 
 0-153 
 
 0-155 
 
 19/11 
 
 0-2048 
 
 0-122 
 
 0-1247 
 
 19/10 
 
 0-2500 
 
 0-100 
 
 0-1034 
 
 37/16 
 
 0-1227 
 
 0-204 
 
 0-2041 
 
 37/15 
 
 0-1551 
 
 0-162 
 
 0-104 
 
 37/14 
 
 0-1913 
 
 0131 
 
 0-1334 
 
 37/13 
 
 0-2534 
 
 0-099 
 
 0-1024 
 
 37 
 
 0-3000 
 
 0-083 
 
 0-087 
 
 37/12 
 
 0-3235 
 
 0-077 
 
 0-081 
 
 37/11 
 
 0-4000 
 
 0-063 
 
 0-068 
 
 37/10 
 
 0-4905 
 
 0-051 
 
 0-057 
 
 61/15 
 
 0-2582 
 
 0-097 
 
 0-1004 
 
 61/14 
 
 0-3185 
 
 0-078 
 
 0-082 
 
 61/13 
 
 0-4218 
 
 0-060 
 
 0-065 
 
 61 
 
 0-5000 
 
 0-050 
 
 0-056 
 
 61/12 
 
 0-5385 
 
 0-046 
 
 0-052 
 
 61 
 
 0-6000 
 
 0-041 
 
 0-048 
 
 61/11 
 
 0-6476 
 
 0-039 
 
 0-0465 
 
 61 
 
 0-7000 
 
 0-0357 
 
 . 0-0435 
 
 61/10 
 
 0-8167 
 
 0-0305 
 
 0-0391 
 
 91/13 
 
 0-6354 
 
 0-0385 
 
 0-0458 
 
 91 
 
 0-7500 
 
 0-0330 
 
 00412 
 
 91/12 
 
 0-8111 
 
 0-0305 
 
 0-0391 
 
 91 
 
 0-9000 
 
 0-0277 
 
 0-0370 
 
 91/11 
 
 1-0000 
 
 0-0250 
 
 0-0350 
 
MEASUREMENT OF ELECTRICAL RESISTANCE. 337 
 
 TABLE XVII. 
 
 Materials Used for Electrical Resistances. 
 
 Material. 
 
 Resistance in microhms per centimetre- 
 cube at 0C. 
 
 Copper (hard drawn) . . . 
 
 Iron (annealed) 
 
 German Silver 
 
 Platinoid 
 
 Manganin 
 
 Eesista 
 
 Beacon 
 
 Eureka 
 
 Cast Iron 
 
 Steel 
 
 Graphite 
 
 Arc Lamp Carbon 
 
 Plumbago and Stour- 
 
 bridge Clay, about 
 
 equal parts mixed and 
 
 well baked. 
 Saturated Solution of 
 
 Sulphate of Copper. 
 Saturated Solution of 
 
 Sulphate of Zinc. 
 Dilute Sulphuric Acid, 
 
 1-2 density. 
 Sodic Sulphate Solution, 
 
 15 per cent. salt. 
 
 From 
 About 
 
 About 
 
 1-626 
 9-0 
 
 20-0 to 30-0 
 40-0 
 
 42-0 to 46*0 
 76-0 
 80-0 
 40-0 
 
 80-0 to 100-0 
 
 15-0 to 50-0 
 
 300-0 to 400-0 
 
 3,000 to 4,000 
 
 100,000 
 
 29-3 xlO 6 
 
 33-7 xlO 6 
 
 l-24x!0 6 
 
 11-37 xlO 6 
 
 microhms. 
 
CHAPTER III. 
 
 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 1. Classification of Electric Currents. Electric currents 
 may be either unidirectional that is, flowing continually in 
 one and the same direction, or alternating that is, periodi- 
 cally changing their direction. 
 
 The character of a current in a conductor is determined 
 by the nature of the field of magnetic force associated with 
 the conductor when it forms part of a circuit in which a 
 current exists. If the direction of the field when tested 
 in any manner at any point outside the conductor is always 
 in the same direction, as indicated, say, by the behaviour of a 
 small magnet held in the field, the current is said to be 
 unidirectional or continuous. If the direction of the field 
 periodically changes, the current in the conductor is said to 
 be alternating or periodic. 
 
 A continuous current may be either uniform or unvarying, 
 or it may be intermittent or pulsatory. An alternating current 
 may, in the same manner, be steadily periodic, or it may be 
 variable and periodic. 
 
 Alternating currents are furthermore divided into monophase 
 and polyphase. In the first case the periodic current exists 
 in a single circuit ; in the second case the circuit in which 
 the current is created is a complex circuit, each elementary 
 circuit of which is traversed by a periodic current, these 
 various currents differing in phase that is to say, not chang- 
 ing their directions at the same instant, but preserving a 
 constant phase difference with respect to each other. 
 
 z2 
 
340 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 In the measurement of electric currents we are concerned 
 with the determination of a quantity capable of having 
 direction as well as magnitude. The magnitude or, as it is 
 sometimes called, the strength is measured by the degree 
 to which some measurable physical effect is produced. The 
 three most important physical effects accompanying or 
 constituting an electric current are : (i.) The production of 
 heat in the conductor; (ii.) the production of a magnetic 
 field around and in the conductor; and (iii.) the production 
 of an electrolytic effect in liquid conductors of a certain 
 kind forming part of the circuit. 
 
 Other things being equal, the heating effects of an unvary- 
 ing current increases as the square of the current when 
 measured in either of the other two ways. That is to say, 
 if there be two currents which, when respectively passed 
 through the same circuit, produce magnetic forces at any one 
 point in the ratio of 1 : x, they produce in the same time 
 chemical decompositions of a given electrolyte inserted in 
 the circuit which, measured by the masses of a liberated ion, 
 are in the ratio of 1 : x. These two currents, however, will 
 produce in any part of the conducting circuit quantities 
 of heat which are in the ratio of 1 : x 2 . Two currents are 
 said to have the same mean square value if they produce in 
 the same time and in the same conductor the same total 
 quantity of heat. 
 
 If a current is periodic or alternating, its effective or virtual 
 value, estimated in its equivalent of continuous current, is that 
 of the unvarying and unidirectional current which will pro- 
 duce in the same conductor the same heat in the same time. 
 This effective value is also called the root-mean-sqiiare (RM.S.) 
 value, because it is equal to the square root of the mean of 
 the squares of the instantaneous current values taken at 
 equidistant and very near intervals of time throughout one 
 complete cycle. The true mean (T.M.) value of a current is 
 the arithmetic mean of its instantaneous values taken at 
 equidistant intervals of time throughout any period. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 341 
 
 We have, therefore, three methods of measuring a current, 
 which may be called respectively the thermal, the magnetic, 
 and the chemical methods. 
 
 The definition of the absolute unit of current in magnetic 
 measure is thus given : 
 
 Let a thin conducting wire be bent into a circle having 
 a radius of r centimetres, and let the pole of a very long 
 linear magnet of strength m be placed at the centre, the 
 other complementary pole being at a considerable distance. 
 Then, if the mechanical force on the magnetic pole placed 
 at the centre is measured in absolute units of force (in dynes), 
 and is represented by /, the absolute magnetic measure of the 
 current (C) is determined by the relation 
 
 The absolute electromagnetic (C.G.S.) unit of current is 
 therefore the current which, when circulating in a circuit of 
 unit radius, exerts on a unit magnetic pole placed at the 
 centre a force of 2?r dynes. The practical unit of current 
 (the ampere) is one-tenth of the above electromagnetic unit 
 in magnitude. 
 
 The Standard or International Ampere, as already explained, has been 
 officially defined as the current which, when passed through a solution of 
 nitrate of silver, made according to a certain specification, deposits 0*001118 
 of a gramme of silver per second on the cathode.* As previously pointed out, 
 there is reason to believe that the unit of current called the International 
 ampere is smaller by about 1 part in 1,000, or 1 part in 800, than the unit of 
 current or ampere defined as one-tenth of the absolute C.G.S. unit of current. 
 This view is confirmed by the discrepancy between the values of the mechanical 
 equivalent of heat, or, as it should be called, the dynamical value of the 
 specific heat of water when determined mechanically and electrically. In the 
 determination of the above equivalent by electrical methods, values obtained 
 by Griffiths exceed those of Rowland, made by mechanical or frictional 
 methods, by about 1 part in 400 at all temperatures between 15deg. and 20deg. 
 on the nitrogen gas thermometer siale. Those of Schuster and Gannon exceed 
 those of Rowland at 19'ldeg. on the same scale by 1 part in 500. Since the 
 current enters as a square, it follows that the above discrepancies would be 
 reconciled by the substitution of O'OOlllQl or 0-0011194 for the electro- 
 chemical equivalent of silver, instead of O'OOlllS, as now adopted. 
 
 * For the electro-chemical equivalents of other metals see Table II., p. 420, 
 at the end of this chapter. 
 
342 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 A careful series of experiments by Patterson and Guthe at Michigan in 
 1898,* showed that the most probable value of the ampere-second silver 
 equivalent is 0*0011192 gramme, and hence a corresponding change must be 
 made in the E.M.F. at 15C. of the Clark cell, which is thereby reduced to 
 1'4327 International volts, instead of 1'4342, as now accepted. 
 
 Dr. K. Kahlef has investigated carefully the silver voltameter, and finds 
 that the electro-chemical equivalent obtained for silver varies slightly with 
 the age of the nitrate of silver solution. He states that with a freshly pre- 
 pared solution the ampere-second equivalent is very nearly 0'001182 gramme, 
 and with an old solution 0*001193 gramme. Some small degree of uncertainty 
 therefore exists as to the actual relation between the International and the 
 True or theoretical ampere, similar to that which occurs in the case of the 
 International and True ohm. 
 
 2. The Measurement of Current by the Electrolysis 
 of a Solution of Copper Sulphate. Standardisation of an 
 Ammeter. The employment of a solution of sulphate of 
 copper as the electrolyte enables an electrochemical deter- 
 mination of a current to be made with less initial outlay than 
 when silver is used. With certain precautions a high degree 
 of accuracy can be obtained. In order that any great degree 
 of exactness may be reached in the measurement of a current, 
 it is essential that the current shall be as nearly as possible 
 constant. To standardise an ampere-balance or ammeter 
 that is to say, to determine the true value in international 
 amperes corresponding to an observed scale reading we 
 proceed as follows : 
 
 The current should be provided from large secondary 
 cells which have been slightly discharged that is, about 
 10 per cent, of their full charge taken out. The ammeter or 
 ampere-balance to be standardised should be joined in series 
 with the cells and with a regulating wire resistance and a 
 carbon rheostat (see page 81), by which to make very small 
 variations in the resistance of the circuit: 
 
 This circuit must also include an electrolytic cell contain- 
 ing a solution of sulphate of copper. The electrolytic cell 
 found most convenient is a round glass jar about 30cm. high 
 
 * See Proc. Amer. Assoc., 47, pp. 154-175, 1898 ; also Science Abstracts^ 
 Vol. II., pp. 39 and 762. 
 
 t Zeitschr. Instrument^., 18, 1898, pp. 229-240 and 267-276. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 343 
 
 and 20cm. in diameter. This is placed on a slab of wood 
 at the sides of which are two vertical wooden rods carrying 
 brass forked strips which project over the top of the jar 
 (see Fig. 1). One of these forks may have three prongs 
 and the other one two. To these prongs are clamped by 
 brass clamps the copper anode and cathode plates. Each 
 plate can be separately removed from the solution. It is 
 convenient to make the two-prong brass fork the cathode. 
 To these forks large screw terminals are attached. The 
 solution placed in the electrolytic cell is made by dissolving 
 
 ioh~fol~~fol" 
 
 FIG. 1. Voltameter for Current Measurement by the Electrolysis of 
 Copper Sulphate. 
 
 pure re-crystallised sulphate of copper in distilled water 
 until a density of 1*15 or 1*18 is obtained. One per cent. 
 by volume of pure sulphuric acid is then added. This 
 addition of free acid is absolutely necessary to obtain good 
 results. No satisfactory determinations can be made with 
 neutral solutions of sulphate of copper. In any case the 
 density of the solution should be between I'l and 1*2. 
 The copper plates should be cut from high-conductivity 
 pure electrolytic copper, and should be 15cm. long and 
 5cm. wide. The corners of the plates should be neatly 
 
344 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 rounded off and all burr on the edges removed. Each 
 plate should be stamped with a number in one corner for 
 recognition, and have a hole near the top edge by means of 
 which the plate can be handled with a wire hook. 
 
 The number and size of these plates to be employed in 
 each experiment is determined by the current to be measured. 
 To obtain an adherent and regular deposit of metal on the 
 cathode plate, it is necessary that the surface exposed should 
 exceed 20 sq. cm. per ampere. An exposed cathode surface 
 of 50cm. per ampere gives excellent results.* 
 
 If, then, the cathode plates are of the dimensions above 
 given and are placed in the electrolyte 10cm. deep, the 
 exposed surface on each plate, assuming both sides used, 
 will be 100 sq. cm., and each plate will be good for 
 2 amperes. The plates selected as cathodes have then to 
 be clamped to the cathode fork so that each row is included 
 between two rows of anode plates, and the number so selected 
 that the above-mentioned current density is not exceeded. 
 These preparations being complete, the cathode plates have to 
 be very carefully cleaned and weighed. The cleaning is best 
 performed by placing the plates in a flat porcelain dish and 
 covering them with strong commercial nitric acid. This 
 immediately evolves copious nitrous fumes, which are very 
 deleterious, and hence the process should be conducted in the 
 open air or in a well-ventilated fume cupboard. The experi- 
 mentalist should carefully avoid inhaling the nitrous vapours. 
 The plates having been left in the acid for a few minutes, 
 or until the acid boils violently, are fished out by the aid of 
 a stout copper wire and dropped into a large jug of clean 
 water. Each plate should then present a clean, bright salmon- 
 coloured surface, without a trace of brown oxide upon it on 
 either side. If the plates are newly cut from sheet copper it 
 will generally be necessary to give them a good scouring with 
 emery-cloth and water before treatment with the nitric acid. 
 
 * See Mr. A. W- Meikle, " On the Electrolysis of Copper Sulphate in Stan- 
 dardising Electrical Instruments." Proc. Phys. Soc. of Glasgow University, 
 Jan. 27, 1888. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 345 
 
 Unless the plates are chemically clean the electrolytically 
 deposited copper will not adhere to them. 
 
 The plates, having been cleansed and washed copiously, 
 are then to be dried between clean white blotting paper as 
 quickly as possible, and completely dried in an air oven 
 or in a dessicating vessel. When thoroughly dry, each plate 
 must be weighed on a good chemical balance, and its weight 
 recorded. In so doing, the plate must not be touched with 
 the fingers, but be handled by a clean copper wire thrust 
 through the hole in the plate. When dried and weighed 
 the plates should, as soon as possible, be placed in the 
 electrolytic cell and the experiment commenced. The circuit 
 must be completed so that the same uniform current flows 
 through the ammeter to be calibrated, and the electrolytic 
 cell and the weighed plates must be made the cathode or 
 negative pole of the cell so that the current deposits copper 
 upon them. The time when the circuit is closed must be 
 noted on a good chronometer, and the current must be kept 
 perfectly constant, as indicated by the observed reading of 
 the ammeter, for a time varying from one to four hours. 
 The circuit is then opened, and the time of so doing is noted. 
 
 The weighed plates should then at once be removed from 
 the electrolytic cell, be washed copiously in water, and be 
 again dried and weighed. The deposit of electrolytic copper 
 should be a bright, clean and adherent film of metal. The 
 increase in weight of each plate is noted, and the total 
 deposit of copper in an observed time thus found. The 
 increase in weight in grammes per second can then at once be 
 calculated, This last figure, divided by the electro-chemical 
 equivalent of copper, gives the mean value in amperes of 
 the current, or true time average of the current during the 
 experiment. 
 
 It was found by experiments conducted in Lord Kelvin's 
 laboratory at Glasgow University that the electro-chemical 
 equivalent of copper varies with the temperature of the 
 electrolyte and with the current density. Hence, in reckoning 
 
346 
 
 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 out results the proper electro-chemical equivalent must be 
 employed as given by Mr. Meikle. The electrochemical 
 equivalent in grammes per ampere-second is a number not far 
 from 0-000328, and it diminishes very slightly both with rise 
 of temperature and increase of cathode surface per ampere. 
 
 The Electro-chemical Equivalent of Copper in grammes per 
 ampere-second. 
 
 Area of cathode 
 surface in 
 square centims. 
 per ampere. 
 
 Temperature of electrolyte. 
 
 2C. 
 
 12C. 
 
 23C. 
 
 28C. 
 
 35C. 
 
 50 
 100 
 150 
 200 
 250 
 300 
 
 0003288 
 0003288 
 0003287 
 0003285 
 0003283 
 0003282 
 
 0003287 
 0003284 
 0003281 
 0003279 
 0003278 
 0003278 
 
 0003286 
 0003283 
 0003280 
 0003277 
 0003275 
 0003272 
 
 0003286 
 0003281 
 0003278 
 0003274 
 0003268 
 0003262 
 
 0003282 
 0003274 
 0003267 
 0003259 
 0003252 
 0003245 
 
 If accurate results are to be obtained, the following precautions must be 
 taken in the employment of the copper voltameter as a means of measuring 
 the time integral of a continuous current : 
 
 No satisfactory results can be reached unless the copper sulphate solution 
 contains free sulphuric acid. On the other hand, copper plates placed in this 
 solution lose in weight at a rate depending on their immersed surface. The 
 plates must, therefore, be most carefully freed from all traces of oxide before 
 being used as the weighed places. The anode plates should also be cleaned, 
 but it is not necessary that they should be of such pure copper as the 
 cathode plates. If, however, the electrolyte is to be frequently used, it is 
 desirable to employ electrolytic c >pper for both sets of plates. It is 
 important to round off the edges and make the cathode plates very smooth, 
 so as to avoid producing a rough deposit of copper or one nodulous or uneven 
 The plate is then not so easily dried, and there is a risk of small particles of 
 copper being detached. 
 
 It need hardly be said that in conducting the observations a good and 
 correct watch or chronometer must be used for determining the time durin g 
 which the experiment lasts. 
 
 The copper voltameter may be advantageously employed in evaluating a 
 steady continuous current and in standardizing an ampere-balance, but it is 
 not so well adapted for current measurement when the current cannot be 
 kept constant for considerable periods of time. 
 
 With the above precautions, however, there is not the slightest difficulty in 
 determining the true value of a steady unidirectional current of the order of 
 10 amperes to within one quarter per cent., and with a little care to within 
 one part in a thousand. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 347 
 
 3. The Measurement of Current by the Electrolysis 
 of Silver Nitrate. The measurement of the time integral 
 of a current when the current is of the order of about one 
 ampere or so, is best effected by the employment of a solution 
 of nitrate of silver, as silver has a higher atomic weight than 
 copper, and, moreover, is a monad element. Hence the mass 
 of silver deposited by a given current is nearly three times 
 that of the copper deposited in the same time. Accordingly 
 there is more mass to weigh, and hence, on that account, a 
 greater possibility of accuracy when dealing with small 
 currents. 
 
 On the other hand, the materials used are expensive 
 compared with the copper method, and there is con- 
 siderably greater difficulty in washing and drying the 
 silver deposit. From a neutral or nearly neutral solution 
 of silver nitrate the deposit of silver on a platinum cathode 
 is apt to be nodulous, crystalline or non-adherent. This 
 irregular deposit occludes small particles of the salt or 
 solution and it is not easy to wash the deposit so as to 
 secure perfect removal of the salt without washing away 
 some of the metal. 
 
 The full detailed specification for performing the operation 
 of electrolysis of silver nitrate in current measurements has 
 already been given (see Chap. I., p. 57), hence there is no need 
 to repeat the details. 
 
 A very careful investigation by Dr. K. Kahle (see Science Abstracts, Vol. II., 
 p. 41, or Zeitschr. Instrumentk., 18, p. 229, 1898), was conducted with the 
 special object of seeing how far the silver voltameter can be relied upon 
 for standardising current. In the course of 115 measurements the amount 
 of silver deposited by the same current acting for 40 minutes varied 
 from G'97134 grammes to 0'97473 grammes. With great care an accuracy 
 of 1 part in 10,000 can be obtained. A clean platinum surface receives 
 rather less deposit than an existing surface of silver, and fresh solutions of 
 silver nitrate deposit less easily than old ones. To free the silver deposit of 
 all silver nitrate solution repeated cold water washing and one final washing 
 in water at 80C. is necessary. 
 
 Dr. Kahle' s value for the mass of silver deposited per ampere-second is 
 0-0011193 from an old solution and '0011182 from a freshly- prepared 
 solution. 
 
348 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 The reader is referred for further information to the 
 following original Papers : 
 LORD RAYLEIGH and MRS. SIDGWICK. " The Electrochemical 
 
 Equivalent of Silver." Phil. Trans. Roy. Soc. Lond., 
 
 1884. 
 K. KAHLE. "The Silver Voltameter and Standard Cells." 
 
 ZeiUchrift fur Instrumentenkunde, 18, 1898, pp. 229, 267. 
 
 H. S. CARHART. " Standards of Measurement." Science, 8, 
 
 p. 326, 1898. 
 G. W. PATTERSON and K. E. GUTHE. " Electrochemical 
 
 Equivalent of Silver." Proc. Amer. Assoc., 47, p. 154, 1898. 
 
 T. W. RICHARDS, E. COLLINS and G. W. HEIMROD. " Electro- 
 chemical Equivalents of Silver and Copper." Proc. Amer. 
 Acad., 35, p. 123, 1899. Science Abstracts, Vol. III., p. 332. 
 
 G. F. C. SEARLE. " The Silver Voltameter." The Electrician, 
 Vol. XXIX., p. 111., 1892. 
 
 Mr. Searle here discusses the various advantages and disadvantages in 
 using different salts of silver. 
 
 FIG. 2. Silver Voltameter for Current Measurement. 
 
 The practical details to which attention must be directed 
 in making a current determination by the silver voltameter 
 are referred to in the above-mentioned article by Mr. Searle. 
 The deposit is best made upon the internal surface of a 
 carefully cleaned platinum bowl (see Fig. 2). The anode 
 should be a plate of pure silver wrapped in white filter paper. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 349 
 
 The washing, drying and weighing of the silver deposit are 
 to be conducted in accordance with the specification given 
 on p. 58, Chap. I. of this volume. 
 
 4. Standard Current Measuring Instruments. Although 
 the official or practical method of determining the value of a 
 current is based upon an electrolytic definition, it is more 
 convenient in ordinary work to rely upon a standard current 
 measuring instrument which operates in virtue of the mag- 
 netic properties of a current-conveying conductor. These 
 instruments may be of such a form that the absolute measure- 
 ment of a current can be made when the geometrical form of 
 the circuits is determined. In this case it is called an absolute 
 standard current-measuring instrument. Of this type are- 
 the absolute tangent galvanometer, or the absolute electro- 
 dynamometer or absolute current balance. 
 
 On the other hand, the instruments may be so constructed 
 that, whilst the same current invariably gives the same- 
 indication, the ampere or absolute value of the current cannot 
 be determined until the instrument has been standardised by 
 passing through it a current the value of which is electro- 
 lytically determined. To this latter class belong the various 
 forms of ampere-balance and standard electro-dynamometer 
 already described in Chap: I. 
 
 It will seldom happen that it is necessary in an ordinary 
 electro-technical laboratory to make an original re-determina- 
 tion of the unit current by means of an absolute instrument,, 
 but it may be convenient to collect here a few elementary 
 principal facts involved in the construction of absolute 
 galvanometers. 
 
 Magnetic Fields of Current-conveying Conductors of Various 
 Forms. (i.) Single Circular Conductor. If a very thin wire 
 is bent into a circle of one turn, the mean radius (r) of 
 the circle being large compared with the diameter of the 
 wire, and if a uniform current is sent through the conductor,. 
 
350 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 the magnetic force (F) in C.G.S. units at the centre is given 
 by the expression 
 
 where A is the current in amperes through the conductor and 
 r is the mean radius of the circle in centimetres. If the 
 point P selected is not at the centre of the plane of the 
 circle, but is a point on the axis or line drawn through that 
 centre at right angles to the plane of the circle, and distant x 
 centimetres from the centre, then the magnetic force there is 
 given by the expression 
 
 r J^A r- 
 
 *~~ 10 (r 8 +*)*' 
 If we write ^for \/r 2 +# 2 , the above becomes 
 
 F _27rA r 2 
 = 10 u* 
 
 where A is the current in amperes through the coil. The 
 above formula may also be written 
 
 where 6 is the angle subtended by the radius r at the point P. 
 The expression for the magnetic force due to a circular 
 current at a point not on the axis is more complicated, and 
 for the detailed proof of the following formulae the reader 
 must be referred to other sources of information. (See 
 Mascart and Joubert's " Electricity and Magnetism," English 
 translation by Atkinson, Vol. II., p. 90, 736 et seq.) 
 
 Let r be the radius of a thin circular wire carrying a current, and x and y 
 the co-ordinates of a point P outside its plane, the centre of the circle being 
 the origin and the axis through the centre perpendicular to the plane of the 
 circle taken as the axis of x. Let X and Y be the components of the 
 magnetic force at P parallel respectively to the axes of x and y, when one 
 absolute or C.G.S. unit of current ( = 10 amperes) flows through the wire. Let 
 M 2 =r 2 +a; 2 , as above. Then it can be shown that, if y is small compared 
 with u, we have, approximately, 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 351 
 
 The above expressions hold good on the assumption that powers of the 
 ratio y/u above the fourth may be neglected. 
 
 The resultant magnetic force at the point P outside the axis is given by 
 the value of N /X 2 + Y 2 , and the inclination 6 to the a-axis by tan 6 = Y/X. 
 
 If the point P is taken in the plane of the circle, then the force at any 
 point not far removed from the centre by a distance y is given by making 
 # = in the above expressions for X and Y. We have then, approximately, 
 
 4r 5 
 Y=0. 
 
 The above formulas are only true when y is, very small compared with r. 
 When this is not the case Y is no longer zero. 
 
 (ii.) Solenoid. Let insulated wire be wound closely in one 
 layer over a cylinder of length 21, so as to cover the whole 
 cylinder. Let r be the mean radius of one circular turn. 
 The magnetic force at any point on the axis of the cylinder 
 may be considered to be the sum of the actions due to a 
 number of circular currents. Take the centre of the cylinder 
 
 FIG. 3. 
 
 as origin, and consider the force at a point P (see Fig. 3) on 
 the axis due to one single circular turn at C occupying a 
 length Sx on the cylinder. Let the distance CP = x. Suppose 
 there are N turns of wire on the cylinder ; then the number 
 of turns per unit of length is N/2J, and the number in a length 
 
 $x is-^r^' Hence the magnetic force in absolute units due 
 
 to this single turn when a current of A amperes traverses the 
 wire is given by the expression 
 
 df 
 
 201 
 
 v i "" j 
 
 Accordingly, the magnetic force at P due to the whole 
 solenoid is 
 
352 IHE MEASUREMENT OF ELECTRIC CURRENT. 
 
 where #=the distance of P from the nearest face of cylinder 
 =AP. 
 Omitting the constant of integration the value of the integral 
 
 x 
 
 Let us call the above integral the cosine of an angle, say 0. 
 Hence, 
 
 2xNA/ a+2l a \ 27rNA 
 
 ~M-U*+(a+2/)s -V^r~20r )S *~ )S *')> 
 
 where and <' are the angles subtended by the radii of the 
 two circular ends of the cylinder at P. 
 
 Suppose we take the point P in the centre of an infinitely 
 long solenoid, and call the length of the cylinder L. Then 
 cos < approximates to 1 and cos <' to 1 . Hence, at the 
 centre of the long solenoid we have a magnetic force F given 
 by the equation 
 
 -p _ 47rNA _ 1 i ampere-turns 
 = TOL~" length 
 
 Or, the magnetic force in the centre is equal to 47T/10 times 
 the ampere-turns per unit of length of the solenoid. 
 
 The above equation holds true approximately for a solenoid 
 the length of which is, say, 20 times its diameter except at 
 regions close to the ends. 
 
 It is easily seen that, in the case of a long solenoid, the 
 force at the centre is just double that at the mouth or 
 entrance to the solenoid, taking the points on the axial line. 
 
 The above formula is also very nearly true for a self-closed 
 or endless solenoid. The calculation of the magnetic field at 
 points not on the axis outside cylindrical solenoids or circular 
 conductors conveying currents involves mathematical pro- 
 cesses of a difficult kind, and the reader must be referred to 
 advanced treatises on the subject. 
 
 5. Absolute Galvanometers. An absolute galvanometer 
 consists of a coil of insulated wire wound in such a form that 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 353 
 
 the field due to a current through it can be calculated at an 
 assigned point. If this coil is arranged so that the coil field 
 at the stated point is at right angles to a known and constant 
 field, such as that of the earth, at the same point, then the 
 ratio of these field strengths can be determined by placing at 
 that point a small magnetic needle and observing its direction. 
 Let C (Fig. 4) be a circular coil of wire, and let F be the 
 magnitude and direction of its field at the point P. Let the 
 coil be arranged so that F is at right angles to the magnetic 
 field H due to the earth ; then if a small magnetic needle is 
 suspended freely at P, it will set its axis in a direction 
 inclined to the magnetic meridian by an angle 6, such that 
 
 FIG. 4. 
 
 F/H tan 0. The current through the coil, reckoned in 
 amperes, is proportional to the magnetic force F at any point. 
 Hence, if G is a constant depending on the geometrical form 
 of the coil, we may write 
 
 F = GA. 
 
 Hence, 
 
 G 
 
 The quantity H/G- is called the galvanometer deflectional 
 constant. 
 
 Accordingly, if the space distribution of magnetic force 
 due to the current in the coil is of such a nature that every- 
 where in the region occupied by the magnetic needle it is 
 at right angles to the magnetic force due to the earth and of 
 
 AA 
 
354 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 constant value, the deflections are strictly proportional to the 
 tangents of the angles of deflection, and the instrument is 
 called a tangent galvanometer. 
 
 Suppose, for instance, that an exceedingly large circular coil of wire of one 
 turn has a very small horizontal magnetic needle hung exactly at the centre 
 of the coil. Let the needle not exceed in length one-hundredth of the 
 radius (r) of the coil. Let the coil be placed with its plane in the magnetic 
 meridian. Then the magnetic force F at the centre of the coil due to a 
 
 2?r A 
 current of A amperes flowing in the wire is F = j~ - Hence, for this coil 
 
 G = 2?r/10r ; and if the magnetic needle takes a deflection under a terrestrial 
 
 horizontal force H we have A= * tan 6. 
 
 2ir 
 
 An arrangement of this kind constitutes an absolute tangent galvanometer, 
 because we can determine the value of the current absolutely from measure- 
 ments of r H, and 0. 
 
 Consider next the case when the magnetic needle is placed with its centre 
 at a point on the axis outside the plane of the circular coil of one turn, and has 
 
 aO 
 
 60 
 
 a length not very small compared with the radius of the coil. Let the current in 
 the wire be 10 amperes or a unit (C.G.S.) current. Let ab (Fig. 5) be the coil seen 
 in section and let the magnetic needle ns have a length 2 and be placed with 
 its centre at P, at a distance x from the centre of the coil. Let each pole 
 of the needle have a strength, m. Then each pole is acted upon by two 
 forces wXi mY 1} ?ftX 2 mY 2 , the values of X and Y being determined by the 
 co-ordinates of the pole, and areas stated in equations (i) and (ii) in 4 on p. 350. 
 This system of forces resolves itself into one resultant force and one resultant 
 couple. If, however, the centre of the neeile is constrained to remain at P, 
 then we need only consider the couple. This couple may be called D, and it 
 has a value such that 
 
 D = ml (X x + X 2 ) cos - ml (Yj + Y 2 ) sin 0. 
 
 By substituting the proper values of Xj. YI, &c., obtained from the equations 
 above mentioned on p. 350, it is not difficult to show that 
 
 1): 
 
 D 
 
 4 
 
 "64 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 355 
 
 la the above equation r is the radius of the coil and u? = r 2 + x z , and it is 
 assumed also that I is so small compared with u that we may neglect powers 
 above the fourth of the ratio l/u. Also, M is written for 2ml or the moment 
 of the magnet. 
 
 If the coil is placed with its plane in the magnetic meridian, then the 
 opposing or controlling couple due to the earth is MH sin 0. If the coil 
 consists of many turns of insulated wire wound on a square-grooved circular 
 
 frame, then in place of the factor 2?r-j we have to write a more complex 
 
 function G, which is obtained as follows : 
 
 Let the windings of the coil be in a square groove having a length 26 
 parallel to the axis of x and a depth 2c = r"-r' parallel to the radius of the 
 coil. Let there be n turns of wire per unit of length of the groove. Consider 
 first, one single layer forming a short solenoid or diameter 2r. It has already 
 been shown that the magnetic force at P due to unit current in this coil 
 would be expressed by 
 
 . . ,- 
 
 r 2 + (x + 6) 2 V r 2 + (x - 
 
 To obtain the magnetic force due to the whole of the windings we have to 
 integrate the above expression between the limits r=r" and r = r' and obtain 
 the value of Gr from the expression. 
 
 G = 2irn a 
 
 Keturning to the expression for the value of the couple D 
 exerted by the unit current on the needle placed with its 
 centre at P. It is seen that if the ratio l/u is so small that 
 we can neglect powers of it above the second, then we can 
 make the correcting factor in the square bracket due to the 
 finite length of the needle reduce to unity, either by making 
 45C 2 = r 2 or by making 1 5 sin 2 $=0. 
 
 The first condition is complied with by placing the centre of 
 the needle at a distance from the plane of the coil equal to 
 half the radius r, and the second by making the reading 
 as nearly as possible in the neighbourhood of the angle 
 
 = VE = 
 
 AA2 
 
356 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 We may, then, summarise the above results as 
 follows : 
 
 If a coil of insulated wire wound in a square-sectioned 
 groove is placed with its plane in the magnetic meridian, and 
 is traversed by a current of A amperes, it exerts a magnetic 
 couple on a needle placed with its centre at a point on 
 the axis of the coil which is determined by the equation for 
 D given at the bottom of p. 354 Let this equation be written 
 
 where G is the coil constant or value of the magnetic force 
 due to unit C.G-.S. current (10 amperes) in one turn of the coil 
 at a point on the axis, and K is a correcting factor for the 
 distribution of the force at points not on the axis. This 
 couple is balanced against the couple MH sin due to the 
 action of the terrestrial magnetic force on the needle. Hence 
 we have 
 
 A _10Htan0 
 = 
 
 If the needle is placed with its centre at a distance from the 
 plane of the coil equal to r/2, then the correcting factor K is 
 reduced to a value 
 
 on the assumption that powers of l/r above the fourth may 
 be neglected. If the length of the needle is not greater than 
 say one-twentieth of the mean radius of the coil, then K 
 becomes sensibly zero and the tangents of the deflections of 
 the needle are proportional to the currents flowing through 
 the coil. 
 
 If the tangent galvanometer consists of a single circular 
 coil of mean radius r, and having the wire wound in n turns 
 in a square-sectioned groove of widtli 2a and radial depth 21, 
 also haying a magnetic needle of length 21 placed at us\ 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 357 
 
 centre, the value for the current in amperes (A) creating a 
 deflection is approximately given by the equation 
 
 A lOrH /-, . I a 2 1 b* 3 / 2 \ A , 15 Z* . 2 <\ . 
 A = _ M+ _ _ JM + _sm 2 0) tana 
 2wn \ 2 r- 3 r 2 4 r 2 / \ 4 7^ / 
 
 In the above equation it will be sufficient to take 21 as 
 equal to 0*82 of the full length of the magnetic needle. 
 (See F. Kohlrausch, " Physical Measurements.") 
 
 A tangent galvanometer of the above type is employed 
 generally in the Postal Telegraph Department. 
 
 Helmholtz Standard Tangent Galvanometer. A better 
 and more practically convenient form of tangent galvano- 
 meter is that devised by Von Helmholtz. In this instru- 
 ment there are two large circular coils of insulated wire, the 
 wire being either wound in a square groove in the edge of a 
 wooden ring or wound in one layer on the edge of a ring 
 which forms the frustrum of a cone. These coils are fixed at 
 a distance apart equal to the mean radius of either coil of 
 wire. If the wire windings lie on the frustrum of a cone the 
 cone angle is selected so that the apex of the cone is the mid- 
 point between the coils. Every turn of wire then complies 
 with the condition that it is separated from another equal 
 circular turn in the other coil by a distance equal to the 
 radius of either. This latter arrangement of the winding is 
 most suitable for an absolute instrument. These coils are 
 fixed to a base so that, whilst remaining at the fixed distance 
 apart, they can be turned round on axes perpendicular to and 
 passing through the mid-point. At the middle point is 
 placed a compass-box containing a short magnetised needle 
 having attached a long aluminium index needle moving over 
 a circular scale of degrees. Otherwise the magnetic needle 
 may be suspended by a fibre of cocoon silk and have attached 
 to it & mirror. If the compass needle has the ordinary jewel 
 centre suspension some device should be added to lift the 
 needle off its pivot when not in use. The length of the needle 
 should not exceed one-twelfth of the radius of either coil. 
 
358 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 To use the instrument it is placed at a distance from all 
 iron or magnets, and the current to be measured is conveyed 
 to it through a length of concentric cable, or through insulated 
 wires twisted together. The current then flows through the 
 coils in such a manner as to produce a uniform field in the 
 space between the coils. The needle then takes a deflection, 
 the tangent of which is proportional to the current. The 
 instrument must be so oriented that if the current is reversed 
 the angular deflection of the needle from the plane of the 
 meridian is in both cases the same in amount though opposite 
 in direction. 
 
 If, then, the dimensions and disposition of the windings is 
 known, the value of the current can be calculated when the 
 magnitude of the earth's horizontal magnetic force H is 
 known at that place. Yery roughly speaking, this has a value 
 lying between 0*15 and 0*18 C.G.S. units in Great Britain ; 
 but its value at any given spot in a laboratory may be greatly 
 affected by the neighbourhood of iron pipes or masses of iron. 
 Hence, a standard tangent galvanometer can only be employed, 
 for purposes where accuracy is required, in a special room set 
 apart for its use and where facilities also exist for determining 
 the value of H as often as required. This constant can, 
 however, be determined with a fair degree of approximation 
 as follows : 
 
 Provide a cylinder of steel carefully magnetised longitudi- 
 nally and measure (in cms.) its length I and mean diameter d. 
 The moment of inertia I of this cylinder round an axis through 
 its centre and perpendicular to its own axis of symmetry is 
 
 12 + : 
 
 where W is the weight of the cylinder in grammes. If this 
 cylinder is suspended in a paper stirrup by a few threads of 
 floss silk and set in vibration round a vertical axis, it is easy 
 to determine, from the time taken to execute, say, 50 complete 
 vibrations, the time t of one vibration. If, then, M is the 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 359 
 magnetic moment of the magnet, it can be shown that 
 
 t = 2 7r ^/^-.* 
 
 Hence, MH=^. 
 
 Then let this magnet be placed in a position with its axis 
 in a horizontal line passing at right angles to the meridian, 
 through the centre of the tangent galvanometer needle, and 
 with its centre at a distance D centimetres from the needle- 
 pivot. Observe the deflection produced on the galvanometer 
 needle. It can be shown that 
 
 M DV, .ItfV 1 
 
 = I j_ + - i 
 
 M_D 3 /. 
 H~~2V 
 
 2DV tan0 ' 
 
 where L is the " magnetic length " or distance between the 
 poles of the cylindrical magnet and D the distance of the 
 centre of the deflecting magnet from the centre of the 
 galvanometer needle ; and the assumption is made that L/D 
 is a quantity so small that its squares and higher powers can 
 be neglected. 
 
 From the two equations for MH and M/H we can find at 
 once the value of H, by taking two sets of observations with 
 the magnet at different distances, D 1 and D 2 , from the 
 galvanometer needle and then eliminating L from the two 
 equations so obtained, viz. : 
 M I 
 
 M 
 
 from which L may be eliminated. 
 The above equations may be written 
 
 " 
 
 * See the Appendix of a book entitled "Magnets and Electric Currents, 
 by J, A, Fleming. 
 
860 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 from which we obviously have 
 
 M_ 1 D^tan^ D 2 5 tanfe 
 H~2 IV-D 2 2 
 
 Hence the ratio M/H is easily calculated when D r D 2 , 9 V 62 
 are found. 
 
 Having, then, the value of the ratio M/H and that of the 
 product MH, we obtain at once the value of H. 
 
 The values of G (the coil constant) having been calculated 
 as already explained, and H determined as described for the 
 locality, we can obtain the ampere value of a current creating 
 any observed galvanometer deflection. 
 
 Standard galvanometers in which fixed coils and magnetic 
 needles are used are, however, almost useless as exact measur- 
 ing appliances unless placed in buildings set apart for the 
 purpose, into the construction of which no iron enters. In 
 ordinary laboratories warmed with iron hot-water pipes or near 
 engines and boilers or machinery, the value of the local 
 terrestrial magnetic force is so constantly varying in amount 
 and direction that the standardization of the instrument 
 changes almost from moment to moment. Hence the use 
 of the tangent galvanometer under these circumstances as an 
 instrument of precision is as impossible as would be the use 
 of the balance if the mass of the standard weights of com- 
 parison were changing from moment to moment. 
 
 6. The Electro -dynamometer. A most valuable substi- 
 tute for the standard galvanometer in the precise measurement 
 of current is the standard electro-dynamometer. In this 
 instrument, as in the commercial form, there are two coils 
 of wire, one fixed and the other movable. In standard 
 instruments both these coils take the Helmholtz form that 
 is to say, they consist of two equal separate circular coils 
 placed with their planes parallel to one another and fixed at a 
 distance equal to the radius of either. The movable coil is 
 suspended by a bifilar suspension consisting generally of the 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 361 
 
 two wires by which the current enters and leaves this movable 
 coil. The coils are held normally with their axes at right 
 angles and centres coincident. When one and the same 
 current is passed through the coils, the electrodynarnic forces 
 tend to turn the coils so that their axes are more in the same 
 direction, and this torque is resisted by the bifilar torque. 
 
 The theory of the electro-dynamometer has been given by 
 Clerk Maxwell (see "Electricity and Magnetism," Vol. IT., 
 p. 337, 2nd edition). The reader is also referred to an 
 excellent series of explanatory articles by Mr. G. R C. Searle, 
 
 FIG. 6. 
 
 on the determination of current in absolute measure in The 
 Electrician, Vol. XXVII. and Vol. XXVIII, for 1892. From 
 these sources the following abbreviated analysis has been 
 taken : 
 
 Consider, in the first case, the electro-dynamometer to 
 consist of two coils only (see Fig. 6). 
 
 Let the inner coil a be the suspended coil, and let its 
 diameter be small compared with the outer or fixed coil A. 
 
 Let G be the galvanometer constant of the large coil, i.e., the 
 magnetic force at the centre due to unit absolute current 
 
362 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 flowing in it. Hence, if i is the current flowing in both 
 coils when joined in series, the magnetic force over the central 
 region of the large coil is nearly equal to Qi. 
 
 Let g be the total area enclosed by all the windings of the 
 small coil ; then gi is the magnetic moment of the small coil. 
 Hence, when the latter is held so that the angle between the 
 axes of the coils is <f>, the magnetic couple or torque on the 
 small coil is i 2 Gg cos 0. If the large coil is placed with its 
 plane in the magnetic meridian there is also a couple due to 
 the earth's force acting on the small coil and equal to giK sin 0. 
 
 The bifilar suspension produces a restoring couple, which may be represented 
 by ju sin 0, since for small angular displacements it is proportional to the sine 
 of the displacement. Hence the equation of equilibrium of the small coil, 
 hung in a uniform magnetic field H and supported by a bifilar suspension, is 
 
 i 2 Gg cos <f> = igU sin + P sin fa 
 or tan = i 2 Gg/(igH + ft). 
 
 It is always possible to make th eterm igR negligible compared with /j. ; so 
 that approximately we have 
 
 If we then take four observations of the deflection of the small coil, first by 
 reversing the direction of the current through the small coil alone and then 
 through the large one alone, and call the several observed angular displace- 
 ments of the small coil fa, 02, 03> 04> it is easy to see that, since 
 
 tan 0! = 
 
 and tan 2 = 
 
 we have & = (tan fa + tan 2 W2G# ; 
 
 and therefore, also, 
 
 i 2 = (tan 0! + tan 2 - tan 3 - tan 4 
 Hence, i is determined in terms of the tangents of the deflections and the 
 constants of the instrument, viz., M, G and g. 
 
 The constants for any instrument can be found as follows : Let M be the 
 mass of the suspended coil. Then /* = XM. Let T be the time of a small 
 vibration of the suspended coil, and K its moment of inertia. Then 
 
 m < 
 
 1-u,,*, XM - 
 
 Affix to the movable coil a bar of mass M', of which the moment of inertia 
 K' is known, and observe the time T' of a small vibration of the new system. 
 
 Then, 
 
 Hence, from the two above equations, we have 
 
 47r 2 K'M 
 
 /* = 
 
 M(T' 2 -T 2 ) + M' 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 363 
 
 In the next place, we have to determine G and g. Suppose the fixed coils 
 have the Helmholtz form, and consist of two coils of mean radius A fixed with 
 centres at a distance B = A/2. Then the magnetic force at the central region 
 for unit current in the coils = G is such that 
 n _ 47rnA 2 
 
 \j __ _- 
 
 or, if B = A/2, G = - 32?m 
 
 Also, g stands for the total area included by all the windings of the small 
 coil. If a is the mean radius of the small coil that is, the radius from the 
 centre to the centre of gravity of the windings, it can be shown that 
 
 where h is the radial depth of the windings supposed to be placed in a 
 rectangular groove, and n' is the number of turns. 
 
 If we substitute the above values of n, G and g in the equation for i, we 
 arrive at the following result : 
 
 2 _ *jv\ ft. / A 2 M'A 
 
 where the symbols have the meanings below : 
 
 x = observed scale deflection. 
 
 d = distance of scale from mirror on movable coil. 
 
 B=half distance of fixed coils. 
 
 A = mean radius of fixed coil. 
 
 a = mean radius of movable coil. 
 M = mass of movable coil. 
 M' = ma<3s of inertia bar. 
 K' = moment of inertia of the above bar. 
 
 T,T' = times of vibration of movable coil with and without inertia bar. 
 n,n' = number of turns of wire on fixed and movable coils respectively. 
 
 Maxwell gives (" Electricity and Magnetism," Vol. II.) the full theory of 
 the action of one circular coil upon another, and shows that if there be two 
 circular coils whose axes intersect at an angle 0, then the co-efficient of 
 mutual induction M can be expressed in a series of zonal harmonics, such that 
 M = GiiP 1 (0) + G 2 2 P 2 (0) + &c., where the constants are G 1} G 2 , &c. The 
 quantities P 1} P 2 , called zonal harmonics, are functions of cos 6 of the form 
 P (0) = l, Pi(0) = cos0, P 2 (0)=i(3cos 2 0-l), P 3 (0) = |(5cos 3 0-3cos0), &c., 
 and have been tabulated and calculated out numerically for various values 
 of 0.* 
 
 The quantities GI, G 2 , &c., are found as follows : Maxwell shows (loc. cit.) 
 that if any point be taken on the axis of a circular current, the magnetic force 
 
 See Prof. John Perry, Phil. Mag., Dec., 1891, 
 
364 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 at that point, F, due to unit current in the coil can be expressed in terms of 
 the distance x of the point from the centre and certain functions of the radius 
 of the coil and the distance of a point of reference on the axis. Consider the 
 case of a circular current of radius A, and take any point as origin on the 
 axis at a distance B Let C 2 = A 2 + B 2 . Then the magnetic f orce F at any 
 point at a distance x from the centre of the circle where x is small compared 
 with C may be expressed by 
 
 F = GI + 2G 2 a- + 3G 3 aj 2 + &c. ; 
 or, if x is large compared with C, by 
 
 F= 2^ 3^ %3 
 
 Off* a 4 X 5 
 
 We have already shown that the magnetic force at a point at distance x 
 from the centre on the axis of a circular current is given by the formula 
 
 27TIA 2 
 
 F= - a- 
 
 Hence, if we expand the above expression in ascending or descending powers 
 of x and equate the co-efficients to those of the above series, we have the 
 values of G and g as follows : 
 
 G 1 = 2 7 rA 2 /C 3 , G 3 =47rA 2 (B2 - |A 2 )C 7 , 
 
 G 2 =37rA 2 B/C 5 , G 4 =57rA 2 B(B 2 - f A 2 )/C 9 . 
 
 - |A 2 ). 
 
 Now in the Helmholtz pattern electro-dynamometer, when we are considering 
 the magnetic force at the centre, we have B = A/2, and, as a consequence, all 
 the terms vanish in the expansion for M between the first and fifth. In 
 other words 
 
 M = Gtf ^(0) + G 5 ? 5 P 5 (0) + 
 
 We need not generally take account of terms beyond the fifth. Hence 
 also if the deflection < of the movable coil is small, and since <f> = ir/2-0, 
 it is easy to show that P 5 (0) = . cos nearly. Under these circumstances 
 
 144 
 
 G 5 = - _ Gi/A 4 , and if a single suspended coil is placed at the centre of the 
 090 
 
 pair of fixed coils, then g. = gO^i- Then we have 
 
 M = Gtf! sin {l - 27a 4 /lCOA 4 }> 
 
 and the couple or torque experienced by the movable coil when both are 
 traversed by a current i is 
 
 i^=G 1 g l cos 0{l - 27a 4 /100A 4 }. 
 
 Hence the factor (1 - 27a 4 /100A 4 ) comes in as a correcting factor to the term 
 Gg cos0 in the equation of equilibrium of the movable coil. 
 
 Space does not permit us to enter more fully into 
 the detailed theory of the electro-dynamometer, but the 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 365 
 
 mathematical reader is referred to the following sources of 
 information : 
 
 For the full mathematical treatment of the action of 
 circular currents on each other see Maxwell, " Electricity 
 and Magnetism," Vol. II., Chap. XIV., 2nd edition. 
 
 Also Mascart and Joubert, " Treatise on Electricity and 
 Magnetism." translated by Atkinson, Vol II., Chap. IV. 
 
 And A. Gray, " Absolute Measurements in Electricity and 
 Magnetism," Vol. II., part 2. 
 
 In addition, the above-mentioned series of articles by 
 Mr. Searle on " Current Measurements " in The Electrician, 
 Vol. XXVII. and XXVIII, may be consulted. 
 
 As an instance of the use of the electro-dynamometer and 
 calculations connected therewith the reader may consult a 
 paper by Mr. Dugald McKichan " On the Number of Electro- 
 static Units in one Electromagnetic Unit," Phil. Trans. Eoy. 
 Soc, 1873. 
 
 7. Current Balances. Dr. Joule was one of the first 
 persons to construct an amperemeter in which a current was 
 measured by observing the apparent increase or decrease in 
 weight of a coil carrying a current produced by the mutual 
 electrodynamic action of another coil conveying a current 
 placed parallel to it. The much more elaborate current 
 balances of Lord Kelvin have already been fully described 
 (see Chapter I.). In these latter instruments the movable 
 coil is placed between two fixed coils. 
 
 In order that stability may be secured, it is necessary that 
 a displacement of the movable coil from its position of rest 
 should not decrease the electrodynamic forces acting upon it. 
 If we place two fixed circular coils parallel to each other, as 
 on the Helmholtz galvanometer, and a smaller movable coil 
 is held between them so that the planes of all three are 
 parallel, then, by suitably arranging the direction of the 
 currents, we can create a force tending to move the movable 
 
366 
 
 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 coil parallel to itself. Maxwell points out that if the 
 diameter of the fixed circular coils is to the distance between 
 their planes as 2 : \/3, then they will produce a nearly 
 uniform force on a much smaller circular coil placed between 
 them and with its plane parallel to those of the fixed coils. 
 
 FIG. 7. 
 
 FIG. 8. Pellat's Ampere Balance. 
 
 A form of standard ampere balance has been designed by M. 
 Pellat for the Laboratoire Central d'Electricite in Paris. It 
 consists (see Figs. 7 and 8) of a fixed horizontal solenoid 
 and an enclosed smaller solenoid attached to the beam of a 
 balance. When a current is passed through the two coils in 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 367 
 
 series it tends to turn round the movable solenoid so as to 
 bring the axes of the coils more into colineation. This torque 
 is resisted by weights put upon the scale pans of the balance. 
 If H is the value of the earth's horizontal magnetic field 
 parallel to the axis of the fixed coil, and if A is the current 
 flowing through the coils, then the resultant magnetic force 
 in the interior of the large coil parallel to its axis is 
 
 F = BA+H. 
 
 If the magnetic moment of the movable coil is M, then 
 
 M-B'A. 
 
 Hence the couple acting on the movable coil when it is in 
 equilibrium is 
 
 C-MF-KK'A'+K'HA. 
 
 If the current in the fixed coil is then reversed, the couple 
 becomes 
 
 C'- -BB'A 2 +B'HA. 
 
 Hence C-C'=>2BB'A 2 , f 
 
 If the couples are produced by weights W and W put in the 
 scale pans attached to the movable coil, then these weights 
 are proportional to the couples, and we have 
 
 A = 
 
 where K is some single constant. If the coil dimensions are 
 measured K can be calculated. The value of K for the 
 Pellat balance in the Laboratoire Central in Paris is 
 K = 0*217682 in terms of the ampere and gramme. 
 
 8. Working or Laboratory Amperemeters. It would be 
 of little use to describe the multitudinous forms of commercial 
 ampere or ammeters which have appeared and disappeared in 
 the last 20 years. Broadly speaking, in addition to the 
 standard instruments already described, the practical elec- 
 trician has need of three classes of current-measuring 
 
368 THE MEASUREMENT OF ELEGTRIG CURRENT. 
 
 direct-reading instruments called respectively galvanometers, 
 table or portable ammeters, and switchboard ammeters. Table 
 or portable ammeters are employed for the numerous occasional 
 measurements of current in practical units made anywhere or 
 everywhere in the laboratory, and those of the third class 
 only in fixed positions and on certain circuits. 
 
 It is necessary that the above two classes of instruments 
 should give at once, by a direct-scale reading, the approxi- 
 mate value of the current in amperes. The first class, or galva- 
 nometers, are not usually direct-reading. They are 'mostly 
 employed to indicate the mere presence or absence of 
 a current in a circuit, and when the ampere value of 
 
 FIG. 9. The Weston Portable Ammeter. 
 
 their indications is required they have to be standardised. 
 The necessary qualifications for a good portable or table 
 ammeter are (i.) that it should be dead-beat that is to say, 
 its indicating needle must come immediately and without 
 oscillations to the scale reading corresponding to the current 
 passing ; (ii.) it should have no dead or undivided part of the 
 scale ; and, (iii.) if possible, the scale divisions for equal 
 increments of current at various portions of the scale should 
 be equal in other words, the scale should be equi-divisional. 
 No laboratory instruments fulfil the above requirements, as 
 far as continuous currents are concerned, so well as the 
 Weston instruments. In these ammeters (see Fig. 9) there 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 369 
 
 is a well-aged magnet which produces a constant magnetic 
 field. In this field is held a circular coil of wire carried on 
 an axis revolving in jewelled centres. The control is produced 
 by a steel spiral spring, like the hair-spring of a watch. 
 
 In all but the ammeters for very small currents the 
 greater portion of the current in the circuit containing the 
 ammeter passes through a shunt, so that the above-mentioned 
 coil only carries a very small portion of the current. The 
 terminals of the instrument are marked + and so as to 
 
 FIG. 10. General Design of Hartmann and Braun Hot Wire Ammeter. 
 
 show how the connections should be made. The instruments 
 are made in various grades, to read from milliamperes to 
 hundreds of amperes, the readable range in each instrument 
 being about 1 to 1,500. These instruments are not, however, 
 available for alternating-current measurement. For this last 
 purpose, a convenient form of ammeter is that depending on 
 the heating of a wire, and therefore called a hot-wire ammeter. 
 A good form of hot-wire ammeter is that of Hartmann and 
 Braun (The Electrician, Oct. 6, 1899). In this instrument (see 
 Figs. 10 and 19) a fine wire is stretched between two fixed 
 
370 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 points, and is heated by the whole or part of the current to 
 be measured. The wire, therefore, extends and "sags/' and 
 the indicating portion of the instrument is a device for accu- 
 rately measuring this sag. The advantage of this arrangement 
 is that the sag is greater than the mere longitudinal extension 
 of the wire. This is easily proved as follows : 
 
 Let an inextensible thread of length 21 be fastened between two supports 
 at a distance 21, and held, therefore, in a straight line. Let one of these 
 supports move towards the other by a small distance, 2x, which is equivalent 
 
 _ L-x 
 
 FIG. 11. 
 
 to assuming a small increment of length, 2x, to be made in the thread. The 
 thread, therefore, will sag down. Let s be the amount of the sag. Then, as 
 seen from Fig. 11, we have the equation 
 
 or s*+x* -21x^0. 
 
 If x is small compared with I, we may neglect x 2 in comparison with 2lx, and 
 we have 
 
 Hence it will be seen that s is very much greater than x provided I is much 
 greater than x. For instance, if 1 = 100mm. and x = 1mm., then s = 141mm. 
 nearly. 
 
 Fm. 12. 
 
 A means of still further multiplying the extension of a wire may be found 
 by allowing the sag of one wire to create a still greater sag in a second. Thus, 
 suppose two wires, each of length 21, are arranged as in Fig. 12, connected 
 to three fixed points, a, 6, c. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 371 
 
 Let the wire cd have its end d attached to the middle point of ab. Let the 
 wire ab increase by a small length 2x. Then, if s is its sag, we have 
 
 or 2xl+x 2 =s 2 , 
 
 or, if x/l is small, s= 
 
 Then, in the same way, for the second wire we have, if s' is its sag, 
 
 or, if xl is small compared with xl?, 
 
 s' 
 Hence, s' is very much greater than x. 
 
 Thus, if <e = 0'lmin. and Z = 100 s' = 21mm. nearly, or the extension is 
 multiplied 210 times. 
 
 In the Hartmann and Braun hot-wire ammeter the wire is 
 mounted between fixed insulated pivots, on a plate of metal 
 having the same coefficient of expansion for heat as the wire. 
 The sag of the wire is measured by causing it to create 
 rotation in an indicating needle, the movement of the needle 
 being resisted by a steel spiral spring which brings it back to 
 zero. 
 
 In the case of ammeters for small currents the whole 
 current passes through the wire and heats it. In the case of 
 ammeters for larger currents, the main portion of the current 
 passes through a shunt. The instrnments are very dead beat 
 and the scale reading is most open at the point at which 
 greatest accuracy is required. The vibrations of the needle 
 are checked by attaching to the needle shaft a light circular 
 disc of copper which moves between the closely placed poles 
 of a strong horse-shoe magnet, thus creating "magnetic 
 friction" by reason of the eddy currents set up in the disc 
 whenever rapid rotation of the disc takes place. 
 
 These instruments are available both for direct and 
 alternating currents, and have many practical advantages. 
 There is, however, a dead portion of the scale below which no 
 scale divisions are engraved ; the lower limit of the scale 
 reading is approximately 10 per cent, of the upper limit. 
 Thus an ammeter reading to 100 amperes would be useless 
 
 BB2 
 
372 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 for measuring less than 10 amperes (see The Electrician, Vol, 
 XLIIL, p. 839). 
 
 For switchboard purposes very popular instruments are 
 those called the Edgewise instruments (see Fig. 13). In this 
 case the scale is a curved circular band, and the needle end 
 projects through a slit in it and has its end turned over so as 
 to be seen against the scale. The instruments take up less 
 room on a switchboard than the circular type, and are more 
 easily read from the floor level. 
 
 FIG. 13. Kelvin Edgewise Switchboard Ammeter. 
 
 For a full discussion of the advantages and disadvantages 
 of various forms of ammeter for switchboard purposes the 
 reader is referred to a paper by Mr. Blakie on " Instruments 
 for Switchboards," in The Electrician, Vol. XLL, p. 209. 
 
 9. Calibration of Laboratory Ammeters. No com- 
 mercial instruments can be taken to be absolutely correct in 
 their scale indications no matter what the makers of them 
 may assert. The practical electrician must proceed first to 
 standardise them in order to obtain the true or most probable 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 373 
 
 real ampere value of any scale-reading by an independant 
 measurement. For this purpose no appliance is so convenient 
 as the potentiometer already described (see Chapter I., 13 
 p. 134) aided by appropriate standard current-carrying resist* 
 ances. For by this means the measurement of a current is 
 reduced to the measurement of a resistance and the electro* 
 motive force of a standard cell, both of which are tolerably 
 permanent values for given well-made instruments. Hence, the 
 standardisation of an ammeter is conducted as follows : 
 
 The ammeter A (see Fig. 14) must be joined up in series 
 with a low resistance standard K of such type that it can 
 
 FIG. 14. 
 
 carry, without injurious heating, the maximum currents to be 
 passed through the ammeter. In series with this should be 
 another adjustable rheostat for varying the current passed 
 through the ammeter, and also a carbon rheostat C for 
 making very small adjustments in the current. From the 
 potential terminals of the standard low resistance are brought 
 two potential wires, which are connected with the potentio- 
 meter wire a 5, as shown in the diagram The potentiometer 
 is first set by means of a Clark or Weston cell so that the fall 
 of potential down the slide- wire is of known amount, obtained 
 by regulating the current flowing from the working battery 
 through the slide-wire. 
 
374 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 If, for instance, a Clark cell is employed, the temperature 
 of which is 15C. and the corresponding E.M.F. 1434 volts, 
 the sliding contact is set to make contact at that division on 
 the slide-wire marked 14,340, and the current down the 
 slide-wire regulated until the reading galvanometer shows no 
 deflection. When this is done, the potential wires connected 
 to the ends of the low resistance are substituted for the 
 connections to the Clark cell, and the fall of potential down 
 the low resistance is read off directly on the potentiometer 
 slide-wire. Hence, knowing the value of this low resistance, 
 we have at once the true current through the resistance, and, 
 
 -2 
 
 1 23456 
 SCALE READING 
 
 NL s A 10 11 1 
 
 FIG. 15. Ammeter Error Curve. 
 
 therefore, that through the ammeter. We can, therefore, 
 write down two columns of figures, one of which gives the 
 observed scale-reading of the ammeter and the other the 
 true ampere value of the corresponding current. The 
 difference between these two figures is the error of the 
 ammeter corresponding to that scale-reading. 
 
 We can then make an error curve for the instrument as 
 follows : Let the various scale readings be plotted out as a" 
 horizontal line (see Fig. 15) and, corresponding to each, let 
 a line be erected the length of which is the error of the 
 ammeter at that reading, the said line being drawn upwards 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 375; 
 
 the error is positive and downwards when the error is 
 negative. Thus if, corresponding to an abscissa 20, denoting 
 a. scale-reading of 20 amperes, the error is +2'2, we draw 
 the line representing 2 '2 upwards, and the true ampere value 
 of the current when the ammeter needle points to 20 on the 
 scale is 20+ 2*2 = 22*2. If,, on the other hand, the error is 
 negative, the line is to be drawn downwards, and the 
 true ampere value corresponding to 20 divisions would be 
 20 -2-2 = 17-8 amperes. 
 
 , Every working ammeter in the laboratory should in this 
 manner have an error curve drawn for it which should be 
 repeatedly verified. The error curve should be taken with 
 ascending as well as descending values of the currents, since, 
 in certain types of ammeter, particularly those containing soft 
 iron masses moved in a magnetic field, there is often con- 
 siderable hysteresis error. The ammeter will not give the 
 s^ime reading for the same current value if it has previously 
 been used with a different and much larger or much smaller 
 current. 
 
 , Hence, in checking an ammeter it is not sufficient. to 
 determine its scale inaccuracy for one cycle of current 
 values : we must know how far the instrument gives the 
 same scale-readings for the same current values independently 
 of the values of the currents previously passed through it 
 At the same time, its zero-keeping quality and dead-beatness 
 can be noted. 
 
 ' If the ammeter is one intended for use with alternating 
 currents, an investigation must be made to determine how far 
 the readings are affected by change in frequency of the 
 current. 
 
 There is no better method of doing this than by calibrating,; 
 first of all, a Siemens' electro-dynamometer and delineating 
 for it a curve showing the torsion in scale degrees corres- 
 ponding to various continuous currents passed through it. : 
 In so doing, it is essential to place the instrument in such 
 a position that the movable coil when in its zero position; 
 
376 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 shall not be affected by the earth's magnetic force. In order 
 that this may be the case the instrument should be so oriented 
 that the axis of the movable coil when in its zero position is 
 in the direction of the local magnetic meridian. To test this 
 try reversing the direction of the current through the movable 
 coil alone, and ascertain if the torsion required to restore the 
 movable coil to the sighted position is the same in both cases- 
 When the instrument has been calibrated for direct currents, 
 it may be used with alternating currents of various 
 frequencies; and employed in series with the ammeter to 
 be tested to calibrate it and to detect if the ammeter reading 
 varies with the frequency. 
 
 10. Direct Measurement of Current by the Potentio- 
 meter. The majority of commercial ammeters are so liable 
 to change of errors that, in order to avoid the expenditure of 
 time in constantly calibrating them, it is better in many cases 
 to rely on the potentiometer directly as a means of measuring 
 current directly. Thus, in the case of the measurement of 
 current through an incandescent lamp, it is necessary to be 
 able to determine a current which may have a value approxi- 
 mately of half an ampere or so to within 1 per cent, at least. 
 No commercial ammeter can be depended upon to measure or 
 indicate correctly a current of this order with the above- 
 mentioned accuracy. Hence incandescent lamp currents are 
 far better measured by inserting in series with the lamp a 
 resistance adapted for carrying 1 ampere to 10 amperes and 
 measuring with the potentiometer the fall of potential 
 down this resistance. If the resistance has a value of 
 1 ohm and is made of manganin, we can, by its aid, deter- 
 mine the current value with great ease to within one-tenth 
 of 1 per cent. 
 
 These measurements may take a little longer than when 
 made with a direct-reading ammeter, but they can be 
 depended upon when made to be accurate within the above- 
 named limits. 
 
THE MEASUREMENT OF ELECTRIC CURRENT 377 
 
 In the same manner, in measuring large currents, such as 
 those given by large dynamos, it is much better to pass the 
 current through a resistance strip of one-thousandth of an 
 ohm resistance and determine the current by the fall of 
 potential down the strip. 
 
 A stock of low-resistance current-carrying resistance strips 
 and a potentiometer is thus a more profitable investment of 
 capital for an electrical laboratory than the purchase of a 
 large number of commercial ammeters of different kinds. 
 
 The measurement of the large currents sent out from 
 continuous-current stations is most accurately effected by the 
 direct measurement of the fall of resistance down a low- 
 resistance strip or strips, the resistance values of which have 
 been carefully determined in absolute measure by a Jones- 
 Lorenz apparatus. 
 
 If a low-resistance strip of known value is not at hand, 
 then a resistance can be constructed by joining in parallel a 
 known number of wires of measured resistance. Thus, if 
 a resistance capable of carrying 1,000 amperes is to be made, 
 it can be constructed by joining in parallel 100 wires each 
 having a resistance of one-tenth of an ohm and each capable 
 of carrying 10 amperes. In making these arrangements a 
 large margin must be allowed in the carrying capacity of the 
 single wires. It does not follow that, if one single bare wire, 
 say of platinoid, No. 36 S.W.G-. size, will carry, without undue 
 heating, one-quarter of an ampere,- that 100 of these wires 
 closely laid in parallel will carry 25 amperes. Owing to the 
 diminution in the radiative power of each wire by its 
 proximity to others, the final temperature of each wire will 
 be much higher, and therefore a less total safe current- 
 carrying capacity results. 
 
 11. Current-carrying Capacity of Wires. In the con- 
 struction of resistances used for the purpose of causing a 
 definite fall in voltage in a current passing through them it is 
 necessary that the rate of generation of heat shall be so 
 
378 TEE MEASUREMENT OP ELECTRIC CURRENT. 
 
 related to the rate of dissipation that the wire does not rise 
 in temperature by an amount sufficient to seriously affect its 
 resistance, or else one of the factors required for the current 
 measurement viz., the resistance of the measuring portion of 
 the circuit is uncertain. The heat generated per second in 
 a bare wire in air by the passage through it of a steady 
 current having a value of A amperes is mechanically equal to 
 A 2 E joules, where E is the resistance of the wire. This 
 energy is dissipated or conveyed away from the surface by 
 radiation and convection, and every surface at a certain 
 temperature has a certain emisssivity, which is defined as the 
 energy passing out per second per square centimetre. The 
 true emissivity is a function of the difference of temperature 
 of the surface of the wire and that of the surrounding vessel 
 or enclosing surface. If the wire is in a vacuum, the 
 dissipated energy is wholly radiant, except in so far as there 
 is conduction out of the ends of the wire. In the case of 
 wires exposed in the air, energy is removed by air convection 
 as well as by radiation, and convection in this case forms an 
 important part of the heat loss. 
 
 Let w stand for the total energy removed from the wire 
 per second per square centimetre of surface, whether by 
 radiation or convection. Then, when a state of thermal 
 equilibrium is reached, we have the equation 
 
 where D is the diameter and L the length of the wire, which 
 we will suppose to have a circular section. Also, if p is the 
 electrical resistivity of its material, we have 
 
 10 9 E=-1 
 
 7T, 
 
 where E is the whole resistance of the wire in ohms and p 
 its resistivity in C.G.S. units. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 379 
 
 If the diameter d of the wire is measured in millimetres, 
 we obtain from the above two equations another, viz., 
 
 A 9 1^0 91AJ<* A -I rfff\ 
 
 A 2 = l-7r 2 l(W, or A =1,570 
 P 
 
 This equation tells us the value of a current in amperes 
 (A) which will bring a circular-sectioned wire of diameter d 
 millimetres to a temperature at which it will be losing 
 energy at a rate equal to w joules per second from each 
 square centimetre of its surface. 
 
 Suppose, for instance, that w = Ol, or that the surface rate of 
 loss of energy is one-tenth of a watt per square centimetre, and 
 that the wire has a diameter of 1 mm. ; then we should have 
 
 A = 1,570 /JL, or p A 2 = 246,490. 
 
 \ 10/3 
 
 Experience shows that when a bare metallic wire is 
 radiating O'l watt per square centimetre, its surface tempera- 
 ture would be about 60C. if surrounded by air at 15C. 
 If we assume the wire to be of copper, then at 60C. its 
 resistivity p would be about 2,000 C.G.S. units. Hence the 
 current carried would approximate to 11 amperes. 
 
 It is generally the custom to specify the diameter of wires 
 in mils, the mil being one-thousandth of an inch. If the 
 resistivity r is measured in microhms per cubic centimetre 
 at the final steady temperature, and d is the diameter in 
 mils, then the above formula for the current carried can be 
 transformed into 
 
 A 1,570 fad* 
 
 8,000V r 
 
 If the rate of loss of energy w reaches one watt per square 
 centimetre of surface for a bare wire, it is far too hot to touch, 
 and is probably at a temperature of about 400deg. If w has 
 a value of 01, then the wire is just hand-hot, or, perhaps, at 
 about 60C. At the above temperature (60C.) the resistivity r- 
 of copper will be 25 per cent, greater than its resistivity at. 
 
380 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 0C. and that of iron 36 per cent., but for platinoid and most 
 resistance alloys, only about 2 per cent, greater. 
 
 Inserting in the formula these values for r and w we have 
 the following convenient but rough empirical formulae for the 
 safe currents in amperes A, carried by round bare wires, of 
 the stated materials, having a diameter of d mils, viz. : 
 
 For copper, 
 
 A = 
 
 -A 
 
 V 
 
 For platinoid or German silver, A= /_ 
 
 V 5, 
 
 500 
 
 For iron, 
 
 A = 
 
 OOP 
 
 d* 
 
 The above formulae only apply to bare wires in air, the 
 wires being either straight or coiled into very open spirals.* 
 
 The following table, embodying experimental results, shows 
 the safe current-carrying capacity of some common sizes of 
 bare wires of copper, iron, brass and German silver in loose 
 or open spirals : 
 
 Safe Current-carrying Capacity in amperes of Bare Wires, 
 ivound into Open Spirals. 
 
 Size of wire 
 in B.W.G. 
 
 Diameter 
 of wire in 
 inches. 
 
 Safe currents carried. Final temperature 
 not exceeding 60C. 
 
 Copper. 
 
 Brass. 
 
 Iron. 
 
 German 
 silver. 
 
 10 
 12 
 14 
 16 
 18 
 20 
 
 0-134 
 0109 
 0-083 
 0-065 
 0-049 
 0-035 
 
 50 amps. 
 
 i- 
 ? :: 
 
 9 
 
 30 
 19 
 15 
 10 
 7 
 5 
 
 19 
 16 
 10 
 8 
 5 
 4 
 
 16 
 13 
 8 
 6 
 4 
 3 
 
 It will, therefore, be seen that the current density or amperes 
 per square inch of section can be very much greater in fine 
 wires than in large ones. In all cases, however, the surface 
 
 * These formulae cannot be applied to extreme cases, such as that of a wire 
 one mil in diameter, but apply generally to ordinary laboratory sizes of wires. 
 
THE MEASUREMENT OP ELECTRIC CURRENT. 381 
 
 of a bare wire in air should approximate to 10 sq. cm. per 
 watt expended on it, if the temperature is not to rise above 
 the point at which it is possible to touch the wire with the 
 hand. 
 
 The result of investigation has been to show that the 
 emissivity of a bare cylindrical wire is not merely a function 
 of the temperature difference between its surface and that of 
 the surrounding envelope, but is also dependent on its form. 
 Prof. Ayrton and Mr. H. Kilgour have deduced the following 
 laws from observations on nine platinum wires varying 
 between l'2mm. and 14mm. in diameter.* 
 
 1. For any temperature the emissivity is higher the finer 
 the wire. 
 
 2. For each wire the emissivity increases with the tempera- 
 ture, the rate of increase being greater the finer the wire. 
 
 3. The effect of surface on the total loss of heat per square 
 centimetre per second per 1C. excess of temperature 
 increases as the temperature rises. 
 
 These authors find that for platinum wires of different 
 diameters the emissivity e, or loss in heat in calories per 
 square centimetre of surface per second per 1C. excess of 
 temperature above the enclosure, can be expressed by the 
 formulae 
 
 At 100C, e = 0-0010360 + 0120776 dr\ 
 At 200C., e = 0-0011113 + 0-0143028^- 1 , 
 At 300C., e = 0-0011353 + 0-016084 d~\ 
 
 where d is the diameter in mils. Hence, whilst the simple 
 theory above given, in which the emissivity is taken as 
 constant, leads to the conclusion that the current required to 
 maintain a wire of given material at a given temperature 
 varies as the diameter of the wire raised to the power of 
 three-halves, as a matter of fact, for very thin wires, the 
 current is more nearly proportional to the diameter simply. 
 
 * See Ayrton and Kilgour, " On the Thermal Emissivity of Thin Wires in 
 Air," Proc. Roy. Soc., November 19, 1891 ; or The Electrician. Vol. XXVIII., 
 page 119. 
 
382 
 
 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 Iii 1884, Sir W. H. Preece gave some measurements of the 
 currents required to fuse fine bare platinum wires Gin. in 
 length and of various diameters. These currents were found 
 to be as follows : 
 
 Diameter of the Wire 
 in inches. 
 
 Fusing Current in 
 amperes. 
 
 0-00050 
 0-00075 
 
 o-ooi 
 
 0-002 
 0-003 
 
 0-277 
 0-356 
 0-437 
 0-790 
 1-150 
 
 It will be seen that these fusing currents are much more 
 nearly proportional to the first power of the diameter of the 
 -wire than to the three-halves power of the diameter. For 
 wires of copper varying in diameter (d) from 8 mils to 
 30 mils he found the observed values of the currents (A) 
 required to make the wires just visibly red hot in the dark 
 (temperature about 500C.) were in very fair agreement with 
 the values calculated from the formula 
 
 A = 0-14587 Vd*. 
 
 For Swedish wrought-iron wires of diameters varying from 
 ] mils to 60 mils the same current could be calculated from 
 the formula 
 
 A = 0-035755 *J&, 
 
 and for German silver wires between 8mm. and 25mm. in 
 diameter from the formula 
 
 A = 0-056376 J3*. 
 
 These experiments made it evident that, whilst for round 
 bare wires in air of diameters between Sjmils and 60 mils 
 the currents required to keep them at constant temperatures 
 could be calculated from a formula of the form current 
 = (constant} X (diameter) , this law does not hold good for 
 wires of much smaller diameter, such as 1 mils to 3 mils, for 
 in this latter case the current varies more nearly as the 
 diameter. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 383 
 
 In connection with this subject a knowledge of the current 
 required to fuse short bare wires of different materials and 
 various diameters in air is practically important. Sir W. H. 
 Preece has given a table (see Table L, end of this chapter) 
 of fuse currents for wires of different sizes of iron, copper, 
 lead and tin. 
 
 The reader may be referred to the following papers for 
 additional information on the heating of conductors by 
 electric currents : 
 
 PROF. G. FORBES. British Association Report, 1882. 
 
 SIR W. H. PREECE. " On the Heating Effects of Electric 
 Currents." Proc. Roy. Soc., April, 1884, or The Electrician, 
 Vol. XII., p. 518. 
 
 PROF. G. FORBES. " On the Diameter of Wires to Prevent Over- 
 heating by Electric Currents." Proc. Inst. Elec. Engineers, 
 London, April, 1884; also The Electrician, Vol. XIII. r 
 pp. 16, 39, 63, 82. 
 
 J. T. BOTTOMLEY, The Electrician, VoL XII., p. 541. 
 
 A. E. KENNELLY. " On the Heating of Conductors by Electric 
 Currents." The Electrician, Vol. XXIV., p. 142. 
 
 12. Calibration of a Galvanometer by the Potentio- 
 meter. The Measurement of Very Small Currents. When 
 
 using a sensitive galvanometer for many purposes it becomes 
 necessary to know the absolute value in amperes of the small 
 current causing an observed deflection. The most simple 
 method of calibrating any form of mirror or deflectional 
 galvanometer is as follows : 
 
 Unless the galvanometer Gr has a high resistance, say 
 2,000 ohms and upwards, it must have a resistance, E, of 
 known value joined in series with it, and the resistance of the 
 galvanometer coil itself must be measured. A potentiometer 
 wire, a b, is then set or adjusted by means of a Clark cell, Ok, 
 so that there is a known fall of voltage down the wire per centi- 
 metre. In the absence of a potentiometer it is always possible 
 
384 
 
 TEE MEASUREMENT OF ELECTRIC CURRENT. 
 
 to improvise an equivalent by stretching a fine uniform 
 platinoid wire along a 2-metre scale and attaching to the ends of 
 the wire a single secondary cell. The galvanometer may then 
 be employed in connection with a Clark cell to discover the 
 length of the wire down which there is a fall in potential 
 equal to the voltage for the moment of the Clark cell. Thus, 
 suppose the connections made as in Fig. 16, and that the 
 Clark cell has an E.M.F. of 1434 volts at 15C. at that 
 temperature, and that we find the fall of potential down 
 80cm. of the wire is equal to 1434 volts ; then the fall of 
 potential per millimetre of the wire is 1434/800 volts. 
 
 FIG. 16. 
 
 This done, remove the Clark cell, attach in series with the 
 galvanometer the known resistance K, and join up the ends of 
 the galvanometer to any two points on the slide- wire separated 
 by such a distance that the resulting galvanometer deflection 
 is the one the current value of which is required. 
 
 Let the galvanometer have a resistance G ohms and be joined 
 in series with a resistance E ohms; let L be the length a x of the 
 slide- wire down which there is a fall of potential equal to the 
 voltage V of the Clark cell ; and let I be the length of slide- 
 wire separating the terminals of the galvanometer circuit 
 when the galvanometer deflection is 8. Then the value of A 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 385 
 
 the current in amperes through the galvanometer which 
 produces this deflection 8 is 
 
 A_ 
 
 ~ 
 
 Hence the galvanometer constant k is equal to A/8. 
 
 The conditions of success are that the value of the resist- 
 ance K+G must be very large compared with the resistance 
 of the length I of the slide-wire, so that the addition of the 
 galvanometer in parallel with a section of the slide- wire does 
 not sensibly affect the current flowing through the slide-wire. 
 
 The galvanometer constant should, in the above manner, 
 be determined for a number of different deflections, and it 
 must not be taken for granted without proof that the constant 
 is constant. If, however, the deflectional constant has been 
 found, the galvanometer may be employed for the measure- 
 ments of large currents by being shunted. 
 
 If the terminals of a galvanometer having a resistance 
 G ohms are joined by a resistance of S ohms, called a 
 shunt, then the combined resistance of the galvanometer 
 
 SG 
 and shunt is ^ -^ ohms. If a steady current A amperes 
 
 is sent through the system, it is divided in the inverse 
 ratio of S and G, and the galvanometer is traversed by a 
 current a, such that 
 
 S 
 S + G' 
 
 Hence, A=fl*t 
 
 o 
 
 But if the current a produces a deflection, 8, and corre- 
 sponding to this deflection we have a constant, K, we then 
 have 
 
 A galvanometer is usually provided by the maker with 
 a set of shunt coils so adjusted for use with it that, by 
 
 cc 
 
386 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 connecting each shunt coil in turn across the terminals 
 of the galvanometer, one-tenth, one-hundredth, or one- 
 thousandth of a current is sent through the galvanometer 
 when the shunted galvanometer is connected in a circuit. 
 
 A universal shunt-box has been designed by Prof. W. E. 
 Ayrton and Mr. Mather which is capable of being applied 
 to any galvanometer. The principle may be explained by 
 reference to the diagram (Fig. 17). 
 
 Let G be a galvanometer having its terminals ab shunted 
 by a resistance consisting of a long fine wire. Let B be 
 a battery having one terminal connected to a and the 
 other to a point, #, on the shunt wire. Then, if the 
 
 FIG. 17. Diagram illustrating the principle of the Ayrton-Mather 
 Universal Shunt-Box. 
 
 resistance of the galvanometer is G, and that of the wire ab 
 is nGr, and the resistance of the fraction of the wire ax 
 is wG, and if C is the current flowing out of the battery 
 and c the current flowing through the galvanometer, we 
 obviously have 
 
 Hence the fraction of the current flowing out of the battery 
 which passes through the galvanometer is independent of 
 the resistance of the galvanometer. Accordingly, if we 
 make n=9 and ra = l, c = OlC; if we make n = 9 and 
 m = 0*l, c = 0'01C, and so on. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 387 
 
 If, then, the shunt wire db remains fixed, but an arrange- 
 ment exists by which the point x can be shifted so as to 
 make ax successively equal to one-tenth, one-hundredth, 
 &c., of ab, we shall have a shunt which can be applied 
 to any galvanometer. It must be noticed, however, that 
 the movement of the point x alters the total resistance 
 between a and x, and therefore affects the total resistance 
 of the circuit, and, as a consequence, the value of the 
 main current, unless some adjustment is made to keep it 
 constant. In the actual arrangement, the shifting of the 
 
 FIG. 18. Ayrton-Mather Universal Shunt-Box. 
 
 contact point x from place to place along the shunt line 
 is achieved either by a plug and block arrangement or by 
 a rubbing contact (see Fig. 18). 
 
 In connection with this matter it may be well to point 
 out that in the ordinary shunt arrangement, in which the 
 galvanometer is provided with a series of shunts, the 
 resistances of which are respectively ^, ^, -g^, &c., of that 
 of the galvanometer, we must not assume that, because steady 
 currents are divided in decimal ratios by the shunts, that 
 therefore sudden impulsive currents or instantaneous dis- 
 charges, as when the galvanometer is used ballistically, are 
 
 cc2 
 
388 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 likewise so divided. Mr. Hockin showed many years ago 
 that the application of the shunt affected the logarithmic 
 decrement or damping of the galvanometer, and hence the 
 instantaneous swing or throw is less than it should be if 
 the shunt merely acted to divide the discharge in the inverse 
 ratio of the resistance of the galvanometer and shunt. 
 
 13. Alternating- Current Measurement. It has already 
 been explained that in the case of alternating or periodic 
 currents we are concerned with either the instantaneous value 
 (i) of the current, or with its maximum value (I), or with 
 its root-mean-square (RM.S.) value, and, occasionally, with 
 the true-mean (T.M.) value. Generally speaking, the measure- 
 ment of an alternating current implies the determination of 
 its root-mean-square value, and most alternating-current 
 ammeters and methods give us this value. In order, there- 
 fore, that an instrument may be useful for alternating-current 
 measurement, it must be based on some principle such that 
 the actual mechanical force, couple or displacement measured 
 varies as the square of the instantaneous value of the current. 
 We may avail ourselves therefore of the heating power of the 
 current, or of the mechanical force between two conductors 
 traversed by the same current, or of the mechanical force 
 between conductors connected to the ends of the circuit 
 traversed by the current, as a means of constructing an 
 ammeter for periodic current measurement, because in each 
 of these cases the observed effects, whether heat pro- 
 duction or mechanical force, varies as the square of the 
 current at any instant, and is therefore independent of its 
 direction. 
 
 We have already described the construction of the instru- 
 ments of the electro-dynamometer class, such as Siemens' 
 electro-dynamometer or the Kelvin ampere balances, which 
 depend for their action upon the mechanical forces existing 
 between fixed and movable conductors traversed by the same 
 current. In using these types of instruments for alternating- 
 
THE MEASUREMENT OF ELECTRIG CURRENT. 389 
 
 current measurement the condition of success is that the 
 periodic time of the alternating current must be small 
 compared with the free time of vibration of the movable part 
 of the instrument. 
 
 There is, however, another very important matter concerned 
 in the proper construction of an instrument of this class in 
 order that it may be available for alternating-current 
 measurement. The instrument must have no metal parts or 
 plates or case near to the coils traversed by the alternating 
 currents. For if there are such metal parts, then the 
 alternating currents in the fixed coils will set up local or 
 eddy currents with these metal parts, and these eddy currents 
 will be nearly in opposition as regards phase with the 
 currents producing them. Hence the eddy currents will 
 react upon the movable coil, and will make the mechanical 
 force upon it different from that which it would be if the 
 eddy currents were absent. This defect may be masked by 
 the opposing action of the currents in the fixed and movable 
 portions of the circuit, and it will in general be more marked 
 if there is a difference in phase between the currents in the 
 fixed and movable circuit. In any case, it is a possible source 
 of serious error, and any electro-dynamometer instrument 
 intended to measure alternating currents which is included 
 in a brass case or has brass or metal parts near the coils 
 should be viewed with suspicion as regards its instrumental 
 accuracy. The Kelvin ampere balances intended for 
 alternating current measurement have their coils wound oil 
 cores of slate, marble or porcelain, and the bases on which 
 the instruments are mounted are also non-metallic. 
 
 The most suitable form of Siemens electro-dynamometer is 
 that called the "Workshop" form, in which the coils are 
 mounted on a wooden base. Even here the instrument 
 maker often fixes the coils to the base by metal straps. 
 These should be removed and ebonite straps used to hold the 
 fixed coil in place. Instrument makers are far too fond of 
 enclosing electrical measuring instruments in lacquered brass 
 
390 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 cases, which look nice but often injuriously affect their 
 performance and accuracy.* 
 
 The measurement of a large alternating current is best 
 effected by some suitable instrument of the electro-dynamo- 
 meter type. This must previously have been calibrated by 
 passing through it a continuous current of known value, as 
 determined by the potentiometer method, and an error curve 
 constructed for the instrument as above described. The 
 instrument may then be used to measure the B.M.S. value of 
 an alternating current since the numerical value of the latter 
 is that of the continuous current which produces the same 
 dynamometer reading. 
 
 The most useful type of hot-wire alternating-current 
 ammeter is that in which the current to be measured passes 
 through a strip resistance of negligible inductance, and from 
 the ends of which connections are made to a very fine wire 
 which is heated by the small portion of the current shunted 
 through it. If the wire is in an enclosure of constant 
 temperature it soon comes to a final steady temperature, 
 which produces a definite elongation of the wire. This 
 expansion is measured by measuring the sag of the wire, its 
 ends being attached to fixed points. Instruments of the 
 above kind are manufactured by Hartmann and Braun (see 
 Eig. 19), and a self-recording hot-wire ammeter is in use, 
 designed by Holden and Pitkin, in which the current to be 
 measured passes through and heats a number of fine wires of 
 platinum or platinum silver arranged in parallel, the sag or 
 extension of these wires being detected and measured by a 
 multiplying gear which actuates a pen moving over a revolving 
 drum. 
 
 The measurement of small alternating currents, such as the 
 magnetising currents of transformers, is best accomplished by 
 
 . * As an instance of the kind of error that may thus result, the reader is 
 referred to a Paper by the Author in the Proc. of the Institution of Electrical 
 Engineers, Vol. XXL, p. 666, 1892, entitled, "Experimental Researches on 
 Alternate Current Transformers," in which reference is made to the results of 
 measurements made with a certain brass-cased wattmeter which were found 
 to be in some cases in error by nearly 50 per cent. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 391 
 
 measuring the fall of potential down a known resistance by 
 means of an electrostatic voltmeter or quadrant electrometer 
 which has been previously standardised by continuous 
 voltage. Thus, for instance, if we have to measure an alter- 
 nating current, say, of about the magnitude of 0*25 ampere, 
 a resistance can be constructed of four strands of No. 36 bare 
 platinoid wire capable of carrying without sensible heating 
 0*25 ampere, the total resistance being, say, 400 ohms. This 
 resistance may be in the cage form described on p. 80. Then 
 the fall in potential down this resistance produced by the 
 current will be nearly 100 volts, and can be measured to 
 
 FIG. 19. Hartmann and Braun Hot- Wire Ammeter. 
 
 within one-tenth per cent, by means of a standardised Kelvin 
 multicellular voltmeter, the only condition necessary for so 
 doing being that we must be able to afford to drop 100 volts 
 in the voltage of the current used. In those cases in which 
 this cannot be done an air-core alternating current trans- 
 former must be employed to effect a transformation. 
 
 If a transformer is constructed without an iron core, the 
 two windings of which have their turns intermingled and in 
 the ratio of 'N l to N 2 , then if to the secondary terminals we 
 connect an electrostatic voltmeter, the scale reading of this 
 
392 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 will be N^N^ times or fractions of the voltage on the primary 
 terminals. If, then, the fall of pressure down the resistance 
 through which the current to be measured is flowing is too 
 small to be measured, say on a Kelvin multicellular voltmeter, 
 we can, by employing an air-core transformer, raise this 
 voltage to a readable value by using a transformer of the 
 kind mentioned having its primary and secondary turns in a 
 known ratio. This transformer should be made with circuits 
 having as large an inductance as possible. It is desirable, 
 however, to calibrate the transformer directly by taking a 
 series of readings, within the range of the same voltmeter if 
 possible, of the observed voltage on the primary and 
 secondary terminals. 
 
 The same arrangement viz., an air-core transformer may 
 be employed as shown by Mr. A. Campbell* to measure 
 currents directly by transformation. In an air-core trans- 
 former the ratio of the maximum value of the primary 
 current I x to that of the secondary current I 2 is 
 
 where K 2 and N are the resistance and inductance of 
 the secondary circuit and M the mutual inductance, and 
 p = 27r times the frequency. Hence, if pN is large compared 
 with ~R%, the ratio of the currents is always N/M, and indepen- 
 dent of frequency. 
 
 By using an air-core transformer with the secondary 
 circuit, made of thick wire and a large number of turns, so 
 that the ratio R 2 /N is at least 50, then, for a frequency of 
 even 50 ^ the ratio of the currents is at most 1 per cent- 
 different from that which it would be for infinite frequency. 
 This ratio of current transformation may, however, be found 
 experimentally. 
 
 Thus, for instance, suppose it is required to measure an 
 alternating current of about 1,000 amperes, and we have 
 
 * Proc. Phys. Soc. Lond., Vol. XIV., p. 279. 
 
THE MEASUREMENT OP ELECTRIC CURRENT. 393 
 
 only a Kelvin ampere balance and a Siemens' electro- 
 dynamometer available, each reading up to 100 amperes. 
 We may construct an air-core transformer having an 
 approximate transformation ratio of 10 : 1 by making it with 
 a thick wire core capable of carrying 1,000 amperes, and 
 a coil of 10 times as many turns capable of carrying 
 100 amperes. The transformer has then to be calibrated 
 by sending through the dynamometer and the thinner circuit 
 a current, say, of 10 amperes, and joining the thicker circuit 
 up in series with an adjustable resistance and the Kelvin 
 balance. Suppose that, when the reading of the dynamometer 
 is 10, the Kelvin ampere balance reads 98*2, we then know 
 that the current transformation ratio is 9*82 to 1, and we 
 can read the value of any current passing through the thick 
 coil by taking the readings of the dynamometer placed in 
 circuit with the thinner coil and multiplying by 9*82. 
 Mr. Campbell has shown that iron ring core transformers 
 may be .used in the same way provided that the resistance 
 of the secondary circuit is sufficiently low. 
 
 Convenient forms of electrostatic voltmeter for measuring 
 alternating currents by means of the fall of potential down a 
 resistance have been devised by Mr. G. L. Addenbrooke.* 
 He constructs a quadrant electrometer with two double 
 quadrant plates each formed of a pair of quadrant-shaped 
 plates. A paddle-shaped aluminum needle is suspended 
 between the plates by a very fine flat phosphor bronze strip 
 (see Fig. 20). The needle carries a mirror as usual. One 
 quadrant is connected to the needle and the two quadrants 
 are connected to the ends of the resistance through which 
 passes the current to be measured. The instrument can be 
 rendered so sensitive that a deflection of 100mm, of a spot 
 of light at 2 metres scale distance, can be obtained with 
 only 1 volt fall of potential down the resistance. The instru- 
 ment, therefore, can be used as an electrostatic voltmeter 
 
 * See a Paper read before the International Congress of Electricians at 
 Paris, 1900 ; also The Electrician, Vol. XLV., p. 901. 
 
394 THE MEASUREMENT OP ELECTRIC CURRENT. 
 
 for the measurement of small potential differences, and also 
 by association with a resistance strip it becomes an alter- 
 nating current ammeter. 
 
 For the measurement of the small alternating currents pass- 
 ing through a transformer on open secondary circuit (magnetiz- 
 
 FIG. 20. The Addenbrooke Electrostatic Voltmeter. 
 
 ing currents) the instrument is especially useful. It can be 
 calibrated by the employment of a battery of Clark cells. Since 
 the deflection is approximately proportional to the square of 
 the potential difference at the terminals of the instrument, 
 the deflections increase very rapidly with the voltages. Some 
 form of low-potential electrostatic voltmeter, such as the one 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 395 
 
 above described, is a valuable acquisition in an electrical 
 testing laboratory. 
 
 14. Wave Form Measurements. One of the most 
 valuable methods of investigating the effects due to alternat- 
 ing currents consists in delineating the wave form that is, 
 drawing a curve to represent the mode of variation of the 
 periodic current or currents and their relative phase differ- 
 ence. This process is called alternate current wave form 
 tracing, or wave delineation. The results are generally 
 expressed by taking a horizontal line to represent the 
 uniform flow of time, and at distances measured from an 
 origin representing the time or epoch, ordinates are set up 
 representing to scale the instantaneous value of the current 
 strength. The curve defined by their upper ends is the 
 current wave form. Innumerable methods have been devised 
 for drawing this wave form curve, but there are two which 
 must be particularly described. These are called the 
 point-by-point method and the oscillograph method. 
 
 The first-mentioned method originated with M. Joubert 
 in 1880, and can be carried out in any laboratory possessing 
 an alternator, or at any place to which alternating current 
 is supplied, provided a synchronous alternating-current motor 
 is at hand. The second method necessitates the possession of 
 a more expensive and special device, called an oscillograph. 
 
 If we desire to know the current wave form of an 
 alternator which is supplying a certain circuit, we may 
 attach to the shaft of the alternator an insulating disc 
 preferably made of a material called stabilit. This disc has a 
 narrow brass strip inserted in its periphery. The strip may 
 be in width about 1 per cent, to 2 per cent, of the 
 periphery of the disc. Against this disc two insulated springs 
 or narrow brushes press, so that when the disc revolves 
 the springs are conductively connected during the moment 
 the brass strip is passing under them. The brushes are 
 carried on a rocking lever which moves over a divided 
 
396 
 
 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 scale, so that they can be shifted round through a known 
 and measured angle. This arrangement is called a revolving 
 contact-maker. It can easily be fitted to any alternator 
 shaft The following arrangement of circuits are then made. 
 In the circuit, the current in which is to be delineated, is 
 inserted a resistance, E, of known value (see Fig. 21), and one 
 end of this resistance is connected to one of the brushes a 
 of the contact-maker c, and the other, 5, to one terminal of 
 an electrostatic voltmeter, V. The other terminal of the 
 voltmeter is connected to the other brush, but arrangements 
 are made for inserting in between a variable number of 
 
 R 
 
 YWWWW 
 
 FIG. 21. 
 
 small (lithanode) secondary cells B. The needle of the 
 voltmeter is thus caused to give a reading at any required 
 part of the scale according to the number of cells in use 
 whenever the brushes are connected together. The terminals 
 of this voltmeter are connected to a condenser K having a 
 capacity of about 0'5 microfarad, to act as a reservoir or 
 flywheel. 
 
 If now the alternator is set in operation, and the brushes 
 occupy a fixed position; every time the brushes are inter- 
 connected by the revolving brass strip, the voltmeter is put 
 momentarily in connection with the ends of the resistance, 
 and after a few revolutions the condenser becomes charged 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 397 
 
 to a potential depending upon the phase of the current 
 at the instant when this contact takes place. The volt- 
 meter reading therefore indicates this potential, plus or minus 
 that due to the cells of the battery B, according as they are 
 connected to act with or against the fall of potential down 
 the resistance. By taking the voltmeter readings as the 
 springs or brushes are shifted over degree by degree through 
 an angle covering the whole period, and correcting each 
 observation by adding or subtracting the cell voltage, we 
 obtain a series of values for the fall in pressure down the 
 
 FIG. 22. 
 
 resistance corresponding to regular time intervals during one 
 complete period. 
 
 Generally speaking, at least 20 observations should be 
 taken at equal intervals during the period. These are then 
 plotted out in a curve and give the wave form (see Tig. 22). 
 They may also be plotted out in the form of a polar curve (see 
 Fig. 23) in which radial lines are drawn at angular intervals 
 representing the time intervals of the observations and 
 lengths set off along these proportional to the instantaneous 
 value of the current. The polar curve defined by the ends 
 
398 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 of these radii vectores has the property that, if we take its 
 area and find the radius of a semi-circle having the same 
 area, this last radius is to the same scale as the root-mean- 
 square (K.M.S.) value of the current.* 
 
 If the alternator supplying the current is not accessible, 
 the same process may be carried out by employing a small 
 synchronous motor to drive the contact-disc in step with 
 the distant alternator. A small synchronous alternating 
 motor is practically a small alternator. A good type of 
 machine to employ for this purpose is the one represented 
 
 in Fig. 24. The motor is a small Kapp alternator having 
 eight magnet poles and an armature consisting of an iron 
 wire core wound over with eight armature bobbins. The 
 field magnets are excited by an independent continuous 
 current, and the armature is connected through a resistance 
 with the circuit supplying the alternating current under 
 investigation. The motor is brought up into step with the 
 supply circuit by passing a strap round its shaft and 
 spinning it up to speed like a top. When in step it will 
 continue to run, and will drive the contact-disc on its shaft 
 
 * For the proof of this propostion see " The Alternate Current Transformer," 
 Fleming, Vol. I., 3rd edition, p. 193. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 399 
 
 so that the circuit of the brushes is closed for an instant at 
 an assigned moment during the phase once during every 
 
 to 
 
 3 
 
 revolution. The process of obtaining graphically the wave 
 form of the alternating current supplied by the circuit 
 
400 
 
 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 is then carried out as above described, using, however, the 
 contact-disc on the motor instead of one on the inaccessible 
 alternator. 
 
 An example of an alternating current wave form plotted 
 out by the point-by-point method is given in Fig. 25. 
 
 The great labour involved in slowly delineating a current 
 wave form by this method led many inventors to devise 
 methods which are susceptible of greater rapidity. In some 
 
 FIG. 25. 
 
 cases these take the form of self-acting potentiometers, in 
 which the instantaneous value of the periodic electromotive 
 force or difference of potential being studied is balanced 
 against the fall of potential down a slide-wire. In this case 
 the galvanometer in the potentiometer circuit is replaced 
 by a very sensitive relay, which operates a mechanism 
 moving the contact point on the slide- wire one way or 
 the other until the current in the relay circuit is zero. A 
 very ingenious instrument of this kind has been devised 
 by Prof. Callendar, and another by Prof. Eosa. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 401 
 
 In the Callendar instrument the essential parts are a 
 form of potentiometer, the contact along the wire being 
 shifted one way or the other by a couple of small motors' 
 The contact-piece carries a pen which records a curve on 
 a slowly revolving drum covered with paper. The contact 
 is driven by the action of a delicate relay, which starts either 
 one motor or the other in revolution unless the current 
 
 FIG. 26. Rosa's Alternating Current Curve Tracer. Revolving Contact. 
 
 through the relay is zero. The relay takes the place of the 
 usual galvanometer used with the potentiometer. Hence, if 
 the instantaneous voltage of a periodic current is balanced 
 against the fall of potential down the potentiometer slide- 
 wire the mechanism will make the pen follow the variations 
 of the periodic voltage as this last varies. The alternator 
 or synchronous motor is provided with a contact-disc and 
 brushes as above described, and these brushes are slowly 
 shifted over by an automatic gearing through an angle equal 
 
 LID 
 
402 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 to one complete period. The pen then draws on the drum 
 the curve corresponding to the wave form of this periodic 
 voltage.* 
 
 The instrument designed by Prof. E. B. Kosaf is not 
 very dissimilar. In it the fall of potential down a 
 potentiometer wire is balanced against the difference of 
 potential between the ends of a resistance traversed by the 
 alternating current and by means of a revolving contact 
 maker with displacable brushes (see Fig. 26). A single value 
 of this periodic potential is selected at an assigned instant 
 during the period for balance. The shifting contact on the 
 potentiometer is coupled to a pantograph, which draws the 
 wave form curve on a uniformly revolving paper-covered drum 
 (see Fig, 27.) 
 
 The other method, making use of an instrument called the 
 Oscillograph, designed for giving a complete view of the 
 whole curve at once, is due originally to M. A. Blondel, 
 who first described it in 1892. 
 
 The oscillograph has been given a very practical and 
 improved form by Mr. Duddell. An oscillograph may be 
 defined as a galvanometer, the needle or coil of which has 
 such a small periodic time of vibration that it is able to 
 follow accurately the variations of a periodic current which 
 runs through its cycle of values in as little as one-hundredth 
 of a second ; the deflections of the needle being proportional 
 to the current. As a laboratory instrument the Duddell 
 oscillograph J has many advantages. It is made as follows : 
 On a base board is fixed a nearly circular electromagnet (see 
 Fig. 28) the coils of which are preferably excited by current 
 at a pressure of 100 volts. This magnet creates a strong 
 magnetic field between two pole pieces. In this field are 
 stretched two loops of flattened phosphor bronze wire, which 
 
 * See Prof. H. L. Callendar on " An Alternating Cycle Curve Recorder," 
 The Electrician, Vol. XLL, p. 582. 
 
 t "An Electric Curve Tracer," bv Prof. E.B.Rosa, The Electrician, Vol. XL. 
 p. 126. 
 
 J Made by the Cambridge Scientific Instrument Company. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 403 
 
 fcO 
 
 J 
 
 DD2 
 
404 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 are kept in tension by a spring. These loops are fixed in the 
 field so that, if traversed by a current, one wire is forced 
 forward by the magnetic force and the other forced back. 
 The straps have attached to them a very small mirror, and 
 the space in which they move is filled with oil. The time of 
 free vibration of the mirror is either -a^jth of a second in 
 one form of the instrument, or Trnhnjth of a second in another 
 form. The first form of instrument is called the projection 
 form. In it a ray of light from an arc lamp is made to fall 
 upon the mirrors attached to the strips, and is reflected back 
 on to another mirror, which is given a rocking action by a 
 small synchronous motor, the rocking taking place round an 
 axis perpendicular to the reflected ray and parallel to the 
 plane of movement or vibration of that ray. The result of 
 the combined action of the mirrors is to reflect a spot of light 
 on to a screen which has a motion in two directions, its 
 displacement horizontally from the zero position being 
 proportional to the phase angle and its displacement 
 perpendicularly being proportional to the current in the 
 oscillograph strips. Accordingly, the spot of light executes a 
 motion on the screen which, in consequence of the persistence 
 of vision, is seen as a luminous curve delineating the wave 
 form of the periodic currents passing through the strip of the 
 oscillograph. The oscillograph is furnished with two strips 
 or loops in order that we may delineate two periodic curves 
 at once. It has also a fixed mirror to project a horizontal 
 datum line on the screen. In the high-frequency instrument 
 this reflected ray of light from the mirrors on the oscillograph 
 wires is received on a uniformly moving photographic film or 
 plate and photographs upon it an exact reproduction of the 
 wave form of the current through the strip. 
 
 In using the instrument to delineate the forms of current 
 and potential difference of the carbons of an alternating 
 current arc lamp, or motor, or other appliance, we attach the 
 terminals of one strip through appropriate resistances to the 
 points between which exists the periodic potential difference 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 405 
 
 FIG. 28. -The Duddell Oscillograph. 
 
406 
 
 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 to be delineated, and we attach the terminals of the other 
 strip through resistance to the ends of a non-inductive 
 resistance in series with the circuit of the apparatus, which 
 is traversed by the current to be studied. We then obtain 
 on the oscillograph screen or plate two curves, which 
 represent the periodic current and potential difference in 
 question. 
 
 The projection pattern of the Duddell oscillograph has 
 sufficiently large mirrors attached to the wires that the light 
 reflected from them will project distinct curves upon a screen 
 at a distance of about 6ft. In the high-frequency instrument 
 the mirrors are necessarily much smaller, and it can only be 
 used as a visual or photographic instrument. 
 
 The following are the approximate data of the two types 
 of Duddell oscillograph: 
 
 
 High-frequency 
 
 Projection 
 
 
 pattern. 
 
 pattern. 
 
 Resistance of the field coils at 15C.... 
 Magnetising current 
 
 360 ohms. 
 0*25 amp. 
 
 180 ohms. 
 0*5 amp. 
 
 Working temperature of oil for correct 
 dampincr 
 
 30 to 35C. 
 
 30 to 35C. 
 
 Periodic time 
 
 O'OOOl sec. 
 
 0-0005 sec. 
 
 Normal working current in strip 
 Resistance of each strip 
 
 0'05 to 01 amp. 
 2 ohms. 
 
 0'5 amp. 
 1 ohm. 
 
 Ditto with fuses 
 
 10 ohms 
 
 3 ohms. 
 
 
 
 
 As it is impossible to recapitulate here a description of 
 more than a fraction of the methods which have been 
 suggested or employed in alternating-current curve tracing, 
 the reader may be referred for further information to the 
 following original Papers and Memoirs, most of which 
 references are taken from a comprehensive Paper on oscillo- 
 graphs by Mr. W. D. B. Duddell.* The references are, for 
 the sake of convenience, divided into groups according to the 
 methods which they describe, and they have, as far as 
 possible, been made complete. 
 
 * Read at the British Association Meeting at Toronto, 1897. 
 Report, 1897 ; or The Electrician, Vol. XXXIX., p. 636. 
 
 See B.A. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 407 
 
 I. Methods Depending on Foint-by-Point Observation and 
 Plotting a Curve. 
 
 M. JOUBERT. Journal de Physique, 1880. 
 
 H. MORTON and B. F. THOMAS. Jour. Amer. Assoc. Ad. of Science, 
 1880, or Trans. Am. Last. Elec. Eng., Vol. IX., p. 263. 
 
 DUNCAN, HUTCHINSON and WILKES. Elec. World., Vol. II., p. 160. 
 H. J. RYAN. Trans. Am. Inst. Elec. Eng., Vol. VII., p. 1. 
 
 L. DUNCAN. The Electrician, Vol. XXVIII., p. 61 ; Trans. Am. 
 Inst. Elec. Eng. Vol. IX., p. 179 ; or Elec. Eng. of New 
 York, Vol. XIX., p. 192. 
 
 F. BEDELL, K. B. MILLER, and C. F. WAGNER. Trans. Am. 
 Inst. Elec. Eng., Vol. X., p. 497. 
 
 J. A. FLEMING. The Electrician, Vol. XXXIV., p. 460. 
 W. M. HICKS. The Electrician, Vol. XXXIV., p. 699. 
 
 B. A. FESSENDEN. Elec. World, Vol. XXVIII., p. 688. 
 
 II. Self-Registering Methods by which a Continuous Curve 
 is Drawn. 
 
 A. BLONDEL. La Lumiere Electrique, Vol. XLL, p. 401 ; Vol. 
 XLIV., p. 185 ; Vol. XLIX., p. 501 ; The Electrician, Vol. 
 XXVIL, p. 603. 
 
 W. E. AYRTON. British Assoc. Report, 1895. 
 
 BARR, BURNIE and RODGERS. The Electrician, Vol. XXXV. 
 p. 719. 
 
 MANJAN LUTOSLAWSKI. Electrotechnische Zeitschrift, Vol. XVII., 
 
 p. 582. 
 
 H. L. CALLENDAR. The Electrician, Vol. XLL, p. 582. 
 E. B. ROSA. The Electrician, Vol. XL., pp. 126, 221, 318. 
 III. Optical or Projection Methods 
 
 (a) With metal diaphragm as the moving part : 
 Q. FROHLICH. Electrotechnische Zeitschrift, Vol. VIII., p. 210 ; 
 
 Vol. X., pp. 65 and 345. 
 E. THOMSON. La Lumiere Electrique, Vol. XXVIL, p. 339. 
 
 C. ROLLEFSON. Eel. Electrique, Vol. L, p. 461. 
 
408 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 (6) With a soft iron needle as the moving parts : 
 A. BLONDEL. Comptes Rendus, Vol. CXVL, pp. 502, 748. 
 
 H, J. HOTCHKISS and F. E. MILLS. Physical Review, Vol. III., 
 pp. 49, 358; Vol. IV., p. 128. 
 
 F. J. A. McKiTTRicK. Trans. Am. Inst. Elec. Eng., Vol. XIII., 
 
 Nos. 6 and 7. 
 
 (e) With a coil of wire carrying the observed currents as the moving part : 
 
 E. GERARD. Bull, de 1'Acad. de Belgique, 1888 ; Phil. Mag., 
 
 Vol. XXIX. 
 
 H. BECKER, G. LAHMEYER and G. D. PICARD. La Lumiere 
 Electrique, Vol. XXXI., p. 16. 
 
 G. S. MOLER. Physical Review, Vol. I., p. 214. 
 
 (d) With the plane of polarization of a beam of light as the moving part : 
 A. C. CREHORE. Physical Review, Vol. II., p. 122 ; Vol. III., 
 
 p. 63. 
 
 J. PIONCHON. Comptes Rendus, Vol. CXX., p. 872. 
 
 (e) With cathode ray in vacuo as the moving part : 
 
 F. BRAUN. Weid. Ann., Vol. LX., p. 552. 
 
 (/) With stream of mercury as the moving part : 
 E. L. NICHOLS. Jour. Amer. Assoc. Ad. Science, Vol. XLIL, p. 57. 
 
 (g) Miscellaneous methods : 
 
 LIPPMAN. 1875. The Electrician, July 17, 1896. (Uses a 
 capillary electrometer.) 
 
 P. JANET. Comptes Rendus, Vol. CXVIII., p. 862 ; Vol. CXIX., 
 pp. 58, 27, 399. (Uses a chemical method.) 
 
 IV. Oscillograph Methods. 
 
 A. BLONDEL. Proc. French Association for the Advancement of 
 Science. 1898. 
 
 H. ABRAHAM. Comptes Rendus, Vol. CXXIV., p. 758. 
 
 W. D. B. DUDDELL. The Electrician, Vol. XXXIX., p. 636. 
 
 DUDDELL and MARCHANT. Journal Inst. E.E., Vol. XXVIII., p. 1. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 409 
 
 The most convenient instrument for ordinary laboratory 
 work will be found to be the projection form of Duddell 
 oscillograph. In using it, a powerful parallel beam of light 
 from a lantern containing a hand-regulated arc lamp with 
 good vertical and horizontal slow-motion screws is thrown on 
 the mirrors of the oscillograph, and a cylindrical lens fixed in 
 front of the mirrors focuses the ray when reflected on to a 
 sheet of tracing paper laid over a curved glass screen. On 
 this tracing paper is then seen, when the oscillograph is in 
 operation, one or two bright sinuous lines of light, which are 
 the wave forms of the currents passing through the oscillo- 
 graph wires. If one of these currents is proportional to the 
 electromotive force in, or the potential difference of, the ends 
 of a circuit, and the other is part or the whole of the current 
 in that circuit, then the two sinuous lines will properly 
 represent the variation of current and voltage, and the 
 curves can be traced on the paper and investigation can be 
 made of their form and phase difference. The oscillograph 
 method has one enormous advantage over the point-by-point 
 method, in that the observer is enabled to see a transient 
 change in the wave form. The oscillograph shows at a 
 glance the whole of one wave, and a change anywhere is 
 instantly visible. 
 
 15. The Use of Transformers in Alternating Current 
 Measurement. The measurement of alternating currents of" 
 moderate value may be carried out as already described by 
 electrodynamic or hot-wire instruments. It often happens 
 however that measurements are required of alternating 
 currents haviDg very large or very small values. It is then 
 possible to bring these within the compass of instruments 
 found in every well-equipped laboratory by employing 
 transformers. Thus, for instance, a large alternating current 
 may be measured by passing it through a low resistance strip 
 of known value and measuring the potential difference of the 
 ends of the strip by means of a step-up transformer and an 
 
410 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 ordinary electrostatic voltmeter reading, say, from 60 to 
 100 volts. 
 
 It has been shown by Mr. A. Campbell* that for the 
 purpose it is necessary to use a transformer with a well closed 
 iron, circuit and a primary coil of low resistance and large 
 inductance. This primary has its terminals connected to the 
 ends of the low resistance strip through which the current to 
 be measured is passing, and its secondary terminals connected 
 to an electrostatic voltmeter. The transformer may con- 
 veniently have a transformation ratio of 1:100. 
 
 As an example of the details of an appropriate transformer 
 Mr. Campbell (loc. cit.) gives the following specification : 
 The primary coil may consist of 100 turns of No. 16 wire, 
 and the secondary of 10,000 turns of No. 40 wire, the coil 
 consisting of iron stampings having a total weight of T5 kilos. 
 
 In the case of the above transformer the variation of the 
 transformation ratio from the value 10 was T9 per cent, at a 
 frequency of 39 and 0'8 per cent, at a frequency of 86. 
 
 Such a transformer can, of course, be adjusted to have any 
 required transformation ratio at a fixed frequency. If it is 
 to be used for varying frequencies, then compensation may 
 be introduced by the employment of a very small additional 
 transformer having its primary in series with that of the 
 main transformer and its secondary joined in reverse direction 
 with that of the secondary of the main transformer. In this 
 case the small transformer can have its turns so adjusted that 
 an increase in frequency causes it to deduct a little from the 
 secondary voltage of the main transformer, and keep the 
 resulting voltage transformation ratio constant. 
 
 The above device enables us to make use of an electro- 
 static voltmeter, reading from, say, 60 to 150 volts, to 
 measure alternating currents covering a wide range in value. 
 \ The advantage of the method is that it introduces no 
 sensible inductance into the circuit of the current to be 
 measured, and that it is applicable to very large currents, 
 
 * Proc. Inat. Elec. Eng., April, 1901. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 411 
 
 such as those which would have to be measured in testing a 
 large alternator. 
 
 We have already mentioned the use of an air-core trans- 
 former to transform alternating currents in known ratios 
 (see page 392), but the method of measuring the volt fall 
 down a low resistance strip by means of a suitable trans- 
 former combination and an electrostatic (preferably reflecting) 
 voltmeter is more convenient. It need hardly be said that 
 the electrostatic voltmeter used should be carefully calibrated 
 in position by means of a potentiometer, a Clark cell and 
 a divided resistance. 
 
 16. Measurement of the Frequency of an Alternating 
 Current. Frequency Tellers. In many alternating current 
 investigations it is necessary to know the periodicity of the 
 current. If the alternator is accessible this can easily be 
 done by ascertaining the speed. If, however, the alternator is 
 in a distant station some appliance is necessary which will 
 measure the frequency of the current as it is supplied on the 
 circuit. Instruments for doing this are called frequency 
 tellers. For this purpose several devices have been invented. 
 In Campbell's frequency teller* a soft iron strip is so held in a 
 frame that it can be caused to protrude more or less from a 
 holding block. The end of the iron strip projects over an 
 electromagnet with laminated core, through the coils of which 
 passes the alternating current to be estimated. The iron 
 strip has a natural free period of vibration, and if the attrac- 
 tive impulses which act on it, due to the period magnetisa- 
 tions of the electromagnet, agree in frequency, the amplitude 
 of vibration of the strip becomes considerable. 
 
 The instrument includes a slow-motion arrangement for 
 pushing the iron strip more or less in or out of the clip which 
 holds it at one end and an indicating needle which magnifies 
 the motion. The observer makes the movement until the 
 sound or visible oscillations of the vibrating iron strip is a 
 
 * See The Electrician, Vol. XXXVIL, p. 437. 
 
412 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 maximum, and then he reads off on the scale of the instru- 
 ment the frequency of the current passing through the coils 
 of the electromagnet. The instrument is graduated by 
 applying to it currents of various frequencies, and is said to 
 read frequency to within 0'2 per cent, 
 
 In another modification due to C. Kinsley* the free period 
 of the strip is altered, not by varying its length, but by 
 sliding along it a non-magnetic rider or weight. 
 
 A third variety of frequency teller, suggested originally by 
 Profs. Ayrton and Perry,f consists of a stretched wire placed 
 between or over the poles of an electromagnet. The wire 
 may be of iron, and the magnet coils may be traversed by 
 the current to be examined. In this case the periodic attrac- 
 tive impulses set the wire in vibration if its free period is in 
 concordance with that of the currents or is some harmonic 
 of it. The free period of the wire is determined by its length, 
 diameter, density and tension, arid is expressed by the equation 
 
 where /=the periodic time, / = the length of wire, r = the 
 semi-diameter, 8 = the density of the wire, and T = its tension 
 in dynes. Hence, if T is varied by using different stretching 
 weights, the free period of vibration of the wire may be made 
 equal to that of the exciting current of the magnet, and 
 when this is the case the vibrations of the wire become a 
 maximum. 
 
 The periodic current may be sent along the wire and the 
 magnet may be a permanent magnet. In this case, however, 
 the determination of the frequency is complicated by the 
 variable rise in temperature of the wire produced by the 
 current. Hence it is better to pass the current examined 
 through the coils of the magnet and use an iron wire or wire 
 with small iron armature attached to it, varying the tension 
 
 * See The Electrician, Vol. XL., p. 258. 
 
 t See " Laboratory Notes on Alternate Current Circuits." Proc. Inst. E. E. 
 Vol. XVIII., p. 310. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 413 
 
 on the wire until unison is produced between its free period 
 of vibration and that of the current through the magnet coil. 
 A fourth method depends upon the use of a telephone 
 If an alternating current is passed through a magneto 
 telephone receiver its diaphragm is set in vibration, and it 
 emits not only a fundamental note corresponding to the 
 frequency of the current, but a series of higher harmonics. 
 The note of the telephone may be examined by testing it 
 with a sliding resonator tube and varying the length of the 
 column of air until resonance is produced. The resonator 
 tube length is altered until two lengths are found which both 
 exalt the note of the telephone. The periodicities corre- 
 sponding to these lengths are then known from the formula 
 
 y=n\ 
 
 where X is the wave-length and V the velocity of sound 
 at the then temperature of the air. The length of the 
 resonator tube which then resounds is obviously one-quarter 
 of a wave-length. 
 
 Thus, if the length of resonator tube is 20cm., we know 
 that the wave-length is 80cm., and hence the frequency n is 
 
 *"* , where t is the temperature of the air. Hence, 
 
 80 
 
 at 15C. n = 427. 
 
 If, for instance, two resonator tube lengths are found, one 
 19'lcm. and the other 16*5cm., corresponding to frequencies 
 of 420 and 480, then these are harmonics, and the greatest 
 common divisor viz., 60 is the frequency of the fundamental. 
 
 For most electrical laboratory purposes, a carefully 
 calibrated Campbell frequency teller will be found to be 
 a most useful instrument, and will give the frequency of 
 usual alternating periodicities within at least 0'5 per cent. 
 
 17. The Measurement of the Phase-difference of 
 Periodic Current Phasemeters. An important measure- 
 ment in connection with alternate-current working is the 
 determination of the phase difference of two currents. If 
 
414 THE MEASUREMENT OP ELECTRIC CURRENT. 
 
 two equi-periodic currents follow a simple sine law of vari- 
 ation, then the angular interval between their maximum or 
 zero values expressed in degrees, taking 360 to represent 
 the complete common period, is called their phase difference. If 
 the two currents can be passed in part or in whole through 
 the two wires of a double oscillograph, then a simple 
 inspection suffices to give the required information. It may 
 be, however, that the observer does not possess an oscillo- 
 graph, and then he may proceed by other means to obtain 
 the desired knowledge. One method is by the use of a 
 soft iron needle, as suggested by Lord Rayleigh.* Let two 
 circular coils of wire be prepared suitable for carrying the 
 two alternating currents which are to be examined as regards 
 difference of phase or lag. Let us, in the first place, assume 
 that these currents are simple periodic currents, or that they 
 are sine-curve curves ; in other words, let the instantaneous 
 value i of either current be represented by an expression of 
 the form, 
 
 i = I sin pt, 
 
 where I is the maximum value and p = 27rn, n being the 
 frequency and t the time reckoned from the instant when 
 i is zero. Let the two currents have the same frequency 
 but different maximum values, and let their phase difference 
 be represented by an angle 0. It is required to determine <. 
 The two currents are then represented by the equations 
 
 i = I sin pt, 
 
 *' = I'sin(/rt-0). 
 
 Hence, the root-mean-square (E.M.S.) value of i is I/\/2, and 
 that of i' is F/V2. 
 
 Suppose, then, that the two currents are passed through the 
 above-mentioned coils, and that these are placed with axes 
 in one line and paralled to each other. At some point 
 between them is placed a short soft iron needle (say 2cm. in 
 length), suspended by a torsion wire or glass fibre and 
 
 * Phil. Mag., May, 1897 ; or The Electrician, Vol. XXXIX., p. 180. j 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 415 
 
 carrying a mirror so that its deflections can be observed by a 
 mirror and scale method as usual. The upper end of the 
 torsion fibre should be carried on a torsion head so that it may 
 be twisted round through a known angle. The needle must 
 be so placed that its axis makes an angle of 45deg. with the line 
 joining the centres of the coils. First let one current, i, be 
 passed through one coil. It will create an alternating mag- 
 netic field, and this field will exert a couple or torque on the 
 soft iron needle proportional to I 2 . This can be measured 
 by the twist necessary to be given to the torsion head to bring 
 the needle back to the original position, or, if the deflection 
 is small, by observing simply the deflectional angle of the 
 needle. 
 
 Next, let the other current be passed alone through its coil, 
 and again observe the angle of deflection or torque acting on 
 the needle. It is proportional to I' 2 . 
 
 In the third place, let both currents be passed at once 
 through their coils, and let the joint field act on the soft iron 
 needle. Then the deflecting couple is proportional to 
 
 I 2 + 1' 2 211' cos 0. 
 
 Hence, if the first observed deflection or torsional angle is 9, 
 the second 9', and the third 6", we have 
 
 I' 2 
 
 where a is some constant depending on the torsion value of 
 the suspension. Hence, if the fields due to each current 
 oppose each other, 
 
 . O+V-O" 
 
 COS0 = -- . . 
 
 2 +/06 1 
 
 Thus, suppose 9 = 9 ' = 40 and 0" = 26J, then cos < = 0'67, 
 = 48deg. If the two equi-periodic currents considered do 
 not follow a simple sine law of variation, then their zero 
 points have not the same phase-difference as their maximum 
 
416 
 
 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 values. Lord Kayleigh shows, in the original Paper, that 
 even if the currents do not follow the sine law, or are not 
 simple periodic currents, the above expression for cos <f> gives 
 us what is called the power-factor of one current with respect 
 to the other. 
 
 If, then, one of the currents is proportional to the voltage 
 of a current and the other to the current flowing in it, the 
 value of cos obtained as above is a factor which, if multi- 
 plied by the K.M.S. values of the current and voltage, will 
 give the true power being taken up electrically by the circuit. 
 
 
 b 
 
 i 
 
 rrrr 
 
 r 
 
 TT7 
 
 ==. 
 
 ^ 
 
 ^ 
 
 \ 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 ^ 
 
 
 y 
 
 =\ 
 
 
 
 
 
 =\ 
 
 
 
 
 
 \ 
 
 1 
 
 
 IT 
 
 7 
 
 FIG. 29. 
 
 Instruments for indicating the phase difference of two 
 simple periodic or harmonic currents are called phasemeters. 
 One convenient form is that invented by Von Dolivo- 
 Dobrowolsky.* 
 
 If two circuits are wound on a frame at right angles to 
 each other (see Fig. 29), and if a disc of soft iron having an 
 indicating needle attached is suspended at the centre, then, as 
 is well known, if there is any difference of phase between 
 periodic currents of equal frequency passing through the two 
 coils, then there will be a torque tending to rotate the iron 
 
 * See The Electrician, Vol. XXXIII., p. 610. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 417 
 
 disc- This torque can be resisted by the action of a spiral 
 spring, and the instrument can be graduated by trial to show 
 on a dial (see Fig. 30) the phase difference of the currents. 
 If i and i' are the instantaneous values of the equi-periodic 
 currents, and if <p is their difference of phase, then the torque 
 T acting on the disc is proportional to n* sin 0. If one of 
 these coils is a high resistance inductionless coil, and is 
 connected to the terminals of any alternating current circuit, 
 then the current through that coil will be proportional to the 
 potential difference of the ends of the said circuit and in step 
 
 FIG. 30. 
 
 with it. If the other coil is traversed by the current entering 
 the above-named circuit, then the indications of the phase- 
 meter are proportional to ^esin^>, where <j> is the angle of 
 phase difference of the current i and the voltage e of the 
 circuit. If the voltage is always the same, then the indica- 
 tions of the instrument are proportional to the idle current, 
 i sin 0, passing into the circuit, and the direction of deflection 
 shows whether this idle current lags or leads. 
 
 The phase-meter may be graduated for a given frequency 
 and RM.S. value of the voltage to read directly on the dial 
 the ampere value of the idle current passing through it. 
 
 E B 
 
418 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 Hence such an instrument is useful, in an alternating current 
 station, to indicate at a glance the so-called wattless current 
 passing out into a circuit. 
 
 Eeferences to appliances and methods for measuring phase 
 difference will be found in the following Papers : 
 
 J. TUMA. Science Abstracts, Vol. I., pp. 148 and 266. 
 
 The author employs a soft iron needle and an arrangement of two coils at 
 right angles carrying the two currents. Otherwise the principle of the 
 apparatus is the same as in the instrument of Lord Rayleigh above described. 
 
 MOLER and BEDELL. The Electrician, Vol. XXXIII., p. 210, 
 Describes an optical phase indicator. 
 
 VON DoLivo-DoBRowoLSKY. See The Electrician, Vol. XXXII., 
 p. 40, and Vol. XXXIII., p. 610, for description of soft iron 
 disc phase meter. 
 
 E. ARNO. Eel. Electr., Vol. XX., 1899, p. 225; also Science 
 Abstracts, Vol. III., p. 71. 
 
 This writer describes an instrument which is a combination of a Weber 
 dynamometer, having separate coils, and an instrument to produce a rotating 
 magnetic field, having separate coils fixed at right angles, and a closed movable 
 circuit placed inside them. 
 
THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 419 
 
 TABLE I. 
 
 Fuse- Wire Currents. (SiR W. H. PBBBCE.) 
 
 Melting currents 
 in amperes. 
 
 Approximate gauge of wire in B.W.G. fused by the 
 stated currents in the case of the metals 
 
 Tin. 
 
 Lead. 
 
 Copper. 
 
 Iron. 
 
 1 
 
 36 
 
 35 
 
 47 
 
 40 
 
 2 
 
 34 
 
 32 
 
 43 
 
 36 
 
 3 
 
 30 
 
 28 
 
 41 
 
 33 
 
 4 
 
 26 
 
 26 
 
 39 
 
 31 
 
 5 
 
 24 
 
 24 
 
 38 
 
 29 
 
 10 
 
 20 
 
 20 
 
 33 
 
 24 
 
 15 
 
 18 
 
 18 
 
 30 
 
 22 
 
 20 
 
 17 
 
 17 
 
 27 
 
 20 
 
 25 
 
 16 
 
 16 
 
 26 
 
 19 
 
 30 
 
 15 
 
 15 
 
 25 
 
 18-5 
 
 35 
 
 14-5 
 
 14 
 
 24 
 
 18 
 
 40 
 
 14 
 
 13 
 
 23 
 
 17-5 
 
 45 
 
 13 
 
 12-5 
 
 22-5 
 
 17 
 
 50 
 
 12 
 
 12 
 
 22 
 
 16 
 
 60 
 
 11-5 
 
 2/15 
 
 21 
 
 15 
 
 70 
 
 10-5 
 
 2/14 
 
 20 
 
 14 
 
 80 
 
 10 
 
 2/13 
 
 19 
 
 13-5 
 
 90 
 
 9-5 
 
 3/15 
 
 18-5 
 
 13 
 
 100 
 
 9 
 
 4/16 
 
 18 
 
 12 
 
 120 
 
 8 
 
 3/13 
 
 17-5 
 
 2/15 
 
 140 
 
 2/10 
 
 4/14 
 
 17 
 
 2/14 
 
 160 
 
 4/13 
 
 4/13 
 
 16-5 
 
 2/18} 
 
 180 
 
 3/11 
 
 4/12 
 
 16 
 
 2/13 
 
 200 
 
 4/12 
 
 5/13 
 
 15 
 
 2/12 
 
 250 
 
 5/12 
 
 5/12 
 
 18} 
 
 5/16 
 
 EE2 
 
420 
 
 THE MEASUREMENT OF ELECTRIC CURRENT. 
 
 TABLE II. 
 
 Electro-chemical Equivalents.* 
 
 Elements. 
 
 T3 
 
 ~ 
 
 ^ rj 
 
 rS 00* 
 
 
 
 Atomic 
 weight. 
 
 Chemical 
 equiva- 
 lent. 
 
 Electro- 
 chemical 
 equivalent 
 in milli- 
 grammes 
 per coulomb 
 
 Coulombs 
 per 
 gramme. 
 
 Electro- 
 chemical 
 equivalent 
 in grammes 
 per ampere 
 hour. 
 
 Electro-Positive. 
 Hydrogen 
 Potassium 
 
 H 1 
 K 1 
 
 1 
 39-04 
 
 1 
 39-04 
 
 0-010384 
 0-40539 
 
 96293-00 
 2467-50 
 
 0-03738 
 1-45950 
 
 Sodium 
 
 Na 1 
 
 22-99 
 
 22-99 
 
 0-23873 
 
 4188-90 
 
 0-85942 
 
 Aluminium 
 
 Al 3 
 
 27-3 
 
 9-1 
 
 0-09449 
 
 1058-30 
 
 0-84016 
 
 Magnesium 
 
 M" 2 
 
 23-94 
 
 11-97 
 
 0-12430 
 
 804-03 
 
 0-44748 
 
 Gold 
 
 An 3 
 
 196-2 
 
 65-4 
 
 0-67911 
 
 1473-50 
 
 2-44480 
 
 Silver 
 
 Ap 1 
 
 107-66 
 
 107-66 
 
 1-11800 
 
 894-41 
 
 4-02500 
 
 Copper (Cupric) ... 
 (Cuprous). . 
 Mercury (Mercuric) 
 ,, (Mercurous) 
 Tin (Stannic) 
 (Stannous) ... 
 Iron (Ferric) 
 ,, (Ferrous) 
 Nickel 
 Zinc 
 
 Cu 2 
 Cu 1 
 Hg* 
 
 Hgi 
 Sn 4 
 
 Sn 2 
 Fe 3 
 Fe 2 
 Ni 2 
 Tin 2 
 
 63 
 63 
 199-8 
 199-8 
 117-8 
 117-8 
 55-9 
 55-9 
 58-6 
 64-9 
 
 31-5 
 63 
 99-9 
 199-8 
 29-45 
 58-9 
 18-64 
 27-95 
 29-3 
 32-45 
 
 0-32709 
 0-65419 
 1-03740 
 2-07470 
 0-30581 
 0-61162 
 0-19356 
 0-29035 
 0-30425 
 0-33696 
 
 3058-60 
 1525-30 
 963-99 
 481-99 
 3270-00 
 1635-00 
 5166-4 
 3445-50 
 3286-80 
 2967-10 
 
 1-17700 
 2-35500 
 3-73450 
 7-46900 
 1-10090 
 2-20180 
 0-69681 
 1-04480 
 1-09530 
 1-21330 
 
 Lead 
 
 Ph 2 
 
 206-4 
 
 103-2 
 
 1-07160 
 
 933-26 
 
 3-85780 
 
 Electro- Negative. 
 Oxygen 
 
 O 2 
 
 15-96 
 
 7-98 
 
 0-08286 
 
 
 
 Chlorine 
 
 ni 1 
 
 35-37 
 
 35-37 
 
 0-36728 
 
 
 
 Iodine 
 
 P 
 
 126-53 
 
 126-53 
 
 1-31390 
 
 
 
 Bromine 
 
 Br 1 
 
 79-75 
 
 79-75 
 
 0-82812 
 
 
 
 Nitrogen . . 
 
 N 3 
 
 14-01 
 
 4-67 
 
 0-04849 
 
 
 
 
 
 
 
 
 
 
 * Taken by permission of " The Electrician " Publishing Company (Ltd.) from 
 the " Electrical Trades' Directory and Handbook." 
 
CHAPTER IV. 
 
 THE MEASUREMENT OF ELECTROMOTIVE FOKCE. 
 
 1. Electromotive Force Measurement. Being provided 
 with a standard of electrical resistance and means for defining 
 or obtaining an electric current, the value of which in amperes 
 or recognised units is known, we can obtain the consistent 
 unit of electromotive force by measuring the fall of potential 
 down the unit of resistance when the unit current flows 
 through it. In practice we may proceed to recover the 
 practical unit of electromotive force, called the International 
 or standard volt as follows : 
 
 Prepare a coil of manganin wire which has a resistance of 
 one International ohm. This wire should be of a gauge 
 or cross section sufficient to carry a current of 1 or 2 
 amperes without sensible heating, and should preferably 
 consist of a bare manganin wire of about No. 16 S.W.G. 
 wound on a wooden frame. The best form for this coil is to 
 construct a short skeleton wooden drum about Sin. in 
 diameter on which may be wound in grooves the necessary 
 length of some 18ft. to 20ft. of the bare manganin wire. 
 
 The drum may be made by putting eight wooden pegs 
 into holes bored near the circumference of two circular 
 wooden discs lOin. or llin. in diameter. Instead of winding 
 on the drum a length of wire having an exact resistance of 
 1 ohm, it will be sufficient to measure with great care the 
 resistance of the length of wire actually wound on it, provided 
 its resistance is nearly 1 ohm. The ends of the wire 
 
422 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 should be silver-soldered to stout copper rods which form the 
 terminals, and between these rods the resistance must be 
 accurately measured. 
 
 This resistance coil is then to be joined up in series with 
 a Kelvin deciampere-balance, which has been previously 
 most carefully standardised by silver deposit (see Chapter III., 
 3, p. 347), and a current having a known value in Inter- 
 national amperes is then sent through this resistance. The 
 product of the values of the known current and known 
 resistance gives us, then, the value in International volts of 
 the potential difference between the copper terminals of the 
 resistance coil. 
 
 In this manner we recover or create a known voltage 
 between two points. It is, however, more convenient to 
 preserve a standard voltage in the form of a standard Clark 
 or Weston cell (see Chapter I., 8, p. 86), and to employ the 
 known voltage obtained as above mentioned to evaluate the 
 electromotive force of the cell. This can be done in the 
 following manner : 
 
 The standard cell to be checked is joined up in series 
 with a very sensitive galvanometer and a wire of high 
 resistance say of 10,000 ohms the two being placed as a 
 shunt across the ends of the above-mentioned 1 ohm 
 resistance. It is well to insert a key, so as to close the 
 circuit of the cell only when required. A current is then 
 passed through the Kelvin deciampere-balance, a carbon 
 rheostat, and the manganin resistance in series with it, and 
 is adjusted to have such a value approximately 1/5 amperes 
 that, when it flows through the manganin 1 ohm resist- 
 ance, it creates a fall of potential down it equal to the 
 electromotive force of the Clark cell. The Clark cell must be 
 so joined up (see Fig. 1) that its positive or mercury pole is 
 in connection with that end of the manganin resistance by 
 which the current enters it. 
 
 When this arrangement of apparatus is complete the experi- 
 mental measurement consists in adjusting the current through 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 423 
 
 the ampere balance until the galvanometer in series with the 
 Clark cell shows no deflection when the key K is down. 
 This being the case, the product of the observed ampere- 
 balance current and the resistance of the manganin wire E 
 is equal to the value of the electromotive force of the Clark 
 cell at the temperature of the day. The Clark cell should 
 be provided with a thermometer by means of which its 
 temperature can be taken. In this manner the recovered 
 standard of voltage can, so to speak, be transferred to a 
 standard cell and be rendered permanent. 
 
 In an electrical testing laboratory the cells used as stan- 
 dards of electromotive force should be checked at intervals 
 so as to re-determine their absolute electromotive force values. 
 
 A Kelvin Deciampere-balance. 
 E, 1 ohm Manganiu Resistance. 
 G High-resistance Galvanometer. 
 Cfc Clark or Weston Standard Cell. 
 
 K Key. 
 
 r Resistance of 10,000 ohms. 
 
 C Adjustable Carbon Rheostat. 
 
 Fm. 1. 
 
 It was by a method of the above kind that Lord Eayleigh 
 made his original measurements of the electromotive force of 
 the Clark cell. An account of his work is found in a Paper 
 by Lord Kayleigh and Mrs. H. Sidgwick in the Phil. Trans. 
 of the Eoyal Society, Part II, 1884, entitled "On the 
 Electrochemical Equivalent of Silver, and on the Absolute 
 Electromotive Force of Clark Cells." In this Paper Lord 
 Eayleigh first describes the construction of an absolute 
 ampere-balance for the evaluation of the current in absolute 
 measure. This consisted of two fixed circular horizontal coils, 
 the distance between their planes being equal to the radius 
 
424 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 of either of them. Between these coils was supported another 
 smaller circular coil, with its plane horizontal and its centre 
 on the line forming the centres of the fixed coils, and 
 midway between them. This third coil was suspended from 
 the beam of a weighing balance, as shown in Fig. 20, p. 71, 
 Chapter I. The movable coil had the current led into and 
 out of it by flexible leads. The current to be measured was 
 passed through all three coils in series, so that the electro- 
 dynamic forces tended either to lift or lower the movable coil 
 and thus decrease or increase its apparent weight. By 
 reversing the current through the fixed coils the direction of 
 the force could be reversed, and hence half the difference 
 between the apparent weight of the movable coil when the 
 current through the fixed coils is reversed gives the force in 
 gravitation units exerted by the fixed upon the movable coil. 
 
 The general theory of the instrument is as follows : Consider 'first two 
 coils only viz., a fixed and a movable co-axial coil. Let n, ri be the respective 
 number of turns of wire on each, i, i r the current in each, and M the 
 coefficient of mutual induction. Then the attraction or repulsion between the 
 coils, in absolute units is equal to 
 
 , 
 
 dx 
 where x is the distance between the parallal planes of the coils. 
 
 The full expression for the attraction between two parallel co-axial circular 
 coils of mean radii A, a, and with centres respectively at distances B, 6 from 
 a point on their common axis, is given by Maxwell ("Electricity and 
 Magnetism," Vol. II., 304) : 
 
 LetC 2 =A 2 + B 2 . Then 
 
 . 
 do C V. C C 
 
 where a and 6 are supposed to be small compared with A. 
 
 In the present case there are two fixed coils, and if we take the origin mid 
 way between them, then 
 
 . 
 Also, approximately, for the fixed coils we have B 2 = |A 2 . 
 
 Hence ^ = 6w^ x 0'2862. 
 
 db A 2 
 
 In other words, the force of attraction / of the fixed coils on the movable is 
 given by /= hnn'i?a?IA z , where h =6?r 2 x 0*2862, and i is the current through 
 the coils. 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 425 
 
 Accordingly, if ft is the ratio of the galvanometer constants of the coils 
 
 that is, if 3= , we have /= hBPi?n' s ln. 
 An 
 
 In the coils used by Lord Rayleigh 
 
 A=24-81016cms. n' = 225 
 a = 10'2473cms. n = 242 
 
 For the elaborate details of the process of weighing the 
 movable coil and reducing the results to calculation we must 
 refer the reader to the original Paper by Lord Eayleigh, 
 which is an example of accurate scientific research of the 
 most perfect kind. 
 
 Having obtained the means of defining in absolute 
 measure a steady electric current, this current was passed 
 through a resistance, and the fall of potential compared, as 
 above described, with the electromotive force of a Clark cell 
 when not sending current. 
 
 Ck 
 
 ll - 
 
 ** > Cy Cy "A/WWWWWW 
 
 A Ampere-balance- I Kj, Rg Resistance Boxes. 
 
 K Resistance Coil. X Commutator. 
 
 Ck Clark Cell. L Two Leclanche" Cells. 
 
 G Galvanometer. | 
 
 FIG. 2. 
 
 In the above arrangement, as employed by Lord Eayleigh, 
 it was not found convenient to alter the main current flowing 
 through the ampere-balance when once started; hence the 
 fall of potential down the resistance was not exactly equal to 
 the electromotive force of the Clark cell. A compensating 
 electromotive force was, however, introduced as follows: 
 Let A (see Fig. 2) be the ampere-balance and E the resistance 
 through which the current traversing the balance is flowing. 
 'Let Ck be the Clark cell and G a sensitive galvanometer of 
 
426 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 high resistance. Then L is another battery, say of two 
 Leclanche' cells, the terminals of which are short-circuited by 
 a large resistance consisting of the coils in two resistance 
 boxes E- 1 , E 2 . A derived circuit is taken from this Leclanche 
 cell circuit, as shown in the figure, so as to insert an assisting 
 or opposing electromotive force in the Clark cell circuit, which 
 can be varied as to direction by a commutator X and as to 
 magnitude by varying the resistances B p K 2 . unplugged out 
 of the circuit of the two resistance boxes subject always to 
 the condition that E 1 + K 2 = 10,000 ohms. In this way the 
 current flowing out of the Leclanche cells is kept constant, 
 but a variable fraction of their electromotive force can be 
 used with or against that of the Clark cell Ck, so as to bring 
 the current in the circuit of the galvanometer G to zero. 
 Then, knowing the resultant electromotive force in the 
 galvanometer circuit, which is equal to the product of 
 the main current and the resistance R, we have only to find 
 the ratio between the electromotive force of the Clark cell and 
 that of the fractional part of the Leclanche cells. This can 
 be done at once by the use of a potentiometer, as described 
 in a subsequent section of this chapter, with any required 
 degree of accuracy. 
 
 By the above process, Lord Bayleigh* found the electro- 
 motive force of the Clark cell, at 15C., to be 1/435 volts, and 
 at tG. it is given by the equation 
 
 E, = 1-435{1 - 0-00077(^-15)} volts. 
 
 Later experiments decided the Board of Trade Committee 
 on Electrical Standards to recommend that the value of the 
 Clark cell electromotive force be taken as T434 International 
 volts at 15C. If, however, the electrochemical equivalent 
 of silver per ampere-second is taken as 0-001119 gramme, 
 instead of 0*001118 gramme as adopted by the Board of 
 Trade, then the corresponding value of the electromotive 
 
 * " The Clark Cell as a Standard of Electromotive Force," by Lord Kayleigh. 
 Trans. Roy. Soc., Part II., 1885. 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 427 
 
 force of the Clark cell will be a number nearer to 1*432 true 
 volts at 15C. The Board of Trade values of the electro- 
 motive force of the Clark cell at various temperatures are 
 given in Table I. at the end of this chapter. 
 
 2. Practical Recovery of a Standard or Known Poten- 
 tial Difference. If the electrical laboratory possesses, as it 
 should do, a Kelvin deciampere-balance, the most convenient 
 practical method of recovering a known potential difference 
 is to standardise this balance most carefully by passing a 
 constant current through it of about 4 or 5 amperes, and 
 then determine by the copper sulphate method of electrolysis 
 the absolute value of this current with all the precautions 
 described in Chapter III. 
 
 Having standardised the balance, it may be employed to 
 measure the ampere-value of a current sent through a resist- 
 ance of known value say, 1 ohm constructed of manganin 
 wire of a sufficient cross-section not to be sensibly heated by 
 the current. If it is desired to obtain a known electromotive 
 force or potential difference of high value such, for instance, 
 as 2,000 volts then the ampere-balance must be one which 
 is suitable for alternating as well as for continuous currents. 
 A wire resistance must then be made having a known value 
 of 2,000 ohms or thereabouts, and an alternating current of 
 1 ampere, measured by the balance, must be passed 
 through it. The exact difference of potential between the 
 terminals of the high resistance then becomes known. 
 Generally speaking, however, the expense of constructing a 
 large current-carrying resistance of 2,000 ohms will be an 
 obstacle to the employment of this method. There is no 
 question, however, that it is the most satisfactory process for 
 conducting with certainty the calibration of high-tension 
 voltmeters. 
 
 The wire resistance must be so constructed as to be as 
 little inductive as possible. This may be done as follows: 
 An ebonite or fibre or pasteboard tube has wound upon it a 
 
428 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 silk-covered manganin wire, or, if bare wire is used, a silk 
 thread must be wound between the convolutions to prevent 
 them from touching each other. The coil so prepared is 
 covered with one layer of mica or shellac paper and another 
 layer of wire wound upon it in an opposite direction. The two 
 layers of wire are joined up at one and the same end, so that if 
 a current is sent through the two layers in series it flows in 
 opposite directions round each layer. A double-layer coil so 
 constructed is practically non-inductive, or but little induc- 
 tive. When traversed by a current there is little or no 
 magnetic field in the neighbourhood of the wire. A series of 
 
 FIG. 3. Skeleton Wooden Drum with Bare Manganin Wire wound 
 non-inductively on it. 
 
 such coils may be joined up in a frame and used as the 
 current-carrying resistance. It is exceedingly useful to 
 provide for the testing laboratory a number of resistances 
 made in this manner of No. 16 S.W.G. manganin wire having 
 resistances of 1 ohm, 10 ohms, 100 ohms, 1,000 ohms and, if 
 possible, 2,000 ohms. This size of wire will carry safely 
 1 ampere for a short time with but little change in resistance. 
 Instead of winding silk-covered wire on a tube, it is better 
 to wind bare wire on a skeleton bobbin made by joining 
 . together two round wooden discs by a number of wooden rods, 
 as shown in Fig. 3. The turns of wire should be kept apart by 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 429 
 
 a paraffined silk thread or cord wound between them. The 
 wire should be wound double, two wires being wound on in 
 parallel and these joined up at one end. The whole wire is, 
 therefore, nearly non-inductive, and the bobbin can be 
 immersed in a vessel of paraffin oil, by which means its 
 temperature can more easily be kept constant and ascertained. 
 
 3. The Potentiometer Measurement of Electromotive 
 Force. Various forms of potentiometer have already been 
 described in Chapter I. Whatever form the instrument takes 
 it consists essentially of a resistance, which may be a series of 
 coils or a long wire stretched over a divided scale. Down 
 this resistance a uniform fall in potential is made by means 
 of a battery working through a rheostat in series with the 
 wire. This battery is called the Working Battery. The 
 working battery should consist of one or more lithanode 
 secondary cells of ample size. The cells should be highly 
 insulated by being placed upon pieces of ebonite. The cells 
 should be well charged, and then about 25 per cent, of the charge 
 taken out by discharging the cell slowly. No good results 
 can be obtained when using a fully and freshly charged cell,, 
 because there are then irregular changes in its electromotive 
 force. The cells should be joined up in series with the 
 potentiometer wire through a carbon plate rheostat. 
 
 The wire rheostats in which wire is wound off one cylinder 
 on to another, or in which a contact spring presses against a 
 wire wound in a helix on a cylinder, give trouble in dusty 
 rooms, because the dust gets under the contact and creates a 
 variable resistance. Whatever form of rheostat is used, the 
 aim must be to cause a perfectly steady current to flow through 
 the potentiometer wire or resistance, and be so adjusted as to 
 value that the wire is not sensibly heated. If a long stretched 
 wire is employed as the potentiometer wire, the greatest care 
 must be taken to secure uniformity in its resistance per 
 centimetre of length, and this uniformity must be proved and 
 not taken for granted. 
 
430 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 The potentiometer is set, or the current in the wire brought 
 to a standard value, by means of a standard cell preferably 
 a Weston cadmium cell made in the Eayleigh H-form, as 
 then temperature correction is negligible. If a Clark cell is 
 employed, it must have a thermometer placed in it, or in the 
 water bath in which it stands, in order that its temperature 
 may be known and the proper correction applied to its 
 nominal value at 15 C. The standard cell must have its 
 positive pole connected to that end of the potentiometer wire 
 to which the positive pole of the working battery is attached. 
 The other pole of the cell is connected through a high 
 resistance galvanometer, or through a sensitive galvanometer 
 with a high resistance in series with it, to a slider or contact 
 maker on the potentiometer wire. The electromotive force of 
 the standard cell being known, it is clear that, if a point is 
 found on the potentiometer wire at which, when connected, 
 the galvanometer shows no current, the fall of potential down 
 the length of potentiometer wire thus intercepted must be 
 equal to the electromotive force of the cell The current in 
 the potentiometer wire can be so adjusted that the fall of 
 potential down it can be read off directly on a divided scale 
 placed against the wire. Thus the electromotive force of the 
 standard cell is, say, 1434 volts ; the potentiometer current 
 can be adjusted by the rheostats to make the fall of poten- 
 tial down the 1,434 division of the wire equal to the above 
 value. 
 
 When this is the case the potentiometer becomes direct 
 reading, and any other electromotive force or potential 
 difference falling within the range of the potentiometer wire 
 can be measured at once by merely attaching the terminals 
 of a circuit formed of the galvanometer in series with this 
 new source of electromotive force to two points on the poten- 
 tiometer wire so selected that the galvanometer shows no 
 current. The positive terminal or highest potential point of 
 this source of electromotive force must be joined to that end 
 of the wire nearest to the positive terminal of the working 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 431 
 
 battery. The source of electromotive force may be another 
 cell, or it may be a difference of potential between two points 
 on another wire traversed by a continuous current. 
 
 4. Measurement of Small Potential Differences. 
 
 To measure an electromotive force or potential difference of 
 about 1 volt or less we attach wires to the terminals of 
 this source of electromotive force (E.M.F.) or potential 
 difference (P.D.), and connect them as above described to the 
 potentiometer, and when it is set we can read off at once on 
 its scale the value of the E.M.F. or P.D. The potentiometer 
 is thus easily employed to give us the terminal voltage of a 
 primary or secondary cell, or the value of a current flowing 
 through a known low resistance, or of a very small current 
 flowing through a known higher resistance, provided always 
 that the P.D. to be measured is less than the whole fall down 
 the potentiometer wire. In making a number of measure- 
 ments of this kind the setting of the potentiometer must be 
 continually tested by coming back on to the Clark or other 
 standard cell. 
 
 In all practical forms of potentiometer, such as Crompton's 
 or Elliott's, there is a double pole switch on the instrument 
 so arranged that, without disturbing the galvanometer con- 
 nections, any cell or terminal wires from any circuit can be 
 quickly substituted for the standard cell in the galvanometer 
 circuit. Hence there is no loss of time in continually 
 re-checking the setting of the potentiometer current, and, if 
 it has varied, bringing it back to its original value by a touch 
 of the rheostat. 
 
 The potentiometer is especially useful in measuring 
 small E.M.F.s, such as that of a thermo-electric couple. 
 The Author designed for certain low temperature, re- 
 searches a combined resistance bridge and potentiometer 
 by means of which a thermo-electromotive force could be 
 measured and immediately afterwards the resistance of a 
 platinum wire giving the temperature of the junction. The 
 
432 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 arrangements of this combined bridge-potentiometer are as 
 follows : 
 
 A length of 2 metres of bare manganin wire (No. 36 
 S.W.G.) is stretched over a scale (see Fig. 4). This wire has 
 a resistance of 26*576 ohms and a diameter 0*0193 centimetre. 
 Over the slide wire moves a slider contact P. The other two 
 arms of the bridge consist of a resistance coil, C, of manganin 
 wire of 5,000 ohms, and a platinum wire used as a platinum 
 thermometer. The bridge is provided with current from a 
 2-cell lithanode battery, B, and a Pitkin-Holden galvano- 
 meter, G-, having a resistance of 4 ohms, is used with it. In 
 the diagram (Fig. 4) XZWY is the 2-metre slide wire 
 having its ends attached to terminal blocks X and Y. B is 
 the 2-cell battery which is connected through a current 
 reverser, D, with the ends of the slide wire, having interposed 
 between one terminal and the block Y either a resistance, E 2 , 
 of 200 ohms when used as a bridge, or a resistance E 1? E 4 and 
 E 3 when used as a potentiometer. E x is a variable resistance 
 of about 5,000 ohms, R 4 a resistance of 18,200 ohms, and E 3 a 
 resistance of 10x25*576 ohms, divided into four sections 
 having ratios of 1, 2, 3 and 4 in magnitude. The galvano- 
 meter is connected to terminals U and V when the 
 instrument is used as a bridge and P is the slide contact 
 maker on the wire ; the other two arms being the 5-ohm coil 
 C and the platinum wire P x used as a thermometer. 
 
 When the instrument is used as a potentiometer the 
 thermo-couple or other source of E.M,F. is joined in 
 series with the galvanometer between the slider P and the 
 end of the resistance coil E 4 . In this case the fall of potential 
 down the slide wire is measured by the Clark cell Ck. In 
 order to make the changes of connection rapidly a seven-cup 
 mercury switch is employed, so that by shifting a pair of 
 copper forks all the necessary changes of connection are made 
 instantly. 
 
 Eeferring to the diagram, ic will be seen that if we connect 
 the mercury cups 4 to 5 and 1 to 7 the arrangement is a 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 433 
 
 FF 
 
434 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 Wheatstone bridge. If we connect cups 3 to 4 and 6 and 7 
 it is changed to a potentiometer to measure E.M.F., and if 
 we connect cups 2 to 3 and 6 to 7 we can set the potentio- 
 meter by the Clark cell. 
 
 This form of combined bridge and potentiometer, devised 
 by the Author,* is of great use in measuring thermo-electro. 
 motive forces from single couples, and at the same time the 
 temperature of the thermo junction may be obtained from the 
 value of the resistance of a platinum wire, P p wound round it. 
 The instrument may be adapted for a variety of uses in 
 measuring E.M.F.S which are functions of temperature. 
 
 Potentiometers in which the whole or part of the resistance 
 is an exposed slide wire have the disadvantage that dust 
 settles on the wire, and then the sliding contact, by which the 
 connection to the galvanometer shunt circuit is made, is 
 uncertain in resistance. It must be borne in mind that, as 
 the position of balance is approached, the effective E.M.F. 
 in . the galvanometer circuit becomes vanishingly small, 
 and hence is unable to break through a dust or oxide 
 film and express itself as a deflection of the galvanometer 
 coil. Accordingly, for workshop purposes a potentiometer is 
 preferable which has no slide wire, but in which the resistance 
 inserted in the circuit of the working battery is wholly of 
 insulated wire coils included in a box. 
 
 A useful form of potentiometer, in which an external or 
 exposed slide wire only forms a 150th part of the whole 
 potentiometer resistance, is made by Messrs. Elliott Bros., 
 and consists essentially of 149 coils of wire joined in series 
 with each other, and with a slide wire equal in resistance 
 to one of them. A perspective view of the instrument is 
 shown in Fig. 5, and a diagram of connections in Fig. 6. 
 
 Each of the 149 sections or coils is about Sin. in length, 
 and they are all adjusted so as to be absolutely equal in 
 
 * See Phil. Mag., July, 1895, p. 95. " On the Thermo-electric Powers of 
 Metals and Alloys between the Temperature of Boiling Water and the Boiling 
 Point of Liquid Air." By J. A. Fleming and J. Dewar. 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 435 
 
 resistance one to the other. The slide portion of the wire 
 KM (Fig. 6) is extremely short, as can be seen in Fig. 5, 
 and is equal in resistance to one coil. Inequalities in the 
 drawing of this wire are compensated for by dividing the 
 scale, over which arm L travels, so that the individual 
 
 !FiG. 5. Elliott Potentiometer. 
 
 divisions of the divided wire EER are exactly multiples of 
 the divisions on the scale. As an example, the fall of 
 potential over 140*7 sections of the divided wire is exactly 
 five times that over 28 divisions of this wire, and 14 
 divisions on the scale. 
 
 PP2 
 
436 
 
 MEASUREMENT OF ELECTROM011VE FORCE. 
 
 A reference to Fig. 6 shows clearly how the arrangement 
 is effected in practice. AB are two terminals, to which the 
 working battery i.e., the one accumulator cell should be 
 attached. At C is a small fuse, which serves to protect the 
 slide wire from injury should too high an E.M.F. be applied 
 to A and B by accident. DE are the galvanometer terminals, 
 and across these is connected a short circuit key X, which in 
 
 F G F, Gi F 2 G 2 
 
 mm 
 
 FIG. 6. Diagram of Connections in the Elliott Potentiometer. 
 
 its normal, or free, position keeps the galvanometer short- 
 circuited, and thus protected against violent deflections. A 
 d'Arsonval galvanometer should always be employed in all 
 these tests. F, G-, F p G 1 , F 2 , G 2 , &c., are the terminals to 
 which wires leading to the various sources of potential 
 differences to be compared should be attached. A multiple 
 double-pole switch V permits of the two common bars Hand 
 
MEASUREMENT OF ELECTROMOTIVE FORCE, 437 
 
 I being connected to any pair of, these terminals at will. 
 EEE is the divided wire, which is laid round in a circular 
 position, and divided in 149 parts of equal resistances, small 
 contacts being placed at each of these 149 points. The 
 whole of this part of the divided wire, which, of course, is the 
 essential part of the whole apparatus, is perfectly protected 
 from mechanical injury by being inside the case. 
 
 At one extremity of this wire N" at the 149th contact it 
 is connected to O, a small fine adjustment rheostat, and so on 
 to P and Q, two other adjustable rheostats in series, and so 
 proportioned that the total resistance value of is rather 
 greater than that of one section of P, and that the total value 
 of all the sections of P are slightly greater than that of one 
 section of Q. P, Q, and O are not adjusted in any definite 
 values they serve simply as adjustments. In practice the 
 whole of Q, P, and are approximately 200 ohms altogether. 
 The divided wire itself, EEE, being about 30 ohms resist- 
 ance, one end of rheostat Q is joined to terminal B. 
 
 The other extremity of the wire EEE is taken up through 
 the top of the instrument at K, where it is led round a curved 
 segment, and where the moving contact arm L can travel over 
 it. A scale is fixed to the top of the instrument, and a 
 pointer is attached to L, so that when the moving contact is 
 on the stud K, the pointer attached to the arm L stands at 
 zero on the scale. When the arm L is moved till the pointer 
 stands at the figure 10, then the moving contact has passed 
 over a length of the divided wire exactly equal in resistance 
 to any of the other 149 sections between K and N. A 
 contact J can travel round the circle of the divided wire and 
 make contact with any of the 149 small contacts fixed to it. 
 This contact J is attached to a large toothed wheel, the edges 
 of which can be seen in Fig. 5 on the right and left of the 
 instrument. This affords a ready means of shifting the 
 position of contact J, and its position with reference to.JT 
 and K can be seen through a small window in the front of 
 the instrument, through which a number shows corresponding 
 
438 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 to the number of the contact on which J lies ; a device is 
 provided to cause J to make contact definitely on either one 
 or other of any pair of adjacent contact studs on the divided 
 wire. A wire is led from J to one on the galvanometer 
 terminals E. 
 
 The travelling contact on arm L is connected through a 
 small key W to the bar of the multiple switch, the other bar 
 H being connected to the second galvanometer terminal D. 
 The key is provided with a small clamping device, so that it 
 can be kept down if desired, and the galvanometer deflections 
 manipulated with key X. Care must be taken that no source 
 of E.M.F. is attached by mistake to terminals F, G-, &c., as, 
 in the event of the key W being clamped down and switch V 
 being in these terminals, a comparatively powerful current 
 might flow through the galvanometer and the slide wire, 
 probably damaging both. The key W, therefore, should only 
 be clamped down when making a series of tests where there is 
 no chance of a wrong connection having been made outside 
 the instrument. 
 
 It will be seen that there exists always between A and B 
 a closed circuit through which the current furnished by the 
 working battery passes from A through C to M, K, RRR, 
 N, 0, P, Q, and so to B. This circuit is of variable resistance, 
 owing to the adjustment of rheostats O, P, and Q ; but in all 
 cases the whole of the wire ERR is in circuit. 
 
 To make an JK.M.F. measurement we proceed as follows: 
 Fig. 7 illustrates the connections. The working battery 
 is connected to AB as usual, the standard cell and 
 resistance to FG. The small separate resistance box is 
 employed, the two terminals marked " Potentiometer " being 
 connected to FG, wires attached to the source of E.M.F. to 
 be measured being connected to terminals on this box, accord- 
 ing to the various ranges used. The terminals marked 
 " Potentiometer " have between them a small fractional part 
 of the whole resistance in the box. Setting the figure 143 at 
 the window, and arm L at 4 on the scale as before, when a 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 439 
 
 balance is obtained with a multiple switch on the standard 
 cell at FG, then each movement of the toothed wheel means 
 0*01 volt, and O'OOOl corresponds to the small whole divisions 
 on the scale. 
 
 Suppose an E.M.F. of about 100 volts is to be measured, 
 the positive wire should be joined to the terminal marked 
 -h on the separate resistance box, and the other to the 
 terminal marked 150. Then, having balanced as above, the 
 instrument is direct reading in volts that is to say, if a 
 balance is obtained with 101 at the window and arm L at 
 
 FIG. 7. The Elliott Potentiometer and Divided Resistance arranged for 
 Measuring Voltages. 
 
 5-3 on the scale, then the E.M.F. under test equals 101'53 
 volts. For readings using the + to 15 terminals on the 
 separate resistance box, the readings must be divided by 10 ; 
 if using terminals -f- to 300, readings must be multiplied 
 by 2 ; if using + to 600, multiply by 4. 
 
 Supposing it is desired to determine exactly an E.M.F. of 
 about 2-2 volts. Obviously, if the standard cell is balanced 
 with 143 at the window and 4 on the scale, the range of the 
 potentiometer is insufficient to compare this directly. If the 
 
440 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 terminals + to 15 on the separate resistance box are used, 
 then the E.M.F. of 2 -2 volts would balance with figure 
 showing at the window. For great accuracy, the following 
 method may be adopted : Connect two accumulator cells in 
 series to AB ; then with switch V (Fig. 6) on FG-, correspond- 
 ing to the terminals of the standard cell, adjust P, Q and 
 so that a balance is obtained with 71 at the window aud 
 arm. L at 7 on the scale (1*434/2 = 0:717). Assuming that 
 the E.M.F. of the standard is taken at 1434 volts at the 
 working temperature, then let wires be brought from the 
 source of E.M.F. to be tested to terminals FG-; then, if a 
 balance is obtained on moving the multiple switch to FG, 
 with 111 at the window and arm L at 4 on the scale, the 
 value of the E.M.F. under test = 1, 114 X 2 = 2-228 volts that 
 is to say, with the standard balanced at the position corre- 
 sponding to half its value, all readings at the window and 
 scale must be double to obtain correct values in volts. 
 
 This process can be carried further, but not more than 6 volts 
 should ever be applied to AB. 
 
 In workshop potentiometers it is desirable to avoid the 
 employment of any slide wire, however short, and to construct 
 the whole potentiometer of coils of wire contained in a box. 
 In the case of a potentiometer designed by the Author, the 
 instrument takes the form of a box having on the ebonite or 
 marble top surface a set of block contacts arranged in circles, 
 and each set associated with a radial arm contact like one of 
 the simple forms of Wheatstone bridge. There are two sets 
 of concentric block contacts, arranged as in Fig. 8, and a pair 
 of concentric brass rings to which the radial arms connect the 
 plugs. Under the top of the box are a series of coils inter- 
 connecting the blocks, as in a dial pattern "Wheatstone bridge, 
 the only difference being that each dial is double. There are 
 three double dials, the coils in between the blocks of the first 
 dial being each of 10 ohms, those between the blocks of the 
 second being 1*0 ohm, and those of the third being each 01 
 of an ohm. 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 441 
 
 The several dials are so joined up that they form one 
 resistance divided into two sections, but of such a nature that 
 increasing the resistance of one section decreases by an equal 
 amount the resistance of the other section. There are 10 
 blocks to each dial and, accordingly, the maximum resistance 
 which can be created in either section is 99*9 ohms ; and, no 
 matter how the dial radial arms are set, the joint resistance of 
 the two sections always has the same value, viz., 99*9 ohms. 
 
 FIG. 8. A Single Dial of the Fleming Potentiometer. 
 
 If, then, a single secondary cell is connected to the ends of 
 this divided resistance, and a high resistance galvanometer 
 and standard cell are connected to the terminals of one 
 section of the resistance, it is possible to move the radial 
 arms in such a manner that the relative magnitude of the 
 resistances of the two sections is varied, but the total value 
 of the two sections remains the same. 
 
 Let the standard cell be a Helmholtz calomel cell, which 
 is constructed to have an E.M.F. of 1 volt. Then it 
 
442 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 is possible to adjust the value of one section of the 
 resistance by moving the radial arm so that the high 
 resistance galvanometer indicates no current when the 
 secondary cell is connected to the terminals of the whole 
 resistance. For this is the case when the fall of potential 
 down the section of the resistance to which the galvanometer 
 is a shunt is 1 volt, and this is so when the sections of the 
 resistance have a certain ratio near equality. 
 
 Suppose, then, that another cell is substituted for the 
 standard cell, and again the radial arms are so moved that 
 the galvanometer shows no current. This movement of 
 the radial arms will not alter the value of the current 
 flowing through the whole resistance, but will alter the 
 ratio of the resistances of the two sections. This ratio 
 may be made such as to bring the galvanometer to zero 
 once more. 
 
 Let K x be the resistance of that section of the whole 
 resistance to which the galvanometer is a shunt when the 
 standard 1-volt cell is in series with the galvanometer, and 
 let K 2 be the resistance of the same section when the second 
 cell is substituted for it. Let us suppose the total constant 
 resistance of the two sections of the box is 99*9 ohms. 
 Let V be the E.M.F. of the cell being tested. Then 
 it is clear that, since the standard cell has an E.M.F. 
 of 1 volt, the volt-fall down the whole resistance in the 
 box is equal to 99'9/K r Hence the E.M.F. V of the cell 
 tested against it must be equal to IV^i volts. 
 
 Accordingly, if the secondary cell attached to the ends 
 of the whole resistance is large and very constant in 
 E.M.F., there is no need to have rheostats and other 
 complications to keep the potentiometer current constant. 
 The only pieces of apparatus necessary for measuring any 
 E.M.F. are the standard 1-volt cell, a high resistance gal- 
 vanometer and keys, the divided resistance above described, 
 and a large secondary cell which has been charged and 
 then partly discharged. 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 443 
 
 5. The Calibration of a Low-Tension Voltmeter. 
 Suppose it is desired to calibrate or check the scale 
 accuracy of a voltmeter reading, say, from zero up to 150 
 volts, by reference to the potential difference of a standard 
 cell, we proceed as follows : A resistance, r 1 r a r 3 (see Fig. 9) 
 must be provided, which is generally called a volt-box, con- 
 sisting of a number of bobbins of manganin wire contained 
 in a box. These coils of wire are arranged in series so as to 
 form a resistance of 10,000 or 20,000 ohms, which is divided 
 
 V Voltmeter. 
 
 B Testing Battery. 
 
 G High-resistance Galvanometer. 
 
 i r 2> r s Divided Resistance. 
 
 a, b Potentiometer Wire. 
 Ck Clark Cell. 
 b Potentiometer Working Cell. 
 
 FIG. 9. Potentiometer Arrangement for Checking Voltmeter. 
 
 in certain ratios by terminal attachments. Thus one set of 
 terminals may be so arranged that the whole resistance is 
 divided into two sections in the ratio of 99 : 1, another set 
 in the ratio of 9:1, another 999 : 1, and so on. This 
 resistance is joined across the terminals of the voltmeter V 
 to be checked, and a proper potential difference applied by 
 means of secondary cells B to give any required reading of 
 
444 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 the voltmeter, For this purpose a set of 100 small lithanode 
 cells are very convenient, giving any required E.M.F. from 
 2 to 200 volts. 
 
 Suppose, for instance, we require to check a voltmeter, 
 reading up to 100 volts, in the neighbourhood of 100 on the 
 scale. We should select those terminals of the volt-box which 
 give us a ratio of 99 : 1 in the whole resistance. Wires 
 would then be taken from the smaller section r x r 2 of the 
 resistance to a potentiometer. We then know that, what- 
 ever may be the value of the fall of potential down the 
 small section r x r 2 of the resistance as measured by the poten- 
 tiometer, the total fall of potential down the whole wire r^ 
 and therefore the actual true voltage applied to the voltmeter 
 terminals, is 100 times as great. In Fig. 9 is shown a 
 diagram of the connections to be made. 
 
 By varying the number of secondary cells in this battery 
 B attached to the terminals of the voltmeter V, we can make 
 various known or measured potential differences on these 
 terminals, and compare these values with the scale reading of 
 the voltmeter. A table can be drawn up of the true poten- 
 tial differences which correspond to various scale readings. 
 We then proceed, as in the case of an ammeter, to make a 
 curve of errors. 
 
 Take a straight horizontal line on a sheet of paper and 
 divide it into equal parts, representing the scale readings of 
 the voltmeter (see Fig. 10). At each point set up a perpen- 
 dicular the length of which is made proportional on same 
 scale to the difference between the scale reading of the volt- 
 meter and the true value found for the potential difference 
 making that reading. Let this perpendicular be drawn 
 upwards when the error of the voltmeter is positive and 
 downwards when the error of the voltmeter is negative. 
 Hence, if, corresponding to a scale reading of 100, the true 
 potential difference is 101*2, then the error is positive 
 that is, we have to add 1*2 volts to the scale reading to 
 arrive at the true voltage corresponding to the scale reading 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 445 
 
 100. In this manner the voltmeter can be calibrated 
 throughout the scale and a curve of errors found for it. 
 
 If the voltmeter is one constructed on an electromagnetic 
 principle, then it is necessary to take a series of ascending 
 and descending scale readings to ascertain if there is sensible 
 hysteresis error. Also tests should be made with the volt- 
 meter in various positions, or with magnets near it, to discover 
 how far it is affected by position or the presence of other 
 magnetic fields. 
 
 In the case of an electrostatic voltmeter it is necessary to 
 be on our guard against errors introduced by contact difference 
 
 FIG. 10. Error Curve of a Voltmeter. 
 
 of potential. Take the case of a Kelvin electrostatic volt- 
 meter. In this instrument the " needle," or movable portion 
 of the instrument, is of aluminium, and the fixed quadrants 
 are made of brass ; hence, when a secondary cell battery is 
 joined in between the terminals of the instrument, the scale 
 reading will be determined by the voltage of this battery plus 
 or minus the Volta contact potential difference of an 
 aluminium-brass couple. This latter amounts to about 0'3 of 
 a volt. Hence we find that an electrostatic voltmeter gives 
 scale readings slightly different when the " needle " is positive 
 from that which it does when the " needle " is made negative 
 
446 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 by reversing the connections of the working battery. Hence, 
 in checking the voltmeter, note must be made of the mode in 
 which the working battery is connected. 
 
 6. Calibration of a High-Tension Voltmeter. Supposing 
 we have calibrated in the manner described in the previous 
 section an electrostatic voltmeter reading up to 100 volts. 
 We may then employ this voltmeter as an intermediate 
 standard instrument to check a high-tension voltmeter 
 reading, say, up to 2,000 volts. For this purpose we require 
 a divided resistance which can be safely placed across a 
 2,000-volt alternating-current circuit. This can be made as 
 follows : 
 
 Provide 100 coils of double silk-covered platinoid wire 
 No. 36, each wire 100ft. in length, coiled up into a coil of 
 
 FIG. 11. 
 
 6in. in diameter, leaving both ends out. Squeeze up each 
 coil into a sort of hank (see Fig. 11) and bind it in the middle 
 with tape. Boil each coil or hank well in melted paraffin 
 wax. The resistance of each hank of wire will be about 
 400 ohms. Make a wooden frame so that 25 of these hanks 
 can be spaced lin. apart and be held by silk string, as shown 
 in Fig. 12. Join up the wires of the hanks in series. Connect 
 four such frames of wood with cross bars and join up all coils 
 in series. Bring the ends of the whole series and of each hank 
 to well-insulated terminals on the outside of the wooden 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 447 
 
 frame. The whole wire will then form a resistance of 40,000 
 ohms in 100 sections, and each section will be perfectly 
 insulated from its neighbour. The wire will bear placing 
 across a 2,000-volt circuit for any length of time without over- 
 heating or risk of failure of the insulation. 
 
 This divided resistance can then be placed across the 
 terminals of the high-tension electrostatic voltmeter, and a 
 calibrated low-tension electrostatic voltmeter joined across 
 the terminals of one section, say ^Vth of the whole wire. 
 Hence, when the high-tension voltmeter is connected to a 
 
 O 
 
 FIG. 12. Inductionless Safety Resistance. 
 
 2,000-volt alternator or transformer, the reading of the low 
 tension voltmeter will give the true volt fall down ^ih of 
 the resistance, and therefore the true voltage at the terminals 
 of the high-tension voltmeter. 
 
 It should be noticed, however, that there is a possible 
 source of error in the above process which arises from the 
 capacity of the low-tension voltmeter. This may be explained 
 as follows : 
 
 Let us suppose, in the first place, for the sake of avoiding mere mathematical 
 complexity, that the divided resistance is entirely non-inductive. Let R and Rj 
 be the resistances of the two sections of this resistance, and let the low-tension 
 electrostatic voltmeter be joined over the section of which the resistance 
 
448 
 
 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 is R (see Fig. 13). Let the capacity of the voltmeter be represented in the 
 figure (Fig. 13) by a condenser C. Then let the instantaneous values of the 
 currents through R, R, and C be i, i t and z 2 , and let the instantaneous values 
 of the potential fall down R, R, and R+Ri be v, Vi, and v'. 
 We have then the following equations : 
 
 }' fby the principle of continuity, 
 ^ l ^=^c,) 
 
 Ohm's law, 
 
 dv 
 and ^ = dt ^ rom definition. 
 
 Also, let v' = V sin pt, the frequency being as usual p/Str. 
 v-'- 
 
 FIG. 13. 
 
 Obviously, then, we have the following equation : 
 dv v ' 
 
 Differentiating with regard to t, we obtain, on re-arranging terms, 
 
 dv 
 
 and eliminating^ between (i) and (ii), and remembering that 0-^= - Cp^v, 
 if the variation of v is harmonic, we obtain finally the equation 
 
 In virtue of a well-known transformation (see "The Alternate^ Current Trans- 
 former," Fleming, Vol. L, p. 161) we can write the above equation in the form 
 
 Hence, if V is the maximum value of v, it follows that 
 
 V^R! 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 449 
 
 or, if we write K a for 1/R, and K for 1/R, we have 
 V_ K, 
 
 V ' 
 
 If, then, C = 0, or if the low-tension voltmeter has no sensible capacity, we 
 
 V R 
 
 have V^R-PR 5 
 
 in other words, the maximum or root mean-square value of the volt fall down 
 the section of the resistance R is to the fall down the whole resistance in the 
 ratio of those resistances. If, however, (J is not zero, or if p is large and if R 
 and Rj are large, then the root-mean-square values of the volt falls are no 
 longer in the exact ratio of the resistances. 
 
 There is no need to complicate the proof by considering the case when these 
 sections of the divided resistance have slight inductance. The same principle 
 holds good. 
 
 Hence, although the use of the divided resistance is 
 a convenient method of stepping from one voltmeter t:> 
 another, it is necessary to take the precaution to check 
 the high-tension voltmeter by the only unexceptionable 
 method viz., by connecting it to the terminals of a high 
 known resistance through which a known measured current 
 is passed. 
 
 7. Self-recording Voltmeters. In many cases it is 
 necessary to secure a continuous record of the difference in 
 potential between two points, and this can be accomplished 
 by the use of a self-recording voltmeter. These instruments 
 consist of two parts a voltmeter part and a paper-carrying 
 drum which is made to revolve by clockwork uniformly. 
 The voltmeter part carries a pen, which is displaced by the 
 voltage applied to the instrument. Hence, if the pen is at 
 rest and the drum revolves, the pen will* draw a line on the 
 paper which will be a straight line when the paper is removed 
 from the drum and spread out. If the pen is displaced by a 
 voltage applied to the instrument, then the line is a sinuous, 
 irregular line. If the displacements of the pen are exactly 
 proportional to the voltage, then the ordinaters of the curve 
 will measure this voltage. If not, then paper ruled up in 
 lines placed at intervals equal to 1 volt or 10 volts is 1 
 
450 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 employed, so that an inspection of the line drawn by the pen 
 suffices to determine the voltage. The voltmeter part may 
 be a hot-wire voltmeter, as in the Pitkin-Holden instrument 
 (see Fig. 14). In this case the expansion of the wire caused 
 by the current flowing through it is made to move the pen 
 arm by an amount increased by the use of a multiplying 
 gear. 
 
 In other cases the voltmeter mechanism is electro- 
 magnetic; as in the Kelvin recording voltmeter (see Fig. 15) 
 or Elliott instrument (see Figs. 16 and 17). In the Kelvin 
 instrument the control is by gravity, and the electro- 
 magnetic action of a solenoid or an iron core lifts or lowers 
 the pen. 
 
 In testing a self-recording voltmeter the clock mechanism 
 must first be examined, to see whether it keeps correct time. 
 Then the voltmeter part must be separately tested by the 
 potentiometer, to ascertain if this portion of the mechanism 
 works properly. 
 
 Self-recording voltmeters are employed to detect the 
 irregularities of pressure in connection with electric supply 
 stations, and to decide whether complaints as to abbreviated 
 lives of glow lamps are due to the qualities of the lamps or 
 to excessive variation of service pressure. A self-recording 
 voltmeter is useful in connection with tests of secondary 
 batteries to determine the exact time at which the voltage 
 per cell has fallen to 1*8 volts, below which voltage no current 
 readings are of any value. They are also necessary in con- 
 nection with life-tests of incandescent lamps. 
 
 8. Extra High-Pressure Yoltmeters. In connection with 
 cable and transformer testing it becomes necessary to employ 
 voltmeters for measuring extra high pressures and voltages 
 such as 20,000 to 60,000 volts. Instruments for this purpose 
 have been designed by Lord Kelvin depending on the 
 attraction exerted between a fixed disc and one suspended 
 over and parallel to it from the arm of a steelyard. The 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 451 
 
452 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 453 
 
 discs are included in a case which is well earthed (see 
 Fig. 18). 
 
 The movement of the suspended disc is limited by stops. 
 The control is a gravity control. The instrument is provided 
 with certain weights which, when hung on the beam, cause 
 the deflection of the scale beam under the electrostatic forces 
 to have a definite and indicated value in volts. 
 
 FIG. 18. Kelvin High-Tension Voltmeter. 
 
 Since the attractive force between two such parallel discs 
 varies as the square of the difference of potential, the 
 instrument is equally well adapted for use with continuous or 
 alternating-current voltages. A modification of this instru- 
 ment has been made by Messrs. Pirelli, of Milan (see Fig. 19), 
 for measuring voltages of 25,000 or so. A fixed plate, A, 
 exerts an attraction on a movable one, B. The two plates are 
 enclosed in a cylindrical copper case, M, and the whole is 
 placed in a glass cup filled with vaseline oil. C is a glass 
 
454 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 P' 
 
 Fio. 19. Pirelli & Co.'s Electrostatic Voltmeter. Scale : 2in. = lft. 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 455 
 
 shade from the top of which the pole P' projects, this being 
 connected with the movable plate by a thin wire, D. The 
 apparatus rests on an ebonite stool, T, having ebonite legs. 
 Two weights are provided : with one weight one scale division 
 corresponds to 500 volts, and with the other a scale division 
 equals 1,000 volts. The instrument can thus read up to 
 60,000 volts. 
 
 Some instrument of the above type is indispensable in 
 testing cables or condensers with high voltage. The instru- 
 ment is best calibrated by the employment of a chain of 
 overlapping instruments, so that we can step up from an 
 electrostatic voltmeter capable of being calibrated directly by 
 
 FIG. 20. Kelvin Water Battery. 
 
 a Clark cell to one of the above type. Thus, if we have three 
 electrostatic voltmeters one reading from 500 to 2,000 volts, 
 one from 1,000 to 5,000, and one from 4,000 to 20,000, we 
 can reduce the readings to their equivalent in terms of the 
 international volt as denned by a Clark or Weston cell. 
 
 Without a chain of overlapping voltmeters there is some 
 difficulty in verifying the indications of an extra high- 
 tension voltmeter, because the construction of a resistance 
 capable of having these very high potentials put on its ends 
 is an expensive matter. One way in which it can be done 
 is by the use of a series of condensers charged by a bat- 
 tery of small cells. Lord Kelvin has designed a small 
 form of water battery consisting of small slips of copper 
 and zinc placed so close together (see Fig. 20) that, when 
 
456 MEASUREMENT OP ELECTROMOTIVE FORCE. 
 
 dipped in water, a small drop is held up by capillary action 
 between the alternate plates. This arrangement may be made 
 to furnish E.M.F. up to 1,000 volts by having a sufficient 
 number of plates. The E.M.F. of the battery can be measured 
 by a standardised voltmeter of the electrostatic type. The 
 cells have, however, such high internal resistance that any 
 attempt to take from them a current, even though exceedingly 
 small, results in a great fall in terminal potential difference. 
 
 In addition to these cells we must be provided with a 
 number of condensers made with glass, paraffined paper or 
 mica as dielectric. These condensers must first be tested to 
 ascertain the rate at which the terminal potential difference of 
 the condenser falls off with lapse of time, after being charged, 
 due to internal or external leakage. If the condenser is 
 charged with the water battery and connected to an electro- 
 static voltmeter we can observe the rate at which the 
 voltmeter deflection decays. This is partly due to leakage in 
 the condenser, and partly to leakage in the voltmeter. The 
 voltmeter must be separately tested, and should have such 
 good insulation that, if charged and left to itself, the poten- 
 tial, as indicated by the needle, does not fall to half its value 
 in a quarter of an hour. 
 
 If the condensers are all found to be equally free from 
 leakage, then they may be arranged in series and all be highly 
 insulated. Each one is then separately charged in the 
 same direction, say to 1,000 volts, by the battery, and the 
 result is that the potential differences are added together, and 
 between the extreme terminals of the series of condensers we 
 have a potential difference represented by nV, where n is the 
 number of condensers and V is the E.M.F. of the batteries. 
 In this experiment both battery and operator must be very 
 highly insulated by being placed on blocks of paraffin wax 
 or sheets of ebonite. 
 
 It is easy to arrange a highly insulated commutator, 
 consisting of a block of paraffin wax having small holes 
 bored in it, to act as mercury cups, and, by means of wire 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 457 
 
 forks attached to ebonite handles, to so connect up the 
 condensers that they can be charged in parallel and then 
 arranged in series. 
 
 Various forms of commutator have been devised to effect 
 such a change quickly. An arrangement was employed by 
 CT. Plante in his researches, and more recently by Prof. 
 Trowbridge. A more effective though expensive arrangement 
 is to employ small secondary cells. Series of 50 small litha- 
 node secondary cells may be arranged in trays so as to give 
 100 volts. These may be supported on shelves on blocks of 
 paraffin, and sets of these 50 cells may be joined up in series. 
 In this manner, high voltages may be created of known value. 
 These may be multiplied by the use of condensers charged 
 in parallel and then joined in series. In this way, by 
 employing series of cells and condensers charged in parallel 
 and then arranged in series, Prof. J. Trowbridge has built 
 up potential differences amounting to two or three million 
 volts, capable of giving electric sparks 7ft. in length. Under 
 these very high KM.F.s he finds the air at ordinary pressures 
 becomes conductive and behaves like the rarefied air in a 
 vacuum tube under lower electromotive force. 
 
 It is not beyond the bounds of possibility to provide in an 
 ordinary electrical testing laboratory a continuous voltage of 
 approximately 10,000 volts. This is best done by setting up 
 small secondary cells in sets of 40 cells. These can be put 
 up in stout glass test tubes, which are carried in holes bored 
 out in blocks of paraffin wax. These cells are joined up in 
 series, and each set can be charged off an ordinary 100- volt 
 circuit through a carbon filament lamp or high resistance. 
 The sets of 40 cells are joined in series, being arranged on 
 ebonite shelves in a sort of cabinet. One hundred arid 
 twenty-five of these sets can be arranged in the cabinet, 
 and give, when charged, an E.M.F. of 10,000 volts. The 
 test-tubes in which the cells are set up may be lin. in 
 diameter and 6in. high, and contain two small plates of 
 lithanode in each cell. Each shelf in the cabinet can be 
 
458 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 made to hold one dozen sets of 40 cells and on 10 or 11 
 shelves the sets requisite to give 10,000 volts can be arranged. 
 The cells can be used to charge mica or glass condensers, 
 and by means of 10 condensers, each having a capacity, say, 
 of O'l of a microfarad, charged in parallel and then arranged 
 in series, we have the means of building up a known potential 
 of 100,000 volts, and for calibrating an electrostatic voltmeter 
 for measuring extra high pressures. 
 
 9. Laboratory and Switchboard Voltmeters. A classi- 
 fication of voltmeters intended for laboratory and dynamo 
 room use, sufficient for present purposes, is as follows: 
 
 A. Classification by Type. 
 (I.) Continuous-current voltmeters. 
 (II.) Alternating-current voltmeters. 
 (III.) Universal voltmeters. 
 
 B. Classification by Principle. 
 (i.) Electrostatic voltmeters, 
 (ii.) Electromagnetic voltmeters, 
 (iii.) Electro- thermal voltmeters. 
 
 C. Classification by Range and Use. 
 
 (a) Laboratory or table voltmeters. 
 
 (b) Switchboard voltmeters. 
 
 (G) Extra high-tension or testing voltmeters. 
 
 It is impossible to describe here all the numerous forms of 
 voltmeter which have been devised. There are certain types 
 which have survived in the struggle for existence because 
 they have proved most convenient. 
 
 In laboratory work, for use with continuous currents only, 
 one of the best forms of table voltmeter is the Weston 
 voltmeter. This instrument is of the electromagnetic type, 
 and consists ot a well-aged magnet, which provides a 
 permanent field. In this field is supported on jewelled 
 centres an axis which carries a circular coil of wire. The 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 459 
 
 coil carries an index needle. In series with the coil is a 
 high non-inductive resistance. The passage of a current 
 through the coil causes it to turn so as to place its magnetic 
 axis more or less in line with the field. This motion is 
 resisted by the torque of a steel spring like the hair spring of 
 a watch. The instruments are so made that the scale 
 division reading in volts or fractions of a volt are equal and 
 there is no dead or undivided portion of the scale. The 
 instruments are very dead-beat. One of the most useful 
 forms is the voltmeter reading from to 150 volts from 
 one pair of terminals, and by the use of another pair 
 reading from to 15 volts over the same range of scale, 
 These voltmeters have a very high resistance from 10,000 
 to 15,000 ohms. Hence the actual current taken is very 
 small. In the next place, for alternating -current laboratory 
 measurement the multicellular electrostatic voltmeter of 
 Lord Kelvin is very valuable. This instrument has already 
 been described in detail (see Chapter I, p. 132). 
 
 Other types of voltmeter available like the electrostatic 
 instruments both for alternating and continuous voltage are 
 the electro-thermal voltmeters represented by the Cardew and 
 Hartmann and Braun hot-wire voltmeters. The Cardew 
 voltmeter consists of a platinum-silver wire well aged by 
 being repeatedly heated and cooled. This is carried on a 
 support which in one form consists of a pair of compound 
 metal rods made of one-third of iron and two-thirds of brass. 
 The platinum-silver wire is fixed to one end of the support 
 and the other end of the wire is attached to a motion- 
 multiplying gear. The object of making the rods partly of 
 iron and partly of brass is to give them the same resultant 
 coefficient of expansion with heat as the platinum-silver wire, 
 so that no external changes of temperature cause any 
 difference of expansion in the wire arid rods ; but the 
 indicating mechanism is only caused to operate when the 
 wire expands more than the rods. The rods, wire and 
 mechanism are enclosed in a brass case. 
 
460 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 In another and better form of instrument the support 
 which carries the wire is not a pair of rods but a tube, partly 
 of brass and partly of iron, which is split longitudinally so 
 as to enable the wire to be easily inserted. This form is 
 called the tube instrument. The split tube is enclosed in 
 another outer casing tube. The resistance of the wire is 
 generally about 300 ohms. Hence, if its ends are attached to 
 a circuit of 100 volts, the wire passes about one-third of an 
 ampere. This causes it to be heated and to expand. The 
 heat radiated by the wire heats the rods or supporting tube 
 and causes it also to expand. After a short time a stationary 
 condition is reached, in which, whilst the wire and rods or 
 tube are both hot, the wire is hotter than the supports, and 
 hence the magnifying mechanism indicates on the dial by the 
 position of the needle a certain relative elongation. Corre- 
 sponding to each particular voltage on the wire there is a 
 position of the indicating needle on the dial. Hence the 
 instrument can be calibrated as a voltmeter. 
 
 In the rod instrument, if the current is switched off the 
 indicating needle goes back to zero and then passes back 
 beyond it. This is due to the fact that the thin wire cools 
 more quickly than the rods, and hence, for a short time, the 
 rods are expanded relatively to the wire. In the tube form 
 of instrument this effect is not so apparent. For the same 
 reason the reading of the instrument must not be taken until 
 the voltage has been kept on it for a few minutes. One 
 objection to the Cardew form of voltmeter is the large power 
 taken up by it. If the wire has a resistance of 300 ohms 
 when hot and with 100 volts on the terminals, then the 
 instrument is taking up about 33 watts, and if kept on the 
 circuit for three hours it uses nearly one-tenth of a Board of 
 Trade unit of electric energy. Hence, relatively to many 
 other electromagnetic instruments, and to electrostatic ones, it 
 is uneconomical for continued use. The Cardew voltmeter 
 should always be fixed with its tube horizontal, as in this 
 position the air convection currents in the tube are less 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 461 
 
 FIG. 21. Hartmami and Brauu Hot- Wire Voltmeter. 
 
 FIG. 22. Kelvin Multicellular Vertical pattern Voltmeter. 
 
462 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 FIG. 23. Kelvin Edgewise Voltmeter. 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 463 
 
 violent than when in a vertical position. If placed with the 
 tube upright, then the air convection currents cause small and 
 frequent changes in temperature in the wire which make the 
 indicating needle "breathe," or move slightly to and fro. 
 The instruments are usually calibrated for use between 
 40 and 150 volts, and hence are not suitable for measuring 
 very low voltages. 
 
 Another form of thermal voltmeter is that of Hartmann and 
 Braun (see Fig. 21). In this instrument the platinum-silver 
 wire is fixed at the ends, but when heated by a current 
 it " sags," and the sag is detected and measured by a delicate 
 multiplying mechanism. The needle is kept from vibration 
 by a damping copper disc attached to it which moves between 
 the poles of a permanent magnet. 
 
 These hot-wire voltmeters, like the electrostatic, are suit- 
 able for use with alternating currents of any frequency, not 
 very high, as well as with continuous currents, since their 
 indication depend upon the heating power of the current, 
 which is proportional to the square of the current, and there- 
 fore to the square of the potential difference of the terminals. 
 
 For switchboard purposes a voltmeter is preferred which 
 has a scale in a vertical plane If the voltmeter is to be 
 kept continuously in connection with a circuit, electrostatic 
 instruments have a great advantage over electromagnetic or 
 electrothermal, in that they take up no sensible amount of 
 power. Moreover, in contrast with electromagnetic instru- 
 ments, they can be employed for direct as well as alternating 
 currents, and in the latter case their indications are indepen- 
 dent of the frequency. 
 
 In the class of voltmeters suitable for switchboard work 
 we may especially include the vertical multicellular pattern 
 of Kelvin electrostatic voltmeter (see Fig. 22), which is made 
 for various ranges of voltage. 
 
 A type of voltmeter for switchboard work, called the Edge- 
 wise pattern (see Fig. 23), is often used on switchboards 
 because of the small space it takes up. This instrument, 
 
464 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 together with the Kelvin engine-room voltmeter, is of the 
 electromagnetic type, and depends for its action upon the 
 attraction of a small, carefully annealed rod of iron by a 
 solenoid. 
 
 In testing a voltmeter for station or workshop use it is 
 necessary to pay attention to the following points : 
 
 First, the accuracy of the scale readings must be checked 
 with the potentiometer if the voltmeter is for continuous 
 currents, or by reference to a carefully-calibrated electrostatic 
 voltmeter if the instrument is for alternating currents. In 
 so doing the voltmeter should be first tested with gradually 
 increasing voltage and then with gradually diminishing 
 voltage, to ascertain if there is any hysteresis error. This is 
 especially necessary in the case of electromagnetic instru- 
 ments containing iron in their construction. 
 
 In the next place, the voltmeter should be tested with the 
 voltage applied in both directions on the terminals, if the 
 instrument permits this being done. This is essential in 
 the case of electrostatic instruments to detect any contact, 
 potential or volta-effects due to contact of different metals. 
 
 In the case of alternating-current voltmeters the effect of 
 varying the frequency should be examined. In all cases the 
 disturbing effects of varying position, or of the proximity 
 of magnets or wires conveying continuous or alternating 
 currents, should be carefully employed. In the case of switch- 
 board instruments this is very necessary, as some types of 
 instrument indicate correctly when isolated but very incor- 
 rectly when in the neighbourhood of conductors conveying 
 strong currents. 
 
 In a vertical pattern electrostatic voltmeter, in which the 
 needle moves on pivots, it is essential that the needle axis 
 should be carried in jewels or on friction wheels. The 
 electrostatic forces brought into play are not large, and if 
 pivot friction exists the instrument will be sluggish and will 
 require a great deal of tapping to make the needle take up 
 its right position when the voltmeter is in the circuit. 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 465 
 
 Another source of error in electrostatic voltmeters is that 
 due to the electrification of the glass front by friction. 
 
 Prof. Ayrton hsfe studied this question, and has devised 
 various transparent varnishes which are sufficiently con- 
 ducting when dry to prevent an electric charge being held 
 on them. The glass front of the voltmeter is covered with 
 a layer of this varnish, and it is impossible to disturb the 
 instrumental readings by electrifying the surface by touching 
 or rubbing. Two of Prof. Ayrton's formulae for a varnish 
 of the above kind are given below : 
 
 (i.) Dissolve |oz. of transparent gelatine in loz. of glacial acetic acid by 
 heating them at 100C. To this add half the volume of dilute 
 sulphuric acid (one part of strong acid to eight of water by 
 volume) and apply this whilst warm to the glass shade. When 
 this film has become hard, apply over it a coating of Griffiths' 
 anti- sulphuric enamel. 
 
 (ii.) Thin the gelatine solution prepared as above by the addition of 
 acetic acid (say, two volumes of acid to one of solution), and, after 
 drying the glass, float this solution over it. Drive off the excess 
 of acetic acid by warming. Allow the glass to cool, and repeat 
 the process. Thin anti-sulphuric enamel by the addition of 
 ether and float it over the gelatine layer. Expel the ether by 
 heating and apply a second layer of anti- sulphuric enamel. 
 
 A glass disc so coated is quite as transparent as one 
 not coated, but it cannot be electrified by touching or 
 rubbing it or holding near it an electrified body. The varnish 
 film acts as a metallic screen would do in preventing elec- 
 trification of the interior portions of the voltmeter.* 
 
 A good switchboard voltmeter should comply with the 
 following conditions : 
 
 (i.) It should not be affected by external magnetic fields, 
 such as exist in the neighbourhood of switch- 
 boards. It is quite common to find that the 
 stray fields on the front of a station switchboard 
 
 * See Ayrton and Mather "Transparent and Conducting Screens for 
 Electric and other Apparatus," Proc. Inst. Elec. Eng., April 12, 1894 ; also 
 The Electrician, Vol. XXXII., p. 693. 
 
 HH 
 
466 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 have a strength of 5 to 10 C.G.S. units that is, 
 25 to 50 times the earth's horizontal field. 
 
 (ii.) It should not be affected by outside electrostatic 
 fields, or by rubbing the dial glass. 
 
 (iii.) It should have no temperature error. 
 
 (iv.) It should have a high resistance, so as to measure 
 - equally accurately the pressure at the station 
 'bus bars or at the ends of long thin pilot wires. 
 
 (v.) It should have as large and open a scale as possible. 
 
 (vi.) It should be dead-beat if possible without the use 
 
 of dashpots. 
 (vii.) If employed with alternating voltages, its readings 
 
 should be independent of frequency. 
 
 (viii.) Its readings should not be affected by variations 
 in external temperature or by vibration, and it 
 should be easy to pack, transport and fix up on 
 a switchboard, and take up as little room as 
 possible. 
 
 Hardly any voltmeter complies perfectly with the whole of 
 these conditions. The electrostatic instruments comply well 
 with (i.), (iii.), (iv.) and (vii.), and the electrothermal with (iii.) 
 and (vi.). Many electromagnetic instruments of the movable 
 coil permanent magnet type are much affected by external 
 magnetic fields. Hence such switchboard voltmeters should 
 be calibrated in position and checked constantly against a 
 tested electrostatic instrument. 
 
 If a switchboard is equipped with electromagnetic volt- 
 meters it is well to have at least one electrostatic instrument 
 in connection with them. 
 
 In selecting these instruments, if not electrostatic, regard 
 should be taken of their resistance and of the amount of 
 power they take up and the energy absorption in watt-hours 
 per year of ordinary use. A voltmeter which has a resist- 
 ance of only 1,000 ohms takes up 10 watts when used on a 
 100-volt circuit, and absorbs therefore 1 B.T.U. in 100 hours 
 of use. Hence the switchboard absorption of power may 
 
MEASUREMENT OF ELECTROMOTIVE FORCE. 467 
 
 amount to a not inconsiderable amount if voltmeters of low 
 resistance are largely employed. 
 
 Prof. Ayrton and Mr. Mather have devised an electro- 
 magnetic astatic voltmeter for switchboard purposes which 
 is, as far as possible, free from liability to disturbance by 
 external magnetic fields. For details of this instrument the 
 reader is referred to the Paper describing it in the Proceedings 
 of the Institution of Electrical Engineers, April 12, 1894, or 
 The Electrician, Vol. XXXII., p. 688, 1894. 
 
 HH2 
 
468 
 
 MEASUREMENT OF ELECTROMOTIVE FORCE. 
 
 TABLE I. 
 
 Electromotive Force of the Clark Cell at Various Temperatures, 
 based on the Board of Trade Value at 15 C. 
 
 Temperature. 
 
 E.M.F. 
 
 Temperature. 
 
 E.M.F. 
 
 6C. 
 
 1-444 
 
 16C. 
 
 1-4331-4329 
 
 7C. 
 
 1-443 
 
 17C. 
 
 1-4321-4318 
 
 8C. 
 
 1-442 
 
 18C. 
 
 1-4311-4307 
 
 9C. 
 
 1-441 
 
 19C. 
 
 1.4301-4296 
 
 10C. 
 
 1-4401-4396 
 
 20C. 
 
 1-428 1-4285 
 
 ire. 
 
 1-488 1-4385 
 
 21C. 
 
 1-4271-4274 
 
 12C. 
 
 1.437_1 -4374 
 
 22C. 
 
 1-426 
 
 13C. 
 
 1-4361-4362 
 
 23C. 
 
 1-425 
 
 14C. 
 
 1-436 1-4851 
 
 24C. 
 
 1-424 
 
 15C. 
 
 1-4341-4340 
 
 25C. 
 
 1-423 
 
 The values from 10C. to 21C. are given to three and also to four places 
 of decimals. 
 
CHAPTER V. 
 
 THE MEASUREMENT OF ELECTRIC POWER. 
 
 1. Electric Power: Mean Power and Power Factor. 
 
 When an electric current exists in a circuit there is an 
 absorption of power by the circuit due to its electrical resis- 
 tance, and this power is ultimately dissipated as heat. If the 
 circuit contains one or more sources of counter-electromotive 
 force against which a current is urged by the external impressed 
 electromotive force, additional work is done and power is 
 expended on the circuit. Considering, first, the case of 
 unvarying continuous or unidirectional electric currents, we 
 can estimate the power expended on the power-absorbing 
 circuit by measuring separately the current through the 
 circuit and the difference of potential of its ends. 
 
 If V be this difference of potential, then the work done 
 in raising a quantity of electricity, Q, through a difference 
 of potential V is QV, and if this work is uniformly per- 
 formed in a time T, then QV/T is the rate of doing work. 
 But Q/T=C, or is the measure of the current in the power- 
 absorbing circuit. Hence, the measure of the power being 
 taken up is the numerical value of the product CV. 
 
 Accordingly, in the case of unvarying unidirectional 
 currents the practical measurement of the power absorbed 
 electrically by any circuit consists in measuring the current 
 in the circuit and the fall in potential down it, and taking 
 the numerical product of these values. These two readings 
 may be taken by separate instruments, an ammeter and a 
 
470 
 
 THE MEASUREMENT OF ELECTRIC POWER. 
 
 voltmeter, or the product may be directly obtained at one 
 reading by the use of a wattmeter, or electric power- 
 measuring instrument. 
 
 If the power taken up from instant to instant varies, the 
 mean value taken at equidistant intervals may be calculated 
 or obtained from a power curve. Thus, if the horizontal 
 distances in the diagram in Fig. 1 represent time and the 
 vertical distances power, then, if observations are taken at 
 certain times of the power being absorbed by a circuit, and 
 ordinates are drawn to scale to represent these values, the 
 curve obtained by joining their upper ends is a power curve. 
 The mean ordinate of this curve is the mean power, and the 
 product of the mean power and the whole time of observation 
 gives us the total energy absorbed by the circuit in that time. 
 
 If the current flowing in the power-absorbing circuit is an 
 alternating current, then we have two cases to consider: 
 first, when the circuit is non-inductive, and second, when 
 it is inductive. In the first case the mean power taken up 
 by the circuit is measured by the product of the root-mean- 
 square (K.M.S.) values of the current and the terminal 
 potential difference or voltage; in other words, by the 
 product of the ammeter and voltmeter readings, employing 
 proper instruments for recording these quantities. When 
 the circuit is inductive, the true mean power is measured by 
 the product of the root-mean-square values of the current 
 and terminal voltage and a factor called the power-factor. In 
 
THE MEASUREMENT OF ELECTRIC POWER. 471 
 
 the case when the current and voltage vary periodically in 
 a simple harmonic manner the power-factor is the cosine of 
 the angle of phase-difference of the current and terminal 
 voltage.* 
 
 Hence, generally, we may say that in all cases the mean 
 power taken up in a circuit is measured by the product of 
 the three quantities the RM.S. value of the terminal 
 voltage, the R.M.S. value of the circuit current, and the 
 power-factor. If the circuit is non-inductive the power- 
 factor is unity, and if the current is continuous the RM.S- 
 value is the same as the unvarying value of this quantity. 
 If the current is alternating the product so obtained is the 
 mean power during this phase. 
 
 2. Measurement of Power in the case of Unvarying 
 Continuous or Direct Currents If a circuit is traversed 
 by a continuous or unvarying current, in order to measure 
 the power taken up we have to measure the current in 
 the circuit and the terminal voltage. The current can be 
 
 T 
 
 FIG. 2. 
 
 measured by a correct ammeter and the voltage by a volt- 
 meter. The voltmeter should preferably be of the electro- 
 static type. If, however, the voltmeter is electromagnetic, or 
 takes up a current, then a correction will be needed in the 
 ammeter reading. 
 
 The voltmeter and ammeter should be arranged as shown 
 in Fig. 2, where A is the ammeter, V the voltmeter and P 
 
 * The term power-factor, defined as above, was first suggested and so used 
 by the Author in a Paper entitled " Experimental Researches on Alternate 
 Current Transformers." See Proc. Inst. E.E ., 1892, Vol. XXII., p. 606. 
 
472 
 
 THE MEASUREMENT OF ELECTRIC POWER. 
 
 the power-absorbing circuit. Then it is necessary to deter- 
 mine the current taken up by the voltmeter, and to deduct 
 this value from the ammeter reading to obtain the true 
 current taken by the power-absorbing circuit alone. This 
 correction is the more necessary in cases in which the current 
 taken by the power-absorbing circuit is small. It may, how- 
 ever, be neglected in many other cases in which the voltmeter 
 current is very small in comparison with the total current. 
 
 If the voltage or the current are either of them very small 
 it may be quite impossible to obtain really good power 
 measurements when using commercial ammeters and volt- 
 
 FIG. 3. 
 
 meters. This is the case in power measurements made on 
 small candle-power low- voltage incandescent lamps. Under 
 these conditions it is better to employ a potentiometer for 
 taking the current and voltage readings. The following 
 arrangement is a very effective one for obtaining quickly 
 good power readings in the case of incandescent lamps. 
 
 The lamp, or power-absorbing circuit P (see Fig. 3), has 
 placed in series with it a manganin resistance E of about 
 1 ohm, and across its terminals a manganin resistance r of, say, 
 10,000 ohms, divided into two sections, having resistances in 
 the ratio of 1 to 99. From the ends of the series resistance 
 
THE MEASUREMENT OF ELECTRIC POWER. 473 
 
 and of the small section of the divided resistance, wires are 
 brought to a potentiometer, and the volt-fall down these 
 known resistances measured. If the series resistance is 
 exactly 1 ohm, these volt-falls give us at once the current 
 through the lamp in amperes and T ^th part of the terminal 
 voltage on the lamp. These voltage measurements are of 
 course referred to that of the Clark or Weston cell, Ck, used 
 to set the potentiometer. 
 
 It is necessary always to apply the above-mentioned cor- 
 rection, and to deduct from the current, through the series 
 resistance, the current passing through the divided resistance 
 attached to the terminals of the lamp. The measurements 
 can be depended upon to a fraction of 1 per cent., provided 
 that the standard cell and the resistances have been previously 
 carefully checked or standardised against correct standards. 
 The potentiometer measurements, and the setting of the 
 potentiometer, can be very quickly accomplished when using 
 a Crompton form of potentiometer. 
 
 The scheme of connections is shown in Fig. 3. The 
 resistance K in series with the power-absorbing circuit P 
 should, if possible, be a 1-ohm resistance, because then 
 calculations are simplified, and the volt-fall down this 
 resistance is the numerical value of the current through 
 the circuit. The divided shunt resistances may be either 
 divided in a 99:1 or 9:1 ratio. By the use of a double- 
 pole switch on the potentiometer, or parallel bars and plugs 
 pp, the readings of the volt-fall down the series and down 
 the decimal fraction of the divided resistance can be taken 
 successively with great expedition. 
 
 The same arrangement may be applied also in measuring 
 the power absorbed by a continuous-current motor, provided 
 that the load on it is steady. 
 
 3. Measurement of Continuous Current Power by the 
 Wattmeter. If it is desired to obtain the measurement of 
 the power absorbed in a circuit traversed by a direct or 
 
474 THE MEASUREMENT OF ELECTRIC POWER. 
 
 unidirectional current by one observation, then a wattmeter 
 of the Siemens type may be used. This instrument has 
 already been described (see p. 181, Chap. I.). In using 
 it to measure continuous current power the fixed circuit 
 of the instrument is joined in series with the power- 
 absorbing circuit, and the movable or shunt coil of the 
 wattmeter is joined across the terminals of that circuit. 
 The fixed coil is then traversed by the current through 
 the power circuit, and the movable coil by a current 
 which is proporti&nal to the P.D. of the ends of this 
 circuit. The electromagnetic torque between the fixed 
 and movable circuits of the wattmeter has then to be 
 balanced by a mechanical torque produced by giving the 
 movable head of the wattmeter a twist. Let be this 
 
 FIG. 4. 
 
 twist in angular degrees or divisions of the wattmeter 
 circular scale. The electromagnetic torque between the 
 wattmeter coils is proportional to the numerical product 
 of the currents in these coils. Let C be the current in 
 the series coil, let c be the currents in the shunt coil, and 
 let K and r be the resistances of these circuits respectively. 
 Then let G be such a constant that G0 = Cc. G is called 
 the wattmeter constant. It can be determined by passing 
 known constant currents, or one and the same current, 
 through the wattmeter coils and observing the twist which 
 must be given to the wattmeter head to bring back the 
 movable coil to its normal position, with its axis at right 
 angles to that of the fixed coil. 
 
 There are two ways in which the movable or shunt coil 
 can be connected. First, it may be joined up as shown in 
 
THE MEASUREMENT OF ELECTRIC POWER. 475 
 
 Fig. 4, where P is the power-absorbing circuit, S the series 
 coil of the wattmeter, and s the shunt coil. In this case 
 the power absorbed in P is equal to the product of the 
 current C and the potential difference of the ends of P, 
 which last is equal to cr - CE. Hence, if we call W the 
 power absorbed in P in watts, we have 
 
 but if G is the wattmeter constant, then G0=Cc, and hence 
 
 In other words, the twist which will have to be given to the 
 head of the wattmeter under the above conditions to bring 
 back the movable coil to its zero position is proportional to 
 the sum of the power absorbed in P and that in S the 
 series coil, and inversely as the resistance of the shunt coil. 
 
 r-A/WWW 
 
 v v v v y v v I 
 
 fWVWVWWWVW 1 ' ,' 
 
 FIG. 5. 
 
 If, on the other hand, the shunt coil of the wattmeter is 
 connected up as shown in Fig. 5, then we have, using the 
 same notation, 
 
 W=cr(C-c)=Ccr-c*r, 
 
 .'. W+cV=G0r, 
 
 and hence the twist is proportional to the sum of the 
 power absorbed in the circuits P and s, and inversely as the 
 resistance of s. 
 
 Accordingly, it will be seen that the scale reading of the 
 wattmeter is never proportional simply to the power 
 absorbed in the circuit under measurement, but it always 
 reckons in as well the power absorbed in one of its own 
 circuits. 
 
476 THE MEASUREMENT OF ELECTRIC POWER. 
 
 This correction may be negligible, but it becomes of 
 importance in the case of circuits taking either very small 
 currents or very small voltages. 
 
 A precaution which must not be neglected in using the 
 dynamometer wattmeter in measuring continuous current 
 power is to set the instrument in such a position that the 
 horizontal magnetic field of the earth does not exercise any 
 action upon the movable coil when this last is traversed by a 
 current. For when a continuous current is passing through 
 the movable coil it becomes a magnet and is directed by the 
 magnetic field of the earth. This may be discovered and 
 neutralised in the following manner : Before beginning an 
 experiment pass a continuous current through the shunt 
 coil of the wattmeter only, and observe whether there is any 
 tendency in this coil to move one way or the other when 
 this current flows through it. If so, turn the wattmeter 
 bodily round into various positions. This may be easily 
 accomplished by placing it on a turntable. A position can 
 be found in which the movable coil of the wattmeter is not 
 changed in position by the passage through it of a current. 
 This will be the case when the magnetic axis of the movable 
 coil coincides with the direction of the earth's magnetic 
 field at that place. The wattmeter must then be used in 
 this position, and we shall know that the current through 
 the movable coil has no effect by itself and apart from the 
 action of that in the fixed coil in causing a displacement of 
 the suspended coil of the wattmeter. 
 
 The wattmeter can of course be calibrated or its constant 
 discovered by sending through its two circuits a current the 
 value of which in amperes is known. We may define the 
 wattmeter constant G, used in the equations above, as the 
 reciprocal of the numerical value of the twist which must be 
 given to the head of the wattmeter to bring the movable coil 
 back to its normal position when a current of 1 ampere flows 
 through both coils joined in series. For the wattmeter 
 constant G is defined by the equation 
 
THE MEASUREMENT OF ELECTRIC POWEE. 477 
 
 where C is the current through one coil and c that through 
 the other. Hence, if C = c = 1, we have 
 
 G=l/ft 
 
 being the restoring twist which must be given to the 
 wattmeter head. Otherwise we may standardise the watt- 
 meter by observing the torsion necessary to be given to the 
 head when it is connected to a power-absorbing circuit 
 through which a known current is flowing and down which 
 there is a known volt-fall. 
 
 4. Measurement of Alternating-Current Power. In the 
 
 case of single-phase alternating-current power measurements, 
 when the current flows in a circuit having a power-factor 
 of unity, or one which is practically non-inductive, we can 
 measure the power taken up by the numerical product of the 
 root-mean-square (E.M.S.) value of the current and the 
 K.M.S. value of the voltage or fall of potential down it. 
 This can be done with any ammeter and voltmeter suitable 
 for measuring the alternating current and voltage in 
 question. 
 
 If, for instance, incandescent lamps are being operated by 
 means of a single-phase alternating current, the power taken 
 up in them, reckoned in watts, is obtained by taking the 
 product of the values of the terminal potential difference in 
 volts, as read by an electrostatic voltmeter, and the current 
 in amperes as given by a hot-wire or other suitable alternat- 
 ing-current ammeter ; or else a wattmeter can be used, with 
 certain precautions, named below, as to its construction, to 
 measure directly the same quantity. If, however, the circuit 
 is not non-inductive, but has a power factor sensibly less 
 than unity, then the product of the E.M.S. values of the ' 
 current through it and the fall of potential down it does not 
 give the true power taken up in that circuit, but gives what' 
 is called the apparent power or, as it is also called, the volt- 
 amperes. 
 
478 THE MEASUREMENT OF ELECTRIC POWER. 
 
 The true power taken up can be obtained by the employ- 
 ment of a properly constructed wattmeter.* In the con- 
 struction of a wattmeter for use with alternating currents it 
 is most important that there should be no metal near to the 
 fixed and movable coils. Instrument makers generally pay 
 no attention to this detail. They delight to devise wattmeters 
 in which the working parts are enclosed in brass cases or are 
 wholly made up of metal. When such an instrument is used 
 with alternating currents, eddy electric currents are set up in 
 the metal portions of the instrument near the coils, and these 
 react upon the movable coil when it is traversed by an 
 .alternating current and create additional and disturbing 
 mechanical forces which displace it. Hence the readings of 
 such a wattmeter may be, and generally are, quite erroneous 
 when it is used with alternating currents, and no reliance 
 can be placed upon them. 
 
 An alternating-current wattmeter must be constructed 
 entirely of non-conducting material, and no metal work 
 should exist in proximity to the coils of the instrument.! 
 
 We can show experimentally that this induction of eddy 
 currents in neighbouring conductors must be a source of 
 error in wattmeter readings when employing alternating 
 currents. Suspend a coil of insulated wire wound on a 
 rectangular or circular frame, and let an alternating current 
 flow through it. The coil may be suspended by a wire or by 
 & bifilar suspension. When traversed by the alternating 
 current, hold a sheet of copper near the coil It will be 
 found to be repelled. This repulsion arises from the reaction 
 of the eddy currents set up in the copper, and is an effect of 
 
 * For a full discussion of the formulae for obtaining the true power taken 
 up in an alternating-current inductive circuit the reader may consult the 
 Author's treatise on "The Alternate Current Transformer." See Vol. I., 
 3rd Edition, pp. 147-157. 
 
 f For an illustration of the errors which may arise by neglecting the above 
 precautions, the reader is referred to a Paper by the Author entitled " Experi- 
 mental Researches on Alternating Current Transformers." See Proc. Inst. 
 E. E., London, Vol. XXI., 1892, p. 666. 
 
THE MEASUREMENT OF ELECTRIC POWER. 479 
 
 the same character as that which gives rise to the phenomena 
 of electromagnetic repulsion* 
 
 It is evident, therefore, that, if mechanical forces are brought 
 to bear on the movable coil of an alternating-current watt- 
 meter due to any other cause than the mutual action between 
 it and the fixed coil, errors in its indications must ensue. 
 
 5. Measurement of the Power taken up in the case of 
 High Tension Alternating Current Circuits, When em- 
 ploying a wattmeter to measure the power taken up by an 
 inductive or non-inductive circuit, the voltage of supply 
 being high, as in the case of alternating-current transformers, 
 certain precautions are necessary for safety arid economy. It 
 is, of course, possible to place the series coil of the wattmeter 
 in series with the power-absorbing circuit and to join the 
 shunt coil of the wattmeter in series with a suitable induc- 
 tionless high resistance, and to place this last circuit as a shunt 
 in the ends of the power-absorbing circuit. If, however, the 
 volt-fall down the power-absorbing circuit is large, this will 
 in general necessitate a great expenditure of power in the 
 wattmeter shunt circuit and associated resistance. The 
 Author therefore devised, in 1892, the following method of 
 working, which has many advantages.* It depends upon the 
 well-known fact that, in the case of a good closed iron circuit 
 alternating-current transformer, not much loaded up on its 
 secondary side, the primary voltage is always exactly opposite 
 in phase to the secondary voltage and proportional to it. 
 
 Hence we may make use of such a transformer (called an 
 auxiliary transformer) to reduce voltage in a known ratio, 
 but still preserve its phase. The wattmeter is accordingly 
 arranged as follows : 
 
 The series coil of the wattmeter is joined in series with 
 the power-absorbing circuit (see Fig. 6). Across the circuit 
 terminals supplying the voltage is connected the primary coil 
 
 ' For a full discussion and description of these effects, the reader is referred 
 to the Author's treatise on " The Alternate Current Transformer," Vol. I., 
 3rd Edition, p. 307. 
 
480 
 
 THE MEASUREMENT OF ELECTRIC POWER. 
 
 of the auxiliary transformer T, and its secondary circuit is 
 joined in series with the shunt coil s of the wattmeter and 
 with one or more incandescent lamps, L, of suitable voltage. 
 Under these conditions the series coil S of the wattmeter W 
 is traversed by the same current as that through the power- 
 absorbing circuit P, and the shunt coil of the wattmeter is 
 traversed by a current which is proportional to the difference 
 of potential of the ends of the power-absorbing circuit and 
 in step with it. Hence the torque, acting on the wattmeter 
 movable coil, will be proportional to the mean power taken 
 up in the power-absorbing circuit. It is desirable to annul 
 certain electrostatic eifects by connecting one end of the 
 
 FIG. 6. 
 
 series coil of the wattmeter with one end of the secondary 
 circuit of the auxiliary transformer nearest to it. 
 
 The wattmeter is then calibrated as follows : A circuit 
 must be provided, consisting of a practically inductionless 
 resistance, r, capable of being placed safely across the high- 
 tension circuit. An electrostatic voltmeter, V, and an 
 ammeter, A, must be provided suitable for measuring the 
 volt-fall down the resistance, called the standardising 
 resistance, and the current through it. We begin by con- 
 necting this inductionless, power-absorbing circuit to the 
 wattmeter, and observe the current through it and volt-fall 
 down it, whilst at the same time we take a wattmeter 
 reading. We then know that the true power taken up in 
 
THE MEASUREMENT OF ELECTRIC POWER. 481 
 
 this inductionless resistance is given by the product of the 
 readings of the ammeter and voltmeter, and we can obtain 
 at once the wattmeter constant by comparing this product 
 with the wattmeter scale reading. We then substitute for 
 the inductionless circuit the inductive circuit P, and take a 
 second wattmeter reading. 
 
 A simple calculation then enables us to deduce the value 
 of the true power taken up in the inductive resistance, for 
 the wattmeter readings in the two cases are proportional 
 to the true power taken up respectively in these circuits ; 
 and in one of these viz., the non-inductive case the actual 
 power is independently obtained in watts as the product 
 of the numerical values of the current through it and its 
 terminal potential difference. 
 
 It is desirable that the wattmeter readings in the two 
 cases should not be very different, or, at any rate, that the 
 power taken up in the inductionless circuit used to stan- 
 dardise the wattmeter should not be less than that taken up 
 in the inductive power-absorbing circuit under investigation. 
 
 6. Power Measurements in the case of Circuits of 
 Small Power Factor. There are greater difficulties in 
 measuring accurately by a wattmeter the true mean power 
 taken up in a circuit of small power factor when supplied 
 with alternating current than in making the same measure- 
 ment when the power factor is large. This arises from the 
 fact that in all cases the small residual inductance of the 
 shunt circuit of the wattmeter causes the current in that 
 circuit to be not quite in step with its terminal potential 
 difference. If the power-absorbing circuit, being examined, 
 has a large power factor, or one approaching unity, then a 
 small shaft or lag in the phase of the shunt coil current 
 behind the phase of the potential difference between the 
 ends of the power-absorbing circuit does not affect the 
 reading of the wattmeter to the same percentage extent 
 as it does if the power factor is large. 
 
 ii 
 
482 THE MEASUREMENT OF ELECTRIC POWER. 
 
 Consider the case of simple harmonic variation. Then, 
 if I is the RM.S. value of the current through the power- 
 absorbing circuit, and V that of the potential difference of 
 its ends, and if <p is the phase difference of these quantities, 
 then the true power, W, taken up on the circuit is IV cos <, 
 where cos <p is the power-factor. Hence, 
 
 W=IVcos0, 
 and cCW/d<j> = I V sin 0. 
 
 dW 
 Therefore -===- = tan <$>d$. 
 
 Accordingly, for a given variation, d<f> of the phase angle 0, 
 the error in the power measurement, which is measured by 
 dW/W, is greater in proportion as </> is greater. 
 
 If, therefore, we are employing a wattmeter of the dynamo- 
 meter type to measure the true power taken up in an open 
 iron-circuit transformer or in a condenser, great precautions 
 must be exercised or else the wattmeter readings will be 
 valueless. For, in the case of an open iron-circuit trans- 
 former or choking coil, the power factor is small, and the 
 current flowing into the circuit lags behind the impressed 
 electromotive force, whilst in the case of a condenser the 
 power factor is also small, but the current is in advance in 
 phase of the impressed electromotive force. If any eddy 
 currents are set up in metallic parts of the wattmeter by 
 the current in its movable or shunt coil, this will cause an 
 increase in the phase difference of the shunt coil current 
 and the current in the series coil, if the series coil current 
 normally lags behind the shunt coil current ; and, accordingly, 
 the reading of the wattmeter will be less than it ought to 
 be. This will be the case when the wattmeter is employed 
 to measure the power being taken up in a choking coil or 
 transformer of small power factor. The reverse is the case 
 with a condenser. 
 
 Then, since the series coil current is normally in advance 
 of the shunt coil current, any eddy currents established in 
 
THE MEASUREMENT OF ELECTRIC POWER. 483 
 
 metal parts of the wattmeter by the shunt coil current will 
 tend to decrease the phase difference of the shunt and series 
 coil currents, and make the wattmeter readings larger than 
 they should be. 
 
 There is, therefore, always a tendency for the power 
 measurement made with the wattmeter on a choking coil or 
 transformer or inductive circuit of small power factor to be 
 too small, and for that made on a condenser or circuit of 
 small power factor having capacity to be too large. 
 
 In these cases wattmeter readings should always be care- 
 fully criticised and not too readily accepted as correct evalua- 
 tions of the true power absorption of the circuit. 
 
 One way in which this difficulty of making power measure- 
 ments on circuits of small power factor may be minimised is 
 by joining in parallel with the circuit under another inductive 
 circuit, or circuit having capacity, as the case may be. The 
 current-phase displacements in the case of the inductive 
 circuit and the permittive circuit (one having capacity) are 
 in opposite directions. Hence, if an inductive circuit in 
 which the current lags behind the impressed electromotive 
 force is joined in parallel with a permittive circuit or 
 condenser in which the current is in advance in phase of 
 the impressed electromotive force, the whole combination has 
 a larger power factor than either of them separately, and the 
 small power factor of one element annuls more or less that 
 of the other. Hence the difficulties which arise from the 
 small power factor in wattmeter measurement may be reduced 
 by taking two wattmeter measurements one on a combined 
 circuit and one on a single circuit. 
 
 Thus, if it is required to measure the power taken up 
 in a concentric cable or other condenser, due to dielectric 
 hysteresis or other causes, when it is subjected to an alter- 
 nating electromotive force, we may proceed as follows : An 
 inductive circuit must be provided, which should be one with- 
 out any iron core in fact, be simply a large coil of insulated 
 copper wire of many turns. The power factor of this inductive 
 
 n2 
 
484 THE MEASUREMENT OF ELECTRIC POWER. 
 
 circuit will be small but positive that is, the current will lag 
 behind the impressed electromotive force. The true power 
 taken up in this inductive circuit must first of all be carefully 
 measured by the wattmeter, or its power factor determined, 
 as described in the following section. It is then joined in 
 parallel with the cable or condenser, and the true power 
 taken up in both together measured. The difference of the 
 two measurements then gives the true power taken up in the 
 condenser. 
 
 If the inductive circuit used is one with no iron core, 
 then the true mean power taken up in it is given at once 
 by taking the quotient of the mean-square value of the 
 impressed electromotive force by the ohmic resistance of the 
 circuit. 
 
 The advantage of combining the inductive circuit with the 
 cable or condenser is that in the latter case the capacity 
 current is in advance in phase of the impressed electromotive 
 force, whilst in the case of the inductive circuit it is in 
 arrear. Hence the opposite phase differences more or less 
 annul each other, and the combined circuit has a larger power 
 factor than either of them separately. 
 
 Instead of joining the ironless inductive circuit in parallel 
 with the cable or condenser, it may, as suggested by Mr. 
 Mather, be connected in series with it.* If the wire of 
 which the inductive circuit is formed is sufficiently stranded 
 to prevent eddy currents being set up in its mass, then the 
 actual power absorption in the circuit is sufficiently nearly 
 found by taking the product of its resistance and the mean- 
 square value of the currents through it. 
 
 It is obviously desirable that this ironless choker should 
 be wound in the form of a coil of maximum self-induciion, as 
 given by Maxwell. 
 
 * The method of employing a choking coil to increase the power factor of 
 a cable or condenser was suggested by Prof. Ayrton in a discussion on a Paper 
 by Mr. Mordey on " Capacity in Alternate Current Working." The plan of 
 using the choker in series is due to Mr. Mather. See The Electrician, Vol. XL VI. 
 1901, pp. 512, 518 and 667. 
 
THE MEASUREMENT OF ELECTRIC POWER. 485 
 
 For a further discussion of the theory of the dynamometer 
 wattmeter the reader is referred to the Author's treatise on 
 "The Alternate Current Transformer," Vol. I., 3rd. Ed., 
 Chap. III., p. 168. It is there shown that if the time 
 constant of the wattmeter shunt circuit is denoted by T, and 
 that of the circuit under test is denoted by T r , and p = 2?r 
 times the frequency, then, when simple harmonic currents 
 are being considered, a correcting factor F must be applied 
 to the wattmeter readings such that 
 
 Hence, if T r is greater than T,, F is a proper fraction, and 
 the wattmeter reading is too high and is corrected by 
 multiplying by F. 
 
 The practical utility of this formula is not, however, very 
 great, as the time-constants of most inductive circuits 
 cannot easily be measured, and if the circuit contains an 
 iron core, or is wound on an iron core, the time-constant or 
 ratio of inductance to resistance is not constant. 
 
 For a discussion of the practical precautions to be employed 
 in using the wattmeter the reader is referred to a Paper by 
 the Author read before the Institution of Electrical Engineers, 
 London, in 1892 (see Proc. Inst. E. E., Lond., Vol. XXL, 
 pp. 623-675). 
 
 Also a Paper may be consulted by Mr. C. V. Drysdale, 
 " On the Theory and Use of the Alternate Current Wattmeter " 
 (see The Electrician, 1901, Vol. XLVI, p. 774). 
 
 A useful discussion on power measurements in the case of 
 cable dielectrics took place after the reading of a Paper by 
 Mr. Mordey on "Capacity in Alternate Current "Working" 
 (see Proc. Inst. E. E., Lond., 1901, and The Electrician, Vol. 
 XLVL, p. 467, et seq.). 
 
 In this discussion the difficulties of such measurements and the precautions 
 which must be taken in dealing with wattmeter readings are well brought 
 out, 
 
486 THE MEASUREMENT OF ELECTRIC POWER. 
 
 7. Power Measurements by Direct Measurement of 
 the Power Factor. It has been shown by Lord Kayleigh* 
 that we can use a shunt and series coil combined with a soft 
 iron indicating needle as a means of measuring either the 
 phase-difference of two currents or of the power factor of an 
 inductive circuit. 
 
 Let two circular coils of wire be placed with their axes in 
 one straight line and their planes parallel, and between them 
 let a soft iron needle be suspended by a glass fibre or torsion 
 wire, so that its centre is on the common axis of the coils and 
 its length at an angle of 45deg. to this line. If, then, a 
 current is passed through one of these coils it will create a 
 magnetic force proportional to the currents and a magnetisa- 
 tion in the iron nearly proportional to the magnetic force. 
 Hence the couple or torque tending to place the axis of the 
 soft iron needle in the direction of the coil axis is proportional 
 to the square of the current in the coil. 
 
 Suppose, in the first place, that the current i varies 
 harmonically and is expressed by the function ^=Isin^, 
 then the mean torque on the soft iron needle, and therefore 
 its angular displacement, if small, varies as the average value 
 throughout a complete period of Fsin 2 ^, or as JI 2 . Suppose, 
 then, that two separate simple periodic currents, differing in 
 phase, are passed through the two coils. Let these currents 
 be represented by the functions I 1 sin^ and I 2 sin(p 0). 
 The torques produced by these currents separately on the 
 soft iron needle will vary as JIi 2 and as JI 2 2 - Also the joint 
 effect, when both currents act together, is to produce a torque 
 on the needle proportional to the average value throughout a 
 complete period of the function 
 
 which varies as J 
 
 If, then, the first current is allowed to act alone on the 
 iron needle, it will produce a small displacement which may 
 
 * See The Electrician, Vol. XXXIX, p. 180, or Phil. Mag., May, 1897. 
 
THE MEASUREMENT OF ELECTRIC POWER. 487 
 
 be represented by D x ; and, in the same way, the second 
 current acting alone will produce a displacement D 2 ; whilst 
 both acting together will produce an effect D 3 . We have 
 then the following equations 
 
 D^W, D 2 = C 2 2 I 2 2 , 
 D 3 = (C^V + C 2 2 I 2 2 + 2C 1 C 2 I 1 I 2 cos 0), 
 
 where C x and C 2 are constants depending on the form of the 
 coils. 
 
 Therefore cos = 
 
 Accordingly, by observing the angular displacements of the 
 iron needle due to each coil acting separately and then that 
 due to the two acting together we can find the phase-difference 
 between the currents in the two coils. 
 
 The same formula holds good even when the currents are not simply 
 periodic, that is, have not a simple sine curve form, but we then derive from 
 the deflections the power factor and not merely the cosine of an angle of 
 phase-difference. For in this last case we have 
 
 D^htfitdt, and Da=t*fifdt, 
 
 where i\ and i% are the instantaneous values of the currents in the coils and p 
 and k are constants depending on the form of the coils, and the integrals are 
 taken throughout one complete period. Also we have 
 
 the + or - sign being used according as the coils act with or against each 
 other. 
 
 In the first case, then, we have 
 PS - D - D 
 
 The quantity on the right-hand side of the above equation is the expression 
 for the power factor of a circuit in which % is the current through that 
 circuit and z' 2 is the fall in voltage down a shunt across that circuit, or the 
 potential difference of the two ends of the circuit. 
 
 The above method gives us, therefore, a means of directly 
 determining the power factor of an inductive circuit for any 
 particular form of single-phase periodic electromotive force. 
 We have to introduce in series with that circuit a coil which 
 will carry the current flowing through the inductive circuit, 
 and we have to place as a shunt across the circuit another 
 
488 THE MEASUREMENT OP ELECTRIC POWER. 
 
 nearly induetionless high-resistance coil, with its plane 
 parallel to that of the series coil and its axis coincident. 
 A short, soft iron needle is then to be suspended by a 
 fibre of glass or quartz, or by a metallic torsion wire of 
 phosphor bronze, in the axial line of the coils. The needle 
 may have a mirror attached to it, so that its small deflec- 
 tions may be read on a scale in the usual way. The coils 
 should be so arranged that the axis of the needle is at 
 45deg. to the line joining the centres of the coils drawn 
 perpendicular to their planes. The series coil should be 
 capable of being short-circuited at pleasure and the shunt 
 coil disconnected. 
 
 We can then observe the small deflections produced on 
 the soft iron needle by the separate actions of the series 
 and shunt-coil currents, and also their joint effect. These 
 deflections give us the quantities called D I} D 2 and D 3 in 
 
 the formula above. Then - / 2 * is the power factor 
 
 of the power-absorbing circuit connected to the coils. 
 
 The coils should be capable of being moved parallel to 
 themselves independently, so as to make the deflections of 
 the soft iron needle small and the deflections due to the 
 series and shunt currents separately approximately equal to 
 each other. 
 
 8. Three- Voltmeter Method of Measuring Alternating 
 Current Power. The following method of measuring the 
 alternating current power absorption of a circuit was first 
 given by Prof. Ayrton and Dr. Sumpner in 1891 : * 
 
 Let AB (see Fig. 7) be an inductive circuit traversed by an 
 alternating current. The first step is to join in series with 
 it another nearly induetionless resistance BC, and to pass 
 a current through both. In many cases, such as in the 
 
 * Sec " The Measurement of the Power given by any Electric Current to any 
 Circuit." By Prof. Ayrton and Dr. Sumpner. Proc. Roy. Soc., Vol. XLIX., 
 1891, p. 424. 
 
THE MEASUREMENT OF ELECTRIC POWER. 489 
 
 measurement of the power absorption of transformers, this 
 necessitates the possession of means for increasing the 
 circuit pressure, so as to enable this additional resistance 
 to be added to the circuit under test. Three measurements 
 of potential difference are then taken, either simultaneously 
 with three voltmeters or, better still, successively with one 
 and the same voltmeter suitable for alternating current 
 measurement. The voltage is measured across AB (call 
 it Vi), down BC (call it V 2 ), and over AC (call it V 3 ). 
 Then let v^ v 2) v 3 be the instantaneous values of these 
 voltages at any moment, and let i be the instantaneous 
 value of the current and U the resistance of the inductionless 
 
 -V 3 -- 
 FIQ. 7. 
 
 part of the circuit. Then, at any moment we have the 
 equality 
 
 therefore vf = v-f + #2 
 
 But v 2 =:~R,i ; 
 
 hence 2R^ ~ v * ~ v ^ = v & 
 
 Multiplying all through by dt, and integrating throughout 
 a complete period T, or from to T, and then multiplying 
 by 1/T to obtain the mean-square values, we have 
 
 2R 
 
 where W is the mean power taken up in the inductive part, 
 AB, of the circuit. 
 
490 THE MEASUREMENT OF ELECTRIC POWER. 
 
 The objection to this method is that great accuracy in 
 the voltmeter readings must be attained if the resulting 
 power value is to be correct to a small percentage. Since 
 the formula involves the difference of squares of voltages, 
 a small error in the measurement of the voltages themselves 
 will make a much larger percentage error in the calculated 
 value of the power. 
 
 If we take the equation given above for the power, viz., 
 
 ^( 
 and differentiate it, we have 
 
 dW= ( 
 
 where dVi, dTV 2 , dV 3 are the errors made in the estimation of the three 
 potential differences, or rather in their R.M.S. values. 
 
 Let dV 3 =eV s , dV 2 =eV 2 , dV l =eV 
 
 where e is a small fraction. The most probable value of (dW) 2 is then 
 
 
 Let the resistance B have such a value that 
 
 V 2 =sV, .......... (2) 
 
 We proceed to find what value x should have that dW/W may be a minimum. 
 Since v 3 =vz+v v we have 
 
 V 8 2 =V 2 2 +V 1 2 +2V 1 V 2 cos0 ........ (3) 
 
 Hence, eliminating V,, V 2 and V 3 from the equations (1), (2) and (3), we 
 have 
 
 dWV (l+a-.aco8) g +l + g 4 ... 
 
 ~~ 
 
 Now cos H independent of x. Hence, if we differentiate the numerator 
 of (4) and equate to zero, we have the value of x which will make dW/W a 
 minimum. We find x=l satisfies this condition ; hence the arrangement 
 which will give the maximum sensibility is when R has such a value that 
 
 Vg = Vi. 
 
 In (4) put g = l. Then 
 
 COS0 
 
 i /7 wr 
 
 But - -=- is the ratio between the percentage error made in determining W 
 
 and that made in determining the potential differences. 
 
 Suppose, then, that the inductive circuit is an ordinary closed iron circuit 
 transformer on open secondary circuit. In this case cos0=0'75 nearly. 
 
THE MEASUREMENT OF ELECTRIC POWER. 
 
 491 
 
 Accordingly, - -=5. Therefore, an error of 1 per cent, made in deter- 
 
 c w 
 
 mining the potential differences by the readings of one common voltmeter 
 would involve an error of 5 per cent, in the estimation of the power taken 
 up by the circuit. It is difficult to obtain commercial voltmeters reading to 
 less than quarter per cent., and therefore the limitation of accuracy in the 
 estimation of power by the three-voltmeter method is rather over 1 per cent. 
 
 In employing the three-voltmeter method to measure the 
 power taken up in an alternating current transformer we 
 proceed as follows : Suppose the transformer under test to 
 take a current at 2,000 volts on its primary circuit, and that 
 we have available the current from an alternator or circuit 
 having a pressure, say, of 100 volts. It is then necessary to 
 
 FIG. 8. 
 
 connect two step-up transformers, T v T 2 (see Fig. 8) with low- 
 tension sides in parallel and high-tension sides in series, 
 so as to create a voltage of 4,000 volts. Across the 
 terminals of this 4,000 volt circuit we join in series an 
 inductionless resistance, E, and the primary circuit of the 
 transformer to be tested. It is convenient to bring potential 
 wires or leads from the ends of the circuits AB, BC and AC 
 to mercury cups, mm, well insulated. A carefully standardised 
 electrostatic voltmeter then has potential wires attached to its 
 terminals, and these wires may be connected to two brass 
 pins carried on an insulating handle, by means of which the 
 
492 THE MEASUREMENT OP ELECTRIC POWER. 
 
 voltmeter can be connected in between any two mercury 
 cups. The voltmeter reading of the required voltages can 
 then be quickly taken. 
 
 If the voltmeter range is only up to about 2,000 volts, then 
 the voltage AC must be measured in two parts by measuring 
 the PD of the terminals of each of the supply transformers 
 separately and adding these voltages together. Hence, if V 
 and V are these last readings and V x and V 2 , as before, the 
 volt-fall down the inductive circuit under test and the induc- 
 tionless resistance E, then the power W taken up in AB is 
 given by 
 
 The previous discussions of the theory of this method 
 shows, however, that it is not well adapted for accurate power 
 measurements in those cases in which the power factor of the 
 tested circuit is small. A modification of the three-voltmeter 
 method which does not necessitate the use of such a large 
 auxiliary resistance has been described by Mr. A. Campbell.* 
 
 9. The Three- Ammeter Method. In cases in which it is 
 not possible to obtain the augmented voltage required by the 
 three-voltmeter method, a variation of it, called the three- 
 ammeter method, proposed by the author in 1891, may be 
 used.f 
 
 In this case the circuit under test, the inductionless resist- 
 ance E, and three ammeters are arranged as in Fig. 9. The 
 first ammeter, AI, measures the current before division, the 
 second, A 2 , the current flowing through the inductionless 
 resistance, and the third, A 3 , the currents through the circuit 
 under test. 
 
 By a similar process of reasoning to that employed in the 
 case of the three-voltmeter method it can be shown that, if 
 
 * See Proc. Phys. Soc., London, 1901, or The Electrician, Vol. XLVL, p. 13, 
 " On a Method of Measuring Power in Alternating Current Circuits," 
 t See The Electrician, May 8, 1891. 
 
THE MEASUREMENT OF ELECTRIC POWER. 
 
 493 
 
 W is the power taken up in the tested inductive circuit and 
 E is the inductionless resistance, then 
 
 where Ii, I 2 , and I 3 are the readings of the three ammeters 
 AI, A? and A 3 respectively. 
 
 For if iiy i^ i s are the instantaneous values of these currents, we have 
 always * 
 
 therefore i 
 
 But Z2=v/R, where v is the potential difference of the ends of the inductive 
 circuit. Hence 
 
 Multiplying all through by dt, and integrating over a period, and then dividing 
 by T, so as to obtain the mean values of each term, we arrive at the formula 
 given above. 
 
 FIG. 9. 
 
 The three-ammeter method labours under the same diffi- 
 culty as the three-voltmeter method. Very small errors 
 in the absolute determination of the three currents make 
 a very much larger percentage error in the result. It is not 
 adapted for power tests on circuits of small power factor. 
 
 10. Dynamometer Methods of Measuring Power. 
 
 Mr. Blakesley gave, in 1891,* a method of measuring alter- 
 nating current power which is independent of the frequency 
 or wave-form and can be employed on any inductive circuit. 
 It involves the use of a split dynamometer or wattmeter, in 
 which the two circuits are traversed by two different currents. 
 
 * See Phil. Mag., April, 1891 p, 346. 
 
494 
 
 THE MEASUREMENT OF ELECTRIC POWER. 
 
 Let P, Fig. 10, be the inductive circuit under test, let R be 
 an inductionless resistance joined in parallel with it, and let 
 an ammeter, A, be employed to measure the current flowing 
 through the inductive circuit. Then a dynamometer, D, of 
 the Siemens type has its two circuits joined as shown in the 
 diagram. 
 
 Let i be the current at any instant in the inductive circuit, 
 ii the current in the inductionless resistance, and 4 the 
 current flowing to both. Then at any instant 
 
 or 
 Therefore 
 
 FIG. 10. 
 
 Let v be the potential fall down the inductionless resist- 
 ance, R ; this is also the potential difference of the ends of the 
 inductive circuit, hence v = R* r Accordingly, from the two 
 last equations we have 
 
 Multiplying all through by dt and integrating throughout 
 the period, or from =0 to t=T, and dividing by T, we 
 obtain the mean value throughout a period of each of the 
 quantities in the above equation. Hence 
 
 i f T R r T . . R r T 
 
 or W=RD-RF, 
 
 where W is the mean power taken up in the inductive 
 circuit in watts, I the R.M.S. value in amperes of the current 
 
THE MEASUREMENT OF ELECTRIC POWER. 495 
 
 through it, D the dynamometer value or mean value of the 
 product of the currents in the two coils throughout a period, 
 and E the ohmic resistance of the non-inductive shunt 
 employed. 
 
 If G- is the dynamometer constant and is the twist which 
 must be given to the torsion head to bring back the movable 
 coil to its zero position when steady currents C and c flow 
 through the coils, then 
 
 GO=Cc = D. 
 
 Accordingly, in the equation for W we can write EG0 for 
 ED, and we have 
 
 W = EG0-EF. 
 
 If we employ a hot-wire ammeter or another dynamometer 
 to measure the current, I, the method is perfectly general 
 and independent either of the frequency or wave-form of the 
 alternating current employed. 
 
 11. Power Measurement in the case of Polyphase 
 Circuits. In the majority of cases the practical measurement 
 of the mean electric power taken up in polyphase circuits 
 offers no greater difficulties than in the case of single-phase 
 alternating-current circuits, although it may involve a 
 multiplication of instrumental readings. The theoretical 
 treatment of the problem is rather more complicated, how- 
 ever, in the case of polyphase circuits, by reason of 
 the phase relations of the various currents involved. In 
 the very simple case of two-phase alternating currents the 
 power taken up in the inductive or inductionless circuit 
 supplied can be estimated by the employment of two watt- 
 meters, one placed in each circuit. Thus, for instance, whether 
 the outgoing line consists of three or four conductors, we can 
 measure the power supplied to a two-phase transformer in 
 motor by the employment of two wattmeters connected into 
 the circuits, as shown in Fig. 11. 
 
 Let Mj, M and M 2 be the two-phase leads and ABC the 
 power-absorbing circuit, whether motor or transformer. Then, 
 
496 
 
 THE MEASUREMENT OF ELECTRIC POWER. 
 
 if two wattmeters, constructed with all the precautions already 
 described for use with alternating currents, are inserted in 
 the two sides of the two-phase circuit, the sum of their 
 readings will be the total power given to the circuit ABC. 
 
 M 
 
 M 
 
 M, 
 
 /-s 1 -- 
 
 r rvvvvv 
 
 ' WVWWVWv* 
 
 v.._SJ] t _..' 
 
 <=> 
 =5 
 
 
 
 ^rWWNAA^ 
 
 Wo 
 Fio. 11. 
 
 A similar arrangement can be applied in the case of three- 
 phase circuits when connected on the star pattern with a 
 common return. 
 
 For if OA, OB, 00, Fig. 12, are the three-phase power- 
 absorbing circuits and M I} M 2 , M 3 the leads, and M the 
 common return, then three wattmeters W lt W a , W 3 may be 
 employed to measure simultaneously the power given to the 
 
 circuits OA, OB, 00. The sum of these wattmeter readings 
 is the power taken up by the three-phase circuit. 
 
 The case of a three-phase circuit arranged on the delta 
 pattern is, however, of particular interest, because then two 
 
THE MEASUREMENT OF ELEVTUW 
 
 497 
 
 wattmeters arranged as in Fig. 11 will give the power 
 absorption, whether the circuit be inductive or induction- 
 less. The problem may, however, be considered on first 
 principles. 
 
 Let ABC (Fig. 13) be a three-phase circuit arranged delta 
 fashion, and let M^M^Ma be the leads through which current 
 
 M 2 
 
 M, 
 
 M 3 
 
 FIG. 13. 
 
 is supplied to it. We may consider, then, in the first place, 
 the following problem : Given the ammeter values of the 
 currents in M x> M 2 and M 3 and the potential differences of 
 the ends of AB, BC, CA find the currents in the delta 
 branches and the mean electrical power taken up in the 
 circuit ABC. 
 
 FIG. 14. 
 
 Let us consider the general relation between the currents 
 in M p M 2 , M 3 , AB, BC, and CA. Eepresent the three-phase 
 system by a network of conductors arranged as in Fig. 14. 
 Let the instantaneous current values in the lines MI, M 2 , M 8 
 be represented by a, 6, c, and those in AB, BC, CA by x, y 
 
 KK 
 
498 THE MEASUREMENT OF ELECTRIC POWER. 
 
 and z\ and let the outer circle represent the armature 
 circuit of the three-phase dynamo or other source of electro- 
 motive force. Then we may represent the relations between 
 the instantaneous values of the currents by the equations 
 
 x-y=a, ...... (i.) 
 
 y-s=&, ...... (ii.) 
 
 zxc ....... (iii.) 
 
 Hence, if we take large letters to represent the maximum 
 values of these currents, and assume a simple periodic mode 
 of variation, it is clear that, on a vector diagram of currents, 
 the line currents A, B, C will be represented by the sides of a 
 triangle, and the delta currents X, Y and Z by lines drawn to 
 the angular points of this triangle from some point in the 
 interior. 
 
 To find the currents X, Y and Z in terms of the line 
 currents A, B and C we may proceed algebraically as 
 follows : Square each of the equations (i.), (ii.) and (iii.) 
 above, multiply each by dt t integrate throughout a complete 
 period, and divide by T the periodic time. Thus 
 
 In other words, equate the mean-square values. 
 
 In the next place, make certain assumptions for the sake 
 of dealing with the simpler .problem first, and therefore 
 elucidating more difficult ones later on. Let us assume the 
 circuits AB, BC, CA are inductionless, and that the currents 
 and electromotive forces vary in a simple harmonic manner. 
 Then the currents x, y and % may be expressed thus 
 
 x = Xsinpt, ..... (v.) 
 
 2/ = Y sin 0^-120), . . (vi.) 
 
 z = Z sin ($t- 240), . (vii.) 
 when p=z2irn as usual, n being the frequency. 
 
THE MEASUREMENT OF ELECTRIC POWER. 499 
 
 If we substitute the values for x, y and z given in the last 
 equation in (iv.) we arrive at equations of the form 
 
 X 2 +XY+Y 2 =A 2 , (viii.) 
 
 Z 2 =B 2 , (ix.) 
 
 C 2 (x.) 
 
 If these equations are solved for X, Y and Z in terms of 
 A, B and C, they will give us the expression for the R.M.S. 
 values of the currents in the delta circuits, which for shortness 
 we will call the delta-currents, in terms of the line currents. 
 Now, unfortunately, the above equations are very intractable. 
 They can be solved algebraically, and those who are fond of 
 algebra can amuse themselves by finding the solutions, which 
 are not very simple. But where algebra fails common sense 
 steps in, and a graphical solution sufficient for practical 
 purposes can easily be obtained. 
 
 It is clear, from an inspection of the equations (viii.), (ix.) 
 and (x.), that they are equivalent to the following geometrical 
 problem: Given a triangle whose sides are A, B, C in 
 length, find a point, P, within that triangle, such that lines 
 drawn from P to the angular points of the triangle are all at 
 120deg. angular distance from each other, and determine the 
 lengths X, Y and Z of these lines in terms of the sides of the 
 triangle. 
 
 It may be possible to solve this geometrical problem by 
 purely Euclidean methods, but it is a waste of labour to 
 attempt it. 
 
 From an electrical engineering point of view the following 
 graphical method gives a solution quite accurate enough for 
 all practical purposes : Procure a celluloid circular protractor 
 and cut out a sector subtending an angle of 120deg. Make 
 a scratch on the protractor forming an angle of 120deg. with 
 both the edges of the sector. The protractor will then look as 
 in Fig. 15. Observe with an ammeter, or with three ammeters, 
 the currents in the main leads M x , M 2 , M 3 . These are the 
 currents A, B, C. On paper set off to scale a triangle whose 
 
 KK2 
 
500 
 
 THE MEASUREMENT OF ELECT RIG POWER. 
 
 sides represent these currents. Put two pins 'at two of the 
 corners of this triangle, I and m (Fig. 16). Then "apply the 
 protractor with the sector edges to these pins and move it 
 about until the scratch lies over the other corner of the 
 triangle nJ Then measure off the lengths, P/, Pra, Prc, where 
 P is the centre of the protractor. These lengths will be the 
 delta currents, X, Y and Z, on the same scale on which the 
 sides of the triangle are the line currents A, B, C. 
 
 FIG. 15. 
 
 Otherwise, in default of a protractor, we may draw on 
 paper three lines making angles of 120deg., and draw on 
 tracing paper the triangle of line currents A, B, C. Place this 
 tracing paper over the other, and trace off the lengths of the 
 
 FIG. 16. 
 
 lines from the centre, P, where the three radial lines inter- 
 sect, to the angular points of the triangle viz., measure the 
 lengths P/, Pm, Pn (see Fig. 17). 
 
 By this simple, graphical construction we can find the 
 ammeter or E.M.S. values of the currents in the delta branches 
 when we are given those in the lines. Hence, multiplying 
 the ampere value of these delta currents by the observed 
 potential differences of the delta corners, and adding the 
 
THE MEASUREMENT OF ELECTRIC POWER. 501 
 
 three products, we have the total power in watts taken up 
 in the inductionless delta circuit. 
 
 It is obvious, if the resistances of the delta branches are 
 all non-inductive and equal, that the three line currents 
 (K.M.S. value) are equal, and also the three delta currents. 
 Also, each delta current is equal to the quotient of each 
 line current by \/3. Accordingly, in the very simple case of 
 a symmetrical inductionless delta circuit, the power taken 
 up in the whole delta is equal to the product of \/3 times 
 either line current and the potential difference of the ends 
 of either delta branch. 
 
 FIG. 17. 
 
 We have next to consider the case when the delta 
 branches are not inductionless, which is an important case, 
 as it involves the testing of three-phase motors and trans- 
 formers worked or constructed on the delta pattern. Let us 
 consider, first, the limited case when the three branches of the 
 delta circuit have equal inductance and resistance. This is 
 always the case with three-phase motors or transformers. A 
 little consideration will, then, show that the same rule given 
 above for finding the currents in the inductionless delta 
 circuits will give also, in the case of equi-inductive delta 
 circuits, the . value of the delta currents. On the other 
 hand, when the delta branches are inductive the current in 
 each branch lags in phase behind the potential difference 
 of the ends or delta corners. Hence we cannot find the 
 
502 
 
 THE MEASUREMENT OF ELECTRIC POWER. 
 
 power taken up in the whole delta circuit until we have 
 discovered the value of this phase difference. 
 
 This may be achieved in the following manner : 
 Draw, as before, the triangle representing the line currents and 
 the radial lines P/, Pm, Pra at angles of 120deg., representing 
 the delta currents. Let the dotted lines on the diagram 
 (see Fig. 18) Pe, P/, P# represent the phase positions of the 
 potential differences of the ends of the delta circuits that is, 
 let the line ~Pe represent the potential difference of the ends 
 of the delta branch in which the current PZ exists. Then the 
 angle is the angle of lag of the current PZ behind the 
 impressed electromotive force Pe acting on that circuit. 
 
 FIQ. 18. 
 
 The angle is equal to the angle 0, minus the angle a. 
 (See Fig. 18.) 
 
 Now the angle is the phase difference between the 
 line current represented by the side ml and the potential 
 difference between the adjacent corners of the delta circuit. 
 The angle a can be measured by a protractor on the triangle of 
 currents. 
 
 Accordingly, we may find all that we require in the 
 following manner : Introduce into one of the lines a series 
 coil, and put across the terminals of one of the delta-branches 
 another high resistance shunt coil. Employ these two coils 
 in conjunction with a soft iron needle to determine, as already 
 described, the phase difference between any one of the line 
 
THE MEASUREMENT OF ELECTRIC POWER. 503 
 
 currents and the potential difference between any two line 
 circuits. This phase difference is the angle <f>. Find from the 
 triangle of currents the angle a, and then the required phase 
 difference 6 = a. 
 
 Hence we can find, assuming sinoidal currents and electro- 
 motive forces, the phase difference between any delta current 
 and the potential difference creating it. The power taken 
 up in the whole delta is then easily found, for it is three 
 times that in any one branch of the delta, and this last 
 is XV cos 0, where X is any delta current (E.M.S. value) and 
 V the potential difference of the ends of that delta branch. 
 
 In place of a soft iron needle and series and shunt coil, a 
 phasemeter of the type devised by Dolivo von Dobrowolsky 
 may be employed. If the delta branches have unequal 
 inductance and resistance, then the above measurements must 
 be repeated on each line, and for the complete calculation 
 of the power taken up in the delta we require, then, to know 
 the value of each line current, the potential difference 
 between each corner of the delta, and the phase difference of 
 the above currents and potential differences. 
 
 The cases of most practical interest are, however, those in 
 which each delta branch has the same inductance and resist- 
 ance, as this involves the testing of three-phase transformers 
 and motors ; and the case when each branch is inductionless 
 but not of equal resistance, as with this we are concerned 
 in a three-phase distribution of current for lighting purposes 
 when unequal numbers of lamps are on each phase. 
 
 But now it is interesting to notice that, although it is 
 difficult to obtain an algebraical expression for the mean 
 power taken up in an inductive delta three-phase circuit, 
 given the line currents and line potential differences only and 
 such phase angles as can easily be measured, yet it is quite 
 easy to determine the power absorption practically by means 
 of two wattmeters or even one instrument properly arranged. 
 
 Consider again the state of the three-phase delta circuit at 
 any instant. Let c } , c z , c 3 be the line currents at any instant, 
 
504 
 
 THE MEASUREMENT OF ELECTRIC POWER. 
 
 let i v i * 3 be the delta branch currents, and let v 1} v 2 , v 3 
 be the line potential differences or delta corner potential 
 
 C 2 
 
 FIG. 19. 
 
 differences respectively (see Fig. 19). Then it is clear that 
 
 Let w be the power absorption in the whole delta at any 
 instant, then 
 
 Fia. 20. Connections for Wattmeter Measurement of Power in Three-Phase 
 
 Circuit. 
 
 If therefore we arrange two wattmeters as in Fig. 20, one of 
 them will give a reading proportional to the average value of 
 
THE MEASUREMENT OF ELECTRIC POWER. 505 
 
 CjV^ and the other will give a reading proportional to the 
 average value of c 3 v 2 , and accordingly the sum of the watt- 
 meter readings will be proportional to the total mean power 
 taken up in the whole delta circuit whether the branches be 
 inductive or not. 
 
 Hence we may arrange two suitable alternating current 
 wattmeters to give the required measurement, or we may 
 arrange one wattmeter and a series of switches which throws 
 over the wattmeter quickly from one side to the other of the 
 delta mains.* 
 
 Lord Kelvin has devised a form of duplex wattmeter 
 suitable for this purpose which is described in the next 
 section. 
 
 12. Practical Forms of Wattmeter The existing prac- 
 tical forms of wattmeter may be classified under two head- 
 ings : (i.) electrodynamic, (ii.) electrostatic instruments. 
 
 The electrodynamic instruments consist of two circuits or 
 coils of wire, one called the series coil and the other called 
 the shunt coil. One of these coils or circuits is fixed, and 
 the other is suspended and free to move over a small range 
 under the influence of the electrodynamic stress existing 
 between the coils when both are traversed by currem . 
 Generally speaking, the series coil is fixed, because it has to 
 carry the larger current, and the difficulty of getting this 
 current in and out of a movable coil is greater than in the 
 case of the smaller current used in the shunt circuit. The 
 movable coil must be restrained and brought back to a fixed 
 zero position by a couple or force due to gravity or a spring 
 control. In any case the conditions which must be complied 
 with are that a small displacement of the movable coil must 
 bring into existence an opposing mechanical force which 
 increases with the displacement. The electrodynamic stress 
 between the coils should be a maximum when the coils are 
 
 * See Science Abstract$, Vol. I., p. 554, M. Aliamet "On Three-phase Power 
 Measurement." 
 
506 
 
 THE MEASUREMENT OF ELECTRIC POWER. 
 
 in their sighted or zero positions. For if the electrodynamic 
 force increases with the displacement, it may increase faster 
 than the opposing mechanical force, and then the equilibrium 
 will be unstable. It is also desirable, though not necessary, 
 that the mutual induction between the coils should be zero 
 when they are in the sighted or normal position. 
 
 In the case of wattmeters intended for use with alternating 
 currents, there must not be any metal enclosing case or metal 
 
 Fia. 21. Siemens Workshop Wattmeter. 
 
 work of any kind near the coils, and the coils themselves 
 must be wound on non-conducting formers or cores. If large- 
 sized wire has to be used for the series coil, it must be 
 stranded or formed of a cable of silk-covered wire twisted 
 together. 
 
 One of the simplest wattmeters for workshop use is the 
 Siemens wattmeter. It consists of a wooden base and 
 support which carries the fixed coil (see Fig. 21) and a 
 
THE MEASUREMENT OF ELECTRIC POWER. 507 
 
 movable coil hung from a torsion head by means of a few 
 fibres of floss silk. In some instruments the ends of the 
 movable coil dip into mercury cups. In the one shown in 
 Fig. 21 the current is led into and out of the movable coil by 
 light flexible connections. The restoring couple is applied to 
 the movable coil by means of a spiral metal spring, one end 
 of which is attached to the movable coil, and the other to the 
 torsion head. In using the instrument the series coil is 
 joined in the circuit of the power-absorbing circuit, and the 
 movable coil is connected as a shunt across the ends of that 
 circuit and the series coil taken together. As already 
 explained, when so connected the reading of the wattmeter 
 is proportional to the power absorbed in the circuit under 
 test and that in the series coil of the wattmeter. If the 
 wattmeter is employed with continuous currents, care must 
 be taken to see that it is placed in such a position that the 
 magnetic field of the earth has no influence on the movable 
 coil when traversed by a current. When both coils have 
 currents through them, the movable coil is twisted round 
 through a small angle as far as a pair of stops will allow it 
 to move. The torsion head is then twisted round in the 
 opposite direction until the movable coil comes back to its 
 original position, and the angular displacement of the torsion 
 head noted. A table is furnished with each instrument, 
 which will then give the power being taken up in watts in 
 the circuit under test. 
 
 In the wattmeter designed by the Author for use with 
 alternating currents, special precautions are taken to obviate 
 sources of error. The wattmeter consists (see Fig. 22) of a 
 teak case about 15in. high and lOin. wide with glass 
 doors on each side. The case stands on levelling screws. 
 On the top surface is a celluloid divided scale. A 
 hollow axis through the centre of this scale carries on 
 its outside an adjustable index arm, and to a support 
 on the inside is suspended the movable coil. This is in a 
 rectangular form, and consists only of a few turns of 
 
508 
 
 THE MEASUREMENT OF ELECTRIC POWER. 
 
 insulated wire kept in shape by shellac. This coil is hung 
 up to the torsion head by a few fibres of floss silk, and to it 
 is attached an index arm of aluminium wire. The torsion 
 spring is a spiral gilt steel chronometer spring, and this is 
 affixed by one end to the torsion head axes and by the other 
 
 FIG. 22. Fleming Alternating Current Wattmeter. 
 
 to the suspended coil. The ends of the coil dip into mercury 
 cups made of vulcanised fibre. The fixed coil is carried on 
 a wooden bar, and has its axis at right angles to the movable 
 coil. The wires bringing the currents to the coils are twisted 
 together. There are no metal parts or screws of any kind 
 
THE MEASUREMENT OF ELECTRIC POWER. 509 
 
 near the coils. This wattmeter is used, as originally suggested 
 by the Author, in conjunction with an auxiliary transformer, 
 the secondary circuit of which is connected through two or 
 three incandescent lamps with the movable coil of the 
 wattmeter. The primary circuit of the transformer is 
 connected as a shunt across the ends of the power-absorbing 
 circuit and the series coil in series with that circuit. The 
 wattmeter is standardised, as already described, by the use of 
 an inductionless standardising resistance and an alternating 
 current ammeter and voltmeter. 
 
 Lord Kelvin's ampere balances are also constructed as 
 wattmeters by forming the fixed coils of thick copper strip, 
 and using them as the series coils, whilst the balanced or 
 movable coils are formed of thinner wire and constitute the 
 shunt coil (see Fig. 23). The shunt coil is made to have a 
 small resistance, and is joined up in series with a large 
 non-inductive resistance outside. 
 
 Lord Kelvin's form of alternating current wattmeter for 
 large powers is shown in Fig. 24. In this case the series coil 
 is a stranded cable bent in a U shape. The shunt coil 
 consists of a pair of balanced coils over it attached to the 
 scale beam arm. The electrodynamic action is the same as 
 in the other balances that is to say, the forces due to the 
 currents tend to raise one balance coil and depress the other. 
 The series coil in the instrument shown in the figure is 
 designed for carrying large currents. This conductor is 
 made up of ropes of insulated copper wire, twisted together 
 so as to form a cable with a hollow core. In order to correct 
 any effect due to the induction of one arm of the coil upon 
 the other the twisting is done in a very careful manner, so 
 that the strands of the cable which are inside on passing 
 the left-hand movable coil on one side are outside on passing 
 the right-hand movable coil on the same side, and are in the 
 reverse direction on the other arm of the U. The core of 
 the cable is hollow, and brass tubes are passed along each arm 
 of the U as far as the bend. The main object of these tubes 
 
510 
 
 THE MEASUREMENT OF ELECTRIC POWER. 
 
THE MEASUREMENT OF ELECTRIC POWER. 
 
 511 
 
512 THE MEASUREMENT OF ELECTRIC POWER. 
 
 is to prevent any deformation in the cable, but they also 
 serve as a means of blowing air through to keep the con- 
 ductor cool, if it should ever be necessary to use it for 
 much heavier currents than those for which the instrument 
 is primarily intended. 
 
 Another form of dynamometer wattmeter is that devised 
 by the Author and Mr. Gimingham. In it there are two 
 helices of wire wound on non-conducting cores. These are 
 so wound as to have similar magnetic poles in the centre, 
 
 FIG. 25. Fleming and Gimingham's Voltmeter (lid removed). 
 
 and are placed parallel to each other. These coils form the 
 series coil of the wattmeter. They are embraced by two 
 circular coils attached to the ends of a bar suspended on a 
 needle point by means of a jewelled centre. These coils are 
 made with aluminium formers, and are wound with fine 
 wire. They constitute the shunt coils. The current is got 
 into and out of this movable coil by means of very fine 
 flexible leads, which do not prevent, the movable coil from 
 swinging freely within narrow limits. To the movable coil 
 
THE MEASUREMENT OF ELECTRIC POWER. 513 
 
 is attached a spiral steel torsion spring, as in the Siemens 
 wattmeter, and its upper end is fixed to a torsion arm 
 moving over a divided scale. The scale can be divided to 
 read directly in watts. The operation of reading consists 
 in turning the torsion head until the movable coil is brought 
 back to its normal or zero position, as shown by a small 
 index needle attached to it. The external appearance of the 
 instrument is shown in Fig. 25. The figure, however, represents 
 the voltmeter designed by the same inventors,but the wattmeter 
 only differs from it in having four terminals instead of two, one 
 pair for the series circuit and one pair for the shunt circuit. 
 
 The above-described instruments are not direct reading. 
 The observer has to move or slide some part of the instru- 
 ment in the process of taking a reading. They are, therefore, 
 not adapted for switchboard purposes. In this latter case 
 an instrument must be employed which shows directly by 
 a needle upon a scale or dial the power passing through it. A 
 form of direct-reading wattmeter has been devised by Lord 
 Kelvin. It consists of a coil of one or two thick turns of 
 copper wire, and a spectacle-shaped fine wire coil in series, 
 with an external resistance. The instrument is adapted as a 
 central station wattmeter, giving indications of power passing 
 through it by means of the movement of a needle attached 
 to the fine wire coil over a scale. The interior is shown in 
 Fig. 26. It has a main circuit formed of a double rectangle 
 of copper rod having sufficient area to carry 200 amperes, 
 and a shunt circuit with two fine wire coils astatically 
 arranged. The main coil is mounted on a slate back so 
 that the rectangles are horizontal. The shunt coils are 
 mounted on a light but strong aluminium frame in the 
 manner shown in Fig. 27. One end of this frame has a 
 circular knife-edged hole fixed to it, and the other end has a 
 straight knife-edge. These two knife-edges rest on two 
 phosphor-bronze hooks attached by insulating supports to 
 the outside ends of the double rectangle. By this method 
 of suspension complete freedom from friction is obtained, 
 
 LL 
 
514 
 
 MEASUREMENT Of ELECTRIC POWER. 
 
 FIG. 26. Kelvin Engine Room Wattmeter. 
 Removed 
 
 General View with Case 
 
 FIG. 27. View of Fine Wire Shunt Coils, showing details of Suspension 
 Springs removed. 
 
THE MEASUREMENT OF ELECTRIC POWER. 
 
 515 
 
 while the movable system is kept in a definite position with- 
 out end guides. 
 
 Each fine wire coil has about 1,000 turns of insulated 
 wire, and its resistance is about 100 ohms. The current is 
 conducted in and out from the movable system by two 
 flat palladium spiral springs, which also supply the restoring 
 force for governing the sensibility of the instrument. Not 
 more than /^th of an ampere is allowed to pass through the 
 fine wire circuit, and in order to regulate this a large non- 
 inductive resistance is rolled on the case of the instrument, 
 which offers a large cooling surface. The scale has nearly 
 uniform divisions, and is graduated to read directly in watts 
 or kilowatts as required. 
 
 Main Coil 
 
 Main Coil 
 
 Fia. 28. Connections of Kelvin's Three-Phase Wattmeter. 
 
 Lord Kelvin has modified his single-phase balance watt- 
 meter to make it suitable for three-phase measurement. 
 It has two sets of fixed coils mounted on the opposite sides 
 of an ebonite or marble slab. Suspended inside these coils 
 are two sets of movable coils carried on the same spindle, 
 the pointer being also carried on the spindle. The only 
 opening in the ebonite slab is for the spindle. The fixed 
 coils are in the two arms of the main circuit, and the shunt 
 coils are connected across through non-induction resistances, 
 as shown in Fig. 28. With instruments for low pressures 
 the inductionless coils are in the case, and for high pressures 
 they are outside and separate. 
 
 LX.2 
 
516 THE MEASUREMENT OF ELECTRIC POWER. 
 
 The use of the Kelvin quadrant electrometer, or some 
 modification of it, as a wattmeter was suggested almost 
 simultaneously by Profs. Ayrton, FitzGerald and Potier. 
 Maxwell showed that, in the case of the Kelvin electro- 
 meter, if A and B are the potentials of the quadrants and 
 C that of the needle, then the deflection of the needle should 
 vary as 
 
 It was shown, however, by Dr. J. Hopkinson, and also 
 by Profs. Ayrton and Perry, that the above law is not 
 fulfilled by every instrument of the quadrant type, but that 
 electrometers can be constructed which do obey it. A form 
 of Kelvin quadrant electrometer has been devised by 
 Messrs. Ayrton, Perry and Sumpner (see Fig. 29), which 
 strictly obeys the above law of deflection. Assuming that, 
 for any particular instrument, the law has been verified, we 
 may use it as a wattmeter as follows : Let AB be an induc- 
 tive circuit through which an alternating current can be set 
 flowing. It is desired to measure the power taken up in AB. 
 Join in series with AB an inductionless resistance BC, and 
 connect the quadrants of the electrometer to the terminals A 
 and B. Then take two readings, one with the needle joined 
 to B and one with it connected to C. Observe the deflections 
 in each case : call them 6 and 0'. Then we have 
 
 where K is an instrumental constant and V A , V B , V c signify 
 the potentials at the points A, B, C respectively. Subtract- 
 ing the equations, we have 
 
 Now (V^ - V B ) is the fall of potential down the inductive 
 
THE MEASUREMENT OF ELECTRIC POWER. 
 
 517 
 
 circuit, and V B V c is the fall of potential down the non- 
 inductive circuit, and is proportional to the current through 
 
 FIG. 29. 
 
 the inductive circuit. The difference of the readings, viz., 
 0', is proportional, therefore, to the mean value of this 
 
518 THE MEASUREMENT OF ELECTRIC POWER. 
 
 product, assuming that the free periodic time of- the needle is 
 large compared with that of the alternating current. 
 
 It has been suggested by MM. Blondlot and Curie that 
 the power may be obtained by a single reading with a 
 double electrometer containing two needles and two pairs of 
 quadrants, the quadrants being connected to the terminals 
 A and B and one " needle " to B and the other needle to C. 
 A careful verification of the right to use the Kelvin quadrant 
 electrometer in the above manner as an alternating-current 
 wattmeter has been given by Prof. E. "Wilson (see Proc. Eoy. 
 Soc., London, Vol. LXIL, 1898, p. 356), but the experimentalist 
 employing any particular instrument should independently 
 verify for himself its obedience to the theoretical law. 
 Mr. G. L. Addenbrooke has devoted particular attention to 
 the improvement of the quadrant electrometer for alternating 
 current measurement, and has arranged a convenient form of 
 electrostatic wattmeter for this purposes. (See abstract of a 
 Paper read at the International Congress of Electricity in 
 Paris, 1900, The Electrician, Vol. XLV., p, 901.) 
 
 The various forms of continuously-recording wattmeters or 
 watt-hour-meters employed as house-meters will be considered 
 in the chapter on " Electric Quantity and Energy Measure- 
 ment." 
 
 13. Wattmeter Testing. Owing to the various disturb- 
 ing actions which tend to render wattmeter readings incorrect, 
 no prudent experimentalist will engage in a course of experi- 
 ments with any one particular instrument without previously 
 making a careful examination of its behaviour under various 
 conditions. Let us assume, in the first place, that the watt- 
 meter is of the dynamometer type and that it is to be 
 employed in measuring continuous-current power with the 
 series coil joined in series with the power-absorbing circuit 
 and the shunt coil joined across the ends of a circuit consist- 
 ing of the power-absorbing circuit and the series coil. The 
 wattmeter should be placed upon a turntable so as to move 
 
THE MEASUREMENT OP ELECTRIC POWER. 519 
 
 it round in azimuth into different positions. The first experi- 
 ment which should be made is to pass the normal current 
 through the shunt coil, no current going through the series 
 coil ; and notice should be taken whether the interruption or 
 reversal of this current through the shunt affects its position 
 when freely suspended and movable. If this is the case, then 
 the wattmeter must be turned round its vertical axis and tests 
 made in different positions to discover if the displacement is 
 due to the earth's magnetic field. If so, an orientation can 
 be found in which the position of the shunt coil is not 
 disturbed by reversing the current through it. If no such 
 position of the wattmeter can be found, then the disturbance 
 may be due to currents flowing in neighbouring wires, and 
 these should be looked for and removed. The next step is 
 to measure the resistance of the series coil and calculate 
 the C 2 K loss in it when the current to be passed through 
 it is used. 
 
 As already explained, the torsion which has to be applied 
 to the wattmeter head to bring the movable shunt coil back 
 to its zero position is proportional to the power taken up in 
 the power-absorbing resistance, plus the power absorbed 
 in the series coil when the connections are made as above 
 described. It is necessary, therefore, to ascertain what pro- 
 portion the power absorbed in the series coil bears to that 
 taken up in the circuit under test, in order that the value 
 of the correction may be estimated. Again, it must not 
 be taken for granted without investigation that the twists 
 given to the wattmeter head as measured in angular dis- 
 placements of the head are proportional to the power taken 
 up in the power-absorbing circuit ; but special experiments 
 must be made with different power absorptions in a circuit 
 under test, and the quotient of true power taken up by the 
 wattmeter head displacement taken. This quotient, should 
 be constant throughout the range of currents within which the 
 wattmeter will be used. This test is best made by passing 
 currents through the wattmeter coils, the values of which are 
 
520 THE MEASUREMENT OP ELECTRIC POWER. 
 
 Independently observed, and also the twist 6 given to the 
 wattmeter head to restore the movable coil to its zero 
 position. Then, if C and c are these currents, we have to 
 prove that, for the particular instrument in question, Cc/0= 
 a constant, in order that the wattmeter may be relied upon to 
 give consistent results when used to measure power. 
 
 In the case of a wattmeter to be used with alternating 
 currents, an additional examination has to be made into 
 its construction and behaviour before accepting its readings 
 as valid. Assuming it to be constructed in accordance with 
 the rules already laid down, we have to ascertain whether 
 its power readings when taken on a circuit of small power 
 factor are in agreement with those taken on circuits of large 
 power factor. For instance, let it be supposed that a watt- 
 meter is to be employed for measuring the power taken up in 
 concentric cables when employed with alternating currents. 
 In this case the power-absorbing circuit, which is the 
 dielectric of the cable, has a small power factor. "We have 
 to assure ourselves first that any wattmeter reading taken 
 on this circuit means the same in true power absorption 
 as when the same indication is found on a power-absorbing 
 circuit of high power factor. A cautious electrician will not 
 take this for granted, knowing, as he should do, that it is 
 quite possible for errors of 300 or 400 per cent, to be made 
 in evaluating by means of a dynamometer wattmeter the 
 power absorption in the case of a small power factor circuit, 
 In order to test the behaviour and trustworthiness of a 
 wattmeter when employed with alternating currents it is 
 essential, therefore, to possess a power-absorbing circuit of 
 known small power factor and known power absorption with 
 various voltages on its ends, and to compare the wattmeter 
 readings taken on this circuit with those taken on a prac- 
 tically inductionless power-absorbing circuit made as already 
 described. 
 
 The question arises, how is such an inductive circuit to be 
 made ? The following principles will guide the construction 
 
THE MEASUREMENT OF ELECTRIC POWER. 521 
 
 of a useful form of inductive resistance for wattmeter testing. 
 It consists in making an ironless choking coil in the form of 
 a Gauss coil of maximum inductance. If a coil of insulated 
 wire is made on a former of circular shape, and if the shape 
 of the cross section of the coil is a square having a length of 
 side equal to a, then it was shown by Maxwell (see " Elec- 
 tricity arid Magnetism," Vol. II., p. 316) that the coil will 
 have a maximum inductance if the mean diameter of the 
 
 Let a core, therefore, be prepared formed by placing cheeks 
 on the sides of a circular disc of wood so as to form a square 
 channel in which insulated wire may be wound, and let the 
 square channel be fitted up with double silk or cotton-covered 
 copper wire well shellaced or paraffined. Let the diameter of 
 the circular former and the depth and breadth of the square 
 channel be such that the outside diameter of the circular coil 
 of wire formed in it is D and the inner diameter D I} and 
 
 these are so chosen that 37( Po ~ Dl )=( P 
 
 also let the width of the coil sideways or parallel to its 
 
 axis be equal to ~ *. The coil will then have the proper- 
 a 
 
 tions which will give it the maximum inductance for the 
 quantity of wire used according to the Gauss and Maxwell 
 rules. 
 
 The inductance of this coil may be calculated approximately 
 as follows : It is shown in the " Treatise on Electricity and 
 Magnetism " by Mascart and Joubert (see Atkinson's English 
 translation, Vol. II., pp. 152 and 153) that for a circular coil 
 of wire of N turns and mean radius a, having a rectangular 
 section of width 26 and depth (radial) 2c, the inductance L is 
 given by the following expression : 
 
 y? 
 
 where ^ and ^ are certain functions of the ratio T which are 
 
 tabulated by Mascart and Joubert, 
 
522 TEE MEASUREMENT OF ELECTRIC POWER. 
 
 The deduction of the above formula from first principles 
 would occupy too much space to give it here in full, and the 
 reader must therefore be referred to the treatise of Mascart 
 and Joubert for details. 
 
 Suppose, now, that the axial width of the coil section is 
 equal to the radial depth, and that the proportions for 
 
 & 
 maximum inductance are fulfilled. That is, let b=:c=^~. 
 
 Corresponding to c/b=l, Mascart and Joubert give the 
 values ^=0-84834 and ^=0-8162. 
 
 Making, therefore, the above substitutions in the general 
 expression for L, we have 
 
 -3784 - 0-82501 = 4?raN 2 X 1*5525, 
 
 or = 
 
 where D = mean diameter of the coil and N = the total 
 number of turns of wire. 
 
 Now let the total length of wire on the coil = I, then 
 
 hence L = 
 
 Let d' be the diameter (over all) of the covered wire used 
 to make the coil ; then the length of the side of the square 
 section is equal to d' \/N. Accordingly, by the Gauss 
 relation, 
 
 and 7rDN=r/= total length of wire. 
 
 Substituting these in the above expression for L, viz., 
 L = 31JN, we have, finally, 
 
 This last expression gives us, therefore, a very simple 
 formula for calculating the self-induction of a square- 
 sectioned circular coil made with the Gauss proportions 
 
THE MEASUREMENT OF ELECTRIC POWER. 523 
 
 for maximum inductance, viz., 3'7 times side of section 
 = mean diameter of coil. 
 
 For example, let a coil of maximum inductance be made 
 with cotton-covered copper wire having an over- all diameter 
 of 2-omm. and, say, 1,600 turns. Calculate the inductance 
 and specify the form of the coil. Here 
 
 d'=0-2o cm., 
 
 N=l,600, 
 
 .-. D = 3-7x0-25x40 = 37cm., 
 
 and side of the section of the coil = 10cm. 
 
 Hence the coil must have an outer diameter of 47cm., 
 an inner diameter of 27cm., a thickness (axially and 
 radially) of 10cm., and its inductance L is such that 
 L' = 36 XJX (1,600)2 X40 
 
 = 36 X 16 X 16 X 10 5 = 921,600,000cm. 
 = 0-9216 henry. 
 
 The resistance of the coil can easily be approximately 
 calculated as follows : Let p denote the specific resistance of 
 copper in C.G.S. units. At 0C for hard- drawn high conduc- 
 tivity copper p has a value near 1,600. The resistance K 
 
 of the coil of wire is equal to -~, where d is the diameter 
 
 ird" 
 
 of the copper wire and I is its length. But / = 7rDN, and 
 ~D = 3'7d r Jy for the maximum inductance coil; hence, 
 R _ 6,400 DIST^ 23,680 flVyff 
 
 This value must, however, be increased by at least 15 per 
 cent, to allow for the temperature rise in the resistance. 
 
 The difference between d' and d is about O'Ol of an inch, 
 or 0*0254 of a centimetre, for double cotton-covered wire, 
 and 0-005 of an inch, or 0*0127 of a centimetre, for double 
 silk-covered wire. Accordingly, when we are given the 
 diameter, d', of the covered wire, its total resistance can 
 easily be calculated. 
 
524 THE MEASUREMENT OP ELECTRIC POWER. 
 
 Having, then, the value of L and K for the coil, we can 
 calculate the impedance ( N/R 2 -}-^ 2 L 2 ) of the coil for simple 
 periodic alternating currents of a frequency n = 27r/p, and 
 find at once the current which will flow through the coil 
 under a given alternating voltage V (K.M.S. value). We 
 then obtain at once the true power W expended in the coil, 
 since it is equal to V 2 /K, and also the apparent power or 
 volt amperes, since this is equal to V 2 / \/R 2 +p' 2 L 2 and the 
 power factor E/ N/K 2 +jp 2 IA 
 
 We are thus able to design an inductance coil with any 
 desired power factor and power absorption and to use it to 
 check a wattmeter. The above formulae are, however, only to 
 be used to give an approximate notion of the power factor 
 and power absorption ; the true values for the coil in ques- 
 tion can best be obtained experimentally as described below. 
 
 One point of considerable importance to which attention 
 must be directed is the energy waste which arises from eddy 
 electric currents set up in solid copper wire when above a 
 certain diameter. If a coil of insulated wire is made, say, of 
 size as large as No. 14 S.W.G., and if this wire is' traversed 
 by an alternating current, the field of each turn embraces 
 and cuts that of other turns and sets up in the mass of the 
 copper eddy currents which dissipate energy. This is in 
 addition to the proper C 2 E loss due to the ohmic resistance of 
 the circuit. As this energy loss is not easily predicted and 
 taken into account, it is necessary to make the conductor of 
 such an ironless inductance coil of stranded wire. Generally 
 speaking, it will not be necessary to insulate each strand. 
 The film of dirt or grease on each constituent wire is usually 
 sufficient to stop the circulation of these eddy currents. If, 
 however, the wire is stranded, then its inductance per unit of 
 length is not quite the same as that of a round-sectioned 
 solid wire of the same cross-sectional area. Stranding the 
 wire reduces the inductance because it increases the average 
 distance of all the filamentary elements into which we may 
 conceive the currents divided. 
 
THE MEASUREMENT OP ELECTRIC POWER. 525 
 
 Hence the calculations made by the above formulae for the 
 inductance and resistance of the copper circuit do not quite 
 exactly give the required quantities. If the wire is solid, 
 then the C 2 E waste in the coil with alternating currents will 
 be under-estimated; and if the wire is stranded, then the 
 inductance will be rather over-estimated when calculated by 
 the above-given rules. 
 
 As an illustration, however, of the use of the above formulae 
 let us for the moment neglect the copper eddy current loss, 
 and proceed to design an ironless choking coil having a power 
 absorption of J H.P., or 375 watts, when submitted to an 
 alternating electromotive force of 2,000 volts at a frequency 
 of 100, the power factor of the coil to be 2 per cent. 
 
 After a few trials we find the specification to be as 
 follows : Take No. 14 double cotton-covered copper wire, say 
 0'2cm. diameter, use 1,225 turns, and make it in the form of a 
 square-sectioned circular Gauss coil. Then 
 
 d = 0-2cm., N=l,225, x/N=35. 
 The inductance L = 36xO'2x35x(l,225) 2 
 = 378,157,500cm. 
 = 0-378 henry. 
 
 The resistance E in ohms at 0C 
 
 =23,680 X 1,225 X 35 X 5 x 10~ 9 =5-076 ohms, 
 or, say, 6 ohms when hot. 
 
 Then ^=2<7r^=200 x 3-1415=628-3, 
 the reactance =Lp=235'6 ohms at 0C, 
 the impedance= N/JR 2 +^ 2 L 2 ='V / 55,508-7 + 25*7=2357 ohms. 
 
 Hence, under an alternating electromotive force of 2,000 
 volts the current in the coil is 2,000/235'7=8*48 amperes. 
 
 The true power absorbed by the coil at 2,000 volts is 
 (8-48) 2 X 5-076=365-3 watts, if we neglect the increase in 
 resistance due to rise in temperature. 
 
 If the current is not kept on more than a few moments, 
 the true power absorption will not exceed 400 watts, 
 
526 THE MEASUREMENT OP ELECTRIC POWER. 
 
 The volt-amperes, or apparent power, taken is equal to 
 2,000x848=16,960, and the power factor=400/16,960 
 =0-023. 
 
 The covered wire will have a diameter, d f , equal to 0*2 2 5cm. 
 
 Then as to the size of the coil. The mean diameter=D 
 =37 X 0-225 X 35 = 291cm., and the side of the square section 
 =a= 0'225 x 35 = 7*9cm. Hence the coil must have an inside 
 diameter of 21'2cm., an outside diameter of 37cm., and a 
 thickness of 7*9cm. It will contain 1,225 turns of No. 14 
 double cotton-covered copper wire. The length of the wire 
 
 will be 7 rDN = ^x291xl,225cm.=112,035crn.=l,250yd. 
 
 nearly. The weight will be about 801b. Hence 801b. of double 
 cotton-covered No. 14 wire will be required to make the coil. 
 
 As a matter of practical construction, it would not be 
 advisable to wind up this weight of cotton-covered wire in 
 one coil, and use it on a high-voltage circuit, because the 
 current would probably jump from layer to layer and destroy 
 the insulation. The coil should be wound like an ordinary 
 induction or spark-coil secondary circuit in a set of side-by- 
 side coils, or sections, insulated from each other by thin 
 ebonite or micanite discs. Before or during winding, the 
 covered wire should be well paraffined, and it is an advantage 
 to keep a coil of this description immersed in insulating 
 oil during experiments with high-tension currents. 
 
 Moreover, as above explained, in practice the wire of 
 which the coil is made should be stranded wire, using a 
 strand the constituent wires of which are not larger than 
 No. 30 S.W.G. Hence, instead of using solid No. 14 S.W.G. 
 copper wire, a stranded 36/30 should be employed. 
 
 Assuming the copper wire to be sufficiently stranded, the 
 actual power absorbed and the power factor at any voltage 
 can, however, best be determined experimentally as follows: 
 Provide a means for regulating the alternating voltage by 
 very small steps say, for instance, by introducing a variable 
 choking coil into the supply circuit, or by varying the 
 
THE MEASUREMENT OF ELECTRIC POWER. 527 
 
 exciting current of the service alternator very gradually by 
 a carbon plate rheostat. Then provide also a supply of 
 continuous current from secondary batteries. Place in series 
 with the inductance coil under test a hot-wire ammeter 
 suitable for use with both continuous and alternating cur- 
 rents, and have at hand calibrated voltmeters for reading 
 accurately the alternating and continuous voltages. Then 
 begin by applying a measured continuous voltage to the 
 inductance coil sufficient to create in it a current equal to 
 that which it will take with the alternating voltage. In the 
 case of the above-described coil, since the resistance is about 
 5 ohms, a continuous voltage of 40 volts will create a 
 current of 8 amperes. Measure very carefully this voltage 
 and current. As soon as the currents become constant, or 
 very nearly so, switch off the continuous voltage and apply 
 an alternating voltage sufficient to maintain the same heating 
 current in the coil. In this case, since the impedance is 
 nearly 250 ohms, about 2,000 alternating volts (RM.S. value) 
 will be required. Measure this alternating voltage carefully. 
 Then, if the ventilation or cooling of the coil is rapid enough 
 to enable these voltages to be measured when the current is 
 practically the same in the two cases, we have at once the 
 power factor and the true power absorbed in the coil. For, 
 if Vc is the continuous voltage required to maintain a cur- 
 rent, A, through the coil, and V A is the equivalent alternating 
 voltage, then V C /V A is the power factor of the coil, and AV C 
 is the true power absorbed by the coil under an alternating 
 voltage V A and an apparent power absorption AV A . 
 
 The inductance coil so made, then, becomes a means of 
 checking a wattmeter. For this purpose we must provide 
 in addition a nearly inductionless resistance, taking up at 
 the 2,000 volts a true power equal, or nearly equal, to that 
 taken up by the inductance coil. For the above case, if 
 we make a resistance coil by winding on a wooden frame 
 non-inductively a length of 1,000 yards of No. 36 S.W.G. 
 cotton-covered platinoid wire, we shall have a resistance 
 
528 THE MEASUREMENT OF ELECTRIC POWER. 
 
 of about 12,000 ohms, which, if properly ventilated, will 
 carry without sensible heating one-sixth of an ampere, or 
 the current it will take under an alternating voltage of 
 2,000 volts. The power absorbed will then be about 333 
 watts. 
 
 We have, then, two resistances, one, the above platinoid 
 resistance, taking up 333 watts or so at 2,000 volts, and 
 having a power factor nearly unity, and the previously- 
 described inductance coil, taking up 360 watts or so, and 
 having a power factor about 0'02. Proceed then to calibrate 
 the wattmeter under test by means of the inductionless 
 platinoid resistance, measuring the pressure with an alter- 
 nating electrostatic high tension voltmeter, and the current 
 through it with a hot-wire ammeter or by a resistance and 
 associated electrostatic low-reading voltmeter ; in this way 
 obtain the constant of the wattmeter on the high power- 
 factor resistance. Then, employing the same instruments on 
 the inductance coil, measure the power taken up calculated 
 out by means of the wattmeter constant observed as above. 
 If this power reading does not agree with the true power 
 absorbed by the inductance coil at that voltage, as already 
 determined by the use of the continuous and alternating 
 currents, then something is wrong with the wattmeter, and 
 it cannot be trusted when used with small power factor 
 circuits. 
 
 An inductance coil made as described, and built up in 
 sections so that one or more sections can be used in series as 
 required, is a very useful implement in a laboratory in which 
 cable testing is being conducted. For, if it is desired to 
 measure the true power absorption in the dielectric of a 
 cable under alternating voltage, then, since the power factor 
 of the dielectric circuit of the cable is small, its measurement 
 directly by a wattmeter becomes a matter of difficulty. But 
 the difficulty is reduced if an inductance coil of suitable 
 power factor is joined, either in parallel or in series, with the 
 dielectric of the cable or condenser, as suggested by Prof. 
 
THE MEASUREMENT OF ELECTRIC POWER. 529 
 
 Ayrton and Mr. Mather,* and the power factor of the two 
 together, cable and coil, becomes greater than either of them 
 separately by reason of the fact that the current leads on the 
 electromotive force in the case of capacity and lags on it in 
 the case of inductance. In order to know approximately 
 how much we may expect to improve the power factor, we 
 must, however, have a rough knowledge of the power factor 
 and current taken in each case separately. Thus, suppose 
 the above-described inductance coil, having a power factor of 
 O02, and taking a current of 8*5 amperes at 2,000 volts, is 
 joined in parallel with a length of 5 miles of a cable 
 having a dielectric power factor of 0*02 and a capacity of 0'3 
 microfarads per mile. Then, under simple periodic currents, 
 the capacity current of the cable (I) would be equal to 
 CpV/10 6 , where C is the total capacity in microfarads, p = 2-n- 
 times the frequency, and V is the voltage. The reader 
 should note that this formula cannot be used to calculate 
 the condenser current when the capacity, inductance and 
 frequency have such values as to create electric resonance 
 in the circuit/)- If, however, resonance is absent, then, since 
 n = 100 and V = 2,000, we have 
 
 T _5x3x 2,000x628-3 
 10^ 
 
 =r885 amperes. 
 
 Hence, to obtain the best result in augmenting the power 
 factor it would be desirable to couple the dielectric of this 
 cable in parallel with an inductance coil having a larger 
 number of turns (about twice as many) than the one above 
 specified, in order that the coil current under 2,000 volts 
 should be about equal in magnitude and opposite in phase, 
 as regards the electromotive force, to the capacity current 
 of the cable. With the assistance of the previously- 
 
 * See Prof. Ayrton's remarks in The Electrician, January 18, 1901, 
 Vol. XLVL, p. 476 ; also January 25, Vol. XL VI., p. 512 ; and Mr. Mather, 
 The Electrician, February 22, Vol. XLVL, p. 667. 
 
 t See Mr. T. Mather, Electrical Review, May 31, 1901 ; also Vol. II. of this 
 Handbook, in the chapter on "Measurement of Capacity." 
 
 MM 
 
530 THE MEASUREMENT OF ELECTRIC POWER. 
 
 explained principles, the reader will have no difficulty in 
 doing this for himself. 
 
 If an ironless inductance coil is joined in parallel with 
 a condenser, and the two are supplied with alternating 
 current from an alternator at constant potential, there is 
 a certain value of the inductance which will, when asso- 
 ciated with a given condenser, make the current coming 
 out of the alternator a minimum. This value may be 
 ascertained as follows : Let i be the instantaneous value 
 of the current coming out of the alternator, i z that of 
 the current into the condenser, and i : that through the 
 inductance. Let C be the capacity of the condenser and 
 L and E the inductance and resistance of the coil. Then, 
 if v is the instantaneous value of the alternator voltage, we 
 have as fundamental equations 
 
 i 2 =i-i v 
 dv. 
 
 Hence, assuming a simple periodic variation of i, we have 
 
 Then, if i = I sin.pt, we shall have * 1 = I 1 sin (pt0\ because 
 there will be a difference of phase between \ and i. Accord- 
 ingly, we obtain, by substitution, 
 
 (1 - VLf)\ sin (pt-Q) H-CRpIiCOS (pt - 0)=I smpt, 
 and hence, by a well-known transformation, 
 
 But I 1= V/\/K 2 -t-/ 2 L 2 ; 
 
 therefore I 
 
 We have, then, to find what value of L will make I a 
 minimum. Differentiate therefore the last expression with 
 
THE MEASUREMENT OP ELECTRIC POWER. 531 
 
 respect to L and equate to zero, and after some simple 
 reductions we have as a result the equation 
 
 C(CLp 2 - 1)(K 2 +^ 2 L 2 )=L{ (1 - C 
 
 1 R 2 
 
 which reduces to L 2 ,-!,= ; - 
 
 Cp 2 p 2 
 
 Hence the solution of the above quadratic equation gives us 
 the value of L which makes I a minimum. It is 
 
 or T _1 Vl-4C 2 Ry 
 
 In this last form the solution of the problem was given by 
 Prof. Ayrton in a discussion at the Institution of Electrical 
 Engineers in 1901. Given a condenser or cable of capacity 
 C farads subjected to an alternating current of frequency 
 n=p/27r, the condenser being shunted by an inductance L of 
 resistance R ; the value of L, calculated from the above 
 equation, is that which will make the total current taken by 
 coil and condenser a minimum. 
 
 END OF VOLUME I. 
 
INDEX. 
 
 Absolute Galvanometer, 352 
 
 Absolute Resistance, Jones-Lorenz Appa- 
 ratus for Determining, 314 
 
 Accumulator Room, 12 
 
 Accumulators for Laboratory Purposes, 12 
 
 Addenbrooke Electrostatic Voltmeter. 394, 
 518 
 
 Alloys, Resistivity of, 263, 326 
 
 Alloys used for Making Resistances, 38 
 
 Alternating Current Curve Tracing, 
 Reference to Papers on, 407 
 
 Alternating Current Measurement, 388 
 
 Alternating Current Measurement, Use of 
 Transformers in, 409 
 
 Alternating Current Power, Measurement 
 of, 477, 479 
 
 Alternating Current Power, Measurement 
 of, by Three Ammeters, 492 
 
 Alternating Current Power, Measurement 
 of, by Three Voltmeters, 488 
 
 Alternating Currents, Delineation of Wave 
 Form of, 395 
 
 Alternating Currents, Generating, 2 
 
 Alternating Currents, Resistance of Con- 
 ductors to, 317 
 
 Alternators, Combined, 6 
 
 Ammeter, Calibration of, 372 
 
 Ammeter, Error Curve of, 374 
 
 Ammeter, Hartmann and Braun, 369 
 
 Ammeter, Hot Wire, 390 
 
 Ammeter, Kelvin Switchboard Form, 372 
 
 Ammeter, Weston Form, 368 
 
 Ammeters, Movable Coil, 142 
 
 Ampere, Board of Trade Specification for 
 the Recovery of the, 57 > 
 
 Ampere, The International, 341 
 Ampere Balance, 60 
 Ampere Balance, Board of Trade, 71 
 Ampere Balance, Pellat's Form, 366 
 Ampere Balance, Use of the, 65 
 Amperemeters, 367 
 Amperemeters, Classification of, 120 
 Ampere Standard, Board of Trade, 30 
 Arrangement of Dynamo Room, 2 
 Atomic Weights, Table of, 320 
 Ayrton Electrostatic Voltmeter, 516 
 Ayrton and Mather Method of Measuring 
 
 Power in Circuits of Small Power Factor, 
 
 529 
 
 Ayrton-Mather Galvanometer, 123 
 Ayrton's N on -Insulating Varnish, 464 
 
 Balance, Standard, 25 
 Ballistic Galvanometer, 128, 173 
 Bar Pattern Wheatstone's Bridge, 164 
 Berlin Reichsanstalt Standard Ohm, 42 
 Bidwell Rheostat, 82 
 
 Blakesley's Method of Measuring Alter- 
 nating Current Power, 493 
 Board of Trade Ampere Standard, 30 
 Board of Trade Electrical Laboratory, 186 
 Board of Trade Ohm Standard, 30 
 Board of Trade Specification for Clark Cell, 
 
 92 
 
 Board of Trade Specification for Unit Cur- 
 rent, 57 
 Board of Trade Standard Ampere Balance, 
 
 71 
 
 Board of Trade Standard Voltmeter. 113, 
 U7 
 
534 
 
 INDEX. 
 
 Board of Trade Volt Standard, 31 
 Bridge, Dial Pattern, Arrangement of Coils, 
 
 in, 163 
 
 Bridge, Kelvin, Double Form, 278 
 Bridge, Plug Form of, 162 
 Bridge, Wheatstone's, 144 
 Bridge for Liquid Resistance Measurement, 
 
 307 
 
 Cadmium Standard Cell, Reichsanstalt 
 Form of, 102 
 
 Cadmium Standard Cell Weston Form of, 
 101 
 
 Calibration of Ammeter, 372 
 
 Calibration of a Slide Wire, 240 
 
 Callendar Clark Cell, 99 
 
 Callendar and Griffith Resistance Bridge, 
 221 
 
 Calomel Cell, 104 
 
 Carbon Plate Rheostat, 81 
 
 Cardew Voltmeter, 459 
 
 Cardew's Method for Measuring High 
 Resistance, 300 
 
 Carey Foster Bridge, 149, 238 
 
 Carhart- Clark Cell, 91 
 
 Circular Conductor, Magnet Field of, 350 
 
 Clark Cell, Board of Trade Specification 
 for, 92 
 
 Clark Cell, Determination of Electromotive 
 Force of, 423 
 
 Clark Cell, Original Form of, 87 
 
 Clark Cell, References to Various Papers 
 on, 108 
 
 Clark Cell, Various Forms of, 87 
 
 Coil of Maximum Inductance, 521 
 
 Combined Resistance Balance and Poten- 
 tiometer, 432 
 
 Conductivity Box, 215 
 
 Conductivity of Metals, 325 
 
 Conductors, Classification of, 292 
 
 Conductors, Networks of, 194 
 
 Construction of Current-Carrying Resist- 
 ances, 53 
 
 Continuous Current Power Measurement, 
 471 
 
 Copper, Conductivity of, 258 
 
 Copper, Temperature Co-efficient of, 261 
 
 Copper Wire, Resistivity of Various 
 Sizes of, 333 
 
 Crompton Galvanometer, 124 
 
 Crompton Potentiometer, 136 
 
 Crompton Water-tube Resistance, 51 
 
 Current Balance, 365 
 Current- Carry ing Capacity of Wires, 377 
 Current-Carrying Resistance?, 49 
 Current Measurement by Electrolysis of 
 Copper Sulphate, 342 
 
 Current Measurement by Electrolysis of 
 
 Silver Nitrate, 347 
 Current Measurement by Potentiometer, 
 
 376 
 
 Current Measuring Instruments, 119 
 Current Measuring Instruments, 349 
 Current, Regulation of, 79 
 Curve Tracer, Rosa's Form, 401 
 
 Daniell Cell, 104 
 
 Density of Metals, 320 
 
 Determination of Mean Temperature Co- 
 efficient of a Wire, 245 
 
 Dial Pattern Wheatstone's Bridge, 163 
 
 Dielectrics, Resistance of, Under Various 
 Electromotive Forces, 294 
 
 Dielectric Resistance, Measurement of, 297 
 
 Dielectrics, Resistivity of, 330 
 
 Differential Bridge, 149 
 
 Differential Bridge, Method of Using, 151 
 
 Dolivo-Dobrowolsky Phasemeters, 416 
 
 Duddell Oscillograph, 405 
 
 Dynamo Room, Arrangement of, 2 
 
 Dynamometer Method of Measuring Power, 
 493 
 
 Electric Current, Methods of Measuring, 
 
 341 
 
 Electric Current, Provision for Obtaining, 2 
 Electric Current, Root Mean Square Value 
 
 of, 340 
 
 Electric Current, Unit of, 29 
 Electric Currents, Classification of, 339 
 Electric Power, Measurement of, 469 
 Electrical Instruments, Foundations for, 9 
 Electrical' Laboratory, Arrangement of an, 8 
 Electrical Laboratory, Board of Trade, 186 
 Electrical Laboratory, Outfit of, 119 
 Electrical Laboratory, University College, 
 
 London, 4 
 Electrical Resistance, Board of Trade 
 
 Standard of, 30 
 Electrical Resistance, Practical Standard 
 
 of, 31 
 
 Electrical Resistance, Unit of, 29 
 Electrical Resistances, Measurement of, 191 
 Electrical Resistivity of Various Materials, 
 
 337 
 
 Electrical Units, 28 
 
 Electrochemical Equivalent of Silver, 58 
 Electrochemical Equivalents, 420 
 Electrodynamometer, 360 
 E lee trodynamo meter, Siemens, 130 
 Electrodynamometer, Theory of, 361 
 Electrolytes, Measurement of Resistivity 
 
 of, 311 
 Electromotive Force, Determination of, 427 
 
INDEX. 
 
 535 
 
 Electromotive Force, Measurement of, 421 
 
 Electromotive Force, Potentiometer 
 Measurement of, 429 
 
 Electromotive Force, Practical Standard 
 of, 86 
 
 Electromotive Force, Unit of, 29 
 
 Electromotive Force of Clark Cell, Deter- 
 mination of, 423 
 
 Electromotive Force of Clark Cell, Table 
 of, 467 
 
 Electrostatic Voltmeter, Ayrton, 516 
 
 Elliott Potentiometer, 434 
 
 Elliott Recording Voltmeter, 452 
 
 Equipment of Test Room, 1 
 
 Equivalents, Electrochemical, Table of, 420 
 
 Error Curve of Voltmeter, 445 
 
 Eureka Alloy, 40 
 
 Evershed's Ohmmeter, 303 
 
 Fleming and Gimingham Wattmeter, 512 
 Fleming Circular Slide-Wire Bridge, 150 
 Fleming Inductionless Resistances, 80 
 Fleming Potentiometer, 441 
 Fleming Standard Daniell Cell, 105 
 Fleming Standard Ohm, 44 
 Fleming Wattmeter, 508 
 Foundations for Electrical Instruments, 9 
 Frequency Tellers, 411 
 Frequency of Alternating Current, Mea- 
 surement of, 411 
 Fundamental Standards, 22 
 Fuse Wire Currents, Table of, 419 
 Fusing Currents of Wires, 382 
 
 Galvanometer Absolute, 352 
 Galvonometer, Ayrton-Mather, 123 
 Galvanometer, Ballistic, 128, 173 
 Galvanometer, Ballistic, Theory of, 173 
 Galvanometer Calibration by Poten- 
 tiometer, 383 
 
 Galvanometer, Crompton, 124 
 Galvanometer, Deflectional Constant, 353 
 Galvanometer, Holden-Pitkin Form, 122 
 Galvanometer Lamps, 11 
 Galvanometer Shunt, 385 
 Galvanometers, Classification of, 120, 126 
 German Silver Alloy, 39 
 Glass, Resistivity of, 293 
 Guard Wire, 289 
 
 Hamilton Dickson Formula for Tempera- 
 ture Variation of Resistance of Platinum, 
 250 
 
 Hartmann and Braun Ammeter, 369 
 Hartmann and Braun Hot Wire Ammeter, 
 391 
 
 Heating Effects of Currents, References to 
 
 Papers on, 383 
 Helmholtz Calomel Cell, 104 
 High Resistance, Measurement of, 293 
 High-Tension Electrostatic Voltmeter, 133 
 High Tension Voltmeter, Kelvin, 453 
 High Tension Voltmeter, Pirelli, 454 
 Holden-Pitkin Galvanometer, 122 
 Holden-Pitkin Hot Wire Ammeter, 390 
 Housman Bridge, 279 
 Hydraulic Speed Indicator, 27 
 
 Indicator, Speed, 27 
 
 Inductance, Rules for Making Coil of 
 
 Maximum, 521 
 
 Insulation of Cables, Measurement of, 290 
 Insulation Resistance, 288 
 Insulation Resistance, Measurement of, 304 
 Insulation, Rules for, 305 
 Insulation Tests, Certificate of, 296 
 Inductionless Resistances, 80 
 International Kilogramme, 23 
 International Metre, 22 
 International Volt, 421 
 International Units, 29 
 Iron, Temperature Co-efficient of, 248 
 
 Kelvin Ammeter, 372 
 
 Kelvin Ampere Balance, 60 
 
 Kelvin Ampere Balance, Various Types, 67 
 
 Kelvin Double Bridge. 270 
 
 Kelvin Double Bridge, Practical Forms of, 
 
 275 
 
 Kelvin Double Bridge, Theory of, 275 
 Kelvin Edgewise Voltmeter, 463 
 Kelvin Electrostatic High-Tension Volt- 
 meter, 133 
 
 Kelvin Engine Room Wattmeter, 514 
 Kelvin High Tension Voltmeter, 453 
 Kelvin Multicellular Electrostatic Volt- 
 meter, 132 
 
 Kelvin Multicellular Vertical Pattern Volt- 
 meter, 462 
 
 Kelvin Multicellular Voltmeter, 118 
 Kelvin Recording Voltmeter, 451 
 Kelvin Standard One Ampere Balance, 77 
 Kelvin-Varley Slide, 273 
 Kelvin Water Battery, 456 
 Kelvin Wattmeter, 509 
 Kelvin Wire Rheostat, 82 
 Key for Wheatstone's Bridge, 220 
 Kilo-ampere Balance, 68 
 Kohlrausch Resistance Bridge, 307 
 
 Laboratory, Electrical, 1 
 Laboratory., Plan for, 14 
 Laboratory Tables, 10 
 
536 
 
 INDEX. 
 
 Length, Unit of, 22 
 
 Lithanode Cells, 12 ITTa. 
 
 Lorenz Apparatus for Absolute Resistance 
 Low Resistances, Determination of, 265 
 Lyon Liquid Rheostat, 85 
 
 Magnetic Field Due to Currents of Various 
 
 Forms, 349 
 Manganin Alloy, 39 
 Manganin Wire, Ageing of, 41 
 Manganin Wire, Resistance of Various 
 
 Sizes of, 332 
 Mass and Volume Resistivity, Relation of. 
 
 253 
 
 Mass Resistivity, Definition of, 253 
 Mass, Unit of, 23 
 
 Matthiessen and Hockin Bridge, 235 
 Matthiessen's Standard for Conductivity 
 
 of Copper, 258 
 Mean Power, 470 
 Mean Solar Second, 23 
 Measurement of Alternating Current 
 
 Power, 477 
 
 Measurement of Electromotive Force, 421 
 Megohm, 56 
 
 Mercury Ohm, Secondary Standard, 36 
 Mercury, Resistance Standard, 33, 34 
 Mercury, Specific Resistance of, 31, 32 
 Mercury Standard Cell, Literature of, 107 
 Mercury, Temperature Co-efficient of, 37 
 Mecury, Temperature Resistance Curve 
 
 of, 251 
 
 Metal Strip Resistances, 50 
 Metals, Conductivity of, 325 
 Metals, Density of, 320 
 Metals, Mass Resistivity of, 321 
 Metals, Volume Resistivity of, 322, 323, 324 
 Motor Alternator Plant, 5 
 Muirhead-Clark Cell, 88 
 Multicellular Electrostatic Voltmeter, 132 
 Multicellular Voltmeter, Lord Kelvin, 118 
 
 Nalder Differential Bridge, 166 
 Nalder Potentiometer, 138 
 Networks of Conductors, 194 
 Non-Inductive Resistance, Construction of, 
 
 428 
 Non-Insulating Varnish, 464 
 
 Ohm, Absolute Dimension of, 48 
 Ohm Standard, Board of Trade, 30 
 Ohm's Law, 192 
 Ohmmeter, 301 
 Ohmmeter, Evershed's, 303 
 Ohmmeter, Theory of, 302 
 One Ampere Kelvin Balance, Standard 
 Form, 77 
 
 Oscillograph, 402 
 
 Oscillograph, Duddell, Description of, 402 
 
 Outfit of Testing Laboratory, 185 
 
 Paul's Carbon Plate Rheostat, 81 
 
 Pender Electrical Engineering Laboratory, 
 
 14 
 Phase Difference of Currents, Measurement 
 
 of, 413 
 
 Phasemeters, 413 
 Phasemeter, Dolivo-Dobrowolsky Form of, 
 
 416 
 Phasemeters, References to Papers on, 
 
 418 
 
 Pirelli High Tension Voltmeter, 454 
 Platinum Silver Alloy, 39 
 Platinum Silver Resistance Coils, 47 
 Platinum, Variation of Resistance with 
 
 Temperature, 250 
 Platinoid Alloy, 40 
 Platinoid Wire, Resistance of Various 
 
 Sizes of, 331 
 Plug Bridge, 162 
 
 Plug Pattern Resistance Bridge, 213 
 Polyphase Circuit Power Measurement, 495 
 Potential Differences, Measurement of 
 
 Small, 431 
 Potentiometer, 134 
 
 Potentiometer and Bridge Combined, 432 
 Potentiometer, Crompton, 136 
 Potentiometer, Elliott, 434 
 Potentiometer, Fleming, 441 
 Potentiometer Measurement of Current, 
 
 376 
 
 Potentiometer, Nalder, 138 
 Potentiometer, Use of, for Determining 
 
 Electromotive Forces, 429 
 Power Factor, 470 
 
 Power Measurement by the Wattmeter, 473 
 Power Measurement by Soft Iron Needle 
 
 Wattmeter, 486 
 Power Measurement by Three Voltmeters, 
 
 Theory of, 489 
 Power Measurement in Ca^e of Circuits of 
 
 Small Power-Factor, 481 
 Power Measurement in case of Continuous 
 
 Currents, 4-71 
 Power Measurement in Case of High- 
 
 Tension Alternating Current Circuits, 
 
 479 
 Power Measurement in Case of Polyphase 
 
 Circuits, 495 
 Power Measurement in Circuits of Small 
 
 Power Factor, Ayrton and Mather 
 
 Method of, 529 
 Power Measurement, Lord Rayleigh's 
 
 Method of, 486 
 
INDEX. 
 
 537 
 
 Power Measurement, Three-Pbase Circuits, 
 497 
 
 Power Measurement, Use of Potentio- 
 meter for, 472 
 
 Preece's Table of Fuse Wire Currents, 
 419 
 
 Prices' Guard Wire, 289 
 
 Rayleigh-Clark Cell, 89 
 
 Rayleigh, Lord, Determination of the 
 
 Absolute Electromotive Force of Clark 
 
 Cells, 423 
 Rayleigh, Lord, Value of Electromotive 
 
 Force of Clark Cell, Found by, 426 
 Regulation of Current, 79 
 Resistance of Conductors to Alternating 
 
 Currents, 317 
 Resistance of Liquids, 306 
 Resistance for Carrying High-Tension 
 
 Currents, 447 
 Resistance, Absolute Measurement of, 312 
 
 Measurement, 314 
 Resistance Alloys, 38, 39 
 Resistance Balance. Nalder, 166 
 Resistance Bridge for Liquid Resistance 
 
 Measurement, Stroud and Henderson's 
 
 Form, 310 
 Resistance Bridge for Low Resistance 
 
 Measurement, Reeves Form, 276 
 Resistance Bridge, Plug Pattern, 213 
 Resistance Bridge, Slide Wire, 147 
 Resistance Coil, Determination of Tempera- 
 ture Co-Efficient, 243 
 Resistance Coil Wound with Bare Wire, 225 
 Resistance Coils for Carrying Large Cur- 
 rents, 49 
 
 Resistance Coils of Platinum Silver, 47 
 Resistance, Insulation, 288 
 Resistance Measuring Instruments, 144 
 Resistance, Measurement of by Fall of 
 
 Potential, 297 
 Resistance Measurement by Galvonometer 
 
 Deflection, 283 
 
 Resistance of Networks of Conductors, 194 
 Resistance of Networks of Conductors, 
 
 Calculation of, 194 
 Resistance Standards, Permanency of 
 
 Wire for, 38 
 
 Reichsanstalt Cadmium Cell, 102 
 Resistances, Determination of Low, 265 
 Resistances, Laboratory Outfit of, 56 
 Reichsanstalt Clark Cell, 95 
 Reicheanstalt Specification for Clark Cell, 
 
 95 
 
 Rheostat, Kelvin Form, 82 
 Rheostat, Lyon, 85 
 Rheostat, Shelford Bidwell's, 82 
 
 Rheostats in University College, London, 
 
 Dynamo Room, 84 
 Rheostats, Power-Absorbing, 86 
 Resistivity of Alloys, 263, 326 
 Resistivity of Copper, 258 
 Resistivity of Dielectrics, 330 
 Resistivity of Hard-Drawn and Annealed 
 
 Copper, 260 
 
 Resistivity of Liquids, 327, 328, 329 
 Re-istiyity of Liquids, Measurement of, 309 
 Resistivity of Pure Metals, 263 
 Resistivity, Reference to Papers on, 264 
 
 Sag of Wire, Calculation of, 370 
 
 Secondary Batteries, 12 
 
 Secondary Standard Mercury Ohm, 36 
 
 Series Plug Pattern of Wheatstone's Bridge 
 216 
 
 Siemens Electrodynamometer, 130 
 
 Siemens Wattmeter, 182, 506 
 
 Silver, Electrochemical Equivalent of, 58 
 
 Slide Wire Bridge, Double Gap, 148 
 
 Slide-Wire Bridge, Fleming Form, 150 
 
 Slide Wire, Calibration of, 240 
 
 Slide Wire Resistance Bridge, 147, 209 
 
 Specific Resistance of Mercury, 31, 32 
 
 Specific Resistance of Metal or Alloy, 
 Determination of, 252 
 
 Speed Counter, 27 
 
 Standard Balance, 25 
 
 Standard Cell, Determination of Electro- 
 motive Force of, 422 
 
 Standard Daniell Cell, Fleming Form of, 
 105 
 
 Standard Megohm, 56 
 
 Standard Mercury Ohm, 34 
 
 Standard Ohm, Berlin Reichsanstalt, 42 
 
 Standard Ohm, Fleming's, 44 
 
 Standard Potential Difference, Recovery of, 
 427 
 
 Standard Voltmeters, 112 
 
 Standard Voltmeter, Board of Trade, 113 
 
 Standards of Length, Mass and Time, 22 
 
 Standards, Mechanical, of Electromotive 
 Force, 112 
 
 Tangent Galvanometer,}Helmholtz Form, 
 
 357 
 
 Tangent Galvanometer, Theory of, 354 
 Temperature Co-efficient, Determination 
 
 of, 243 
 
 Temperature Co-efficient of Iron, 248 
 Temperature Co-efficient of Mercury, 37 
 Terrestial Magnetic Field, Determination 
 
 of, 359 
 
 Testing Laboratory, Hints on Outfit of, 185 
 Testing of Wattmeters, 518 
 
538 
 
 INDEX. 
 
 Test Room Equipment, 1 
 
 The Electrolytic Measurement of Current. 
 
 342 
 
 Three-Phase Power Measurement, 497 
 Time, Unit of, 23 
 Trotter Resistance Bridge, 229 
 Trowbridge Researches on High Tension 
 
 Discharges, 457 
 
 Unit Electric Current, Recovery of, 57 
 
 Unit of Electric Current, 29 
 
 Unit of Electrical Resistance, 29 
 
 Unit of Electromotive Force, 29 
 
 Unit of Length, 22 
 
 Unit of Mass, 23 
 
 Unit of Time, 23 
 
 Units, Electrical, 28 
 
 Units, International, 29 
 
 Universal Shunt Box, Ayrton-Mather 
 Form, 386 
 
 University College, London, Electrical 
 Laboratory, 14 
 
 University College, London, Dynamo Rheo- 
 stats, 84 
 
 University College, London, Dynamo Room, 
 6 
 
 Vibration Effects, Overcoming, 9 
 
 Volt, International, 421 
 
 Volt Standard, Board of Trade, 31 
 
 Voltmeter, Addenbrooke Electrostatic, 518 
 
 Voltmeter, Calibration of a High Tension, 
 
 446 
 
 Voltmeter, Calibration of Low Tension. 443 
 Voltmeter, Cardew, 459 
 Voltmeter, Effect of Capacity of, 447 
 Voltmeter, Electrostatic, Addenbrooke 
 
 Form, 394 
 
 Voltmeter, Elliott Recording, 452 
 Voltmeter, Error Curve of, 445 
 Voltmeter, Hartmann and Braun Hot 
 
 Wire, 461 
 
 Voltmeter, Kelvin Edgewise, 463 
 Voltmeter, Kelvin Multicellular Vertical 
 
 Pattern, 462 
 
 Voltmeter, Kelvin Recording, 451 
 Voltmeter, Pitkin-Holden Hot- Wire, 450 
 Voltmeter, Practical Forms of, 505 
 Voltmeter, Self-Recording, 449 
 Voltmeter, Standard, 112 
 Volmeter Switchboard, Requirements iu a, 
 
 465 
 
 Voltmeters, Classification of, 458 
 Voltmeters, High Tension, 453 
 
 Volume and Mass Resistivity, Determina- 
 tion of for Metals, 257 
 Volume Restivity, Definition of, 252 
 
 Water Battery, 456 
 
 Water- tube Resistance, 51 
 
 Wattmeter, Fleming, 508 
 
 Wattmeter, Fleming and Gimingham, 512 
 
 Wattmeter, Kelvin, 509 
 
 Wattmeter, Kelvin Engine Room, 514 
 
 Wattmeter, Power Measurement by, 474, 
 
 475 
 
 Wattmeter, Siemens, 182, 506 
 Wattmeter Testing, 518 
 Wattmeter, Theory of, 485 
 Wattmeter for Alternating Current 
 
 Measurement, Construction of, 478 
 Wattmeters, 181 
 Wave Form of Current, Measurement of, 
 
 395 
 
 Weston Ammeter, 368 
 Weston Cadmium Cell, 101 
 Wheats tone Bridge, Housman Form, 279 
 Wheatstone Bridge, Kohlrausch's Form of, 
 
 307 
 
 Wheatstone's Bridge, 144 
 Wheatstone's Bridge, Bar Pattern, 164 
 Wheatstone's Bridge Battery Key, 220 
 Wheatstone Bridge, Best Arrangement of 
 
 Conductors for, 235 
 Wheatstone's Bridge, Callendar and 
 
 Griffith Form, 221 
 
 Wheatstone's Bridge, Dial Pattern of, 163 
 Wheatstone's Bridge, Fleming Form, 150 
 Wheatstone's Bridge, Fleming Workshop 
 
 Pattern, 168 
 Wheatstone's Bridge, Foster's Method of 
 
 Using, 149 
 Wheatstone Bridge, Matthiessen and Hockin 
 
 Form, 235 
 
 Wheatstone's Bridge, Method of Using, 145 
 Wheatstone's Bridge, Nalder Form, 166 
 Wheatstone's Bridge, Plug Pattern, 216 
 Wheatstone Bridge, Portable Forms of, 228 
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 ELECTROMAGNETIC THEORY. 
 
 BY OLIVER HEAVISIDE. 
 
 EXTRACT FROM PREFACE TO VOL. I. 
 
 This work is something approaching a connected treatise on electrical theory, though without 
 the strict formality usually associated with a treatise. The following are some of the leading 
 points in this volume. The first chapter is introductory. The second consists of an outline scheme of 
 the fundamentals of electromagnetic theory from the Faraday -Max well point of view, with some 
 email modifications and extensions upon Maxwell's equations. The third chapter is devoted to 
 vector algebra and analysis, in the form used by me in former papers. The fourth chapter is 
 devoted to the theory of plane electromagnetic waves, and, being mainly descriptive, may perhaps be 
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 I have included in the present volume the application of the theory (in duplex form) to straight 
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 significance in present practice as well as in possible future developments. 
 EXTRACT FROM PREFACE TO VOL. II. 
 
 From one point of view this volume consists essentially of a detailed development of the 
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 development of the theory of the propagation of waves along wires. But on account of the 
 important applications, ranging from Atlantic telegraphy, through ordinary telegraphy and 
 telephony, to Hertzian waves along wires, the author has usually preferred to express results in 
 terms of the concrete voltage and current, rather than the specific electric and magnetic forces 
 belonging to a single tube of flux of energy. . . . The theory of the latest kind of so called 
 wireless telegraphy (Lodge. Marconi, &c.) has been somewhat anticipated, since the waves sent up 
 the vertical wire are hemispherical, with their equatorial bases on the ground or sea, which they 
 run along in expanding. (See 60, Vol. I. ; also 393 in this volume.) The author's old predictions 
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 MAGNETIC INDUCTION IN IRON AND OTHER METALS. 
 
 BY PBOF. J. A. EWINQ, M.A., B.So., F.B.S., 
 
 Professor of Mechanism and Applied Mechanics in the University of Cambridge. 
 
 SYNOPSIS OF CONTENTS. 
 
 After an introductory chapter, which attempts to explain the fundamental ideas and the 
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 magnetic quality of metals. Examples are then quoted, showing the results of such measurements) 
 for various specimens of iron, steel, nickel and cobalt. A chapter on Magnetic Hysteresis folk 
 and then the distinctive features of induction by very weak and by very strong magnetic foi 
 are separately described, with further description of experimental methods, and with additional) 
 numerical results. The influence of Temperature and the influence of Stress are next discussed. 
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 important subject of Practical Magnetic Testing has been added. _ 
 
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 ELECTRIC LAMPS AND ELECTRIC LIGHTING. 
 
 By PROF. J. A. FLEMING, M.A., D.Sc., F.R.S., M.R.I., 
 
 Professor of Electrical Engineering in University College, London. 
 SYNOPSIS OF CONTENTS. 
 
 I. A Retrospect over 25 Years Present Condition of Electric Lighting Chief Properties of an Electric 
 Current Names of Electrical Units Chemical Power of an Electric Current Hydraulic Analogies Electric 
 Pressure Fall of Electric Pressure Down a Conductor Ohm's Law Joule's Law Units of Work and Power 
 The Watt as a Unit of Power Incandescence of a Platinum Wi?e Spectroscopic Examination of a Heated 
 Wire Visible and Invisible Radiation Luminous Efficiency Radiation from Bodies at Various Temperature; 
 -Efficiency of Various Sources of Light The Glow Lamp and Arc Lamp as Illuminants Colours and Wave- 
 ^engths of Rays of Light Similar and Dissimilar Sources of Light Colour-Distinguishing Power Causes o 
 Colour Comparison of Brightness and Colour Principles of Photometry Limitations Due to the Eye 
 Luminosity and Candle Power Standards of Light Standards of Illumination The Candle Foot Comparison 
 of Sunlight and Moonlight Comparison of Lights Ritchie's Wedsje Rumf ord and Bunsen Photometers 
 Comparison of Lights of Different Colours Spe'ctro- Photometers Results of Investigations. 
 
 II. The Evolution of the Incandescent Lamp The Nature of the Problem Necessary Conditions 
 Allotropic Forms of Carbon The Modern Glow Lamp Processes for the Manufacture of the Filament Edison- 
 Swan Lamps The Expansion of Carbon when Heated Various Forms of Glow Lamps Velocity of Molecules of 
 Gases Kinetic Theory of Gases Processes for the Production of High Vacua Necessity for a Vacuum Mean 
 Free Path of Gaseous Molecules -Voltage, Current and Candle Power of Lamps Watts per Candle Power- 
 Characteristic Curves of L imps Life of Glow Lamps Molecular Shadows Blackening of Glow Lamps Salf- 
 Recording Voltmeters Necessity for Constant Pressure of Supply Changes Produced in Lamps by Age- 
 Smashing Point Efficiency of Glow Lamps Statistics of Age Variation of Candle Power with Varying Voltage 
 Cost of Incandescent Lighting Useful Life of Lamps Importance of Careful " Wiring "Average Energy 
 Consumption of Lamps in Various Places Load Factors Methods of Glow Lamp Illumination for Production 
 of Best Effects Artistic Electric Lighting Molecular Physics of the Glow Lamp-High Voltage Lamps- 
 Varieties of Carbon Densities and Resistances Deterioration of Carbon Lamps High Efficiency Lamps 
 Hecently Suggested Improvements. 
 
 III. Forms of Electric Discharge Vacuum Tubes Sparking Distance The Electric Arc The Optical 
 Projection of the Arc The Arc a Flexible Conductor The High Temperature of the Arc Non- Arcing Metals- 
 Lightning Protectors The Distribution of Light from the Arc Continuous and Alternating Current Arcs 
 VoUage Required to Produce an Arc The Physical Actions in the Arc The Changes in the Carbons The 
 Distribution of a Potential in the Arc The Unilateral Conductivity of the Arc The Temperature of the Crater 
 Comparison with Solar Temperature The "Watte per Candle" of the Sun Intrinsic Brightness and Dissi- 
 patiye Power of Heated Surfaces Comparison of Glow Lamp, Arc Lamp and Sun in Respect of Brightness and 
 Radiation Arc Lamp Mechanism Arc Lamp Carbons The Hissing of Arc Lamps The Applications of Arc 
 Lamps Inverted Arcs Series and Parallel Arc Lighting The Enclosed Arc Lamp. 
 
 IV. The Generation and Distribution of Electric Current The Magnetic Action of an Electric Current 
 The Magnetic Field of a Spiral Current The Induction of Electric Currents The Peculiar Magnetic Property 
 of Iron Iron and Air Magnetic Circuits The Typical Cases of an Iron Conduit With and Without Air Gaps 
 The Prototypical Forms of Dynamo and Transformer The Transformation of Electrical Energy Hydraulic 
 Illustrations The Mechanical Analogue of a Transformer The Mode of Construction of an Alternate Current 
 Transformer The Fundamental Principle of all Dynamo Electric Machines Alternating and Direct Current 
 Dynamos Alternating Current Systems of Electrical Distribution Description of the Electric Lighting Station 
 in Rome The Tivoli-Rome Electric Transmission Views of the Tivoli Station Continuous Current Systems 
 The Three- Wire System Description of St. Pancras Vestry Electric Lighting Station Liverpool, Glasgow and 
 Brussels Electric Lighting Stations Direct Driven Dynamos Alternating and Continuous Current Systems 
 Contrasted Secondary Batteries House and Maximum Demand Meters. 
 
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 THE ALTERNATE CURRENT TRANSFORMER 
 
 IN THEORY AND PRACTICE. 
 
 By J. A. FLEMING, M.A., D.Sc., F.K.S., M.R.I., &c., 
 
 Professor of Electrical Engineering at University College, London. 
 
 Since the first edition of this Treatise was published, the study of the properties and applications of 
 alternating electric currents has made enormous progress. . . . The author has, accordingly, rewritten the 
 greater part of the chapters, and availed himself of various criticisms, with the desire of removing mistakes and 
 remedying defects of treatment. In the hope that this will be found to render the book still useful to the increas- 
 ing numbers of those who are practically engaged in alternating- current work, he has sought, as far as possible, 
 to avoid academic methods and keep in touch with the necessities of the student who has to deal with the 
 subject not as a basis for mathematical gymnastics but with Hie object of acquiring practically useful knowledge. 
 
 SYNOPSIS OF CONTENTS OF VOL. I. 
 
 CHAPTER I. Introductory. Faraday's Electrical Researches Faraday's Theories Magneto-Electric 
 Induction Views of Maxwell, Helmholtz and Kelvin Action at a Distance The Electro-Magnetic Medium 
 J*%eph Henry'* investigations. 
 
 CHAPTER II. Electro-Magnetic Induction. Magnetic Force and Magnetic Fields MagnetitfForce 
 t'M Conductors Typical Cases Magneto-Motive Force and Magnetic Induction Flux of Force Magnetic 
 I ermeability Lines of Induction -Faraday's Law of Induction Electromotive Force One to the Change of Induc- 
 tion The Magnetic Circuit Magnetic Resistance Lines of Induction of Closed and Open Magnetic Circuits 
 Fundamental Delations Between Magnetic Force and Magnetic Induction Intensity of Magnetisa' ion Magnetic 
 Moment Lines and Tubes of Magnetic Induction Curves of Magnetisation Permeability Curves Determina- 
 tion of Permeability Magnetic Hysteresis Hysteresis Curves H.B. Diagram Effect of Temperature on Hyster- 
 esis Electromotive Force of Induction Graphical Representations Electromotive Force of Self-Induction. 
 a CHAPTER III. The Theory of Simple Periodic Currents. Variable and Steady Flow Current 
 and Electromotive Force Curves Fourier's Theorem Mechanical Harmonographs Mathematical Sketch of 
 Fourier's Theorem Practical Application of Fourier's Theorem to the Harmonic Analysis of a Periodic Curve 
 Simple Periodic Currents and Electromotive Forces Description of a Simple Periodic Curve The Mean Value 
 of the Ordinate of a Sine Curve The Square Root of the Mean of the Squares of the Ordinates of a Simple 
 Periodic Curve Derived Curves Inductance and Inductive Circuits; Inductance, Resistance and Capacity of 
 Circuits ; Inductive and Non-inductive Circuits Faraday's and Henry's Experiments on Self-induction - Edlund's 
 and Maxwells Arrangement for Exhibiting Inductance of Circuits -Electro-Magnetic Momentum Electrot-nic 
 State and Electromagnetic Energy Co-efficient of Mutual Induction; Energy of Two Circuits The Unit of 
 Inductance Value of the Self-Induction in Henry's for Various Instruments Current Growth in Inductive 
 Circuits Analogy of Current and Velocity Change ; Fundamental Equations for Current Growth in Inductive 
 Circuits Equation for the Establishment of a Steady Current in Inductive Circuits Time Constant of an 
 Inductive Circuit- Logarithmic Curves Instantaneous Value of Simple Periodic Current Solution of Current 
 Equation -Impedance of Inductive Circuit Relations of Impressed Electromotive Force, Current and Im- 
 pedance- Geomet ical Illustrations Impressed and Effecive Electromotive Forces clock Diagram of Electro- 
 motive Forces in Inductive Circuit Triangle Representing Resistance, Impedance and Reactance of Circuit 
 The Mean Value of the Power of a Periodic Current Geometrical Theorem Power Curves for Inductive and 
 B on-Inductive Circuits Experimental Measurement of Periodic Currents and Electromotive Forces Mean 
 Square Value Method of Measuring the True Mean Power Given to an Inductive Circuit Theory of the 
 Wattmeter Divided Circuits Important Trigonometrical Lemma Impedance of Branched Circuits Watt- 
 meter Measurement of Periodic Power Mutual Induction of Two Circuits of Constant Induct mce The 
 low of Simple Periodic Currents into a Condenser Time Constant of a Condenser Charging a Condenser 
 through a Resistance-Condenser equation Annulment of Inductance by Capacity Representation of Periodic 
 Currents by Polar Diagrams -Initial Conditions on Starting Current Flow in Inductive Circuits Complex 
 Periodic Pun ctions Apparent and True Power given to Inductive Circuits Power Factor. 
 , CHAPTER IV. -Mutual and Self-Induction. The Researches of Joseph Henry Experiments with 
 toils ai d Bobbins ; Discovery of Self-induction Mutual Induction Induction at a Distance Induction between 
 Telephone Circuits-Induction over Great Distances Induced Currents of Higher Orders Inductive Effects by 
 Qsient Electric Currents Magnetic Screening -Direction of Induced Currents Various Qualities of au 
 Induced Current Elementary Theory of Mutual Induction of Two Circuits Theory of Induction Coil with Non- 
 Magnetic Core Comparison of Theory and Experiment Duration of Induced Currents Magnetic Screening 
 Action of Good-Conducting Masses Faraday's and Henry's Experiments Willoughby Smith's Investigations on 
 Magnetic Screening -Doves Experiments and Henry's Views on same The Reaction of the Secondary Currents 
 on the Primary Circuit in the Case of an Induction Coil Induction Balance and Sonometer Transmission of 
 Alternating Currents through Conductors Prof. Hughes' Experiments Lord Rayleigh's Researches Flow of 
 uum through Conductor- Surface Flow of Alternating Currents Increased Resistance of Conductors for 
 natmg Currents of High Frequency Limiting Size of Conductors for Conveyance of Alternating Currents 
 btep^ans Analogies Electro-Magnetic Repulsion Elihu Thomson's Experiments Electro-Magnetic Rotations. 
 CHAPTER V, Dynamical Theory of Induction. Electro-Magnetic Theory Faraday's Concep- 
 >r an Electro-Magneto Medium Maxwell's Suggestion The Lumini erous Ether Maxwells Theory of 
 Jtnc Displacement Electric Elasticity of the Medium-Displacetient and Conduction Currents Electro- 
 motive Intensity-Displacement Currents and Displacement Waves-Theory of Molecular Vortices Mechanical 
 Analogy comparison of Theory and Experiment Maxwell's Law Connecting Dielectric Constant and Refrac- 
 wvity or a Dielectric Tables of Comparison Velocity of Propagation of Electro-Magnetic Disturbances 
 rtftvfn j v "~ Vector Potential Electrical Oscillation Charge and Discharge of Leyden Jar The Function 
 01 in- condenser in an Induction Coil Impulsive Discharges and Relation of Inductance Thereto Impulsive 
 impettunce Ifertz's Researches Experimental Determination of the Velocity of Electro- Magnetic Waves. 
 th T F VI.- The Induction Coil and Transformer. Gem ral Description of the Action of 
 
 rvT v sformer or Induction Coil The Delineation ol Periodic Curves of Current and Electromotive Force 
 s iracers Transformer Diagrams -Curves of Electromotive Force- Cuircnt and Induction in Cases of 
 various .transformers Taken off Various Alternators Open-Circuit Cuirtnt of Transformers Symmetry of 
 rs, >rme c . u r v es Harmonic Analysis of Transformer Curves Power and Hysteresis Curves Hysteresis 
 uurve f \anous Transformers Efficiency of Transformers Efficiency Curves of Transformers Tables of 
 ri pH n p- eS ~? U -!r rent Dia 8 rams of a Transformer Tables of Complete Tests-The Power Factor-Open and 
 ivSS ^ ir ? ult Transformers- Magnetic Leakage ami Secondary Drop Various Causes of Secondary Drop 
 ijeiermination of Magetic Leakage Investigations of the Author and Dr. Roessler Form Factor and Amplitude 
 ctor of a Periodic Curve-General Analytical Theory of the Trausfc rmer and Induction Coil. 
 
"The Electrician" Printing and Publishing Co., Ltd. 
 "THE ELECTRICIAN" SERIES continued. 
 
 THIRD ISSUE. More than 600 pages and over SOO illustrations. Price 12s. 6d., post free; 
 
 abroad, 13s. 
 
 THE ALTERNATE CURRENT TRANSFORMER 
 
 IN THEORY AND PRACTICE. 
 
 By J. A. FLEMING, M.A., D.Sa, F.R.S., M.E.I., &c., 
 
 Professor of Electrical Engineering in University College London, 
 
 SYNOPSIS OF CONTENTS OF VOL. 2. 
 CHAP. I. Historical Development of Induction Coil and Transformer. 
 
 The Evolution of the Induction Coil Page's Researches Callan's Induction Apparatus- 
 Sturgeon's Induction Coil Bachhoffner's Researches Callan's Further Researches Callan'g 
 Great Induction Coil Page's Induction Coil Abbot's Coil Automatic Contact Breakers 
 Ruhmkorff's Coils Poggendorff's Experiments Stohrer's, Hoarder's, Ritchie's Induction 
 Apparatus Grove's Experiments Apps' Large Induction Coils Jablochkoff's Patent Fuller's 
 Transformer Early Pioneers Gaulard and Gibbs Zipernowsky's Transformers Improvements 
 of Rankin Kennedy, Hopkinson, Ferranti, and others The Modern Transformer since 1885. 
 
 CHAP. II. Distribution of Electrical Energy by Transformers. 
 
 Detailed Descriptions of Large Alternate-Current Electric Stations using Transformers in 
 Italy, England, and United States Descriptions of the Systems of Zipernowsky-D6ri-Blathy, 
 Westinghouse, Thomson-Houston, Mordey, Lowrie-Hall, Ferranti, and others Plans, Sections, 
 and Details of Central Stations using Transformers Illustrations of Alternators and Transformers 
 in Practical Use in all the chief British, Continental, and American Transformer Stations. 
 
 CHAP. III. Alternate-Current Electric Stations. 
 
 General Design of Alternating-Current Stations, Engines, Dynamos, Boilers Proper Choice 
 of Units Water Power Parallel Working of Alternators Underground Conductors Various 
 Systems Concentric Cables Capacity Effects dependent on Use of Concentric Cables Phenomena 
 of Ferranti Tubular Mains Safety Devices Regulation of Pressure Choice of Frequency 
 Methods of Transformer Distribution Sub-Stations Automatic Switches. 
 
 CHAP. IV. The Construction and Action of Transformers. 
 
 Transformer Indicator Diagrams Ryan's Curves Curves of Current Electromotive Force 
 and InductionrAnalysis of Transformer Diagrams Predetermination of Eddy Current and 
 Hysteresis Loss in Iron Cores Calculation and Design of Transformers Practical Predetermina- 
 tion of Constants Practical Construction of Transformers Experimental Tests of Transformers 
 Measurement of Efficiency of Transformers Calometric Dynamometer and Wattmeter Methods 
 Reduction of Results. 
 
 CHAP. V. Further Practical Application of Transformers. 
 
 Electrical Welding and Heating Transformers for producing Large Currents of Low Electro- 
 motive Force Theory of Electric Welding Other Practical Applications Conclusion. 
 
 NEW EDITION. Fully Illustrated. Price 6s. nett, post free; abroad 6s. 3d. 
 STUIXEJMTS' GTJXOE TO 
 
 SUBMARINE CABLE TESTING. 
 
 By H. K. C. FISHER and J. C. H. DARBY. 
 
 The authors of this book have, for some years past, been engaged in the practical work of Submarine Cable 
 Testing in the Eastern Extension Telegraph Company's service, and have embodied their experience in a Guide 
 for the use of those in the Telegraph Service who desire to qualify themselves for the examinations which the 
 Cable Companies have recently instituted. To those desirous of entering the Cable Service, Messrs. Fisher and 
 Darby's book is indispensable, as it is now necessary for probationers to pass these examinations as part of the 
 qualification for service. 
 
 1, 2 and 3, Salisbury Court, Fleet Street London, E.G. 
 
8 "The Electrician" Printing and Publishing Co., JLtd. 
 "THE ELECTRICIAN" SERIES continued. 
 
 In Two Volumes, 2s. 6d. each, post free 2s. 9d. each. Single Primers, 2d., post free 
 In quantities of 12, Is. 9d. post free. 
 
 "THE ELECTRICIAN" PRIMERS. 
 
 (FULLY ILLUSTRATED.) 
 
 A Series o-F Helpful Primers on Electrical Subjects for the use of those seeking a 
 Knowledge of Electricity-Theoretical and Practical. 
 
 OF CONTENTS. 
 
 Volumell. PRACTICE. 
 
 Primer 
 
 No. 
 
 21. The Electric Telegraph. 
 
 22. Automatic and Duplex 
 
 Telegraphy. 
 
 23. The Laying and Repair of 
 
 Submarine Cables. 
 
 24. Testing Submarine Cables. 
 
 25. The Telephone. 
 
 26. Dynamos. 
 
 27. Motors. 
 
 28. Transformers. 
 
 29. The Arc Lamp. 
 
 30. The Incandescent Lamp. 
 
 31. Underground Mains. 
 
 32. Electric Meters. 
 
 33. Electric Light Safety De- 
 
 vices. 
 
 34. Systems of Electric Distri- 
 
 bution. 
 
 35. Electric Transmission ol 
 
 Energy. 
 
 36. Electric Traction. 
 
 37. Electro-Deposition. 
 
 _ 38. Electric Welding. 
 
 A DIGEST OF THE 
 
 LAW OF ELECTEIC LIGHTING, ELECTEIC TEACTION, 
 AND OTHEE SUBJECTS. 
 
 By A. C. CUKTIS-HAYWAKD, B.A., M.I.E.E. Price 3s., post free. 
 
 Being a full critical abstract of the Electric Lighting Acts, 1882 and 1889, of the Tramways Act, 1870, and ol 
 
 Volume I. THEORY. 
 
 Primer 
 
 Mo. 
 
 1. The Effects of an Electric 
 
 Current. 
 
 2. Conductors and Insulators. 
 8. Ohm's Law. 
 
 4. Primary Batteries. 
 
 0. Arrangement of Batteries. 
 
 6. Electrolysis. 
 
 7. Secondary Batteries. 
 
 8. Lines of Force. 
 
 9. Magnets. 
 
 10. Electrical Units. 
 
 11. The Galvanometer. 
 
 12. Electrical Measuring In- 
 
 struments. 
 
 13. The Wheatstone Bridge. 
 
 14. The Electrometer. 
 
 15. The Induction CoiL 
 
 16. Alternating Currents. 
 
 17. The Leyden Jar. 
 
 18. Influence Machines. 
 
 19. Lightning Protectors. 
 80. Thermopiles. 
 
 The object of "The Electrician ' 
 Primers is to briefly describe in sim- 
 ple and correct language the present 
 state of electrical knowledge. Each 
 Primer is short and completein itself, 
 and is devoted to the elucidation of 
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 of some special application. Theo- 
 retical discussion is as far as possible 
 avoided, the principal facts being 
 stated and made clear by reference 
 to the uses to which they have been 
 put. Both volumes are suited to 
 readers having little previous ac- 
 quaintance with the subject. The 
 matter is brought up to date, and 
 the illustrations refer to instruments 
 and machinery in actual use at the 
 present time. It is hoped that the 
 Primers will be found of use where- 
 ever the want of a somewhat 
 popularly written work on electricity 
 
 and its industrial applications, pub- 
 lished at a popular price, has been 
 felt. Electricity Committees of 
 
 Town Councils will find the Primers 
 of great service. Artisans will find 
 the Primers useful in enabling 
 them to obtain clear notions of the 
 essential principles underlying the 
 apparatus of which they may be 
 called upon to take charge. 
 
 Supply Undertakings. The Digest treats first of the manner in which person* desirous of supplying electricity 
 must set to work, and then of their rights and obligations after obtaining Parliamentary powers ; and gives in a 
 succinct form information of great value to Local Authorities, Electric Light Contractors, &c., up to date. The 
 Board of Trade Regulations as to the Supply of Electrical Energy, the London County Council Regulations as to 
 Overhead Wires, Theatre Lighting, &c., together with the Bye-laws enforced in pursuance of Part II. of the 
 Public Health Acts Amendment Act, 1890, by the various Urban Sanitary Authorities are also given. 
 
 Fully illustrated. Price Is. 6d., post free Is. 9d. 
 
 THE MANUFACTURE OF ELECTRIC LIGHT CARBONS. 
 
 A Practical Guide to the Establishment of a Carbon Manufactory. 
 
 NOW READY. With Numerous Illustrations. 
 
 THE THEORY OP 
 
 Demy 8vo. Paper Covevs. 2/6 net, post free. 
 
 COMMUTATION- 
 
 By C. C. HAWKINS, M.A., M.I.E.E. 
 
 11 THE THEORY OF COMMUTATION " deals with commutation in the continuous-current dynamo, and has 
 special reference to Prof. Arnold and Dr. Mie's method of taking into account the contact resistance of the 
 copper or carbon brushes in the mathematical equation of the short-circuit current. 
 
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 MOTIVE POWER AND GEARING 
 
 FOR ELECTRICAL MACHINERY: 
 
 A Treatise on the Theory and Practice of the Mechanical Equipment of Power Stations for Electric 
 
 Supply, and for Electric Traction. 
 
 BY E. TREMLETT CARTER, C.E., M.I.E.E., F.R.A.S., F.P.S. (Lond.), &c, 
 
 550 pages, 900 Illustrations, Scale Drawings and Folding Plates, and over 80 Tables of E igineering Data 
 
 IN ONE VOLUME. 
 
 Part I. Introductory. Part II. The Steam Engine Eartlll. Gas aid Oil Engines. 
 
 Part IV. Water Power Plant. Part V. Gearing. Part VI. Types rf Power Stations 
 
 This work presents to consulting engineers contractors, central-station engineers, and 
 engineering students the latest and most approved practice in the equipment and working of 
 mechanical plant in electric-power generating stations. Every part of the work ha ebeen brought 
 completely up to date ; and especially in the matter of the costs of equipment and working the 
 latest available information has been given. The treatise deals with Steam, Gas, Oil and Hydraulic 
 Plant and Gearing ; and it deals with these severally from the three standpoints of (1) Tbrory 
 (2) Practice and (3) Costs. 
 
 "MOTIVE POWER AND GEARING FOR ELECTRICAL MACHINERY" is a handbook of modem 
 electrical engineering practice in all pan -:f the world. It offers to the reader a means of 
 comparing the central-station practice of the United Kingdom with that of America, the Colonies 
 or other places abroad ; and it enables him to study the scientific, economic and financial principles 
 upon which the relative suitability of various forms of practice is based, and to apply these 
 principles to the design or working of plant for any given kind of work, whether for electrical 
 supply or for electric traction. It is a treatise which should be in the hands of every electrical 
 engineer throughout the world, as it constitutes the only existing treatise on the Economics of 
 Motive Power and Gearing for Electrical Machinery. 
 
 NEW EDITION. 
 
 Over 400 pages, nearly 250 illustrations. Price 10s. 6d., post free ; abroad, 11s, 
 
 ELECTRIC MOTIVE POWER. 
 
 By ALBION T. SNELL, Assoo.M.lNST.C.E., M.I.E.E. 
 
 The rapid spread of electrical work in collieries, mines, and elsewhere has created a demand for a practical 
 book on the subject of transmission of power. Though much had been written, there was no single work dealing 
 with the question in a sufficiently comprehensive and yet practical manner to be of real use to the mechanical 
 or mining engineer ; either the treatment was adapted for specialists, or it was fragmentary, and power work 
 was regarded as subservient to the question of lighting. The Author has felt the want of such a book in dealing 
 with his clients and others, and in " ELECTRIC MOTIVE POWER " has endeavoured to supply it. 
 
 In the introduction the limiting conditions and essentials of a power plant are analysed, and in the 
 subsequent chapters the power plant is treated synthetically. The dynamo, motor, line, and details are 
 discussed both as to function and design. The various systems of transmitting and distributing power by con- 
 tinuous and alternate currents are fully enlarged upon, and much practical informatio gathered from actual 
 experience, is distributed under the various divisions. The last two chapters deal exhaustively with the 
 applications of electricity to mining work in Great Britain, the Continent .and America, particularly with 
 reference to collieries and coal-getting, and the results of the extensive experience gained in this field are 
 embodied. 
 
 In general, the Author's aim has been to give a sound digest of the theory and practice of the electrical 
 transmission of power, which will be of real use to the practical engineer, and to avoid controversial ^points 
 which lie in the province of the specialist, and elementary proofs which properly belong to text-books on 
 electricity and magnetism. 
 
 To meet the convenience of Continental readers and others, the Author has prepared 
 In tabular form and in parallel columns the working equations used in this work in inch* 
 potmd-minute and centimetre-gramme-second units, so that they may be readily used in 
 either system. 
 
 1, 2 and 3, Salisbury Court, Fleet Street, London, E.G. 
 
10 "The Electrician" Printing and Publishing Co., Ltd. 
 "THE ELECTRICIAN" SERIEScontmtcoZ. 
 
 Price 5S., post free ; abroad, 5s. 6d. 180 pages and over 100 illustrations. 
 
 THE LOCALISATION FAULTS IN ELECTRIC LIGHT MAINS. 
 
 By F. CHAKLES RAPHAEL. 
 
 Although the localisation of faults in telegraph cables has been dealt with fully in several 
 hand-books and pocket-books, the treatment of faulty electric light and power cables has never been 
 discussed in an equally comprehensive manner. Beyond a few short articles which have appeared 
 In the technical journals from time to time, nothing has been written on the subject. The condi- 
 tions of the problems presented for solution are, however, very different in the two cases ; faults in 
 telegraph cables are seldom localised before their resistance has become low compared with the 
 resistance of the cable itself, while in electric light work the contrary almost always obtains. This 
 fact alone entirely changes the method of treatment required in the latter case, and it has been the 
 author's endeavour, by dealing with the matter systematically, and as a separate subject, to 
 adequately fill a gap which has hitherto existed in technical literature. 
 
 The various methods of insulation testing during working have been collected and discussed, as 
 these tests may be considered to belong to the subject. 
 
 Price 6s., post free ; abroad 6s. 6d, 
 
 THE POTENTIOMETER AND ITS ADJUNCTS. 
 
 (A UNIVERSAL SYSTEM OF ELECTRICAL MEASUREMENT.) 
 By W. CLAEK FISHER. 
 
 The extended use of the Potentiometer System of Electrical Measurement will, it is hoped, be 
 sufficient excuse for the publication of this work, which, while dealing with the main instrument, 
 Its construction, use and capabilities, would necessarily be incomplete without similar treatment of 
 the various apparatus which, as adjuncts, extend the range and usefulness of the whole system. 
 
 Electrical testing may be said to have passed through two stages. First that which may be 
 called the elementary, in which first principles were evolved ; secondly, the adaptation of the same 
 to the needs of the telegraph and cable engineer. But with the advent of electric lighting and 
 other undertakings, such testing might be said to have passed into the third or practical and com- 
 mercial stage, where large quantities have to be dealt with, and where the old order of things 
 change th. 
 
 The engineer or practical man demands that he shall be shown results quickly, plainly and 
 accurately with a minimum of trouble, understanding, and consequently "Time," and on that 
 fuicount prefers like all good mechanics to have one good instrument, which, once understood 
 and easily manipulated, can be used in a variety of ways to suit his needs. It is to this fact un- 
 doubtedly that the " Potentiometer " method of measurement owes its popularity. Its accuracy 
 Is rarely, if ever, impunged. Measurements made by it are universally accepted amongst engineers, 
 and it might be well termed a " universal " instrument in " universal " use. 
 
 Over 400 pages and 200 specially drawn Illust,, unions. Price 12s. 6d., post free. 
 
 SUBMARINE CABLE-LAYING AND REPAIRING. 
 
 By H. D. WILKINSON, M.I.E.E., &c., <fec. 
 
 This work describes the procedure on board ship when removing a fault or break in a submerged cable 
 and the mechanical gear used in different vessels for this purpose ; and considers the best and most recent 
 practice as regards the electrical tests in use for the detection and localisation of faults, and the various 
 difficulties that occur to the beginner. It gives a detailed technical summary of modern practice in Manu- 
 factt^wg, Laying, Testing and Repairing a Submarine Telegraph Cable. The testing section and details of 
 boardshit. $aaaer. have been prepared with the object and hope of helping men in the cable services who are 
 looking further Into these branches. The description of the equipment of cable ships and the mechanical and 
 electrical work carried on during the laying and repairing of a submarine cable will also prove to some not 
 directly engaged in the profession, but nevertheless interested hs fee enterprise, a means of informing them- 
 selves as to the work which has to be done from the moment a new cable is projected until it is successfully 
 laid and worked. 
 
 The Chapter on " Testing " is especially valuable and up to date. 
 
 1 f 2 and 3, Salisbury Court, Fleet Street, London, E.G. 
 
"The Electrician" Printing and Publishing Co., Ltd., 11 
 
 "THE ELECTRICIAN " SERIES continued. 
 Over SOO pages, 106 illustrations. Price 10s. 6d., post free. 
 
 The ART ol ELECTROLYTIC SEPARATION of METALS 
 
 (THEOEETICAL AND PRACTICAL). 
 By GEORGE GORE, LL.D., F.R.S. 
 
 THE ONLY BOOK ON THIS IMPORTANT SUBJECT IN ANY LANGUAGE. 
 
 SYNOPSIS OF CONTENTS. 
 HISTORICAL SKETCH. 
 
 Discovery of Voltaic and Magneto-Electricity First Application of Electrolysis to the 
 Refining of Copper List of Electrolytic Refineries. 
 
 THEORETICAL DIVISION. 
 
 Section A. : Chief Electrical Facts and Principles of the Subject. Electric Polarity and 
 Induction, Quantity, Capacity, Potential Electromotive Force Electric Current Conduction 
 and Insulation Electric Conduction Resistance. 
 
 Section B. : Chief Thermal Phenomena. Heat of Conduction Resistance Thermal Units 
 Symbols, and Formulae. 
 
 Section C. : Chief Chemical Facts and Principles of the Subject. Explanation of Chemical 
 Terms Symbols and Atomic Weights Chemical Formulae and Molecular Weights Relation of 
 Heat to Chemical Action. 
 
 Section D.: Chief Facts of Chemico-Electric or Voltaic Action. Electrical Theory of 
 Chemistry Relation of Chemical Heat to Volta Motive Force Volta-Electric Relationb to 
 Metals in Electrolytes Voltaic Batteries Relative Amounts of Voltaic Current produced by 
 Different Metals. 
 
 Section B. : Chief Facts of Electro-Chemical Action. Definition of Electrolysis Arrange- 
 ments for Producing Electrolysis Modes of Preparing Solutions Nomenclature Physical 
 Structure of Electro-Deposited Metals Incidental Phenomena attending Electrolysis Decom- 
 posability of Electrolytes Electro-Chemical Equivalents of Substances Consumption of Electrifl 
 Energy in Electrolysis. 
 
 Section F. : The Generation of Electric Currents by Dynamo Machines. Definition of a 
 Dynamo and of a Magnetic Field Electro-Magnetic Induction Lines of Magnetic Force. 
 
 PRACTICAL DIVISION. 
 
 Section G. Establishing and Working an Electrolytic Copper Refinery. Planning a Refinery 
 Kinds of Dynamos Employed Choice and Care of Dynamo The Depositing Room The Vats 
 The Electrodes The Main Conductors Expenditure of Mechanical Power and Electric 
 Energy Cost of Electrolytic Refining. 
 
 Section H. : Other Applications of Electrolysis in Separating and Refining Metals. Elec- 
 trolytic Refining of Copper by other Methods Extraction of Copper from Minerals and Mineral 
 Waters Electrolytic Refining of Silver Bullion and of Lead Separation of Antimony, of Tin, of 
 Aluminium, of Zinc, of Magnesium, of Sodium and Potassium, of Gold Electrolytic Refining of 
 Nickel Electric Smelting. 
 
 Appendix. Useful Tables and Data. 
 
 Second Edition , price 2s., post free. 
 
 ELECTRO-CHEMISTRY. 
 
 By GEORGE GORE, LL.D., F.R.S. 
 S20 pages, 155 illustrations. Price 6s. 6d., post free. 
 
 PRACTICAL NOTES FOR ELECTRICAL STUDENTS. 
 
 LAWS, UNITS, AND SIMPLE MEASURING INSTRUMENTS. 
 By A. E. KENNELLY and H. D. WILKINSON, M.I.E.E. 
 
 Chapter I. Introductory. 
 II. Batteries. 
 
 ,, III. Electromotive Force and Potential. 
 IV. Resistance. 
 .. V. Current. 
 
 CONTENTS. 
 
 Chapter VI. Current Indicators. 
 VII. Simple Tests with Indicators. 
 VIII. Calibration of Current Indicators. 
 IX. Magnetic Fields and their Measure- 
 ment. 
 
 I, 2 and 3, Salisbury Court, Fleet Street, London, E.G. 
 
12 "The Electrician" Printing and Publishing Co., Ltd. 
 "THE ELECTRICIAN" SERIES continued. 
 
 Electrical Laboratory Notes & Forms. 
 
 ARRANGED AKD PREPARED BY 
 
 Dr. J. A. FLEMIIVO, M.A., F.R.S. 
 
 Professor of Electrical Engineering in University College, London. 
 
 These " Laboratory Notes and Forms " have been prepared to assist Teachers, Demonstrators 
 and Students in Electrical Laboratories, and to enable the Teacher to economise time. They 
 consist of a series of (about) Twenty Elementary and (about) Twenty Advanced Exercises 
 fa Practical Electrical Measurements and Testing. For each of these Exercises a four-page Report 
 Sheet has been prepared, two pages of which are occupied with a condensed account of the theory 
 and practical instructions for performing the particular Experiment, the other two pages being 
 ruled up in lettered columns, to be filled in by the Student with the observed and calculated 
 quantities. Where simple diagrams will assist the Student, these have been supplied. These 
 Exercises are for the most part based on the methods in use in the Electrical Engineering 
 Laboratories of University College, London ; but they are perfectly general, and can be put into 
 practice in any Electrical Laboratory. 
 
 Each Form is supplied either singly at 3d. nett, or at 3s. 6d. per dozen nett (assorted or 
 otherwise as required) ; in sets of any three at Is. nett ; or the set of (about) Twenty Elementary 
 (or Advanced) Exercises can be obtained, price 5s. 6d. nett. The complete set of Elementary 
 and Advanced Exercises are price 10s. 6d. nett, or in a handy Portfolio, 12s. nett, or bound in 
 strong cloth case, price 12s. 6d. nett. 
 
 Spare Tabulated Sheets for Observations, price Id. each nett. 
 
 Strong Portfolios, price Is. 6d. each. 
 
 The very best quality foolscap sectional paper (16in. by 13in.) can be supplied, price Is. 
 per dozen sheets nett. 
 
 NOW READY. Cheaper edition of "Electrical Laboratory Notes and Forms." These 
 cheaper Forms have been prepared for the use of students and teachers at the Polytechnic and 
 other science classes throughout the country. These new Forms, which differ only from the higher- 
 priced set in being printed on smaller and cheaper paper and with less space for tabulated records, 
 are issued at half the price of the above set. Bound in strong case, 8s. 6d. 
 
 SERIES. 
 
 1. The Exploration of Magnetic Fields. 
 
 2. The Magnetic Field of a Circular Current. 
 
 3. The Standardisation of a Tangent Galvanometer by the Water Voltameter 
 
 4. The Measurement of Electrical Resistance by the Divided Wire Bridge. 
 
 5. The Calibration of the Ballistic Galvanometer. 
 
 6. The Determination of Magnetic Field Strength. 
 
 7. Experiments with Standard Magnetic Fields 
 
 8. The Determination of the Magnetic Field in Air Gap of an Eleccro-magnet. 
 
 9. The Determinaticn of Resistance with the Post Office Pattern Wheatstone Bridge. 
 
 10. The Determination of Potential Difference by the Potentiometer. 
 
 11. The Measurement of a Current by the Potentiometer. 
 
 12. A Complete Report on a Primary Battery. 
 
 18. The Standardisation of a Voltmeter by the Potentiometer. 
 
 14. The Photometric Examination of an Incandescent Lamp. 
 
 15. The Determination of the Absorptive Powers of Semi-Transparent Screens. 
 
 16. The Determination of the Reflective Power of Various Surfaces. 
 
 17. The Determination of the Electrical Efficiency of an Electromotor by the Cradle Method. 
 
 18. The Determination of the Efficiency of an Electromotor by the Brake Method. 
 
 19. The Efficiency Test of a Combined Motor-Generator Plant. 
 
 20. Efficiency Test of a Gas Engine and Dynamo Plant. 
 
 ADVANCED SERIES. 
 
 2L The Determination of the Electrical Resistivity of a Sample of Metallic Wire. 
 
 22. The Measurement of Low Resistances by the Potentiometer. 
 
 23. The Measurement of Armature Resistances. 
 
 24. The Standardisation of an Ammeter by Copper Deposit. 
 
 25. The Standardisation of a Voltmeter by the Potentiometer. 
 
 26. The Standardisation of an Ammeter by the Potentiometer. 
 
 27. The Determination of the Magnetic Permeability of a Sample of Ironi 
 
 28. The Standardisation of a High Tension Voltmeter. 
 
 29. The Examination of an Alternate-Current Ammeter. 
 
 80. The Delineation of Alternating Current Curves. 
 
 81. The Efficiency Test of a Transformer. 
 
 82. The Efficiency Test of an Alternator. 
 
 83. The Photometric Examination of an Arc Lamp. 
 
 84. The Measurement of Insulation and High Resistance 
 
 35. The Complete Efficiency Test of a Secondary Battery. 
 
 36. The Calibration of Electric Meters. 
 
 37. The Delineation of Hysteresis Curves of Iron. 
 
 88 The Examination of a Sample of Iron for Magnetic Hysteresis Loss 
 
 39. fhe Determination of the Capacity of a Concentric Cable 
 
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